def __init__(self, centroidFindType=CentroidFindType.RandomWalk):
"""Instantiate the class of CompensableImage.
Parameters
----------
centroidFindType : enum 'CentroidFindType', optional
Algorithm to find the centroid of donut. (the default is
CentroidFindType.RandomWalk.)
"""
self._image = Image(centroidFindType=centroidFindType)
self.defocalType = DefocalType.Intra
# Field coordinate in degree
self.fieldX = 0
self.fieldY = 0
# Initial image before doing the compensation
self.image0 = None
# Coefficient to do the off-axis correction
self.offAxisCoeff = np.array([])
# Defocused offset in files of off-axis correction
self.offAxisOffset = 0.0
# Ture if the image gets the over-compensation
self.caustic = False
# Padded mask for use at the offset planes
self.pMask = np.array([], dtype=int)
# Non-padded mask corresponding to aperture
self.cMask = np.array([], dtype=int)
def __init__(self, centroidFindType=CentroidFindType.RandomWalk):
self._image = Image(centroidFindType=centroidFindType)
self.defocalType = DefocalType.Intra
# Field coordinate in degree
self.fieldX = 0
self.fieldY = 0
# Initial image before doing the compensation
self.image0 = None
# Coefficient to do the off-axis correction
self.offAxisCoeff = np.array([])
# Defocused offset in files of off-axis correction
self.offAxisOffset = 0.0
# True if the image gets the over-compensation
self.caustic = False
# Padded mask for use at the offset planes
self.mask_comp = np.array([], dtype=int)
# Non-padded mask corresponding to aperture
self.mask_pupil = np.array([], dtype=int)
def setUp(self):
self.testDataDir = os.path.join(getModulePath(), "tests", "testData")
self.imgFile = os.path.join(self.testDataDir, "testImages",
"LSST_NE_SN25", "z11_0.25_intra.txt")
self.img = Image()
self.img.setImg(imageFile=self.imgFile)
def setImg(self, fieldXY, image=None, imageFile=None, atype=None):
"""
Set the wavefront image.
Arguments:
fieldXY {[float]} -- Position of donut on the focal plane in degree.
Keyword Arguments:
image {[float]} -- Array of image. (default: {None})
imageFile {[string]} -- Path of image file. (default: {None})
atype {[string]} -- Type of image. It should be "intra" or "extra". (default: {None})
Raises:
TypeError -- Error if the atype is not "intra" or "extra".
"""
# Instantiate the image object
self.__image = Image()
# Read the file if there is no input image
self.__image.setImg(image=image, imageFile=imageFile)
# Make sure the image size is n by n
if (self.__image.image.shape[0] != self.__image.image.shape[1]):
raise RuntimeError("Only square image stamps are accepted.")
elif (self.__image.image.shape[0] % 2 == 1):
raise RuntimeError("Number of pixels cannot be odd numbers.")
# Dimension of image
self.sizeinPix = self.__image.image.shape[0]
# Donut position in degree
self.fieldX, self.fieldY = fieldXY
# Save the initial image if we want the compensator always start from this
self.image0 = None
# We will need self.fldr to be on denominator
self.fldr = np.max((np.hypot(self.fieldX, self.fieldY), 1e-8))
# Check the type of image
if atype.lower() not in (self.INTRA, self.EXTRA):
raise TypeError("Image defocal type must be 'intra' or 'extra'.")
self.atype = atype
# Coefficient to do the off-axis correction
self.offAxis_coeff = None
# Defocal distance (Baseline is 1.5mm. The configuration file now is 1mm.)
self.offAxisOffset = 0
# Check the image has the problem or not
self.caustic = False
# Reset all mask related parameters
self.pMask = None
self.cMask = None
def __init__(self):
"""Instantiate the class of CompensableImage."""
self._image = Image()
self.defocalType = DefocalType.Intra
# Field coordinate in degree
self.fieldX = 0
self.fieldY = 0
# Initial image before doing the compensation
self.image0 = None
# Coefficient to do the off-axis correction
self.offAxisCoeff = np.array([])
# Defocused offset in files of off-axis correction
self.offAxisOffset = 0.0
# Ture if the image gets the over-compensation
self.caustic = False
# Padded mask for use at the offset planes
self.pMask = np.array([], dtype=int)
# Non-padded mask corresponding to aperture
self.cMask = np.array([], dtype=int)
def setUp(self):
self.testDataDir = os.path.join(getModulePath(), "tests", "testData")
self.imgFile = os.path.join(self.testDataDir, "testImages",
"LSST_NE_SN25", "z11_0.25_intra.txt")
self.img = Image()
self.img.setImg(imageFile=self.imgFile)
def setUp(self):
# Get the path of module
modulePath = getModulePath()
# Define the algorithm folder
algoFolderPath = os.path.join(modulePath, "configData", "cwfs", "algo")
# Define the image folder and image names
# Image data -- Don't know the final image format.
# It is noted that image.readFile inuts is based on the txt file
imageFolderPath = os.path.join(modulePath, "tests", "testData",
"testImages", "LSST_NE_SN25")
imgName = "z11_0.25_intra.txt"
# Image files Path
imgFile = os.path.join(imageFolderPath, imgName)
# There is the difference between intra and extra images
self.img = Image()
self.img.setImg(imageFile=imgFile)
def testZeroImg(self):
# Creat a zero image
zeroImg = Image()
zeroImg.setImg(image=np.zeros([4, 4]))
self.assertEqual(np.sum(zeroImg.image), 0)
# Update Image
zeroImg.updateImage(np.ones([4, 4]))
self.assertEqual(np.sum(zeroImg.image), 16)
realcx, realcy, realR, imgBinary = zeroImg.getCenterAndR_ef(
randNumFilePath=None, checkEntropy=True)
self.assertEqual(realcx, [])
# update to the random image
zeroImg.updateImage(np.random.rand(100, 100))
realcx, realcy, realR, imgBinary = zeroImg.getCenterAndR_ef(
randNumFilePath=None, checkEntropy=True)
self.assertEqual(realcx, [])
def testGetCenterAndR_ef_withEntropyCheck(self):
# Creat a zero image
zeroImg = Image()
zeroImg.setImg(image=np.ones([4, 4]))
realcx, realcy, realR, imgBinary = \
zeroImg.getCenterAndR_ef(checkEntropy=True)
self.assertEqual(realcx, [])
# update to the random image
zeroImg.updateImage(np.random.rand(100, 100))
realcx, realcy, realR, imgBinary = \
zeroImg.getCenterAndR_ef(checkEntropy=True)
self.assertEqual(realcx, [])
class TestImage(unittest.TestCase):
"""Test the Image class."""
def setUp(self):
self.testDataDir = os.path.join(getModulePath(), "tests", "testData")
self.imgFile = os.path.join(self.testDataDir, "testImages",
"LSST_NE_SN25", "z11_0.25_intra.txt")
self.img = Image()
self.img.setImg(imageFile=self.imgFile)
def testGetImg(self):
img = self.img.getImg()
self.assertEqual(img.shape, (120, 120))
def testGetImgFilePath(self):
imgFilePath = self.img.getImgFilePath()
self.assertEqual(imgFilePath, self.imgFile)
def testSetImgByImageArray(self):
newImg = np.random.rand(5, 5)
self.img.setImg(image=newImg)
self.assertTrue(np.all(self.img.getImg() == newImg))
self.assertEqual(self.img.getImgFilePath(), "")
def testSetImgByFitsFile(self):
opdFitsFile = os.path.join(self.testDataDir, "opdOutput", "9005000",
"opd_9005000_0.fits.gz")
self.img.setImg(imageFile=opdFitsFile)
img = self.img.getImg()
self.assertEqual(img.shape, (255, 255))
imgFilePath = self.img.getImgFilePath()
self.assertEqual(imgFilePath, opdFitsFile)
def testUpdateImage(self):
newImg = np.random.rand(5, 5)
self.img.updateImage(newImg)
self.assertTrue(np.all(self.img.getImg() == newImg))
def testUpdateImageWithNoHoldImage(self):
img = Image()
newImg = np.random.rand(5, 5)
self.assertWarns(UserWarning, img.updateImage, newImg)
def testGetCenterAndR_ef(self):
realcx, realcy, realR, imgBinary = \
self.img.getCenterAndR_ef(checkEntropy=True)
self.assertEqual(int(realcx), 61)
self.assertEqual(int(realcy), 61)
self.assertGreater(int(realR), 35)
def testGetCenterAndR_ef_withEntropyCheck(self):
# Creat a zero image
zeroImg = Image()
zeroImg.setImg(image=np.ones([4, 4]))
realcx, realcy, realR, imgBinary = \
zeroImg.getCenterAndR_ef(checkEntropy=True)
self.assertEqual(realcx, [])
# update to the random image
zeroImg.updateImage(np.random.rand(100, 100))
realcx, realcy, realR, imgBinary = \
zeroImg.getCenterAndR_ef(checkEntropy=True)
self.assertEqual(realcx, [])
def testGetSNR(self):
# Add the noise to the image
image = self.img.getImg()
noisedImg = image + np.random.random(image.shape) * 0.1
self.img.setImg(image=noisedImg)
snr = self.img.getSNR()
self.assertGreater(snr, 15)
class CompensableImage(object):
"""Instantiate the class of CompensableImage.
Parameters
----------
centroidFindType : enum 'CentroidFindType', optional
Algorithm to find the centroid of donut. (the default is
CentroidFindType.RandomWalk.)
"""
def __init__(self, centroidFindType=CentroidFindType.RandomWalk):
self._image = Image(centroidFindType=centroidFindType)
self.defocalType = DefocalType.Intra
# Field coordinate in degree
self.fieldX = 0
self.fieldY = 0
# Initial image before doing the compensation
self.image0 = None
# Coefficient to do the off-axis correction
self.offAxisCoeff = np.array([])
# Defocused offset in files of off-axis correction
self.offAxisOffset = 0.0
# True if the image gets the over-compensation
self.caustic = False
# Padded mask for use at the offset planes
self.mask_comp = np.array([], dtype=int)
# Non-padded mask corresponding to aperture
self.mask_pupil = np.array([], dtype=int)
def getDefocalType(self):
"""Get the defocal type.
Returns
-------
enum 'DefocalType'
Defocal type.
"""
return self.defocalType
def getImgObj(self):
"""Get the image object.
Returns
-------
Image
Image object.
"""
return self._image
def getImg(self):
"""Get the image.
Returns
-------
numpy.ndarray
Image.
"""
return self._image.getImg()
def getImgSizeInPix(self):
"""Get the image size in pixel.
Returns
-------
int
Image size in pixel.
"""
return self.getImg().shape[0]
def getOffAxisCoeff(self):
"""Get the coefficients to do the off-axis correction.
Returns
-------
numpy.ndarray
Coefficients to do the off-axis correction.
float
Defocused offset in files of off-axis correction.
"""
return self.offAxisCoeff, self.offAxisOffset
def getImgInit(self):
"""Get the initial image before doing the compensation.
Returns
-------
numpy.ndarray
Initial image before doing the compensation.
"""
return self.image0
def isCaustic(self):
"""The image is caustic or not.
The image might be caustic from the over-compensation.
Returns
-------
bool
True if the image is caustic.
"""
return self.caustic
def getPaddedMask(self):
"""Get the padded mask use at the offset planes.
Returns
-------
numpy.ndarray[int]
Padded mask.
"""
return self.mask_comp
def getNonPaddedMask(self):
"""Get the non-padded mask corresponding to aperture.
Returns
-------
numpy.ndarray[int]
Non-padded mask
"""
return self.mask_pupil
def getFieldXY(self):
"""Get the field x, y in degree.
Returns
-------
float
Field x in degree.
float
Field y in degree.
"""
return self.fieldX, self.fieldY
def setImg(self, fieldXY, defocalType, image=None, imageFile=None):
"""Set the wavefront image.
Parameters
----------
fieldXY : tuple or list
Position of donut on the focal plane in degree (field x, field y).
defocalType : enum 'DefocalType'
Defocal type of image.
image : numpy.ndarray, optional
Array of image. (the default is None.)
imageFile : str, optional
Path of image file. (the default is None.)
"""
self._image.setImg(image=image, imageFile=imageFile)
self._checkImgShape()
self.fieldX, self.fieldY = fieldXY
self.defocalType = defocalType
self._resetInternalAttributes()
def _checkImgShape(self):
"""Check the image shape.
Raises
------
RuntimeError
Only square image stamps are accepted.
RuntimeError
Number of pixels cannot be odd numbers.
"""
img = self.getImg()
if img.shape[0] != img.shape[1]:
raise RuntimeError("Only square image stamps are accepted.")
elif img.shape[0] % 2 == 1:
raise RuntimeError("Number of pixels cannot be odd numbers.")
def _resetInternalAttributes(self):
"""Reset the internal attributes."""
self.image0 = None
self.offAxisCoeff = np.array([])
self.offAxisOffset = 0.0
self.caustic = False
# Reset all mask related parameters
self.mask_pupil = np.array([], dtype=int)
self.mask_comp = np.array([], dtype=int)
def updateImage(self, image):
"""Update the image of donut.
Parameters
----------
image : numpy.ndarray
Donut image.
"""
self._image.updateImage(image)
def updateImgInit(self):
"""Update the backup of initial image.
This will be used in the outer loop iteration, which always uses the
initial image (image0) before each iteration starts.
"""
# Update the initial image for future use
self.image0 = self.getImg().copy()
def imageCoCenter(self, inst, fov=3.5, debugLevel=0):
"""Shift the weighting center of donut to the center of reference
image with the correction of projection of fieldX and fieldY.
Parameters
----------
inst : Instrument
Instrument to use.
fov : float, optional
Field of view (FOV) of telescope. (the default is 3.5.)
debugLevel : int, optional
Show the information under the running. If the value is higher, the
information shows more. It can be 0, 1, 2, or 3. (the default is
0.)
"""
# Calculate the weighting center (x, y) and radius
x1, y1 = self._image.getCenterAndR()[0:2]
# Show the co-center information
if debugLevel >= 3:
print("imageCoCenter: (x, y) = (%8.2f,%8.2f)\n" % (x1, y1))
# Calculate the center position on image
# 0.5 is the half of 1 pixel
dimOfDonut = inst.getDimOfDonutOnSensor()
stampCenterx1 = dimOfDonut / 2 + 0.5
stampCentery1 = dimOfDonut / 2 + 0.5
# Shift in the radial direction
# The field of view (FOV) of LSST camera is 3.5 degree
offset = inst.getDefocalDisOffset()
pixelSize = inst.getCamPixelSize()
radialShift = fov * (offset / 1e-3) * (10e-6 / pixelSize)
# Calculate the projection of distance of donut to center
fieldDist = self._getFieldDistFromOrigin()
radialShift = radialShift * (fieldDist / (fov / 2))
# Do not consider the condition out of FOV of lsst
if fieldDist > (fov / 2):
radialShift = 0
# Calculate the cos(theta) for projection
I1c = self.fieldX / fieldDist
# Calculate the sin(theta) for projection
I1s = self.fieldY / fieldDist
# Get the projected x, y-coordinate
stampCenterx1 = stampCenterx1 + radialShift * I1c
stampCentery1 = stampCentery1 + radialShift * I1s
# Shift the image to the projected position
self.updateImage(
np.roll(self.getImg(), int(np.round(stampCentery1 - y1)), axis=0))
self.updateImage(
np.roll(self.getImg(), int(np.round(stampCenterx1 - x1)), axis=1))
def _getFieldDistFromOrigin(self, fieldX=None, fieldY=None, minDist=1e-8):
"""Get the field distance from the origin.
Parameters
----------
fieldX : float, optional
Field x in degree. If the input is None, the value of self.fieldX
will be used. (the default is None.)
fieldY : float, optional
Field y in degree. If the input is None, the value of self.fieldY
will be used. (the default is None.)
minDist : float, optional
Minimum distace. In some cases, the field distance will be the
denominator in other functions. (the default is 1e-8.)
Returns
-------
float
Field distance from the origin.
"""
if fieldX is None:
fieldX = self.fieldX
if fieldY is None:
fieldY = self.fieldY
fieldDist = np.hypot(fieldX, fieldY)
if fieldDist == 0:
fieldDist = minDist
return fieldDist
def compensate(self, inst, algo, zcCol, model):
"""Calculate the image compensated from the affection of wavefront.
Parameters
----------
inst : Instrument
Instrument to use.
algo : Algorithm
Algorithm to solve the Poisson's equation. It can by done by the
fast Fourier transform or serial expansion.
zcCol : numpy.ndarray
Coefficients of wavefront.
model : str
Optical model. It can be "paraxial", "onAxis", or "offAxis".
Raises
------
RuntimeError
input:size zcCol in compensate needs to be a numTerms row column
vector.
"""
# Check the condition of inputs
numTerms = algo.getNumOfZernikes()
if (zcCol.ndim == 1) and (len(zcCol) != numTerms):
raise RuntimeError(
"input:size",
"zcCol in compensate needs to be a %d row column vector. \n" %
numTerms,
)
# Dimension of image
sm, sn = self.getImg().shape
# Dimension of projected image on focal plane
projSamples = sm
# Let us create a look-up table for x -> xp first.
luty, lutx = np.mgrid[-(projSamples / 2 - 0.5):(projSamples / 2 + 0.5),
-(projSamples / 2 - 0.5):(projSamples / 2 +
0.5), ]
sensorFactor = inst.getSensorFactor()
lutx = lutx / (projSamples / 2 / sensorFactor)
luty = luty / (projSamples / 2 / sensorFactor)
# Set up the mapping
lutxp, lutyp, J = self._aperture2image(inst, algo, zcCol, lutx, luty,
projSamples, model)
show_lutxyp = self._showProjection(lutxp,
lutyp,
sensorFactor,
projSamples,
raytrace=False)
if np.all(show_lutxyp <= 0):
self.caustic = True
return
# Extend the dimension of image by 20 pixel in x and y direction
show_lutxyp = padArray(show_lutxyp, projSamples + 20)
# Get the binary matrix of image on pupil plane if raytrace=False
struct0 = generate_binary_structure(2, 1)
struct = iterate_structure(struct0, 4)
struct = binary_dilation(struct, structure=struct0,
iterations=2).astype(int)
show_lutxyp = binary_dilation(show_lutxyp, structure=struct)
show_lutxyp = binary_erosion(show_lutxyp, structure=struct)
# Extract the region from the center of image and get the original one
show_lutxyp = extractArray(show_lutxyp, projSamples)
# Recenter the image
imgRecenter = self.centerOnProjection(self.getImg(),
show_lutxyp.astype(float),
window=20)
self.updateImage(imgRecenter)
# Construct the interpolant to get the intensity on (x', p') plane
# that corresponds to the grid points on (x,y)
yp, xp = np.mgrid[-(sm / 2 - 0.5):(sm / 2 + 0.5),
-(sm / 2 - 0.5):(sm / 2 + 0.5)]
xp = xp / (sm / 2 / sensorFactor)
yp = yp / (sm / 2 / sensorFactor)
# Put the NaN to be 0 for the interpolate to use
lutxp[np.isnan(lutxp)] = 0
lutyp[np.isnan(lutyp)] = 0
# Construct the function for interpolation
ip = RectBivariateSpline(yp[:, 0], xp[0, :], self.getImg(), kx=1, ky=1)
# Construct the projected image by the interpolation
lutIp = ip(lutyp, lutxp, grid=False)
# Calculate the image on focal plane with compensation based on flux
# conservation
# I(x, y)/I'(x', y') = J = (dx'/dx)*(dy'/dy) - (dx'/dy)*(dy'/dx)
self.updateImage(lutIp * J)
if self.defocalType == DefocalType.Extra:
self.updateImage(np.rot90(self.getImg(), k=2))
# Put NaN to be 0
imgCompensate = self.getImg()
imgCompensate[np.isnan(imgCompensate)] = 0
# Check the compensated image has the problem or not.
# The negative value means the over-compensation from wavefront error
if np.any(imgCompensate < 0) and np.all(self.image0 >= 0):
print(
"WARNING: negative scale parameter, image is within caustic, zcCol (in um)=\n"
)
self.caustic = True
# Put the overcompensated part to be 0
imgCompensate[imgCompensate < 0] = 0
self.updateImage(imgCompensate)
def _aperture2image(self, inst, algo, zcCol, lutx, luty, projSamples,
model):
"""Calculate the x, y-coordinate on the focal plane and the related
Jacobian matrix.
Parameters
----------
inst : Instrument
Instrument to use.
algo : Algorithm
Algorithm to solve the Poisson's equation. It can by done by the
fast Fourier transform or serial expansion.
zcCol : numpy.ndarray
Coefficients of optical basis. It is Zernike polynomials in the
baseline.
lutx : numpy.ndarray
X-coordinate on pupil plane.
luty : numpy.ndarray
Y-coordinate on pupil plane.
projSamples : int
Dimension of projected image. This value considers the
magnification ratio of donut image.
model : str
Optical model. It can be "paraxial", "onAxis", or "offAxis".
Returns
-------
numpy.ndarray
X coordinate on the focal plane.
numpy.ndarray
Y coordinate on the focal plane.
numpy.ndarray
Jacobian matrix between the pupil and focal plane.
"""
# Get the radius: R = D/2
R = inst.getApertureDiameter() / 2
# Calculate C = -f(f-l)/l/R^2. This is for the calculation of reduced
# coordinate.
defocalDisOffset = inst.getDefocalDisOffset()
if self.defocalType == DefocalType.Intra:
l = defocalDisOffset
elif self.defocalType == DefocalType.Extra:
l = -defocalDisOffset
focalLength = inst.getFocalLength()
myC = -focalLength * (focalLength - l) / l / R**2
# Get the functions to do the off-axis correction by numerical fitting
# Order to do the off-axis correction. The order is 10 now.
offAxisPolyOrder = algo.getOffAxisPolyOrder()
polyFunc = self._getFunction("poly%d_2D" % offAxisPolyOrder)
polyGradFunc = self._getFunction("poly%dGrad" % offAxisPolyOrder)
# Calculate the distance to center
lutr = np.sqrt(lutx**2 + luty**2)
# Calculated the extended ring radius (delta r), which is to extended
# the available pupil area.
# 1 pixel larger than projected pupil. No need to be EF-like, anything
# outside of this will be masked off by the computational mask
sensorFactor = inst.getSensorFactor()
onepixel = 1 / (projSamples / 2 / sensorFactor)
# Get the index that the point is out of the range of extended pupil
obscuration = inst.getObscuration()
idxout = (lutr > 1 + onepixel) | (lutr < obscuration - onepixel)
# Define the element to be NaN if it is out of range
lutx[idxout] = np.nan
luty[idxout] = np.nan
# Get the index in the extended area of outer boundary with the width
# of onepixel
idxbound = (lutr <= 1 + onepixel) & (lutr > 1)
# Calculate the extended x, y-coordinate (x' = x/r*r', r'=1)
lutx[idxbound] = lutx[idxbound] / lutr[idxbound]
luty[idxbound] = luty[idxbound] / lutr[idxbound]
# Get the index in the extended area of inner boundary with the width
# of onepixel
idxinbd = (lutr < obscuration) & (lutr > obscuration - onepixel)
# Calculate the extended x, y-coordinate (x' = x/r*r', r'=obscuration)
lutx[idxinbd] = lutx[idxinbd] / lutr[idxinbd] * obscuration
luty[idxinbd] = luty[idxinbd] / lutr[idxinbd] * obscuration
# Get the corrected x, y-coordinate on focal plane (lutxp, lutyp)
if model == "paraxial":
# No correction is needed in "paraxial" model
lutxp = lutx
lutyp = luty
elif model == "onAxis":
# Calculate F(x, y) = m * sqrt(f^2-R^2) / sqrt(f^2-(x^2+y^2)*R^2)
# m is the mask scaling factor
myA2 = (focalLength**2 - R**2) / (focalLength**2 - lutr**2 * R**2)
# Put the unphysical value as NaN
myA = myA2.copy()
idx = myA < 0
myA[idx] = np.nan
myA[~idx] = np.sqrt(myA2[~idx])
# Mask scaling factor (for fast beam)
maskScalingFactor = algo.getMaskScalingFactor()
# Calculate the x, y-coordinate on focal plane
# x' = F(x,y)*x + C*(dW/dx), y' = F(x,y)*y + C*(dW/dy)
lutxp = maskScalingFactor * myA * lutx
lutyp = maskScalingFactor * myA * luty
elif model == "offAxis":
# Get the coefficient of polynomials for off-axis correction
tt = self.offAxisOffset
cx = (self.offAxisCoeff[0, :] - self.offAxisCoeff[2, :]) * (
tt + l) / (2 * tt) + self.offAxisCoeff[2, :]
cy = (self.offAxisCoeff[1, :] - self.offAxisCoeff[3, :]) * (
tt + l) / (2 * tt) + self.offAxisCoeff[3, :]
# This will be inverted back by typesign later on.
# We do the inversion here to make the (x,y)->(x',y') equations has
# the same form as the paraxial case.
cx = np.sign(l) * cx
cy = np.sign(l) * cy
# Do the orthogonalization: x'=1/sqrt(2)*(x+y), y'=1/sqrt(2)*(x-y)
# Calculate the rotation angle for the orthogonalization
fieldDist = self._getFieldDistFromOrigin()
costheta = (self.fieldX + self.fieldY) / fieldDist / np.sqrt(2)
if costheta > 1:
costheta = 1
elif costheta < -1:
costheta = -1
sintheta = np.sqrt(1 - costheta**2)
if self.fieldY < self.fieldX:
sintheta = -sintheta
# Create the pupil grid in off-axis model. This gives the
# x,y-coordinate in the extended ring area defined by the parameter
# of onepixel.
# Get the mask-related parameters
maskCa, maskRa, maskCb, maskRb = self._interpMaskParam(
self.fieldX, self.fieldY, inst.getMaskOffAxisCorr())
lutx, luty = self._createPupilGrid(
lutx,
luty,
onepixel,
maskCa,
maskCb,
maskRa,
maskRb,
self.fieldX,
self.fieldY,
)
# Calculate the x, y-coordinate on focal plane
# First rotate back to reference orientation
lutx0 = lutx * costheta + luty * sintheta
luty0 = -lutx * sintheta + luty * costheta
# Use the mapping at reference orientation
lutxp0 = polyFunc(cx, lutx0, y=luty0)
lutyp0 = polyFunc(cy, lutx0, y=luty0)
# Rotate back to focal plane
lutxp = lutxp0 * costheta - lutyp0 * sintheta
lutyp = lutxp0 * sintheta + lutyp0 * costheta
# Zemax data are in mm, therefore 1000
dimOfDonut = inst.getDimOfDonutOnSensor()
pixelSize = inst.getCamPixelSize()
reduced_coordi_factor = 1e-3 / (dimOfDonut / 2 * pixelSize /
sensorFactor)
# Reduced coordinates, so that this can be added with the dW/dz
lutxp = lutxp * reduced_coordi_factor
lutyp = lutyp * reduced_coordi_factor
else:
print("Wrong optical model type in compensate. \n")
return
# Obscuration of annular aperture
zobsR = algo.getObsOfZernikes()
# Calculate the x, y-coordinate on focal plane
# x' = F(x,y)*x + C*(dW/dx), y' = F(x,y)*y + C*(dW/dy)
# In Model basis (zer: Zernike polynomials)
if zcCol.ndim == 1:
lutxp = lutxp + myC * ZernikeAnnularGrad(zcCol, lutx, luty, zobsR,
"dx")
lutyp = lutyp + myC * ZernikeAnnularGrad(zcCol, lutx, luty, zobsR,
"dy")
# Make the sign to be consistent
if self.defocalType == DefocalType.Extra:
lutxp = -lutxp
lutyp = -lutyp
# Calculate the Jacobian matrix
# In Model basis (zer: Zernike polynomials)
if zcCol.ndim == 1:
if model == "paraxial":
J = (1 + myC *
ZernikeAnnularJacobian(zcCol, lutx, luty, zobsR, "1st") +
myC**2 *
ZernikeAnnularJacobian(zcCol, lutx, luty, zobsR, "2nd"))
elif model == "onAxis":
xpox = maskScalingFactor * myA * (
1 + lutx**2 * R**2.0 / (focalLength**2 - R**2 * lutr**2)
) + myC * ZernikeAnnularGrad(zcCol, lutx, luty, zobsR, "dx2")
ypoy = maskScalingFactor * myA * (
1 + luty**2 * R**2.0 / (focalLength**2 - R**2 * lutr**2)
) + myC * ZernikeAnnularGrad(zcCol, lutx, luty, zobsR, "dy2")
xpoy = maskScalingFactor * myA * lutx * luty * R**2 / (
focalLength**2 - R**2 * lutr**2
) + myC * ZernikeAnnularGrad(zcCol, lutx, luty, zobsR, "dxy")
ypox = xpoy
J = xpox * ypoy - xpoy * ypox
elif model == "offAxis":
xp0ox = (polyGradFunc(cx, lutx0, luty0, "dx") * costheta -
polyGradFunc(cx, lutx0, luty0, "dy") * sintheta)
yp0ox = (polyGradFunc(cy, lutx0, luty0, "dx") * costheta -
polyGradFunc(cy, lutx0, luty0, "dy") * sintheta)
xp0oy = (polyGradFunc(cx, lutx0, luty0, "dx") * sintheta +
polyGradFunc(cx, lutx0, luty0, "dy") * costheta)
yp0oy = (polyGradFunc(cy, lutx0, luty0, "dx") * sintheta +
polyGradFunc(cy, lutx0, luty0, "dy") * costheta)
xpox = (xp0ox * costheta - yp0ox * sintheta
) * reduced_coordi_factor + myC * ZernikeAnnularGrad(
zcCol, lutx, luty, zobsR, "dx2")
ypoy = (xp0oy * sintheta + yp0oy * costheta
) * reduced_coordi_factor + myC * ZernikeAnnularGrad(
zcCol, lutx, luty, zobsR, "dy2")
temp = myC * ZernikeAnnularGrad(zcCol, lutx, luty, zobsR,
"dxy")
# if temp==0,xpoy doesn't need to be symmetric about x=y
xpoy = (xp0oy * costheta -
yp0oy * sintheta) * reduced_coordi_factor + temp
# xpoy-flipud(rot90(ypox))==0 is true
ypox = (xp0ox * sintheta +
yp0ox * costheta) * reduced_coordi_factor + temp
J = xpox * ypoy - xpoy * ypox
return lutxp, lutyp, J
def _getFunction(self, name):
"""Decide to call the function of _poly10_2D() or _poly10Grad().
This is to correct the off-axis distortion. A numerical solution with
2-dimensions 10 order polynomials to map between the telescope
aperture and defocused image plane is used.
Parameters
----------
name : str
Function name to call.
Returns
-------
numpy.ndarray
Corrected image after the correction.
Raises
------
RuntimeError
Raise error if the function name does not exist.
"""
# Construct the dictionary table for calling function.
# The reason to use the dictionary is for the future's extension.
funcTable = dict(poly10_2D=self._poly10_2D,
poly10Grad=self._poly10Grad)
# Look for the function to call
if name in funcTable:
return funcTable[name]
# Error for unknown function name
raise RuntimeError("Unknown function name: %s" % name)
def _poly10_2D(self, c, data, y=None):
"""Correct the off-axis distortion by fitting with a 10 order
polynomial equation.
Parameters
----------
c : numpy.ndarray
Parameters of off-axis distrotion.
data : numpy.ndarray
X, y-coordinate on aperture. If y is provided this will be just
the x-coordinate.
y : numpy.ndarray, optional
Y-coordinate at aperture. (the default is None.)
Returns
-------
numpy.ndarray
Corrected parameters for off-axis distortion.
"""
# Decide the x, y-coordinate data on aperture
if y is None:
x = data[0, :]
y = data[1, :]
else:
x = data
# Correct the off-axis distortion
# Need to reorder the coefficients for use with GalSim:
carr = np.zeros((11, 11))
carr[np.tril_indices(11)] = c
for i in range(0, 11):
carr[:, i] = np.roll(carr[:, i], -i)
return horner2d(x, y, carr)
def _poly10Grad(self, c, x, y, atype):
"""Correct the off-axis distortion by fitting with a 10 order
polynomial equation in the gradient part.
Parameters
----------
c : numpy.ndarray
Parameters of off-axis distrotion.
x : numpy.ndarray
X-coordinate at aperture.
y : numpy.ndarray
Y-coordinate at aperture.
atype : str
Direction of gradient. It can be "dx" or "dy".
Returns
-------
numpy.ndarray
Corrected parameters for off-axis distortion.
Raises
------
ValueError
If atype is not 'dx' or 'dy'.
"""
if atype not in ["dx", "dy"]:
raise ValueError(f"Unknown atype: {atype}")
carr = np.zeros((11, 11))
carr[np.tril_indices(11)] = c
for i in range(0, 11):
carr[:, i] = np.roll(carr[:, i], -i)
grad = np.zeros(carr.shape, dtype=np.float64)
if atype == "dx":
for (i, j) in zip(*np.nonzero(carr)):
if i > 0:
grad[i - 1, j] = carr[i, j] * i
elif atype == "dy":
for (i, j) in zip(*np.nonzero(carr)):
if j > 0:
grad[i, j - 1] = carr[i, j] * j
return horner2d(x, y, grad)
def _createPupilGrid(self, lutx, luty, onepixel, ca, cb, ra, rb, fieldX,
fieldY):
"""Create the pupil grid in off-axis model.
This function gives the x,y-coordinate in the extended ring area
defined by the parameter of onepixel.
Parameters
----------
lutx : numpy.ndarray
X-coordinate on pupil plane.
luty : numpy.ndarray
Y-coordinate on pupil plane.
onepixel : float
Extended delta radius.
ca : float
Center of outer ring on the pupil plane.
cb : float
Center of inner ring on the pupil plane.
ra : float
Radius of outer ring on the pupil plane.
rb : float
Radius of inner ring on the pupil plane.
fieldX : float
X-coordinate of donut on the focal plane in degree.
fieldY : float
Y-coordinate of donut on the focal plane in degree.
Returns
-------
numpy.ndarray
X-coordinate of extended ring area on pupil plane.
numpy.ndarray
Y-coordinate of extended ring area on pupil plane.
"""
# Rotate the mask center after the off-axis correction based on the
# position of fieldX and fieldY
cax, cay, cbx, cby = self._rotateMaskParam(ca, cb, fieldX, fieldY)
# Get x, y coordinate of extended outer boundary by the linear
# approximation
lutx, luty = self._approximateExtendedXY(lutx, luty, cax, cay, ra,
ra + onepixel, "outer")
# Get x, y coordinate of extended inner boundary by the linear
# approximation
lutx, luty = self._approximateExtendedXY(lutx, luty, cbx, cby,
rb - onepixel, rb, "inner")
return lutx, luty
def _approximateExtendedXY(self, lutx, luty, cenX, cenY, innerR, outerR,
config):
"""Calculate the x, y-coordinate on pupil plane in the extended ring
area by the linear approximation, which is used in the off-axis
correction.
Parameters
----------
lutx : numpy.ndarray
X-coordinate on pupil plane.
luty : numpy.ndarray
Y-coordinate on pupil plane.
cenX : float
X-coordinate of boundary ring center.
cenY : float
Y-coordinate of boundary ring center.
innerR : float
Inner radius of extended ring.
outerR : float
Outer radius of extended ring.
config : str
Configuration to calculate the x,y-coordinate in the extended ring.
"inner": inner extended ring; "outer": outer extended ring.
Returns
-------
numpy.ndarray
X-coordinate of extended ring area on pupil plane.
numpy.ndarray
Y-coordinate of extended ring area on pupil plane.
"""
# Calculate the distance to rotated center of boundary ring
lutr = np.sqrt((lutx - cenX)**2 + (luty - cenY)**2)
# Define NaN to be 999 for the comparison in the following step
tmp = lutr.copy()
tmp[np.isnan(tmp)] = 999
# Get the available index that the related distance is between innderR
# and outerR
idxbound = (~np.isnan(lutr)) & (tmp >= innerR) & (tmp <= outerR)
# Deside R based on the configuration
if config == "outer":
R = innerR
# Get the index that the related distance is bigger than outerR
idxout = tmp > outerR
elif config == "inner":
R = outerR
# Get the index that the related distance is smaller than innerR
idxout = tmp < innerR
# Put the x, y-coordinate to be NaN if it is inside/ outside the pupil
# that is after the off-axis correction.
lutx[idxout] = np.nan
luty[idxout] = np.nan
# Get the x, y-coordinate in this ring area by the linear approximation
lutx[idxbound] = (lutx[idxbound] - cenX) / lutr[idxbound] * R + cenX
luty[idxbound] = (luty[idxbound] - cenY) / lutr[idxbound] * R + cenY
return lutx, luty
def _rotateMaskParam(self, ca, cb, fieldX, fieldY):
"""Rotate the mask-related parameters of center.
Parameters
----------
ca : float
Mask-related parameter of center.
cb : float
Mask-related parameter of center.
fieldX : float
X-coordinate of donut on the focal plane in degree.
fieldY : float
Y-coordinate of donut on the focal plane in degree.
Returns
-------
float
Projected x element after the rotation.
float
Projected y element after the rotation.
float
Projected x element after the rotation.
float
Projected y element after the rotation.
"""
# Calculate the sin(theta) and cos(theta) for the rotation
fieldDist = self._getFieldDistFromOrigin(fieldX=fieldX,
fieldY=fieldY,
minDist=0)
if fieldDist == 0:
c = 0
s = 0
else:
# Calculate cos(theta)
c = fieldX / fieldDist
# Calculate sin(theta)
s = fieldY / fieldDist
# Projected x and y coordinate after the rotation
cax = c * ca
cay = s * ca
cbx = c * cb
cby = s * cb
return cax, cay, cbx, cby
def centerOnProjection(self, img, template, window=20):
"""Center the image to the template's center.
Parameters
----------
img : numpy.array
Image to be centered with the template. The input image needs to
be a n-by-n matrix.
template : numpy.array
Template image to have the same dimension as the input image
('img'). The center of template is the position of input image
tries to align with.
window : int, optional
Size of window in pixel. Assume the difference of centers of input
image and template is in this range (e.g. [-window/2, window/2] if
1D). (the default is 20.)
Returns
-------
numpy.array
Recentered image.
"""
# Calculate the cross-correlate
corr = correlate(img, template, mode="same")
# Calculate the shifts of center
# Only consider the shifts in a certain window (range)
# Align the input image to the center of template
length = template.shape[0]
center = length // 2
r = window // 2
mask = np.zeros(corr.shape)
mask[center - r:center + r, center - r:center + r] = 1
idx = np.argmax(corr * mask)
# The above 'idx' is an interger. Need to rematch it to the
# two-dimension position (x and y)
xmatch = idx % length
ymatch = idx // length
dx = center - xmatch
dy = center - ymatch
# Shift/ recenter the input image
return np.roll(np.roll(img, dx, axis=1), dy, axis=0)
def setOffAxisCorr(self, inst, order):
"""Set the coefficients of off-axis correction for x, y-projection of
intra- and extra-image.
This is for the mapping of coordinate from the telescope aperture to
defocal image plane.
Parameters
----------
inst : Instrument
Instrument to use.
order : int
Up to order-th of off-axis correction.
"""
# List of configuration
configList = ["cxin", "cyin", "cxex", "cyex"]
# Get all files in the directory
instDir = inst.getInstFileDir()
fileList = [
f for f in os.listdir(instDir)
if os.path.isfile(os.path.join(instDir, f))
]
# Read files
offAxisCoeff = []
for config in configList:
# Construct the configuration file name
for fileName in fileList:
m = re.match(r"\S*%s\S*.yaml" % config, fileName)
if m is not None:
matchFileName = m.group()
break
filePath = os.path.join(instDir, matchFileName)
corrCoeff, offset = self._getOffAxisCorrSingle(filePath)
offAxisCoeff.append(corrCoeff)
# Give the values
self.offAxisCoeff = np.array(offAxisCoeff)
self.offAxisOffset = offset
def _getOffAxisCorrSingle(self, confFile):
"""Get the image-related parameters for the off-axis distortion by the
linear approximation with a series of fitted parameters with LSST
ZEMAX model.
Parameters
----------
confFile : str
Path of configuration file.
Returns
-------
numpy.ndarray
Coefficients for the off-axis distortion based on the linear
response.
float
Defocal distance in m.
"""
fieldDist = self._getFieldDistFromOrigin(minDist=0.0)
# Read the configuration file
paramReader = ParamReader()
paramReader.setFilePath(confFile)
cdata = paramReader.getMatContent()
# Record the offset (defocal distance)
offset = cdata[0, 0]
# Take the reference parameters
c = cdata[:, 1:]
# Get the ruler, which is the distance to center
# ruler is between 1.51 and 1.84 degree here
ruler = np.sqrt(c[:, 0]**2 + c[:, 1]**2)
# Get the fitted parameters for off-axis correction by linear
# approximation
corr_coeff = self._linearApprox(fieldDist, ruler, c[:, 2:])
return corr_coeff, offset
def _interpMaskParam(self, fieldX, fieldY, maskParam):
"""Get the mask-related parameters for the off-axis distortion and
vignetting correction by the linear approximation with a series of
fitted parameters with LSST ZEMAX model.
Parameters
----------
fieldX : float
X-coordinate of donut on the focal plane in degree.
fieldY : float
Y-coordinate of donut on the focal plane in degree.
maskParam : numpy.ndarray
Fitted coefficients for the off-axis distortion and vignetting
correction.
Returns
-------
float
'ca' coefficient for the off-axis distortion and vignetting
correction based on the linear response.
float
'ra' coefficient for the off-axis distortion and vignetting
correction based on the linear response.
float
'cb' coefficient for the off-axis distortion and vignetting
correction based on the linear response.
float
'rb' coefficient for the off-axis distortion and vignetting
correction based on the linear response.
"""
# Calculate the distance from donut to origin (aperture)
filedDist = np.sqrt(fieldX**2 + fieldY**2)
# Get the ruler, which is the distance to center
# ruler is between 1.51 and 1.84 degree here
ruler = np.sqrt(2) * maskParam[:, 0]
# Get the fitted parameters for off-axis correction by linear
# approximation
param = self._linearApprox(filedDist, ruler, maskParam[:, 1:])
# Define related parameters
ca = param[0]
ra = param[1]
cb = param[2]
rb = param[3]
return ca, ra, cb, rb
def _linearApprox(self, fieldDist, ruler, parameters):
"""Get the fitted parameters for off-axis correction by linear
approximation.
Parameters
----------
fieldDist : float
Field distance from donut to origin (aperture).
ruler : numpy.ndarray
A series of distance with available parameters for the fitting.
parameters : numpy.ndarray
Referenced parameters for the fitting.
Returns
-------
numpy.ndarray
Fitted parameters based on the linear approximation.
"""
# Sort the ruler and parameters based on the magnitude of ruler
sortIndex = np.argsort(ruler)
ruler = ruler[sortIndex]
parameters = parameters[sortIndex, :]
# Compare the distance to center (aperture) between donut and standard
compDis = ruler >= fieldDist
# fieldDist is too big and out of range
if fieldDist > ruler.max():
# Take the coefficients in the highest boundary
p2 = parameters.shape[0] - 1
p1 = 0
w1 = 0
w2 = 1
# fieldDist is too small to be in the range
elif fieldDist < ruler.min():
# Take the coefficients in the lowest boundary
p2 = 0
p1 = 0
w1 = 1
w2 = 0
# fieldDist is in the range
else:
# Find the boundary of fieldDist in the known data
p2 = compDis.argmax()
p1 = p2 - 1
# Calculate the weighting ratio
w1 = (ruler[p2] - fieldDist) / (ruler[p2] - ruler[p1])
w2 = 1 - w1
# Get the fitted parameters for off-axis correction by linear
# approximation
param = w1 * parameters[p1, :] + w2 * parameters[p2, :]
return param
def makeMaskList(self, inst, model):
"""Calculate the mask list based on the obscuration and optical model.
Parameters
----------
inst : Instrument
Instrument to use.
model : str
Optical model. It can be "paraxial", "onAxis", or "offAxis".
Returns
-------
numpy.ndarray
The list of mask.
"""
# Masklist = [center_x, center_y, radius_of_boundary,
# 1/ 0 for outer/ inner boundary]
obscuration = inst.getObscuration()
if model in ("paraxial", "onAxis"):
if obscuration == 0:
masklist = np.array([[0, 0, 1, 1]])
else:
masklist = np.array([[0, 0, 1, 1], [0, 0, obscuration, 0]])
else:
# Get the mask-related parameters
maskCa, maskRa, maskCb, maskRb = self._interpMaskParam(
self.fieldX, self.fieldY, inst.getMaskOffAxisCorr())
# Rotate the mask-related parameters of center
cax, cay, cbx, cby = self._rotateMaskParam(maskCa, maskCb,
self.fieldX,
self.fieldY)
masklist = np.array([
[0, 0, 1, 1],
[0, 0, obscuration, 0],
[cax, cay, maskRa, 1],
[cbx, cby, maskRb, 0],
])
return masklist
def _showProjection(self,
lutxp,
lutyp,
sensorFactor,
projSamples,
raytrace=False):
"""Calculate the x, y-projection of image on pupil.
This can be used to calculate the center of projection in compensate().
Parameters
----------
lutxp : numpy.ndarray
X-coordinate on pupil plane. The value of element will be NaN if
that point is not inside the pupil.
lutyp : numpy.ndarray
Y-coordinate on pupil plane. The value of element will be NaN if
that point is not inside the pupil.
sensorFactor : float
Sensor factor.
projSamples : int
Dimension of projected image. This value considers the
magnification ratio of donut image.
raytrace : bool, optional
Consider the ray trace or not. If the value is true, the times of
photon hit will aggregate. (the default is False.)
Returns
-------
numpy.ndarray
Projection of image. It will be a binary image if raytrace=False.
"""
# Dimension of pupil image
n1, n2 = lutxp.shape
# Construct the binary matrix on pupil. It is noted that if the
# raytrace is true, the value of element is allowed to be greater
# than 1.
show_lutxyp = np.zeros((n1, n2))
# Get the index in pupil. If a point's value is NaN, this point is
# outside the pupil.
idx = ~np.isnan(lutxp)
# Calculate the projected x, y-coordinate in pixel
# x=0.5 is center of pixel#1
xR = np.zeros((n1, n2))
yR = np.zeros((n1, n2))
xR[idx] = np.round((lutxp[idx] + sensorFactor) *
(projSamples / sensorFactor) / 2 + 0.5)
yR[idx] = np.round((lutyp[idx] + sensorFactor) *
(projSamples / sensorFactor) / 2 + 0.5)
# Check the projected coordinate is in the range of image or not.
# If the check passes, the times will be recorded.
mask = np.bitwise_and(
np.bitwise_and(np.bitwise_and(xR > 0, xR < n2), yR > 0), yR < n1)
# Check the projected coordinate is in the range of image or not.
# If the check passes, the times will be recorded.
if raytrace:
for ii, jj in zip(
np.array(yR - 1, dtype=int)[mask],
np.array(xR - 1, dtype=int)[mask]):
show_lutxyp[ii, jj] += 1
else:
show_lutxyp[np.array(yR - 1, dtype=int)[mask],
np.array(xR - 1, dtype=int)[mask]] = 1
return show_lutxyp
def makeMask(self, inst, model, boundaryT, maskScalingFactorLocal):
"""Get the binary mask which considers the obscuration and off-axis
correction.
There will be two mask parameters to be calculated:
mask_comp: computation mask, i.e. padded mask,
for use at the offset planes
mask_pupil: pupil mask, i.e. non-padded mask,
corresponding to aperture
Parameters
----------
inst : Instrument
Instrument to use.
model : str
Optical model. It can be "paraxial", "onAxis", or "offAxis".
boundaryT : int
Extended boundary in pixel. It defines how far the computation mask
extends beyond the pupil mask. And, in fft, it is also the width of
Neuman boundary where the derivative of the wavefront is set to
zero.
maskScalingFactorLocal : float
Mask scaling factor (for fast beam) for local correction.
"""
dimOfDonut = inst.getDimOfDonutOnSensor()
self.mask_pupil = np.ones(dimOfDonut, dtype=int)
self.mask_comp = self.mask_pupil.copy()
apertureDiameter = inst.getApertureDiameter()
focalLength = inst.getFocalLength()
offset = inst.getDefocalDisOffset()
rMask = apertureDiameter / (2 * focalLength /
offset) * maskScalingFactorLocal
# Get the mask list
pixelSize = inst.getCamPixelSize()
xSensor, ySensor = inst.getSensorCoor()
masklist = self.makeMaskList(inst, model)
for ii in range(masklist.shape[0]):
# Distance to center on pupil
r = np.sqrt((xSensor - masklist[ii, 0])**2 +
(ySensor - masklist[ii, 1])**2)
# Find the indices that correspond to the mask element, set them to
# the pass/ block boolean
# Get the index inside the aperture
idx = r <= masklist[ii, 2]
# Get the higher and lower boundary beyond the pupil mask by
# extension.
# The extension level is dicided by boundaryT.
# In fft, this is also the Neuman boundary where the derivative of
# the wavefront is set to zero.
if masklist[ii, 3] >= 1:
aidx = np.nonzero(r <= masklist[ii, 2] *
(1 + boundaryT * pixelSize / rMask))
else:
aidx = np.nonzero(r <= masklist[ii, 2] *
(1 - boundaryT * pixelSize / rMask))
# Initialize both mask elements to the opposite of the pass/ block
# boolean
mask_pupil_ii = (1 - int(masklist[ii, 3])) * np.ones(
[dimOfDonut, dimOfDonut], dtype=int)
mask_comp_ii = mask_pupil_ii.copy()
mask_pupil_ii[idx] = int(masklist[ii, 3])
mask_comp_ii[aidx] = int(masklist[ii, 3])
# Multiplicatively add the current mask elements to the model
# masks.
# This is try to find the common mask region.
# non-padded mask corresponding to aperture
self.mask_pupil = self.mask_pupil * mask_pupil_ii
# padded mask for use at the offset planes
self.mask_comp = self.mask_comp * mask_comp_ii
class TestImage(unittest.TestCase):
"""Test the Image class."""
def setUp(self):
# Get the path of module
modulePath = getModulePath()
# Define the algorithm folder
algoFolderPath = os.path.join(modulePath, "configData", "cwfs", "algo")
# Define the image folder and image names
# Image data -- Don't know the final image format.
# It is noted that image.readFile inuts is based on the txt file
imageFolderPath = os.path.join(modulePath, "tests", "testData",
"testImages", "LSST_NE_SN25")
imgName = "z11_0.25_intra.txt"
# Image files Path
imgFile = os.path.join(imageFolderPath, imgName)
# There is the difference between intra and extra images
self.img = Image()
self.img.setImg(imageFile=imgFile)
def testZeroImg(self):
# Creat a zero image
zeroImg = Image()
zeroImg.setImg(image=np.zeros([4, 4]))
self.assertEqual(np.sum(zeroImg.image), 0)
# Update Image
zeroImg.updateImage(np.ones([4, 4]))
self.assertEqual(np.sum(zeroImg.image), 16)
realcx, realcy, realR, imgBinary = zeroImg.getCenterAndR_ef(
randNumFilePath=None, checkEntropy=True)
self.assertEqual(realcx, [])
# update to the random image
zeroImg.updateImage(np.random.rand(100, 100))
realcx, realcy, realR, imgBinary = zeroImg.getCenterAndR_ef(
randNumFilePath=None, checkEntropy=True)
self.assertEqual(realcx, [])
def testImg(self):
realcx, realcy, realR, imgBinary = self.img.getCenterAndR_ef(
randNumFilePath=None, checkEntropy=True)
self.assertEqual(int(realcx), 61)
self.assertEqual(int(realcy), 61)
self.assertGreater(int(realR), 35)
# Calculate the S/N
# Add the noise to the image
noisedImg = self.img.image + np.random.random(
self.img.image.shape) * 0.1
self.img.setImg(image=noisedImg)
snr = self.img.getSNR()
self.assertGreater(snr, 15)
def _runWep(self, imgIntraName, imgExtraName, offset, model):
# Cut the donut image from input files
centroidFindType = CentroidFindType.Otsu
imgIntra = Image(centroidFindType=centroidFindType)
imgExtra = Image(centroidFindType=centroidFindType)
imgIntraPath = os.path.join(self.testImgDir, imgIntraName)
imgExtraPath = os.path.join(self.testImgDir, imgExtraName)
imgIntra.setImg(imageFile=imgIntraPath)
imgExtra.setImg(imageFile=imgExtraPath)
xIntra, yIntra, _ = imgIntra.getCenterAndR()
imgIntraArray = imgIntra.getImg()[int(yIntra) - offset:int(yIntra) +
offset,
int(xIntra) - offset:int(xIntra) +
offset, ]
xExtra, yExtra, _ = imgExtra.getCenterAndR()
imgExtraArray = imgExtra.getImg()[int(yExtra) - offset:int(yExtra) +
offset,
int(xExtra) - offset:int(xExtra) +
offset, ]
# Set the images
fieldXY = (0, 0)
imgCompIntra = CompensableImage(centroidFindType=centroidFindType)
imgCompIntra.setImg(fieldXY, DefocalType.Intra, image=imgIntraArray)
imgCompExtra = CompensableImage(centroidFindType=centroidFindType)
imgCompExtra.setImg(fieldXY, DefocalType.Extra, image=imgExtraArray)
# Calculate the wavefront error
# Set the instrument
instDir = os.path.join(getConfigDir(), "cwfs", "instData")
instAuxTel = Instrument(instDir)
instAuxTel.config(CamType.AuxTel,
imgCompIntra.getImgSizeInPix(),
announcedDefocalDisInMm=0.8)
# Set the algorithm
algoFolderPath = os.path.join(getConfigDir(), "cwfs", "algo")
algoAuxTel = Algorithm(algoFolderPath)
algoAuxTel.config("exp", instAuxTel)
algoAuxTel.runIt(imgCompIntra, imgCompExtra, model)
return algoAuxTel.getZer4UpInNm()
class TestImage(unittest.TestCase):
"""Test the Image class."""
def setUp(self):
self.testDataDir = os.path.join(getModulePath(), "tests", "testData")
self.imgFile = os.path.join(
self.testDataDir, "testImages", "LSST_NE_SN25", "z11_0.25_intra.txt"
)
self.img = Image()
self.img.setImg(imageFile=self.imgFile)
def testGetCentroidFind(self):
centroidFind = self.img.getCentroidFind()
self.assertTrue(isinstance(centroidFind, CentroidRandomWalk))
def testGetImg(self):
img = self.img.getImg()
self.assertEqual(img.shape, (120, 120))
def testGetImgFilePath(self):
imgFilePath = self.img.getImgFilePath()
self.assertEqual(imgFilePath, self.imgFile)
def testSetImgByImageArray(self):
newImg = np.random.rand(5, 5)
self.img.setImg(image=newImg)
self.assertTrue(np.all(self.img.getImg() == newImg))
self.assertEqual(self.img.getImgFilePath(), "")
def testSetImgByFitsFile(self):
opdFitsFile = os.path.join(
self.testDataDir, "opdOutput", "9006000", "opd_9006000_0.fits.gz"
)
self.img.setImg(imageFile=opdFitsFile)
img = self.img.getImg()
self.assertEqual(img.shape, (255, 255))
imgFilePath = self.img.getImgFilePath()
self.assertEqual(imgFilePath, opdFitsFile)
def testUpdateImage(self):
newImg = np.random.rand(5, 5)
self.img.updateImage(newImg)
self.assertTrue(np.all(self.img.getImg() == newImg))
def testUpdateImageWithNoHoldImage(self):
img = Image()
newImg = np.random.rand(5, 5)
self.assertWarns(UserWarning, img.updateImage, newImg)
def testGetCenterAndR_ef(self):
realcx, realcy, realR = self.img.getCenterAndR()
self.assertEqual(int(realcx), 61)
self.assertEqual(int(realcy), 61)
self.assertGreater(int(realR), 35)
def testGetSNR(self):
# Add the noise to the image
image = self.img.getImg()
noisedImg = image + np.random.random(image.shape) * 0.1
self.img.setImg(image=noisedImg)
snr = self.img.getSNR()
self.assertGreater(snr, 15)
class CompensationImageDecorator(object):
# Constant
INTRA = "intra"
EXTRA = "extra"
def __init__(self):
"""
Instantiate the class of CompensationImageDecorator.
"""
self.__image = None
# Parameters used for transport of intensity equation (TIE)
self.sizeinPix = None
self.fieldX = None
self.fieldY = None
self.image0 = None
self.fldr = None
self.atype = None
self.offAxis_coeff = None
self.offAxisOffset = None
self.caustic = False
self.pMask = None
self.cMask = None
def __getattr__(self, attributeName):
"""
Use the functions and attributes hold by the object.
Arguments:
attributeName {[str]} -- Name of attribute or function.
Returns:
[str] -- Returned values.
"""
return getattr(self.__image, attributeName)
def setImg(self, fieldXY, image=None, imageFile=None, atype=None):
"""
Set the wavefront image.
Arguments:
fieldXY {[float]} -- Position of donut on the focal plane in degree.
Keyword Arguments:
image {[float]} -- Array of image. (default: {None})
imageFile {[string]} -- Path of image file. (default: {None})
atype {[string]} -- Type of image. It should be "intra" or "extra". (default: {None})
Raises:
TypeError -- Error if the atype is not "intra" or "extra".
"""
# Instantiate the image object
self.__image = Image()
# Read the file if there is no input image
self.__image.setImg(image=image, imageFile=imageFile)
# Make sure the image size is n by n
if (self.__image.image.shape[0] != self.__image.image.shape[1]):
raise RuntimeError("Only square image stamps are accepted.")
elif (self.__image.image.shape[0] % 2 == 1):
raise RuntimeError("Number of pixels cannot be odd numbers.")
# Dimension of image
self.sizeinPix = self.__image.image.shape[0]
# Donut position in degree
self.fieldX, self.fieldY = fieldXY
# Save the initial image if we want the compensator always start from this
self.image0 = None
# We will need self.fldr to be on denominator
self.fldr = np.max((np.hypot(self.fieldX, self.fieldY), 1e-8))
# Check the type of image
if atype.lower() not in (self.INTRA, self.EXTRA):
raise TypeError("Image defocal type must be 'intra' or 'extra'.")
self.atype = atype
# Coefficient to do the off-axis correction
self.offAxis_coeff = None
# Defocal distance (Baseline is 1.5mm. The configuration file now is 1mm.)
self.offAxisOffset = 0
# Check the image has the problem or not
self.caustic = False
# Reset all mask related parameters
self.pMask = None
self.cMask = None
def updateImage0(self):
"""
Update the backup of initial image. This will be used in the outer loop iteration, which
always uses the initial image (image0) before each iteration starts.
"""
# Update the initial image for future use
self.image0 = self.__image.image.copy()
def imageCoCenter(self, inst, fov=3.5, debugLevel=0):
"""
Shift the weighting center of donut to the center of reference image with the correction of
projection of fieldX and fieldY.
Arguments:
inst {[Instrument]} -- Instrument to use.
Keyword Arguments:
fov {[float]} -- Field of view (FOV) of telescope. (default: {3.5})
debugLevel {[int]} -- Show the information under the running. If the value is higher,
the information shows more. It can be 0, 1, 2, or 3. (default: {0})
"""
# Calculate the weighting center (x, y) and radius
x1, y1 = self.getCenterAndR_ef()[0:2]
# Show the co-center information
if (debugLevel >= 3):
print("imageCoCenter: (x, y) = (%8.2f,%8.2f)\n" % (x1, y1))
# Calculate the center position on image
# 0.5 is the half of 1 pixel
sensorSamples = inst.parameter["sensorSamples"]
stampCenterx1 = sensorSamples / 2. + 0.5
stampCentery1 = sensorSamples / 2. + 0.5
# Shift in the radial direction
# The field of view (FOV) of LSST camera is 3.5 degree
offset = inst.parameter["offset"]
pixelSize = inst.parameter["pixelSize"]
radialShift = fov * (offset / 1e-3) * (10e-6 / pixelSize)
# Calculate the projection of distance of donut to center
radialShift = radialShift * (self.fldr / (fov / 2))
# Do not consider the condition out of FOV of lsst
if (self.fldr > (fov / 2)):
radialShift = 0
# Calculate the cos(theta) for projection
I1c = self.fieldX / self.fldr
# Calculate the sin(theta) for projection
I1s = self.fieldY / self.fldr
# Get the projected x, y-coordinate
stampCenterx1 = stampCenterx1 + radialShift * I1c
stampCentery1 = stampCentery1 + radialShift * I1s
# Shift the image to the projected position
self.__image.updateImage(
np.roll(self.__image.image,
int(np.round(stampCentery1 - y1)),
axis=0))
self.__image.updateImage(
np.roll(self.__image.image,
int(np.round(stampCenterx1 - x1)),
axis=1))
def compensate(self, inst, algo, zcCol, model):
"""
Calculate the image compensated from the affection of wavefront.
Arguments:
inst {[Instrument]} -- Instrument to use.
algo {[Algorithm]} -- Algorithm to solve the Poisson's equation. It can by done
by the fast Fourier transform or serial expansion.
zcCol {[float]} -- Coefficients of wavefront.
model {[string]} -- Optical model. It can be "paraxial", "onAxis", or "offAxis".
Raises:
Exception -- Number of terms of normal/ annular Zernike polynomilas does
not match the needed number for compensation to use.
"""
# Check the condition of inputs
numTerms = algo.parameter["numTerms"]
if ((zcCol.ndim == 1) and (len(zcCol) != numTerms)):
raise RuntimeError(
"input:size",
"zcCol in compensate needs to be a %d row column vector. \n" %
numTerms)
# Dimension of image
sm, sn = self.__image.image.shape
# Dimenstion of projected image on focal plane
projSamples = sm
# Let us create a look-up table for x -> xp first.
luty, lutx = np.mgrid[-(projSamples / 2 - 0.5):(projSamples / 2 + 0.5),
-(projSamples / 2 - 0.5):(projSamples / 2 + 0.5)]
sensorFactor = inst.parameter["sensorFactor"]
lutx = lutx / (projSamples / 2 / sensorFactor)
luty = luty / (projSamples / 2 / sensorFactor)
# Set up the mapping
lutxp, lutyp, J = self.__aperture2image(inst, algo, zcCol, lutx, luty,
projSamples, model)
show_lutxyp = self.__showProjection(lutxp,
lutyp,
sensorFactor,
projSamples,
raytrace=False)
if (np.all(show_lutxyp <= 0)):
self.caustic = True
return
# Calculate the weighting center (x, y) and radius
realcx, realcy = self.__image.getCenterAndR_ef()[0:2]
# Extend the dimension of image by 20 pixel in x and y direction
show_lutxyp = padArray(show_lutxyp, projSamples + 20)
# Get the binary matrix of image on pupil plane if raytrace=False
struct0 = generate_binary_structure(2, 1)
struct = iterate_structure(struct0, 4)
struct = binary_dilation(struct, structure=struct0,
iterations=2).astype(int)
show_lutxyp = binary_dilation(show_lutxyp, structure=struct)
show_lutxyp = binary_erosion(show_lutxyp, structure=struct)
# Extract the region from the center of image and get the original one
show_lutxyp = extractArray(show_lutxyp, projSamples)
# Calculate the weighting center (x, y) and radius
projcx, projcy = self.__image.getCenterAndR_ef(
image=show_lutxyp.astype(float))[0:2]
# Shift the image to center of projection on pupil
# +(-) means we need to move image to the right (left)
shiftx = projcx - realcx
# +(-) means we need to move image upward (downward)
shifty = projcy - realcy
self.__image.image = np.roll(self.__image.image,
int(np.round(shifty)),
axis=0)
self.__image.image = np.roll(self.__image.image,
int(np.round(shiftx)),
axis=1)
# Construct the interpolant to get the intensity on (x', p') plane
# that corresponds to the grid points on (x,y)
yp, xp = np.mgrid[-(sm / 2 - 0.5):(sm / 2 + 0.5),
-(sm / 2 - 0.5):(sm / 2 + 0.5)]
xp = xp / (sm / 2 / sensorFactor)
yp = yp / (sm / 2 / sensorFactor)
# Put the NaN to be 0 for the interpolate to use
lutxp[np.isnan(lutxp)] = 0
lutyp[np.isnan(lutyp)] = 0
# Construct the function for interpolation
ip = RectBivariateSpline(yp[:, 0],
xp[0, :],
self.__image.image,
kx=1,
ky=1)
# Construct the projected image by the interpolation
lutIp = np.zeros(lutxp.shape[0] * lutxp.shape[1])
for ii, (xx, yy) in enumerate(zip(lutxp.ravel(), lutyp.ravel())):
lutIp[ii] = ip(yy, xx)
lutIp = lutIp.reshape(lutxp.shape)
# Calaculate the image on focal plane with compensation based on flux conservation
# I(x, y)/I'(x', y') = J = (dx'/dx)*(dy'/dy) - (dx'/dy)*(dy'/dx)
self.__image.image = lutIp * J
if (self.atype == "extra"):
self.__image.image = np.rot90(self.__image.image, k=2)
# Put NaN to be 0
self.__image.image[np.isnan(self.__image.image)] = 0
# Check the compensated image has the problem or not.
# The negative value means the over-compensation from wavefront error
if (np.any(self.__image.image < 0) and np.all(self.image0 >= 0)):
print(
"WARNING: negative scale parameter, image is within caustic, zcCol (in um)=\n"
)
self.caustic = True
# Put the overcompensated part to be 0.
self.__image.image[self.__image.image < 0] = 0
def __aperture2image(self, inst, algo, zcCol, lutx, luty, projSamples,
model):
"""
Calculate the x, y-coordinate on the focal plane and the related Jacobian matrix.
Arguments:
inst {[Instrument]} -- Instrument to use.
algo {[Algorithm]} -- Algorithm to solve the Poisson's equation. It can by done
by the fast Fourier transform or serial expansion.
zcCol {[float]} -- Coefficients of optical basis. It is Zernike polynomials in the
baseline.
lutx {[float]} -- x-coordinate on pupil plane.
luty {[float]} -- y-coordinate on pupil plane.
projSamples {[int]} -- Dimension of projected image. This value considers the
magnification ratio of donut image.
model {[string]} -- Optical model. It can be "paraxial", "onAxis", or "offAxis".
Returns:
[float] -- x, y-coordinate on the focal plane.
[float] -- Jacobian matrix between the pupil and focal plane.
"""
# Get the radius: R = D/2
R = inst.parameter["apertureDiameter"] / 2.0
# Calculate C = -f(f-l)/l/R^2. This is for the calculation of reduced coordinate.
if (self.atype == self.INTRA):
l = inst.parameter["offset"]
elif (self.atype == self.EXTRA):
l = -inst.parameter["offset"]
focalLength = inst.parameter["focalLength"]
myC = -focalLength * (focalLength - l) / l / R**2
# Get the functions to do the off-axis correction by numerical fitting
# Order to do the off-axis correction. The order is 10 now.
offAxisPolyOrder = algo.parameter["offAxisPolyOrder"]
polyFunc = self.__getFunction("poly%d_2D" % offAxisPolyOrder)
polyGradFunc = self.__getFunction("poly%dGrad" % offAxisPolyOrder)
# Calculate the distance to center
lutr = np.sqrt(lutx**2 + luty**2)
# Calculated the extended ring radius (delta r), which is to extended the available
# pupil area.
# 1 pixel larger than projected pupil. No need to be EF-like, anything
# outside of this will be masked off by the computational mask
sensorFactor = inst.parameter["sensorFactor"]
onepixel = 1 / (projSamples / 2 / sensorFactor)
# Get the index that the point is out of the range of extended pupil
obscuration = inst.parameter["obscuration"]
idxout = (lutr > 1 + onepixel) | (lutr < obscuration - onepixel)
# Define the element to be NaN if it is out of range
lutx[idxout] = np.nan
luty[idxout] = np.nan
# Get the index in the extended area of outer boundary with the width of onepixel
idxbound = (lutr <= 1 + onepixel) & (lutr > 1)
# Calculate the extended x, y-coordinate (x' = x/r*r', r'=1)
lutx[idxbound] = lutx[idxbound] / lutr[idxbound]
luty[idxbound] = luty[idxbound] / lutr[idxbound]
# Get the index in the extended area of inner boundary with the width of onepixel
idxinbd = (lutr < obscuration) & (lutr > obscuration - onepixel)
# Calculate the extended x, y-coordinate (x' = x/r*r', r'=obscuration)
lutx[idxinbd] = lutx[idxinbd] / lutr[idxinbd] * obscuration
luty[idxinbd] = luty[idxinbd] / lutr[idxinbd] * obscuration
# Get the corrected x, y-coordinate on focal plane (lutxp, lutyp)
if (model == "paraxial"):
# No correction is needed in "paraxial" model
lutxp = lutx
lutyp = luty
elif (model == "onAxis"):
# Calculate F(x, y) = m * sqrt(f^2-R^2) / sqrt(f^2-(x^2+y^2)*R^2)
# m is the mask scaling factor
myA2 = (focalLength**2 - R**2) / (focalLength**2 - lutr**2 * R**2)
# Put the unphysical value as NaN
myA = myA2.copy()
idx = (myA < 0)
myA[idx] = np.nan
myA[~idx] = np.sqrt(myA2[~idx])
# Mask scaling factor (for fast beam)
maskScalingFactor = algo.parameter["maskScalingFactor"]
# Calculate the x, y-coordinate on focal plane
# x' = F(x,y)*x + C*(dW/dx), y' = F(x,y)*y + C*(dW/dy)
lutxp = maskScalingFactor * myA * lutx
lutyp = maskScalingFactor * myA * luty
elif (model == "offAxis"):
# Get the coefficient of polynomials for off-axis correction
tt = self.offAxisOffset
cx = (self.offAxis_coeff[0, :] - self.offAxis_coeff[2, :]) * (tt+l)/(2*tt) + \
self.offAxis_coeff[2, :]
cy = (self.offAxis_coeff[1, :] - self.offAxis_coeff[3, :]) * (tt+l)/(2*tt) + \
self.offAxis_coeff[3, :]
# This will be inverted back by typesign later on.
# We do the inversion here to make the (x,y)->(x',y') equations has
# the same form as the paraxial case.
cx = np.sign(l) * cx
cy = np.sign(l) * cy
# Do the orthogonalization: x'=1/sqrt(2)*(x+y), y'=1/sqrt(2)*(x-y)
# Calculate the rotation angle for the orthogonalization
costheta = (self.fieldX + self.fieldY) / self.fldr / np.sqrt(2)
if (costheta > 1):
costheta = 1
elif (costheta < -1):
costheta = -1
sintheta = np.sqrt(1 - costheta**2)
if (self.fieldY < self.fieldX):
sintheta = -sintheta
# Create the pupil grid in off-axis model. This gives the x,y-coordinate
# in the extended ring area defined by the parameter of onepixel.
# Get the mask-related parameters
maskCa, maskRa, maskCb, maskRb = self.__interpMaskParam(
self.fieldX, self.fieldY, inst.maskParam)
lutx, luty = self.__createPupilGrid(lutx, luty, onepixel, maskCa,
maskCb, maskRa, maskRb,
self.fieldX, self.fieldY)
# Calculate the x, y-coordinate on focal plane
# First rotate back to reference orientation
lutx0 = lutx * costheta + luty * sintheta
luty0 = -lutx * sintheta + luty * costheta
# Use the mapping at reference orientation
lutxp0 = polyFunc(cx, lutx0, y=luty0)
lutyp0 = polyFunc(cy, lutx0, y=luty0)
# Rotate back to focal plane
lutxp = lutxp0 * costheta - lutyp0 * sintheta
lutyp = lutxp0 * sintheta + lutyp0 * costheta
# Zemax data are in mm, therefore 1000
sensorSamples = inst.parameter["sensorSamples"]
pixelSize = inst.parameter["pixelSize"]
reduced_coordi_factor = 1e-3 / (sensorSamples / 2 * pixelSize /
sensorFactor)
# Reduced coordinates, so that this can be added with the dW/dz
lutxp = lutxp * reduced_coordi_factor
lutyp = lutyp * reduced_coordi_factor
else:
print('Wrong optical model type in compensate. \n')
return
# Obscuration of annular aperture
zobsR = algo.parameter["zobsR"]
# Calculate the x, y-coordinate on focal plane
# x' = F(x,y)*x + C*(dW/dx), y' = F(x,y)*y + C*(dW/dy)
# In Model basis (zer: Zernike polynomials)
if (zcCol.ndim == 1):
lutxp = lutxp + myC * ZernikeAnnularGrad(zcCol, lutx, luty, zobsR,
"dx")
lutyp = lutyp + myC * ZernikeAnnularGrad(zcCol, lutx, luty, zobsR,
"dy")
# Make the sign to be consistent
if (self.atype == "extra"):
lutxp = -lutxp
lutyp = -lutyp
# Calculate the Jacobian matrix
# In Model basis (zer: Zernike polynomials)
if (zcCol.ndim == 1):
if (model == "paraxial"):
J = 1 + myC * ZernikeAnnularJacobian(zcCol, lutx, luty, zobsR, "1st") + \
myC**2 * ZernikeAnnularJacobian(zcCol, lutx, luty, zobsR, "2nd")
elif (model == "onAxis"):
xpox = maskScalingFactor * myA * (1 + \
lutx**2 * R**2. / (focalLength**2 - R**2 * lutr**2)) + \
myC * ZernikeAnnularGrad(zcCol, lutx, luty, zobsR, "dx2")
ypoy = maskScalingFactor * myA * (1 + \
luty**2 * R**2. / (focalLength**2 - R**2 * lutr**2)) + \
myC * ZernikeAnnularGrad(zcCol, lutx, luty, zobsR, "dy2")
xpoy = maskScalingFactor * myA * \
lutx * luty * R**2 / (focalLength**2 - R**2 * lutr**2) + \
myC * ZernikeAnnularGrad(zcCol, lutx, luty, zobsR, "dxy")
ypox = xpoy
J = xpox * ypoy - xpoy * ypox
elif (model == "offAxis"):
xp0ox = polyGradFunc(cx, lutx0, luty0, "dx") * costheta - \
polyGradFunc(cx, lutx0, luty0, "dy") * sintheta
yp0ox = polyGradFunc(cy, lutx0, luty0, "dx") * costheta - \
polyGradFunc(cy, lutx0, luty0, "dy") * sintheta
xp0oy = polyGradFunc(cx, lutx0, luty0, "dx") * sintheta + \
polyGradFunc(cx, lutx0, luty0, "dy") * costheta
yp0oy = polyGradFunc(cy, lutx0, luty0, "dx") * sintheta + \
polyGradFunc(cy, lutx0, luty0, "dy") * costheta
xpox = (xp0ox*costheta - yp0ox*sintheta)*reduced_coordi_factor + \
myC*ZernikeAnnularGrad(zcCol, lutx, luty, zobsR, "dx2")
ypoy = (xp0oy*sintheta + yp0oy*costheta)*reduced_coordi_factor + \
myC*ZernikeAnnularGrad(zcCol, lutx, luty, zobsR, "dy2")
temp = myC * ZernikeAnnularGrad(zcCol, lutx, luty, zobsR,
"dxy")
# if temp==0,xpoy doesn't need to be symmetric about x=y
xpoy = (xp0oy * costheta -
yp0oy * sintheta) * reduced_coordi_factor + temp
# xpoy-flipud(rot90(ypox))==0 is true
ypox = (xp0ox * sintheta +
yp0ox * costheta) * reduced_coordi_factor + temp
J = xpox * ypoy - xpoy * ypox
return lutxp, lutyp, J
def __getFunction(self, name):
"""
Decide to call the function of __poly10_2D() or __poly10Grad(). This is to correct
the off-axis distortion. A numerical solution with 2-dimensions 10 order polynomials
to map between the telescope aperature and defocused image plane is used.
Arguments:
name {[string]} -- Function name to call.
Returns:
[float] -- Corrected image after the correction.
Raises:
RuntimeError -- Raise error if the function name does not exist.
"""
# Construnct the dictionary table for calling function.
# The reason to use the dictionary is for the future's extension.
funcTable = dict(poly10_2D=self.__poly10_2D,
poly10Grad=self.__poly10Grad)
# Look for the function to call
if name in funcTable:
return funcTable[name]
# Error for unknown function name
raise RuntimeError("Unknown function name: %s" % name)
def __poly10_2D(self, c, data, y=None):
"""
Correct the off-axis distortion by fitting with a 10 order polynomial
equation.
Arguments:
c {[float]} -- Parameters of off-axis distrotion.
data {[float]} -- x, y-coordinate on aperature. If y is provided,
this will be just the x-coordinate.
Keyword Arguments:
y {[float]} -- y-coordinate at aperature (default: {None}).
Returns:
[float] -- Corrected parameters for off-axis distortion.
"""
# Decide the x, y-coordinate data on aperature
if (y is None):
x = data[0, :]
y = data[1, :]
else:
x = data
# Correct the off-axis distortion
return poly10_2D(c, x.flatten(), y.flatten()).reshape(x.shape)
def __poly10Grad(self, c, x, y, atype):
"""
Correct the off-axis distortion by fitting with a 10 order polynomial
equation in the gradident part.
Arguments:
c {[float]} -- Parameters of off-axis distrotion.
x {[type]} -- x-coordinate at aperature.
y {[float]} -- y-coordinate at aperature.
atype {[string]} -- Direction of gradient. It can be "dx" or "dy".
Returns:
[float] -- Corrected parameters for off-axis distortion.
"""
return poly10Grad(c, x.flatten(), y.flatten(), atype).reshape(x.shape)
def __createPupilGrid(self,
lutx,
luty,
onepixel,
ca,
cb,
ra,
rb,
fieldX,
fieldY=None):
"""
Create the pupil grid in off-axis model. This function gives the x,y-coordinate in the
extended ring area defined by the parameter of onepixel.
Arguments:
lutx {[float]} -- x-coordinate on pupil plane.
luty {[float]} -- y-coordinate on pupil plane.
onepixel {[float]} -- Exteneded delta radius.
ca {[float]} -- Center of outer ring on the pupil plane.
cb {float} -- Center of inner ring on the pupil plane.
ra {[float]} -- Radius of outer ring on the pupil plane.
rb {[float]} -- Radius of inner ring on the pupil plane.
fieldX {[float]} -- x-coordinate of donut on the focal plane in degree.
If only fieldX is given, this will be fldr = sqrt(2)*fieldX
actually.
Keyword Arguments:
fieldY {[float]} -- y-coordinate of donut on the focal plane in degree. (default: {None})
Returns:
[float] -- x, y-coordinate of extended ring area on pupil plane.
"""
# Calculate fieldX, fieldY if only input of fieldX (= fldr = sqrt(2)*fieldX actually)
# is provided
if (fieldY is None):
# Input of filedX is fldr actually
fldr = fieldX
# Divide fldr by sqrt(2) to get fieldX = fieldY
fieldX = fldr / np.sqrt(2)
fieldY = fieldX
# Rotate the mask center after the off-axis correction based on the position
# of fieldX and fieldY
cax, cay, cbx, cby = self.__rotateMaskParam(ca, cb, fieldX, fieldY)
# Get x, y coordinate of extended outer boundary by the linear approximation
lutx, luty = self.__approximateExtendedXY(lutx, luty, cax, cay, ra,
ra + onepixel, "outer")
# Get x, y coordinate of extended inner boundary by the linear approximation
lutx, luty = self.__approximateExtendedXY(lutx, luty, cbx, cby,
rb - onepixel, rb, "inner")
return lutx, luty
def __approximateExtendedXY(self, lutx, luty, cenX, cenY, innerR, outerR,
config):
"""
Calculate the x, y-cooridnate on puil plane in the extended ring area by the linear
approxination, which is used in the off-axis correction.
Arguments:
lutx {[float]} -- x-coordinate on pupil plane.
luty {[float]} -- y-coordinate on pupil plane.
cenX {[float]} -- x-coordinate of boundary ring center.
cenY {[float]} -- y-coordinate of boundary ring center.
innerR {[float]} -- Inner radius of extended ring.
outerR {[float]} -- Outer radius of extended ring.
config {[string]} -- Configuration to calculate the x,y-coordinate in the extended ring.
"inner": inner extended ring;
"outer": outer extended ring.
Returns:
[float] -- x, y-coordinate of extended ring area on pupil plane.
"""
# Catculate the distance to rotated center of boundary ring
lutr = np.sqrt((lutx - cenX)**2 + (luty - cenY)**2)
# Define NaN to be 999 for the comparison in the following step
tmp = lutr.copy()
tmp[np.isnan(tmp)] = 999
# Get the available index that the related distance is between innderR and outerR
idxbound = (~np.isnan(lutr)) & (tmp >= innerR) & (tmp <= outerR)
# Deside R based on the configuration
if (config == "outer"):
R = innerR
# Get the index that the related distance is bigger than outerR
idxout = (tmp > outerR)
elif (config == "inner"):
R = outerR
# Get the index that the related distance is smaller than innerR
idxout = (tmp < innerR)
# Put the x, y-coordiate to be NaN if it is inside/ outside the pupil that is
# after the off-axis correction.
lutx[idxout] = np.nan
luty[idxout] = np.nan
# Get the x, y-coordinate in this ring area by the linear approximation
lutx[idxbound] = (lutx[idxbound] - cenX) / lutr[idxbound] * R + cenX
luty[idxbound] = (luty[idxbound] - cenY) / lutr[idxbound] * R + cenY
return lutx, luty
def __rotateMaskParam(self, ca, cb, fieldX, fieldY):
"""
Rotate the mask-related parameters of center.
Arguments:
ca {[float]} -- Mask-related parameter of center.
cb {float} -- Mask-related parameter of center.
fieldX {[float]} -- x-coordinate of donut on the focal plane in degree.
fieldY {[float]} -- y-coordinate of donut on the focal plane in degree.
Returns:
[float] -- Projected x, y elements
"""
# Calculate the sin(theta) and cos(theta) for the rotation
fldr = np.sqrt(fieldX**2 + fieldY**2)
if (fldr == 0):
c = 0
s = 0
else:
# Calculate cos(theta)
c = fieldX / fldr
# Calculate sin(theta)
s = fieldY / fldr
# Projected x and y coordinate after the rotation
cax = c * ca
cay = s * ca
cbx = c * cb
cby = s * cb
return cax, cay, cbx, cby
def getOffAxisCorr(self, instDir, order):
"""
Map the coefficients of off-axis correction for x, y-projection of intra- and
extra-image. This is for the mapping of coordinate from the telescope apearature
to defocal image plane.
Arguments:
instDir {[string]} -- Path to specific instrument directory.
order {[int]} -- Up to order-th of off-axis correction.
"""
# List of configuration
configList = ["cxin", "cyin", "cxex", "cyex"]
# Get all files in the directory
fileList = [
f for f in os.listdir(instDir)
if os.path.isfile(os.path.join(instDir, f))
]
# Read files
temp = []
for config in configList:
# Construct the configuration file name
for fileName in fileList:
m = re.match(r"\S*%s\S*.txt" % config, fileName)
if (m is not None):
matchFileName = m.group()
break
filePath = os.path.join(instDir, matchFileName)
# Read the file
corr_coeff, offset = self.__getOffAxisCorr_single(filePath)
temp.append(corr_coeff)
# Give the values
self.offAxis_coeff = np.array(temp)
self.offAxisOffset = offset
def __getOffAxisCorr_single(self, confFile):
"""
Get the image-related pamameters for the off-axis distortion by the linear
approximation with a series of fitted parameters with LSST ZEMAX model.
Arguments:
confFile {[string]} -- Path of configuration file.
Returns:
[float] -- Coefficients for the off-axis distortion based on the linear
response.
[float] -- Defocal distance in m.
"""
# Calculate the distance from donut to origin (aperature)
fldr = np.sqrt(self.fieldX**2 + self.fieldY**2)
# Read the configuration file
cdata = np.loadtxt(confFile)
# Record the offset (defocal distance)
offset = cdata[0, 0]
# Take the reference parameters
c = cdata[:, 1:]
# Get the ruler, which is the distance to center
# ruler is between 1.51 and 1.84 degree here
ruler = np.sqrt(c[:, 0]**2 + c[:, 1]**2)
# Get the fitted parameters for off-axis correction by linear approximation
corr_coeff = self.__linearApprox(fldr, ruler, c[:, 2:])
return corr_coeff, offset
def __interpMaskParam(self, fieldX, fieldY, maskParam):
"""
Get the mask-related pamameters for the off-axis distortion and vignetting correction
by the linear approximation with a series of fitted parameters with LSST ZEMAX model.
Arguments:
fieldX {[float]} -- x-coordinate of donut on the focal plane in degree.
fieldY {[float]} -- y-coordinate of donut on the focal plane in degree.
maskParam {[string]} -- Fitted coefficient file for the off-axis distortion and
vignetting correction
Returns:
[float] -- Coefficients for the off-axis distortion and vignetting correction based
on the linear response.
"""
# Calculate the distance from donut to origin (aperature)
fldr = np.sqrt(fieldX**2 + fieldY**2)
# Load the mask parameter
c = np.loadtxt(maskParam)
# Get the ruler, which is the distance to center
# ruler is between 1.51 and 1.84 degree here
ruler = np.sqrt(2) * c[:, 0]
# Get the fitted parameters for off-axis correction by linear approximation
param = self.__linearApprox(fldr, ruler, c[:, 1:])
# Define related parameters
ca = param[0]
ra = param[1]
cb = param[2]
rb = param[3]
return ca, ra, cb, rb
def __linearApprox(self, fldr, ruler, parameters):
"""
Get the fitted parameters for off-axis correction by linear approximation
Arguments:
fldr {[float]} -- Distance from donut to origin (aperature).
ruler {[float]} -- A series of distance with available parameters for the fitting.
parameters {[float]} -- Referenced parameters for the fitting.
Returns:
[float] -- Fitted parameters based on the linear approximation.
"""
# Sort the ruler and parameters based on the magnitude of ruler
sortIndex = np.argsort(ruler)
ruler = ruler[sortIndex]
parameters = parameters[sortIndex, :]
# Compare the distance to center (aperature) between donut and standard
compDis = (ruler >= fldr)
# fldr is too big and out of range
if (fldr > ruler.max()):
# Take the coefficients in the highest boundary
p2 = parameters.shape[0] - 1
p1 = 0
w1 = 0
w2 = 1
# fldr is too small to be in the range
elif (fldr < ruler.min()):
# Take the coefficients in the lowest boundary
p2 = 0
p1 = 0
w1 = 1
w2 = 0
# fldr is in the range
else:
# Find the boundary of fldr in the known data
p2 = compDis.argmax()
p1 = p2 - 1
# Calculate the weighting ratio
w1 = (ruler[p2] - fldr) / (ruler[p2] - ruler[p1])
w2 = 1 - w1
# Get the fitted parameters for off-axis correction by linear approximation
param = w1 * parameters[p1, :] + w2 * parameters[p2, :]
return param
def makeMaskList(self, inst, model):
"""
Calculate the mask list based on the obscuration and optical model.
Arguments:
inst {[Instrument]} -- Instrument to use.
model {[string]} -- Optical model. It can be "paraxial", "onAxis", or "offAxis".
"""
# Masklist = [center_x, center_y, radius_of_boundary, 1/ 0 for outer/ inner boundary]
obscuration = inst.parameter["obscuration"]
if (model in ("paraxial", "onAxis")):
if (obscuration == 0):
masklist = np.array([0, 0, 1, 1])
else:
masklist = np.array([[0, 0, 1, 1], [0, 0, obscuration, 0]])
else:
# Get the mask-related parameters
maskCa, maskRa, maskCb, maskRb = self.__interpMaskParam(
self.fieldX, self.fieldY, inst.maskParam)
# Rotate the mask-related parameters of center
cax, cay, cbx, cby = self.__rotateMaskParam(
maskCa, maskCb, self.fieldX, self.fieldY)
masklist = np.array([[0, 0, 1, 1], [0, 0, obscuration, 0],
[cax, cay, maskRa, 1], [cbx, cby, maskRb, 0]])
return masklist
def __showProjection(self,
lutxp,
lutyp,
sensorFactor,
projSamples,
raytrace=False):
"""
Calculate the x, y-projection of image on pupil. This can be used to calculate
the center of projection in compensate().
Arguments:
lutxp {[float]} -- x-coordinate on pupil plane. The value of element will be
NaN if that point is not inside the pupil.
lutyp {[float]} -- y-coordinate on pupil plane. The value of element will be
NaN if that point is not inside the pupil.
sensorFactor {[float]} -- ? (Need to check the meaning of this.)
projSamples {[int]} -- Dimension of projected image. This value considers the
magnification ratio of donut image.
raytrace {[bool]} -- Consider the ray trace or not. If the value is true, the
times of photon hit will aggregate. (default: {False})
Returns:
[float] -- Projection of image. It will be a binary image if raytrace=False.
"""
# Dimension of pupil image
n1, n2 = lutxp.shape
# Construct the binary matrix on pupil. It is noted that if the raytrace is true,
# the value of element is allowed to be greater than 1.
show_lutxyp = np.zeros([n1, n2])
# Get the index in pupil. If a point's value is NaN, this point is outside the pupil.
idx = (~np.isnan(lutxp)).nonzero()
for ii, jj in zip(idx[0], idx[1]):
# Calculate the projected x, y-coordinate in pixel
# x=0.5 is center of pixel#1
xR = int(
np.round((lutxp[ii, jj] + sensorFactor) * projSamples /
sensorFactor / 2 + 0.5))
yR = int(
np.round((lutyp[ii, jj] + sensorFactor) * projSamples /
sensorFactor / 2 + 0.5))
# Check the projected coordinate is in the range of image or not.
# If the check passes, the times will be recorded.
if (xR > 0 and xR < n2 and yR > 0 and yR < n1):
# Aggregate the times
if raytrace:
show_lutxyp[yR - 1, xR - 1] += 1
# No aggragation of times
else:
if (show_lutxyp[yR - 1, xR - 1] < 1):
show_lutxyp[yR - 1, xR - 1] = 1
return show_lutxyp
def makeMask(self, inst, model, boundaryT, maskScalingFactorLocal):
"""
Get the binary mask which considers the obscuration and off-axis correction.
There will be two mask parameters to be calculated:
pMask: padded mask for use at the offset planes
cMask: non-padded mask corresponding to aperture
Arguments:
inst {[Instrument]} -- Instrument to use.
model {[string]} -- Optical model. It can be "paraxial", "onAxis", or "offAxis".
boundaryT {[int]} -- Extended boundary in pixel. It defines how far the
computation mask extends beyond the pupil mask. And,
in fft, it is also the width of Neuman boundary where
the derivative of the wavefront is set to zero.
maskScalingFactorLocal {[float]} -- Mask scaling factor (for fast beam) for
local correction.
"""
sensorSamples = inst.parameter["sensorSamples"]
self.pMask = np.ones(sensorSamples, dtype=int)
self.cMask = self.pMask.copy()
apertureDiameter = inst.parameter["apertureDiameter"]
focalLength = inst.parameter["focalLength"]
offset = inst.parameter["offset"]
rMask = apertureDiameter / (2 * focalLength /
offset) * maskScalingFactorLocal
# Get the mask list
masklist = self.makeMaskList(inst, model)
for ii in range(masklist.shape[0]):
# Distance to center on pupil
r = np.sqrt((inst.xSensor - masklist[ii, 0])**2 +
(inst.ySensor - masklist[ii, 1])**2)
# Find the indices that correspond to the mask element, set them to
# the pass/ block boolean
# Get the index inside the aperature
idx = (r <= masklist[ii, 2])
# Get the higher and lower boundary beyond the pupil mask by extension.
# The extension level is dicided by boundaryT.
# In fft, this is also the Neuman boundary where the derivative of the
# wavefront is set to zero.
pixelSize = inst.parameter["pixelSize"]
if (masklist[ii, 3] >= 1):
aidx = np.nonzero(r <= masklist[ii, 2] *
(1 + boundaryT * pixelSize / rMask))
else:
aidx = np.nonzero(r <= masklist[ii, 2] *
(1 - boundaryT * pixelSize / rMask))
# Initialize both mask elements to the opposite of the pass/ block boolean
pMaskii = (1 - masklist[ii, 3]) * \
np.ones([sensorSamples, sensorSamples], dtype=int)
cMaskii = pMaskii.copy()
pMaskii[idx] = masklist[ii, 3]
cMaskii[aidx] = masklist[ii, 3]
# Multiplicatively add the current mask elements to the model masks.
# This is try to find the common mask region.
# padded mask for use at the offset planes
self.pMask = self.pMask * pMaskii
# non-padded mask corresponding to aperture
self.cMask = self.cMask * cMaskii
def testUpdateImageWithNoHoldImage(self):
img = Image()
newImg = np.random.rand(5, 5)
self.assertWarns(UserWarning, img.updateImage, newImg)
class CompensableImage(object):
def __init__(self):
"""Instantiate the class of CompensableImage."""
self._image = Image()
self.defocalType = DefocalType.Intra
# Field coordinate in degree
self.fieldX = 0
self.fieldY = 0
# Initial image before doing the compensation
self.image0 = None
# Coefficient to do the off-axis correction
self.offAxisCoeff = np.array([])
# Defocused offset in files of off-axis correction
self.offAxisOffset = 0.0
# Ture if the image gets the over-compensation
self.caustic = False
# Padded mask for use at the offset planes
self.pMask = np.array([], dtype=int)
# Non-padded mask corresponding to aperture
self.cMask = np.array([], dtype=int)
def getDefocalType(self):
"""Get the defocal type.
Returns
-------
enum 'DefocalType'
Defocal type.
"""
return self.defocalType
def getImgObj(self):
"""Get the image object.
Returns
-------
Image
Imgae object.
"""
return self._image
def getImg(self):
"""Get the image.
Returns
-------
numpy.ndarray
Image.
"""
return self._image.getImg()
def getImgSizeInPix(self):
"""Get the image size in pixel.
Returns
-------
int
Image size in pixel.
"""
return self.getImg().shape[0]
def getOffAxisCoeff(self):
"""Get the coefficients to do the off-axis correction.
Returns
-------
numpy.ndarray
Coefficients to do the off-axis correction.
float
Defocused offset in files of off-axis correction.
"""
return self.offAxisCoeff, self.offAxisOffset
def getImgInit(self):
"""Get the initial image before doing the compensation.
Returns
-------
numpy.ndarray
Initial image before doing the compensation.
"""
return self.image0
def isCaustic(self):
"""The image is caustic or not.
The image might be caustic from the over-compensation.
Returns
-------
bool
True if the image is caustic.
"""
return self.caustic
def getPaddedMask(self):
"""Get the padded mask use at the offset planes.
Returns
-------
numpy.ndarray[int]
Padded mask.
"""
return self.pMask
def getNonPaddedMask(self):
"""Get the non-padded mask corresponding to aperture.
Returns
-------
numpy.ndarray[int]
Non-padded mask
"""
return self.cMask
def getFieldXY(self):
"""Get the field x, y in degree.
Returns
-------
float
Field x in degree.
float
Field y in degree.
"""
return self.fieldX, self.fieldY
def setImg(self, fieldXY, defocalType, image=None, imageFile=None):
"""Set the wavefront image.
Parameters
----------
fieldXY : tuple or list
Position of donut on the focal plane in degree (field x, field y).
defocalType : enum 'DefocalType'
Defocal type of image.
image : numpy.ndarray, optional
Array of image. (the default is None.)
imageFile : str, optional
Path of image file. (the default is None.)
"""
self._image.setImg(image=image, imageFile=imageFile)
self._checkImgShape()
self.fieldX, self.fieldY = fieldXY
self.defocalType = defocalType
self._resetInternalAttributes()
def _checkImgShape(self):
"""Check the image shape.
Raises
------
RuntimeError
Only square image stamps are accepted.
RuntimeError
Number of pixels cannot be odd numbers.
"""
img = self._image.getImg()
if (img.shape[0] != img.shape[1]):
raise RuntimeError("Only square image stamps are accepted.")
elif (img.shape[0] % 2 == 1):
raise RuntimeError("Number of pixels cannot be odd numbers.")
def _resetInternalAttributes(self):
"""Reset the internal attributes."""
self.image0 = None
self.offAxisCoeff = np.array([])
self.offAxisOffset = 0.0
self.caustic = False
# Reset all mask related parameters
self.pMask = np.array([], dtype=int)
self.cMask = np.array([], dtype=int)
def updateImage(self, image):
"""Update the image of donut.
Parameters
----------
image : numpy.ndarray
Donut image.
"""
self._image.updateImage(image)
def updateImgInit(self):
"""Update the backup of initial image.
This will be used in the outer loop iteration, which always uses the
initial image (image0) before each iteration starts.
"""
# Update the initial image for future use
self.image0 = self._image.getImg().copy()
def imageCoCenter(self, inst, fov=3.5, debugLevel=0):
"""Shift the weighting center of donut to the center of reference
image with the correction of projection of fieldX and fieldY.
Parameters
----------
inst : Instrument
Instrument to use.
fov : float, optional
Field of view (FOV) of telescope. (the default is 3.5.)
debugLevel : int, optional
Show the information under the running. If the value is higher, the
information shows more. It can be 0, 1, 2, or 3. (the default is
0.)
"""
# Calculate the weighting center (x, y) and radius
x1, y1 = self._image.getCenterAndR_ef()[0:2]
# Show the co-center information
if (debugLevel >= 3):
print("imageCoCenter: (x, y) = (%8.2f,%8.2f)\n" % (x1, y1))
# Calculate the center position on image
# 0.5 is the half of 1 pixel
dimOfDonut = inst.getDimOfDonutOnSensor()
stampCenterx1 = dimOfDonut / 2 + 0.5
stampCentery1 = dimOfDonut / 2 + 0.5
# Shift in the radial direction
# The field of view (FOV) of LSST camera is 3.5 degree
offset = inst.getDefocalDisOffset()
pixelSize = inst.getCamPixelSize()
radialShift = fov*(offset/1e-3)*(10e-6/pixelSize)
# Calculate the projection of distance of donut to center
fieldDist = self._getFieldDistFromOrigin()
radialShift = radialShift * (fieldDist / (fov / 2))
# Do not consider the condition out of FOV of lsst
if (fieldDist > (fov / 2)):
radialShift = 0
# Calculate the cos(theta) for projection
I1c = self.fieldX / fieldDist
# Calculate the sin(theta) for projection
I1s = self.fieldY / fieldDist
# Get the projected x, y-coordinate
stampCenterx1 = stampCenterx1 + radialShift*I1c
stampCentery1 = stampCentery1 + radialShift*I1s
# Shift the image to the projected position
self._image.updateImage(
np.roll(self._image.getImg(), int(np.round(stampCentery1 - y1)), axis=0))
self._image.updateImage(
np.roll(self._image.getImg(), int(np.round(stampCenterx1 - x1)), axis=1))
def _getFieldDistFromOrigin(self, fieldX=None, fieldY=None, minDist=1e-8):
"""Get the field distance from the origin.
Parameters
----------
fieldX : float, optional
Field x in degree. If the input is None, the value of self.fieldX
will be used. (the default is None.)
fieldY : float, optional
Field y in degree. If the input is None, the value of self.fieldY
will be used. (the default is None.)
minDist : float, optional
Minimum distace. In some cases, the field distance will be the
denominator in other functions. (the default is 1e-8.)
Returns
-------
float
Field distance from the origin.
"""
if (fieldX is None):
fieldX = self.fieldX
if (fieldY is None):
fieldY = self.fieldY
fieldDist = np.hypot(fieldX, fieldY)
if (fieldDist == 0):
fieldDist = minDist
return fieldDist
def compensate(self, inst, algo, zcCol, model):
"""Calculate the image compensated from the affection of wavefront.
Parameters
----------
inst : Instrument
Instrument to use.
algo : Algorithm
Algorithm to solve the Poisson's equation. It can by done by the
fast Fourier transform or serial expansion.
zcCol : numpy.ndarray
Coefficients of wavefront.
model : str
Optical model. It can be "paraxial", "onAxis", or "offAxis".
Raises
------
RuntimeError
input:size zcCol in compensate needs to be a numTerms row column
vector.
"""
# Check the condition of inputs
numTerms = algo.getNumOfZernikes()
if ((zcCol.ndim == 1) and (len(zcCol) != numTerms)):
raise RuntimeError("input:size",
"zcCol in compensate needs to be a %d row column vector. \n" % numTerms)
# Dimension of image
sm, sn = self._image.getImg().shape
# Dimenstion of projected image on focal plane
projSamples = sm
# Let us create a look-up table for x -> xp first.
luty, lutx = np.mgrid[-(projSamples/2 - 0.5):(projSamples/2 + 0.5),
-(projSamples/2 - 0.5):(projSamples/2 + 0.5)]
sensorFactor = inst.getSensorFactor()
lutx = lutx/(projSamples/2/sensorFactor)
luty = luty/(projSamples/2/sensorFactor)
# Set up the mapping
lutxp, lutyp, J = self._aperture2image(inst, algo, zcCol, lutx, luty,
projSamples, model)
show_lutxyp = self._showProjection(lutxp, lutyp, sensorFactor,
projSamples, raytrace=False)
if (np.all(show_lutxyp <= 0)):
self.caustic = True
return
# Calculate the weighting center (x, y) and radius
realcx, realcy = self._image.getCenterAndR_ef()[0:2]
# Extend the dimension of image by 20 pixel in x and y direction
show_lutxyp = padArray(show_lutxyp, projSamples+20)
# Get the binary matrix of image on pupil plane if raytrace=False
struct0 = generate_binary_structure(2, 1)
struct = iterate_structure(struct0, 4)
struct = binary_dilation(struct, structure=struct0, iterations=2).astype(int)
show_lutxyp = binary_dilation(show_lutxyp, structure=struct)
show_lutxyp = binary_erosion(show_lutxyp, structure=struct)
# Extract the region from the center of image and get the original one
show_lutxyp = extractArray(show_lutxyp, projSamples)
# Calculate the weighting center (x, y) and radius
projcx, projcy = self._image.getCenterAndR_ef(image=show_lutxyp.astype(float))[0:2]
# Shift the image to center of projection on pupil
# +(-) means we need to move image to the right (left)
shiftx = projcx - realcx
# +(-) means we need to move image upward (downward)
shifty = projcy - realcy
self._image.updateImage(np.roll(self._image.getImg(), int(np.round(shifty)), axis=0))
self._image.updateImage(np.roll(self._image.getImg(), int(np.round(shiftx)), axis=1))
# Construct the interpolant to get the intensity on (x', p') plane
# that corresponds to the grid points on (x,y)
yp, xp = np.mgrid[-(sm/2 - 0.5):(sm/2 + 0.5), -(sm/2 - 0.5):(sm/2 + 0.5)]
xp = xp/(sm/2/sensorFactor)
yp = yp/(sm/2/sensorFactor)
# Put the NaN to be 0 for the interpolate to use
lutxp[np.isnan(lutxp)] = 0
lutyp[np.isnan(lutyp)] = 0
# Construct the function for interpolation
ip = RectBivariateSpline(yp[:, 0], xp[0, :], self._image.getImg(), kx=1, ky=1)
# Construct the projected image by the interpolation
lutIp = np.zeros(lutxp.shape[0]*lutxp.shape[1])
for ii, (xx, yy) in enumerate(zip(lutxp.ravel(), lutyp.ravel())):
lutIp[ii] = ip(yy, xx)
lutIp = lutIp.reshape(lutxp.shape)
# Calaculate the image on focal plane with compensation based on flux
# conservation
# I(x, y)/I'(x', y') = J = (dx'/dx)*(dy'/dy) - (dx'/dy)*(dy'/dx)
self._image.updateImage(lutIp * J)
if (self.defocalType == DefocalType.Extra):
self._image.updateImage(np.rot90(self._image.getImg(), k=2))
# Put NaN to be 0
holdedImg = self._image.getImg()
holdedImg[np.isnan(holdedImg)] = 0
self._image.updateImage(holdedImg)
# Check the compensated image has the problem or not.
# The negative value means the over-compensation from wavefront error
if (np.any(self._image.getImg() < 0) and np.all(self.image0 >= 0)):
print("WARNING: negative scale parameter, image is within caustic, zcCol (in um)=\n")
self.caustic = True
# Put the overcompensated part to be 0
holdedImg = self._image.getImg()
holdedImg[holdedImg < 0] = 0
self._image.updateImage(holdedImg)
def _aperture2image(self, inst, algo, zcCol, lutx, luty, projSamples,
model):
"""Calculate the x, y-coordinate on the focal plane and the related
Jacobian matrix.
Parameters
----------
inst : Instrument
Instrument to use.
algo : Algorithm
Algorithm to solve the Poisson's equation. It can by done by the
fast Fourier transform or serial expansion.
zcCol : numpy.ndarray
Coefficients of optical basis. It is Zernike polynomials in the
baseline.
lutx : numpy.ndarray
X-coordinate on pupil plane.
luty : numpy.ndarray
Y-coordinate on pupil plane.
projSamples : int
Dimension of projected image. This value considers the
magnification ratio of donut image.
model : str
Optical model. It can be "paraxial", "onAxis", or "offAxis".
Returns
-------
numpy.ndarray
X coordinate on the focal plane.
numpy.ndarray
Y coordinate on the focal plane.
numpy.ndarray
Jacobian matrix between the pupil and focal plane.
"""
# Get the radius: R = D/2
R = inst.getApertureDiameter() / 2
# Calculate C = -f(f-l)/l/R^2. This is for the calculation of reduced
# coordinate.
defocalDisOffset = inst.getDefocalDisOffset()
if (self.defocalType == DefocalType.Intra):
l = defocalDisOffset
elif (self.defocalType == DefocalType.Extra):
l = -defocalDisOffset
focalLength = inst.getFocalLength()
myC = -focalLength*(focalLength - l)/l/R**2
# Get the functions to do the off-axis correction by numerical fitting
# Order to do the off-axis correction. The order is 10 now.
offAxisPolyOrder = algo.getOffAxisPolyOrder()
polyFunc = self._getFunction("poly%d_2D" % offAxisPolyOrder)
polyGradFunc = self._getFunction("poly%dGrad" % offAxisPolyOrder)
# Calculate the distance to center
lutr = np.sqrt(lutx**2 + luty**2)
# Calculated the extended ring radius (delta r), which is to extended
# the available pupil area.
# 1 pixel larger than projected pupil. No need to be EF-like, anything
# outside of this will be masked off by the computational mask
sensorFactor = inst.getSensorFactor()
onepixel = 1/(projSamples/2/sensorFactor)
# Get the index that the point is out of the range of extended pupil
obscuration = inst.getObscuration()
idxout = (lutr > 1+onepixel) | (lutr < obscuration-onepixel)
# Define the element to be NaN if it is out of range
lutx[idxout] = np.nan
luty[idxout] = np.nan
# Get the index in the extended area of outer boundary with the width
# of onepixel
idxbound = (lutr <= 1+onepixel) & (lutr > 1)
# Calculate the extended x, y-coordinate (x' = x/r*r', r'=1)
lutx[idxbound] = lutx[idxbound]/lutr[idxbound]
luty[idxbound] = luty[idxbound]/lutr[idxbound]
# Get the index in the extended area of inner boundary with the width
# of onepixel
idxinbd = (lutr < obscuration) & (lutr > obscuration-onepixel)
# Calculate the extended x, y-coordinate (x' = x/r*r', r'=obscuration)
lutx[idxinbd] = lutx[idxinbd]/lutr[idxinbd]*obscuration
luty[idxinbd] = luty[idxinbd]/lutr[idxinbd]*obscuration
# Get the corrected x, y-coordinate on focal plane (lutxp, lutyp)
if (model == "paraxial"):
# No correction is needed in "paraxial" model
lutxp = lutx
lutyp = luty
elif (model == "onAxis"):
# Calculate F(x, y) = m * sqrt(f^2-R^2) / sqrt(f^2-(x^2+y^2)*R^2)
# m is the mask scaling factor
myA2 = (focalLength**2 - R**2) / (focalLength**2 - lutr**2 * R**2)
# Put the unphysical value as NaN
myA = myA2.copy()
idx = (myA < 0)
myA[idx] = np.nan
myA[~idx] = np.sqrt(myA2[~idx])
# Mask scaling factor (for fast beam)
maskScalingFactor = algo.getMaskScalingFactor()
# Calculate the x, y-coordinate on focal plane
# x' = F(x,y)*x + C*(dW/dx), y' = F(x,y)*y + C*(dW/dy)
lutxp = maskScalingFactor*myA*lutx
lutyp = maskScalingFactor*myA*luty
elif (model == "offAxis"):
# Get the coefficient of polynomials for off-axis correction
tt = self.offAxisOffset
cx = (self.offAxisCoeff[0, :] - self.offAxisCoeff[2, :]) * (tt+l)/(2*tt) + \
self.offAxisCoeff[2, :]
cy = (self.offAxisCoeff[1, :] - self.offAxisCoeff[3, :]) * (tt+l)/(2*tt) + \
self.offAxisCoeff[3, :]
# This will be inverted back by typesign later on.
# We do the inversion here to make the (x,y)->(x',y') equations has
# the same form as the paraxial case.
cx = np.sign(l)*cx
cy = np.sign(l)*cy
# Do the orthogonalization: x'=1/sqrt(2)*(x+y), y'=1/sqrt(2)*(x-y)
# Calculate the rotation angle for the orthogonalization
fieldDist = self._getFieldDistFromOrigin()
costheta = (self.fieldX + self.fieldY) / fieldDist / np.sqrt(2)
if (costheta > 1):
costheta = 1
elif (costheta < -1):
costheta = -1
sintheta = np.sqrt(1 - costheta**2)
if (self.fieldY < self.fieldX):
sintheta = -sintheta
# Create the pupil grid in off-axis model. This gives the
# x,y-coordinate in the extended ring area defined by the parameter
# of onepixel.
# Get the mask-related parameters
maskCa, maskRa, maskCb, maskRb = self._interpMaskParam(
self.fieldX, self.fieldY, inst.getMaskOffAxisCorr())
lutx, luty = self._createPupilGrid(
lutx, luty, onepixel, maskCa, maskCb, maskRa, maskRb,
self.fieldX, self.fieldY)
# Calculate the x, y-coordinate on focal plane
# First rotate back to reference orientation
lutx0 = lutx*costheta + luty*sintheta
luty0 = -lutx*sintheta + luty*costheta
# Use the mapping at reference orientation
lutxp0 = polyFunc(cx, lutx0, y=luty0)
lutyp0 = polyFunc(cy, lutx0, y=luty0)
# Rotate back to focal plane
lutxp = lutxp0*costheta - lutyp0*sintheta
lutyp = lutxp0*sintheta + lutyp0*costheta
# Zemax data are in mm, therefore 1000
dimOfDonut = inst.getDimOfDonutOnSensor()
pixelSize = inst.getCamPixelSize()
reduced_coordi_factor = 1e-3/(dimOfDonut/2*pixelSize/sensorFactor)
# Reduced coordinates, so that this can be added with the dW/dz
lutxp = lutxp*reduced_coordi_factor
lutyp = lutyp*reduced_coordi_factor
else:
print('Wrong optical model type in compensate. \n')
return
# Obscuration of annular aperture
zobsR = algo.getObsOfZernikes()
# Calculate the x, y-coordinate on focal plane
# x' = F(x,y)*x + C*(dW/dx), y' = F(x,y)*y + C*(dW/dy)
# In Model basis (zer: Zernike polynomials)
if (zcCol.ndim == 1):
lutxp = lutxp + myC*ZernikeAnnularGrad(zcCol, lutx, luty, zobsR, "dx")
lutyp = lutyp + myC*ZernikeAnnularGrad(zcCol, lutx, luty, zobsR, "dy")
# Make the sign to be consistent
if (self.defocalType == DefocalType.Extra):
lutxp = -lutxp
lutyp = -lutyp
# Calculate the Jacobian matrix
# In Model basis (zer: Zernike polynomials)
if (zcCol.ndim == 1):
if (model == "paraxial"):
J = 1 + myC * ZernikeAnnularJacobian(zcCol, lutx, luty, zobsR, "1st") + \
myC**2 * ZernikeAnnularJacobian(zcCol, lutx, luty, zobsR, "2nd")
elif (model == "onAxis"):
xpox = maskScalingFactor * myA * (
1 + lutx**2 * R**2. / (focalLength**2 - R**2 * lutr**2)) + \
myC * ZernikeAnnularGrad(zcCol, lutx, luty, zobsR, "dx2")
ypoy = maskScalingFactor * myA * (
1 + luty**2 * R**2. / (focalLength**2 - R**2 * lutr**2)) + \
myC * ZernikeAnnularGrad(zcCol, lutx, luty, zobsR, "dy2")
xpoy = maskScalingFactor * myA * \
lutx * luty * R**2 / (focalLength**2 - R**2 * lutr**2) + \
myC * ZernikeAnnularGrad(zcCol, lutx, luty, zobsR, "dxy")
ypox = xpoy
J = xpox*ypoy - xpoy*ypox
elif (model == "offAxis"):
xp0ox = polyGradFunc(cx, lutx0, luty0, "dx") * costheta - \
polyGradFunc(cx, lutx0, luty0, "dy") * sintheta
yp0ox = polyGradFunc(cy, lutx0, luty0, "dx") * costheta - \
polyGradFunc(cy, lutx0, luty0, "dy") * sintheta
xp0oy = polyGradFunc(cx, lutx0, luty0, "dx") * sintheta + \
polyGradFunc(cx, lutx0, luty0, "dy") * costheta
yp0oy = polyGradFunc(cy, lutx0, luty0, "dx") * sintheta + \
polyGradFunc(cy, lutx0, luty0, "dy") * costheta
xpox = (xp0ox*costheta - yp0ox*sintheta)*reduced_coordi_factor + \
myC*ZernikeAnnularGrad(zcCol, lutx, luty, zobsR, "dx2")
ypoy = (xp0oy*sintheta + yp0oy*costheta)*reduced_coordi_factor + \
myC*ZernikeAnnularGrad(zcCol, lutx, luty, zobsR, "dy2")
temp = myC*ZernikeAnnularGrad(zcCol, lutx, luty, zobsR, "dxy")
# if temp==0,xpoy doesn't need to be symmetric about x=y
xpoy = (xp0oy*costheta - yp0oy*sintheta)*reduced_coordi_factor + temp
# xpoy-flipud(rot90(ypox))==0 is true
ypox = (xp0ox*sintheta + yp0ox*costheta)*reduced_coordi_factor + temp
J = xpox*ypoy - xpoy*ypox
return lutxp, lutyp, J
def _getFunction(self, name):
"""Decide to call the function of _poly10_2D() or _poly10Grad().
This is to correct the off-axis distortion. A numerical solution with
2-dimensions 10 order polynomials to map between the telescope
aperature and defocused image plane is used.
Parameters
----------
name : str
Function name to call.
Returns
-------
numpy.ndarray
Corrected image after the correction.
Raises
------
RuntimeError
Raise error if the function name does not exist.
"""
# Construnct the dictionary table for calling function.
# The reason to use the dictionary is for the future's extension.
funcTable = dict(poly10_2D=self._poly10_2D, poly10Grad=self._poly10Grad)
# Look for the function to call
if name in funcTable:
return funcTable[name]
# Error for unknown function name
raise RuntimeError("Unknown function name: %s" % name)
def _poly10_2D(self, c, data, y=None):
"""Correct the off-axis distortion by fitting with a 10 order
polynomial equation.
Parameters
----------
c : numpy.ndarray
Parameters of off-axis distrotion.
data : numpy.ndarray
X, y-coordinate on aperature. If y is provided this will be just
the x-coordinate.
y : numpy.ndarray, optional
Y-coordinate at aperature. (the default is None.)
Returns
-------
numpy.ndarray
Corrected parameters for off-axis distortion.
"""
# Decide the x, y-coordinate data on aperature
if (y is None):
x = data[0, :]
y = data[1, :]
else:
x = data
# Correct the off-axis distortion
return poly10_2D(c, x.flatten(), y.flatten()).reshape(x.shape)
def _poly10Grad(self, c, x, y, atype):
"""Correct the off-axis distortion by fitting with a 10 order
polynomial equation in the gradident part.
Parameters
----------
c : numpy.ndarray
Parameters of off-axis distrotion.
x : numpy.ndarray
X-coordinate at aperature.
y : numpy.ndarray
Y-coordinate at aperature.
atype : str
Direction of gradient. It can be "dx" or "dy".
Returns
-------
numpy.ndarray
Corrected parameters for off-axis distortion.
"""
return poly10Grad(c, x.flatten(), y.flatten(), atype).reshape(x.shape)
def _createPupilGrid(self, lutx, luty, onepixel, ca, cb, ra, rb, fieldX,
fieldY):
"""Create the pupil grid in off-axis model.
This function gives the x,y-coordinate in the extended ring area
defined by the parameter of onepixel.
Parameters
----------
lutx : numpy.ndarray
X-coordinate on pupil plane.
luty : numpy.ndarray
Y-coordinate on pupil plane.
onepixel : float
Exteneded delta radius.
ca : float
Center of outer ring on the pupil plane.
cb : float
Center of inner ring on the pupil plane.
ra : float
Radius of outer ring on the pupil plane.
rb : float
Radius of inner ring on the pupil plane.
fieldX : float
X-coordinate of donut on the focal plane in degree.
fieldY : float
Y-coordinate of donut on the focal plane in degree.
Returns
-------
numpy.ndarray
X-coordinate of extended ring area on pupil plane.
numpy.ndarray
Y-coordinate of extended ring area on pupil plane.
"""
# Rotate the mask center after the off-axis correction based on the
# position of fieldX and fieldY
cax, cay, cbx, cby = self._rotateMaskParam(ca, cb, fieldX, fieldY)
# Get x, y coordinate of extended outer boundary by the linear
# approximation
lutx, luty = self._approximateExtendedXY(lutx, luty, cax, cay, ra,
ra+onepixel, "outer")
# Get x, y coordinate of extended inner boundary by the linear
# approximation
lutx, luty = self._approximateExtendedXY(lutx, luty, cbx, cby,
rb-onepixel, rb, "inner")
return lutx, luty
def _approximateExtendedXY(self, lutx, luty, cenX, cenY, innerR, outerR,
config):
"""Calculate the x, y-cooridnate on puil plane in the extended ring
area by the linear approxination, which is used in the off-axis
correction.
Parameters
----------
lutx : numpy.ndarray
X-coordinate on pupil plane.
luty : numpy.ndarray
Y-coordinate on pupil plane.
cenX : float
X-coordinate of boundary ring center.
cenY : float
Y-coordinate of boundary ring center.
innerR : float
Inner radius of extended ring.
outerR : float
Outer radius of extended ring.
config : str
Configuration to calculate the x,y-coordinate in the extended ring.
"inner": inner extended ring; "outer": outer extended ring.
Returns
-------
numpy.ndarray
X-coordinate of extended ring area on pupil plane.
numpy.ndarray
Y-coordinate of extended ring area on pupil plane.
"""
# Catculate the distance to rotated center of boundary ring
lutr = np.sqrt((lutx - cenX)**2 + (luty - cenY)**2)
# Define NaN to be 999 for the comparison in the following step
tmp = lutr.copy()
tmp[np.isnan(tmp)] = 999
# Get the available index that the related distance is between innderR
# and outerR
idxbound = (~np.isnan(lutr)) & (tmp >= innerR) & (tmp <= outerR)
# Deside R based on the configuration
if (config == "outer"):
R = innerR
# Get the index that the related distance is bigger than outerR
idxout = (tmp > outerR)
elif (config == "inner"):
R = outerR
# Get the index that the related distance is smaller than innerR
idxout = (tmp < innerR)
# Put the x, y-coordiate to be NaN if it is inside/ outside the pupil
# that is after the off-axis correction.
lutx[idxout] = np.nan
luty[idxout] = np.nan
# Get the x, y-coordinate in this ring area by the linear approximation
lutx[idxbound] = (lutx[idxbound]-cenX)/lutr[idxbound]*R + cenX
luty[idxbound] = (luty[idxbound]-cenY)/lutr[idxbound]*R + cenY
return lutx, luty
def _rotateMaskParam(self, ca, cb, fieldX, fieldY):
"""Rotate the mask-related parameters of center.
Parameters
----------
ca : float
Mask-related parameter of center.
cb : float
Mask-related parameter of center.
fieldX : float
X-coordinate of donut on the focal plane in degree.
fieldY : float
Y-coordinate of donut on the focal plane in degree.
Returns
-------
float
Projected x element after the rotation.
float
Projected y element after the rotation.
float
Projected x element after the rotation.
float
Projected y element after the rotation.
"""
# Calculate the sin(theta) and cos(theta) for the rotation
fieldDist = self._getFieldDistFromOrigin(fieldX=fieldX, fieldY=fieldY,
minDist=0)
if (fieldDist == 0):
c = 0
s = 0
else:
# Calculate cos(theta)
c = fieldX / fieldDist
# Calculate sin(theta)
s = fieldY / fieldDist
# Projected x and y coordinate after the rotation
cax = c * ca
cay = s * ca
cbx = c * cb
cby = s * cb
return cax, cay, cbx, cby
def setOffAxisCorr(self, inst, order):
"""Set the coefficients of off-axis correction for x, y-projection of
intra- and extra-image.
This is for the mapping of coordinate from the telescope apearature to
defocal image plane.
Parameters
----------
inst : Instrument
Instrument to use.
order : int
Up to order-th of off-axis correction.
"""
# List of configuration
configList = ["cxin", "cyin", "cxex", "cyex"]
# Get all files in the directory
instDir = inst.getInstFileDir()
fileList = [f for f in os.listdir(instDir)
if os.path.isfile(os.path.join(instDir, f))]
# Read files
offAxisCoeff = []
for config in configList:
# Construct the configuration file name
for fileName in fileList:
m = re.match(r"\S*%s\S*.yaml" % config, fileName)
if (m is not None):
matchFileName = m.group()
break
filePath = os.path.join(instDir, matchFileName)
corrCoeff, offset = self._getOffAxisCorrSingle(filePath)
offAxisCoeff.append(corrCoeff)
# Give the values
self.offAxisCoeff = np.array(offAxisCoeff)
self.offAxisOffset = offset
def _getOffAxisCorrSingle(self, confFile):
"""Get the image-related pamameters for the off-axis distortion by the
linear approximation with a series of fitted parameters with LSST
ZEMAX model.
Parameters
----------
confFile : str
Path of configuration file.
Returns
-------
numpy.ndarray
Coefficients for the off-axis distortion based on the linear
response.
float
Defocal distance in m.
"""
fieldDist = self._getFieldDistFromOrigin(minDist=0.0)
# Read the configuration file
paramReader = ParamReader()
paramReader.setFilePath(confFile)
cdata = paramReader.getMatContent()
# Record the offset (defocal distance)
offset = cdata[0, 0]
# Take the reference parameters
c = cdata[:, 1:]
# Get the ruler, which is the distance to center
# ruler is between 1.51 and 1.84 degree here
ruler = np.sqrt(c[:, 0]**2 + c[:, 1]**2)
# Get the fitted parameters for off-axis correction by linear
# approximation
corr_coeff = self._linearApprox(fieldDist, ruler, c[:, 2:])
return corr_coeff, offset
def _interpMaskParam(self, fieldX, fieldY, maskParam):
"""Get the mask-related pamameters for the off-axis distortion and
vignetting correction by the linear approximation with a series of
fitted parameters with LSST ZEMAX model.
Parameters
----------
fieldX : float
X-coordinate of donut on the focal plane in degree.
fieldY : float
Y-coordinate of donut on the focal plane in degree.
maskParam : numpy.ndarray
Fitted coefficients for the off-axis distortion and vignetting
correction.
Returns
-------
float
'ca' coefficient for the off-axis distortion and vignetting
correction based on the linear response.
float
'ra' coefficient for the off-axis distortion and vignetting
correction based on the linear response.
float
'cb' coefficient for the off-axis distortion and vignetting
correction based on the linear response.
float
'rb' coefficient for the off-axis distortion and vignetting
correction based on the linear response.
"""
# Calculate the distance from donut to origin (aperature)
filedDist = np.sqrt(fieldX**2 + fieldY**2)
# Get the ruler, which is the distance to center
# ruler is between 1.51 and 1.84 degree here
ruler = np.sqrt(2)*maskParam[:, 0]
# Get the fitted parameters for off-axis correction by linear
# approximation
param = self._linearApprox(filedDist, ruler, maskParam[:, 1:])
# Define related parameters
ca = param[0]
ra = param[1]
cb = param[2]
rb = param[3]
return ca, ra, cb, rb
def _linearApprox(self, fieldDist, ruler, parameters):
"""Get the fitted parameters for off-axis correction by linear
approximation.
Parameters
----------
fieldDist : float
Field distance from donut to origin (aperature).
ruler : numpy.ndarray
A series of distance with available parameters for the fitting.
parameters : numpy.ndarray
Referenced parameters for the fitting.
Returns
-------
numpy.ndarray
Fitted parameters based on the linear approximation.
"""
# Sort the ruler and parameters based on the magnitude of ruler
sortIndex = np.argsort(ruler)
ruler = ruler[sortIndex]
parameters = parameters[sortIndex, :]
# Compare the distance to center (aperature) between donut and standard
compDis = (ruler >= fieldDist)
# fieldDist is too big and out of range
if (fieldDist > ruler.max()):
# Take the coefficients in the highest boundary
p2 = parameters.shape[0] - 1
p1 = 0
w1 = 0
w2 = 1
# fieldDist is too small to be in the range
elif (fieldDist < ruler.min()):
# Take the coefficients in the lowest boundary
p2 = 0
p1 = 0
w1 = 1
w2 = 0
# fieldDist is in the range
else:
# Find the boundary of fieldDist in the known data
p2 = compDis.argmax()
p1 = p2 - 1
# Calculate the weighting ratio
w1 = (ruler[p2]-fieldDist)/(ruler[p2]-ruler[p1])
w2 = 1-w1
# Get the fitted parameters for off-axis correction by linear
# approximation
param = w1*parameters[p1, :] + w2*parameters[p2, :]
return param
def makeMaskList(self, inst, model):
"""Calculate the mask list based on the obscuration and optical model.
Parameters
----------
inst : Instrument
Instrument to use.
model : str
Optical model. It can be "paraxial", "onAxis", or "offAxis".
Returns
-------
numpy.ndarray
The list of mask.
"""
# Masklist = [center_x, center_y, radius_of_boundary,
# 1/ 0 for outer/ inner boundary]
obscuration = inst.getObscuration()
if (model in ("paraxial", "onAxis")):
if (obscuration == 0):
masklist = np.array([0, 0, 1, 1])
else:
masklist = np.array([[0, 0, 1, 1],
[0, 0, obscuration, 0]])
else:
# Get the mask-related parameters
maskCa, maskRa, maskCb, maskRb = self._interpMaskParam(
self.fieldX, self.fieldY, inst.getMaskOffAxisCorr())
# Rotate the mask-related parameters of center
cax, cay, cbx, cby = self._rotateMaskParam(
maskCa, maskCb, self.fieldX, self.fieldY)
masklist = np.array([[0, 0, 1, 1], [0, 0, obscuration, 0],
[cax, cay, maskRa, 1], [cbx, cby, maskRb, 0]])
return masklist
def _showProjection(self, lutxp, lutyp, sensorFactor, projSamples,
raytrace=False):
"""Calculate the x, y-projection of image on pupil.
This can be used to calculate the center of projection in compensate().
Parameters
----------
lutxp : numpy.ndarray
X-coordinate on pupil plane. The value of element will be NaN if
that point is not inside the pupil.
lutyp : numpy.ndarray
Y-coordinate on pupil plane. The value of element will be NaN if
that point is not inside the pupil.
sensorFactor : float
Sensor factor.
projSamples : int
Dimension of projected image. This value considers the
magnification ratio of donut image.
raytrace : bool, optional
Consider the ray trace or not. If the value is true, the times of
photon hit will aggregate. (the default is False.)
Returns
-------
numpy.ndarray
Projection of image. It will be a binary image if raytrace=False.
"""
# Dimension of pupil image
n1, n2 = lutxp.shape
# Construct the binary matrix on pupil. It is noted that if the
# raytrace is true, the value of element is allowed to be greater
# than 1.
show_lutxyp = np.zeros([n1, n2])
# Get the index in pupil. If a point's value is NaN, this point is
# outside the pupil.
idx = (~np.isnan(lutxp)).nonzero()
for ii, jj in zip(idx[0], idx[1]):
# Calculate the projected x, y-coordinate in pixel
# x=0.5 is center of pixel#1
xR = int(np.round((lutxp[ii, jj]+sensorFactor)*projSamples/sensorFactor/2 + 0.5))
yR = int(np.round((lutyp[ii, jj]+sensorFactor)*projSamples/sensorFactor/2 + 0.5))
# Check the projected coordinate is in the range of image or not.
# If the check passes, the times will be recorded.
if (xR > 0 and xR < n2 and yR > 0 and yR < n1):
# Aggregate the times
if raytrace:
show_lutxyp[yR-1, xR-1] += 1
# No aggragation of times
else:
if (show_lutxyp[yR-1, xR-1] < 1):
show_lutxyp[yR-1, xR-1] = 1
return show_lutxyp
def makeMask(self, inst, model, boundaryT, maskScalingFactorLocal):
"""Get the binary mask which considers the obscuration and off-axis
correction.
There will be two mask parameters to be calculated:
pMask: padded mask for use at the offset planes
cMask: non-padded mask corresponding to aperture
Parameters
----------
inst : Instrument
Instrument to use.
model : str
Optical model. It can be "paraxial", "onAxis", or "offAxis".
boundaryT : int
Extended boundary in pixel. It defines how far the computation mask
extends beyond the pupil mask. And, in fft, it is also the width of
Neuman boundary where the derivative of the wavefront is set to
zero.
maskScalingFactorLocal : float
Mask scaling factor (for fast beam) for local correction.
"""
dimOfDonut = inst.getDimOfDonutOnSensor()
self.pMask = np.ones(dimOfDonut, dtype=int)
self.cMask = self.pMask.copy()
apertureDiameter = inst.getApertureDiameter()
focalLength = inst.getFocalLength()
offset = inst.getDefocalDisOffset()
rMask = apertureDiameter/(2*focalLength/offset)*maskScalingFactorLocal
# Get the mask list
pixelSize = inst.getCamPixelSize()
xSensor, ySensor = inst.getSensorCoor()
masklist = self.makeMaskList(inst, model)
for ii in range(masklist.shape[0]):
# Distance to center on pupil
r = np.sqrt((xSensor - masklist[ii, 0])**2 +
(ySensor - masklist[ii, 1])**2)
# Find the indices that correspond to the mask element, set them to
# the pass/ block boolean
# Get the index inside the aperature
idx = (r <= masklist[ii, 2])
# Get the higher and lower boundary beyond the pupil mask by
# extension.
# The extension level is dicided by boundaryT.
# In fft, this is also the Neuman boundary where the derivative of
# the wavefront is set to zero.
if (masklist[ii, 3] >= 1):
aidx = np.nonzero(r <= masklist[ii, 2]*(1+boundaryT*pixelSize/rMask))
else:
aidx = np.nonzero(r <= masklist[ii, 2]*(1-boundaryT*pixelSize/rMask))
# Initialize both mask elements to the opposite of the pass/ block
# boolean
pMaskii = (1 - masklist[ii, 3]) * \
np.ones([dimOfDonut, dimOfDonut], dtype=int)
cMaskii = pMaskii.copy()
pMaskii[idx] = masklist[ii, 3]
cMaskii[aidx] = masklist[ii, 3]
# Multiplicatively add the current mask elements to the model
# masks.
# This is try to find the common mask region.
# padded mask for use at the offset planes
self.pMask = self.pMask * pMaskii
# non-padded mask corresponding to aperture
self.cMask = self.cMask * cMaskii
def _calcWfErrAuxTel(self, imgIntraName, imgExtraName, offset, model):
# Cut the donut image from input files
centroidFindType = CentroidFindType.Otsu
imgIntra = Image(centroidFindType=centroidFindType)
imgExtra = Image(centroidFindType=centroidFindType)
imgIntraPath = os.path.join(self.testImgDir, imgIntraName)
imgExtraPath = os.path.join(self.testImgDir, imgExtraName)
imgIntra.setImg(imageFile=imgIntraPath)
imgExtra.setImg(imageFile=imgExtraPath)
xIntra, yIntra = imgIntra.getCenterAndR()[0:2]
imgIntraArray = imgIntra.getImg()[int(yIntra) - offset:int(yIntra) +
offset,
int(xIntra) - offset:int(xIntra) +
offset, ]
xExtra, yExtra = imgExtra.getCenterAndR()[0:2]
imgExtraArray = imgExtra.getImg()[int(yExtra) - offset:int(yExtra) +
offset,
int(xExtra) - offset:int(xExtra) +
offset, ]
# Calculate the wavefront error
fieldXY = (0, 0)
wfErr = self.calcWfErr(
centroidFindType,
fieldXY,
CamType.AuxTel,
"exp",
0.8,
model,
imageIntra=imgIntraArray,
imageExtra=imgExtraArray,
)
return wfErr