class TestInstrument(unittest.TestCase):
"""Test the Instrument class."""
def setUp(self):
self.instDir = os.path.join(getConfigDir(), "cwfs", "instData")
self.inst = Instrument(self.instDir)
self.dimOfDonutOnSensor = 120
self.inst.config(CamType.LsstCam,
self.dimOfDonutOnSensor,
announcedDefocalDisInMm=1.5)
def testConfigWithUnsupportedCamType(self):
self.assertRaises(ValueError, self.inst.config, "NoThisCamType", 120)
def testGetInstFileDir(self):
instFileDir = self.inst.getInstFileDir()
ansInstFileDir = os.path.join(self.instDir, "lsst")
self.assertEqual(instFileDir, ansInstFileDir)
def testGetAnnDefocalDisInMm(self):
annDefocalDisInMm = self.inst.getAnnDefocalDisInMm()
self.assertEqual(annDefocalDisInMm, 1.5)
def testSetAnnDefocalDisInMm(self):
annDefocalDisInMm = 2.0
self.inst.setAnnDefocalDisInMm(annDefocalDisInMm)
self.assertEqual(self.inst.getAnnDefocalDisInMm(), annDefocalDisInMm)
def testGetInstFilePath(self):
instFilePath = self.inst.getInstFilePath()
self.assertTrue(os.path.exists(instFilePath))
self.assertEqual(os.path.basename(instFilePath), "instParam.yaml")
def testGetMaskOffAxisCorr(self):
maskOffAxisCorr = self.inst.getMaskOffAxisCorr()
self.assertEqual(maskOffAxisCorr.shape, (9, 5))
self.assertEqual(maskOffAxisCorr[0, 0], 1.07)
self.assertEqual(maskOffAxisCorr[2, 3], -0.090100858)
def testGetDimOfDonutOnSensor(self):
dimOfDonutOnSensor = self.inst.getDimOfDonutOnSensor()
self.assertEqual(dimOfDonutOnSensor, self.dimOfDonutOnSensor)
def testGetObscuration(self):
obscuration = self.inst.getObscuration()
self.assertEqual(obscuration, 0.61)
def testGetFocalLength(self):
focalLength = self.inst.getFocalLength()
self.assertEqual(focalLength, 10.312)
def testGetApertureDiameter(self):
apertureDiameter = self.inst.getApertureDiameter()
self.assertEqual(apertureDiameter, 8.36)
def testGetDefocalDisOffset(self):
defocalDisInM = self.inst.getDefocalDisOffset()
# The answer is 1.5 mm
self.assertEqual(defocalDisInM * 1e3, 1.5)
def testGetCamPixelSize(self):
camPixelSizeInM = self.inst.getCamPixelSize()
# The answer is 10 um
self.assertEqual(camPixelSizeInM * 1e6, 10)
def testGetMarginalFocalLength(self):
marginalFL = self.inst.getMarginalFocalLength()
self.assertAlmostEqual(marginalFL, 9.4268, places=4)
def testGetSensorFactor(self):
sensorFactor = self.inst.getSensorFactor()
self.assertAlmostEqual(sensorFactor, 0.98679, places=5)
def testGetSensorCoor(self):
xSensor, ySensor = self.inst.getSensorCoor()
self.assertEqual(xSensor.shape,
(self.dimOfDonutOnSensor, self.dimOfDonutOnSensor))
self.assertAlmostEqual(xSensor[0, 0], -0.97857, places=5)
self.assertAlmostEqual(xSensor[0, 1], -0.96212, places=5)
self.assertEqual(ySensor.shape,
(self.dimOfDonutOnSensor, self.dimOfDonutOnSensor))
self.assertAlmostEqual(ySensor[0, 0], -0.97857, places=5)
self.assertAlmostEqual(ySensor[1, 0], -0.96212, places=5)
def testGetSensorCoorAnnular(self):
xoSensor, yoSensor = self.inst.getSensorCoorAnnular()
self.assertEqual(xoSensor.shape,
(self.dimOfDonutOnSensor, self.dimOfDonutOnSensor))
self.assertTrue(np.isnan(xoSensor[0, 0]))
self.assertTrue(np.isnan(xoSensor[60, 60]))
self.assertEqual(yoSensor.shape,
(self.dimOfDonutOnSensor, self.dimOfDonutOnSensor))
self.assertTrue(np.isnan(yoSensor[0, 0]))
self.assertTrue(np.isnan(yoSensor[60, 60]))
def testCalcSizeOfDonutExpected(self):
self.assertAlmostEqual(self.inst.calcSizeOfDonutExpected(),
121.60589604,
places=7)
def testDataAuxTel(self):
inst = Instrument(self.instDir)
inst.config(CamType.AuxTel, 160, announcedDefocalDisInMm=0.8)
self.assertEqual(inst.getObscuration(), 0.3525)
self.assertEqual(inst.getFocalLength(), 21.6)
self.assertEqual(inst.getApertureDiameter(), 1.2)
self.assertEqual(inst.getDefocalDisOffset(), 0.041 * 0.8)
self.assertEqual(inst.getCamPixelSize(), 10.0e-6)
self.assertAlmostEqual(inst.calcSizeOfDonutExpected(),
182.2222222,
places=7)
def testDataAuxTelZWO(self):
inst = Instrument(self.instDir)
inst.config(CamType.AuxTelZWO, 160, announcedDefocalDisInMm=0.5)
self.assertEqual(inst.getObscuration(), 0.3525)
self.assertEqual(inst.getFocalLength(), 21.6)
self.assertEqual(inst.getApertureDiameter(), 1.2)
self.assertEqual(inst.getDefocalDisOffset(), 0.0205)
self.assertEqual(inst.getCamPixelSize(), 15.2e-6)
self.assertAlmostEqual(inst.calcSizeOfDonutExpected(),
74.92690058,
places=7)
class TestInstrument(unittest.TestCase):
"""Test the Instrument class."""
def setUp(self):
self.instDir = os.path.join(getConfigDir(), "cwfs", "instData")
self.inst = Instrument(self.instDir)
self.dimOfDonutOnSensor = 120
self.inst.config(CamType.LsstCam, self.dimOfDonutOnSensor,
announcedDefocalDisInMm=1.5)
def testConfigWithUnsupportedCamType(self):
self.assertRaises(ValueError, self.inst.config, CamType.LsstFamCam, 120)
def testGetInstFileDir(self):
instFileDir = self.inst.getInstFileDir()
ansInstFileDir = os.path.join(self.instDir, "lsst")
self.assertEqual(instFileDir, ansInstFileDir)
def testGetAnnDefocalDisInMm(self):
annDefocalDisInMm = self.inst.getAnnDefocalDisInMm()
self.assertEqual(annDefocalDisInMm, 1.5)
def testSetAnnDefocalDisInMm(self):
annDefocalDisInMm = 2.0
self.inst.setAnnDefocalDisInMm(annDefocalDisInMm)
self.assertEqual(self.inst.getAnnDefocalDisInMm(), annDefocalDisInMm)
def testGetInstFilePath(self):
instFilePath = self.inst.getInstFilePath()
self.assertTrue(os.path.exists(instFilePath))
self.assertEqual(os.path.basename(instFilePath), "instParam.yaml")
def testGetMaskOffAxisCorr(self):
maskOffAxisCorr = self.inst.getMaskOffAxisCorr()
self.assertEqual(maskOffAxisCorr.shape, (9, 5))
self.assertEqual(maskOffAxisCorr[0, 0], 1.07)
self.assertEqual(maskOffAxisCorr[2, 3], -0.090100858)
def testGetDimOfDonutOnSensor(self):
dimOfDonutOnSensor = self.inst.getDimOfDonutOnSensor()
self.assertEqual(dimOfDonutOnSensor, self.dimOfDonutOnSensor)
def testGetObscuration(self):
obscuration = self.inst.getObscuration()
self.assertEqual(obscuration, 0.61)
def testGetFocalLength(self):
focalLength = self.inst.getFocalLength()
self.assertEqual(focalLength, 10.312)
def testGetApertureDiameter(self):
apertureDiameter = self.inst.getApertureDiameter()
self.assertEqual(apertureDiameter, 8.36)
def testGetDefocalDisOffset(self):
defocalDisInM = self.inst.getDefocalDisOffset()
# The answer is 1.5 mm
self.assertEqual(defocalDisInM * 1e3, 1.5)
def testGetCamPixelSize(self):
camPixelSizeInM = self.inst.getCamPixelSize()
# The answer is 10 um
self.assertEqual(camPixelSizeInM * 1e6, 10)
def testGetMarginalFocalLength(self):
marginalFL = self.inst.getMarginalFocalLength()
self.assertAlmostEqual(marginalFL, 9.4268, places=4)
def testGetSensorFactor(self):
sensorFactor = self.inst.getSensorFactor()
self.assertAlmostEqual(sensorFactor, 0.98679, places=5)
def testGetSensorCoor(self):
xSensor, ySensor = self.inst.getSensorCoor()
self.assertEqual(xSensor.shape,
(self.dimOfDonutOnSensor, self.dimOfDonutOnSensor))
self.assertAlmostEqual(xSensor[0, 0], -0.97857, places=5)
self.assertAlmostEqual(xSensor[0, 1], -0.96212, places=5)
self.assertEqual(ySensor.shape,
(self.dimOfDonutOnSensor, self.dimOfDonutOnSensor))
self.assertAlmostEqual(ySensor[0, 0], -0.97857, places=5)
self.assertAlmostEqual(ySensor[1, 0], -0.96212, places=5)
def testGetSensorCoorAnnular(self):
xoSensor, yoSensor = self.inst.getSensorCoorAnnular()
self.assertEqual(xoSensor.shape,
(self.dimOfDonutOnSensor, self.dimOfDonutOnSensor))
self.assertTrue(np.isnan(xoSensor[0, 0]))
self.assertTrue(np.isnan(xoSensor[60, 60]))
self.assertEqual(yoSensor.shape,
(self.dimOfDonutOnSensor, self.dimOfDonutOnSensor))
self.assertTrue(np.isnan(yoSensor[0, 0]))
self.assertTrue(np.isnan(yoSensor[60, 60]))
class Algorithm(object):
def __init__(self, algoDir):
"""Initialize the Algorithm class.
Algorithm used to solve the transport of intensity equation to get
normal/ annular Zernike polynomials.
Parameters
----------
algoDir : str
Algorithm configuration directory.
"""
self.algoDir = algoDir
self.algoParamFile = ParamReader()
self._inst = Instrument("")
# Show the calculation message based on this value
# 0 means no message will be showed
self.debugLevel = 0
# Image has the problem or not from the over-compensation
self.caustic = False
# Record the Zk coefficients in each outer-loop iteration
# The actual total outer-loop iteration time is Num_of_outer_itr + 1
self.converge = np.array([])
# Current number of outer-loop iteration
self.currentItr = 0
# Record the coefficients of normal/ annular Zernike polynomials after
# z4 in unit of nm
self.zer4UpNm = np.array([])
# Converged wavefront.
self.wcomp = np.array([])
# Calculated wavefront in previous outer-loop iteration.
self.West = np.array([])
# Converged Zk coefficients
self.zcomp = np.array([])
# Calculated Zk coefficients in previous outer-loop iteration
self.zc = np.array([])
# Padded mask for use at the offset planes
self.pMask = None
# Non-padded mask corresponding to aperture
self.cMask = None
# Change the dimension of mask for fft to use
self.pMaskPad = None
self.cMaskPad = None
def reset(self):
"""Reset the calculation for the new input images with the same
algorithm settings."""
self.caustic = False
self.converge = np.zeros(self.converge.shape)
self.currentItr = 0
self.zer4UpNm = np.zeros(self.zer4UpNm.shape)
self.wcomp = np.zeros(self.wcomp.shape)
self.West = np.zeros(self.West.shape)
self.zcomp = np.zeros(self.zcomp.shape)
self.zc = np.zeros(self.zc.shape)
self.pMask = None
self.cMask = None
self.pMaskPad = None
self.cMaskPad = None
def config(self, algoName, inst, debugLevel=0):
"""Configure the algorithm to solve TIE.
Parameters
----------
algoName : str
Algorithm configuration file to solve the Poisson's equation in the
transport of intensity equation (TIE). It can be "fft" or "exp"
here.
inst : Instrument
Instrument to use.
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.)
"""
algoParamFilePath = os.path.join(self.algoDir, "%s.yaml" % algoName)
self.algoParamFile.setFilePath(algoParamFilePath)
self._inst = inst
self.debugLevel = debugLevel
self.caustic = False
numTerms = self.getNumOfZernikes()
outerItr = self.getNumOfOuterItr()
self.converge = np.zeros((numTerms, outerItr + 1))
self.currentItr = 0
self.zer4UpNm = np.zeros(numTerms - 3)
# Wavefront related parameters
dimOfDonut = self._inst.getDimOfDonutOnSensor()
self.wcomp = np.zeros((dimOfDonut, dimOfDonut))
self.West = self.wcomp.copy()
# Used in model basis ("zer").
self.zcomp = np.zeros(numTerms)
self.zc = self.zcomp.copy()
# Mask related variables
self.pMask = None
self.cMask = None
self.pMaskPad = None
self.cMaskPad = None
def setDebugLevel(self, debugLevel):
"""Set the debug level.
If the value is higher, the information shows more. It can be 0, 1, 2,
or 3.
Parameters
----------
debugLevel : int
Show the information under the running.
"""
self.debugLevel = int(debugLevel)
def getDebugLevel(self):
"""Get the debug level.
If the value is higher, the information shows more. It can be 0, 1, 2,
or 3.
Returns
-------
int
Debug level.
"""
return self.debugLevel
def getZer4UpInNm(self):
"""Get the coefficients of Zernike polynomials of z4-zn in nm.
Returns
-------
numpy.ndarray
Zernike polynomials of z4-zn in nm.
"""
return self.zer4UpNm
def getPoissonSolverName(self):
"""Get the method name to solve the Poisson equation.
Returns
-------
str
Method name to solve the Poisson equation.
"""
return self.algoParamFile.getSetting("poissonSolver")
def getNumOfZernikes(self):
"""Get the maximum number of Zernike polynomials supported.
Returns
-------
int
Maximum number of Zernike polynomials supported.
"""
return int(self.algoParamFile.getSetting("numOfZernikes"))
def getZernikeTerms(self):
"""Get the Zernike terms in using.
Returns
-------
numpy.ndarray
Zernkie terms in using.
"""
numTerms = self.getNumOfZernikes()
zTerms = np.arange(numTerms) + 1
return zTerms
def getObsOfZernikes(self):
"""Get the obscuration of annular Zernike polynomials.
Returns
-------
float
Obscuration of annular Zernike polynomials
"""
zobsR = self.algoParamFile.getSetting("obsOfZernikes")
if (zobsR == 1):
zobsR = self._inst.getObscuration()
return float(zobsR)
def getNumOfOuterItr(self):
"""Get the number of outer loop iteration.
Returns
-------
int
Number of outer loop iteration.
"""
return int(self.algoParamFile.getSetting("numOfOuterItr"))
def getNumOfInnerItr(self):
"""Get the number of inner loop iteration.
This is for the fast Fourier transform (FFT) solver only.
Returns
-------
int
Number of inner loop iteration.
"""
return int(self.algoParamFile.getSetting("numOfInnerItr"))
def getFeedbackGain(self):
"""Get the gain value used in the outer loop iteration.
Returns
-------
float
Gain value used in the outer loop iteration.
"""
return self.algoParamFile.getSetting("feedbackGain")
def getOffAxisPolyOrder(self):
"""Get the number of polynomial order supported in off-axis correction.
Returns
-------
int
Number of polynomial order supported in off-axis correction.
"""
return int(self.algoParamFile.getSetting("offAxisPolyOrder"))
def getCompensatorMode(self):
"""Get the method name to compensate the wavefront by wavefront error.
Returns
-------
str
Method name to compensate the wavefront by wavefront error.
"""
return self.algoParamFile.getSetting("compensatorMode")
def getCompSequence(self):
"""Get the compensated sequence of Zernike order for each iteration.
Returns
-------
numpy.ndarray[int]
Compensated sequence of Zernike order for each iteration.
"""
compSequenceFromFile = self.algoParamFile.getSetting("compSequence")
compSequence = np.array(compSequenceFromFile, dtype=int)
# If outerItr is large, and compSequence is too small,
# the rest in compSequence will be filled.
# This is used in the "zer" method.
outerItr = self.getNumOfOuterItr()
compSequence = self._extend1dArray(compSequence, outerItr)
compSequence = compSequence.astype(int)
return compSequence
def _extend1dArray(self, origArray, targetLength):
"""Extend the 1D original array to the taget length.
The extended value will be the final element of original array. Nothing
will be done if the input array is not 1D or its length is less than
the target.
Parameters
----------
origArray : numpy.ndarray
Original array with 1 dimension.
targetLength : int
Target length of new extended array.
Returns
-------
numpy.ndarray
Extended 1D array.
"""
if (len(origArray) < targetLength) and (origArray.ndim == 1):
leftOver = np.ones(targetLength - len(origArray))
extendArray = np.append(origArray, origArray[-1] * leftOver)
else:
extendArray = origArray
return extendArray
def getBoundaryThickness(self):
"""Get the boundary thickness that the computation mask extends beyond
the pupil mask.
It is noted that in Fast Fourier transform (FFT) algorithm, it is also
the width of Neuman boundary where the derivative of the wavefront is
set to zero
Returns
-------
int
Boundary thickness.
"""
return int(self.algoParamFile.getSetting("boundaryThickness"))
def getFftDimension(self):
"""Get the FFT pad dimension in pixel.
This is for the fast Fourier transform (FFT) solver only.
Returns
-------
int
FFT pad dimention.
"""
fftDim = int(self.algoParamFile.getSetting("fftDimension"))
# Make sure the dimension is the order of multiple of 2
if (fftDim == 999):
dimToFit = self._inst.getDimOfDonutOnSensor()
else:
dimToFit = fftDim
padDim = int(2**np.ceil(np.log2(dimToFit)))
return padDim
def getSignalClipSequence(self):
"""Get the signal clip sequence.
The number of values should be the number of compensation plus 1.
This is for the fast Fourier transform (FFT) solver only.
Returns
-------
numpy.ndarray
Signal clip sequence.
"""
sumclipSequenceFromFile = self.algoParamFile.getSetting("signalClipSequence")
sumclipSequence = np.array(sumclipSequenceFromFile)
# If outerItr is large, and sumclipSequence is too small, the rest in
# sumclipSequence will be filled.
# This is used in the "zer" method.
targetLength = self.getNumOfOuterItr() + 1
sumclipSequence = self._extend1dArray(sumclipSequence, targetLength)
return sumclipSequence
def getMaskScalingFactor(self):
"""Get the mask scaling factor for fast beam.
Returns
-------
float
Mask scaling factor for fast beam.
"""
# m = R'*f/(l*R), R': radius of the no-aberration image
focalLength = self._inst.getFocalLength()
marginalFL = self._inst.getMarginalFocalLength()
maskScalingFactor = focalLength / marginalFL
return maskScalingFactor
def itr0(self, I1, I2, model):
"""Calculate the wavefront and coefficients of normal/ annular Zernike
polynomials in the first iteration time.
Parameters
----------
I1 : Image
Intra- or extra-focal image.
I2 : Image
Intra- or extra-focal image.
model : str
Optical model. It can be "paraxial", "onAxis", or "offAxis".
"""
# Reset the iteration time of outer loop and decide to reset the
# defocal images or not
self._reset(I1, I2)
# Solve the transport of intensity equation (TIE)
self._singleItr(I1, I2, model)
def runIt(self, I1, I2, model, tol=1e-3):
"""Calculate the wavefront error by solving the transport of intensity
equation (TIE).
The inner (for fft algorithm) and outer loops are used. The inner loop
is to solve the Poisson's equation. The outer loop is to compensate the
intra- and extra-focal images to mitigate the calculation of wavefront
(e.g. S = -1/(delta Z) * (I1 - I2)/ (I1 + I2)).
Parameters
----------
I1 : Image
Intra- or extra-focal image.
I2 : Image
Intra- or extra-focal image.
model : str
Optical model. It can be "paraxial", "onAxis", or "offAxis".
tol : float, optional
Tolerance of difference of coefficients of Zk polynomials compared
with the previours iteration. (the default is 1e-3.)
"""
# To have the iteration time initiated from global variable is to
# distinguish the manually and automatically iteration processes.
itr = self.currentItr
while (itr <= self.getNumOfOuterItr()):
stopItr = self._singleItr(I1, I2, model, tol)
# Stop the iteration of outer loop if converged
if (stopItr):
break
itr += 1
def nextItr(self, I1, I2, model, nItr=1):
"""Run the outer loop iteration with the specific time defined in nItr.
Parameters
----------
I1 : Image
Intra- or extra-focal image.
I2 : Image
Intra- or extra-focal image.
model : str
Optical model. It can be "paraxial", "onAxis", or "offAxis".
nItr : int, optional
Outer loop iteration time. (the default is 1.)
"""
# Do the iteration
ii = 0
while (ii < nItr):
self._singleItr(I1, I2, model)
ii += 1
def _singleItr(self, I1, I2, model, tol=1e-3):
"""Run the outer-loop with single iteration to solve the transport of
intensity equation (TIE).
This is to compensate the approximation of wavefront:
S = -1/(delta Z) * (I1 - I2)/ (I1 + I2)).
Parameters
----------
I1 : Image
Intra- or extra-focal image.
I2 : Image
Intra- or extra-focal image.
model : str
Optical model. It can be "paraxial", "onAxis", or "offAxis".
tol : float, optional
Tolerance of difference of coefficients of Zk polynomials compared
with the previours iteration. (the default is 1e-3.)
Returns
-------
bool
Status of iteration.
"""
# Use the zonal mode ("zer")
compMode = self.getCompensatorMode()
# Define the gain of feedbackGain
feedbackGain = self.getFeedbackGain()
# Set the pre-condition
if (self.currentItr == 0):
# Check this is the first time of running iteration or not
if (I1.getImgInit() is None or I2.getImgInit() is None):
# Check the image dimension
if (I1.getImg().shape != I2.getImg().shape):
print("Error: The intra and extra image stamps need to be of same size.")
sys.exit()
# Calculate the pupil mask (binary matrix) and related
# parameters
boundaryT = self.getBoundaryThickness()
I1.makeMask(self._inst, model, boundaryT, 1)
I2.makeMask(self._inst, model, boundaryT, 1)
self._makeMasterMask(I1, I2, self.getPoissonSolverName())
# Load the offAxis correction coefficients
if (model == "offAxis"):
offAxisPolyOrder = self.getOffAxisPolyOrder()
I1.setOffAxisCorr(self._inst, offAxisPolyOrder)
I2.setOffAxisCorr(self._inst, offAxisPolyOrder)
# Cocenter the images to the center referenced to fieldX and
# fieldY. Need to check the availability of this.
I1.imageCoCenter(self._inst, debugLevel=self.debugLevel)
I2.imageCoCenter(self._inst, debugLevel=self.debugLevel)
# Update the self-initial image
I1.updateImgInit()
I2.updateImgInit()
# Initialize the variables used in the iteration.
self.zcomp = np.zeros(self.getNumOfZernikes())
self.zc = self.zcomp.copy()
dimOfDonut = self._inst.getDimOfDonutOnSensor()
self.wcomp = np.zeros((dimOfDonut, dimOfDonut))
self.West = self.wcomp.copy()
self.caustic = False
# Rename this index (currentItr) for the simplification
jj = self.currentItr
# Solve the transport of intensity equation (TIE)
if (not self.caustic):
# Reset the images before the compensation
I1.updateImage(I1.getImgInit().copy())
I2.updateImage(I2.getImgInit().copy())
if (compMode == "zer"):
# Zk coefficient from the previous iteration
ztmp = self.zc
# Do the feedback of Zk from the lower terms first based on the
# sequence defined in compSequence
if (jj != 0):
compSequence = self.getCompSequence()
ztmp[int(compSequence[jj - 1]):] = 0
# Add partial feedback of residual estimated wavefront in Zk
self.zcomp = self.zcomp + ztmp*feedbackGain
# Remove the image distortion if the optical model is not
# "paraxial"
# Only the optical model of "onAxis" or "offAxis" is considered
# here
I1.compensate(self._inst, self, self.zcomp, model)
I2.compensate(self._inst, self, self.zcomp, model)
# Check the image condition. If there is the problem, done with
# this _singleItr().
if (I1.isCaustic() is True) or (I2.isCaustic() is True):
self.converge[:, jj] = self.converge[:, jj - 1]
self.caustic = True
return
# Correct the defocal images if I1 and I2 are belong to different
# sources, which is determined by the (fieldX, field Y)
I1, I2 = self._applyI1I2pMask(I1, I2)
# Solve the Poisson's equation
self.zc, self.West = self._solvePoissonEq(I1, I2, jj)
# Record/ calculate the Zk coefficient and wavefront
if (compMode == "zer"):
self.converge[:, jj] = self.zcomp + self.zc
xoSensor, yoSensor = self._inst.getSensorCoorAnnular()
self.wcomp = self.West + ZernikeAnnularEval(
np.concatenate(([0, 0, 0], self.zcomp[3:])), xoSensor,
yoSensor, self.getObsOfZernikes())
else:
# Once we run into caustic, stop here, results may be close to real
# aberration.
# Continuation may lead to disatrous results.
self.converge[:, jj] = self.converge[:, jj - 1]
# Record the coefficients of normal/ annular Zernike polynomials after
# z4 in unit of nm
self.zer4UpNm = self.converge[3:, jj]*1e9
# Status of iteration
stopItr = False
# Calculate the difference
if (jj > 0):
diffZk = np.sum(np.abs(self.converge[:, jj]-self.converge[:, jj-1]))*1e9
# Check the Status of iteration
if (diffZk < tol):
stopItr = True
# Update the current iteration time
self.currentItr += 1
# Show the Zk coefficients in interger in each iteration
if (self.debugLevel >= 2):
tmp = self.zer4UpNm
print("itr = %d, z4-z%d" % (jj, self.getNumOfZernikes()))
print(np.rint(tmp))
return stopItr
def _solvePoissonEq(self, I1, I2, iOutItr=0):
"""Solve the Poisson's equation by Fourier transform (differential) or
serial expansion (integration).
There is no convergence for fft actually. Need to add the difference
comparison and X-alpha method. Need to discuss further for this.
Parameters
----------
I1 : Image
Intra- or extra-focal image.
I2 : Image
Intra- or extra-focal image.
iOutItr : int, optional
ith number of outer loop iteration which is important in "fft"
algorithm. (the default is 0.)
Returns
-------
numpy.ndarray
Coefficients of normal/ annular Zernike polynomials.
numpy.ndarray
Estimated wavefront.
"""
# Calculate the aperature pixel size
apertureDiameter = self._inst.getApertureDiameter()
sensorFactor = self._inst.getSensorFactor()
dimOfDonut = self._inst.getDimOfDonutOnSensor()
aperturePixelSize = apertureDiameter*sensorFactor/dimOfDonut
# Calculate the differential Omega
dOmega = aperturePixelSize**2
# Solve the Poisson's equation based on the type of algorithm
numTerms = self.getNumOfZernikes()
zobsR = self.getObsOfZernikes()
PoissonSolver = self.getPoissonSolverName()
if (PoissonSolver == "fft"):
# Use the differential method by fft to solve the Poisson's
# equation
# Parameter to determine the threshold of calculating I0.
sumclipSequence = self.getSignalClipSequence()
cliplevel = sumclipSequence[iOutItr]
# Generate the v, u-coordinates on pupil plane
padDim = self.getFftDimension()
v, u = np.mgrid[
-0.5/aperturePixelSize: 0.5/aperturePixelSize: 1./padDim/aperturePixelSize,
-0.5/aperturePixelSize: 0.5/aperturePixelSize: 1./padDim/aperturePixelSize]
# Show the threshold and pupil coordinate information
if (self.debugLevel >= 3):
print("iOuter=%d, cliplevel=%4.2f" % (iOutItr, cliplevel))
print(v.shape)
# Calculate the const of fft:
# FT{Delta W} = -4*pi^2*(u^2+v^2) * FT{W}
u2v2 = -4 * (np.pi**2) * (u*u + v*v)
# Set origin to Inf to result in 0 at origin after filtering
ctrIdx = int(np.floor(padDim/2.0))
u2v2[ctrIdx, ctrIdx] = np.inf
# Calculate the wavefront signal
Sini = self._createSignal(I1, I2, cliplevel)
# Find the just-outside and just-inside indices of a ring in pixels
# This is for the use in setting dWdn = 0
boundaryT = self.getBoundaryThickness()
struct = generate_binary_structure(2, 1)
struct = iterate_structure(struct, boundaryT)
ApringOut = np.logical_xor(binary_dilation(self.pMask, structure=struct),
self.pMask).astype(int)
ApringIn = np.logical_xor(binary_erosion(self.pMask, structure=struct),
self.pMask).astype(int)
bordery, borderx = np.nonzero(ApringOut)
# Put the signal in boundary (since there's no existing Sestimate,
# S just equals self.S as the initial condition of SCF
S = Sini.copy()
for jj in range(self.getNumOfInnerItr()):
# Calculate FT{S}
SFFT = np.fft.fftshift(np.fft.fft2(np.fft.fftshift(S)))
# Calculate W by W=IFT{ FT{S}/(-4*pi^2*(u^2+v^2)) }
W = np.fft.fftshift(np.fft.irfft2(np.fft.fftshift(SFFT/u2v2), s=S.shape))
# Estimate the wavefront (includes zeroing offset & masking to
# the aperture size)
# Take the estimated wavefront
West = extractArray(W, dimOfDonut)
# Calculate the offset
offset = West[self.pMask == 1].mean()
West = West - offset
West[self.pMask == 0] = 0
# Set dWestimate/dn = 0 around boundary
WestdWdn0 = West.copy()
# Do a 3x3 average around each border pixel, including only
# those pixels inside the aperture
for ii in range(len(borderx)):
reg = West[borderx[ii] - boundaryT:
borderx[ii] + boundaryT + 1,
bordery[ii] - boundaryT:
bordery[ii] + boundaryT + 1]
intersectIdx = ApringIn[borderx[ii] - boundaryT:
borderx[ii] + boundaryT + 1,
bordery[ii] - boundaryT:
bordery[ii] + boundaryT + 1]
WestdWdn0[borderx[ii], bordery[ii]] = \
reg[np.nonzero(intersectIdx)].mean()
# Take Laplacian to find sensor signal estimate (Delta W = S)
del2W = laplace(WestdWdn0)/dOmega
# Extend the dimension of signal to the order of 2 for "fft" to
# use
Sest = padArray(del2W, padDim)
# Put signal back inside boundary, leaving the rest of
# Sestimate
Sest[self.pMaskPad == 1] = Sini[self.pMaskPad == 1]
# Need to recheck this condition
S = Sest
# Define the estimated wavefront
# self.West = West.copy()
# Calculate the coefficient of normal/ annular Zernike polynomials
if (self.getCompensatorMode() == "zer"):
xSensor, ySensor = self._inst.getSensorCoor()
zc = ZernikeMaskedFit(West, xSensor, ySensor, numTerms,
self.pMask, zobsR)
else:
zc = np.zeros(numTerms)
elif (PoissonSolver == "exp"):
# Use the integration method by serial expansion to solve the
# Poisson's equation
# Calculate I0 and dI
I0, dI = self._getdIandI(I1, I2)
# Get the x, y coordinate in mask. The element outside mask is 0.
xSensor, ySensor = self._inst.getSensorCoor()
xSensor = xSensor * self.cMask
ySensor = ySensor * self.cMask
# Create the F matrix and Zernike-related matrixes
F = np.zeros(numTerms)
dZidx = np.zeros((numTerms, dimOfDonut, dimOfDonut))
dZidy = dZidx.copy()
zcCol = np.zeros(numTerms)
for ii in range(int(numTerms)):
# Calculate the matrix for each Zk related component
# Set the specific Zk cofficient to be 1 for the calculation
zcCol[ii] = 1
F[ii] = np.sum(dI*ZernikeAnnularEval(zcCol, xSensor, ySensor, zobsR))*dOmega
dZidx[ii, :, :] = ZernikeAnnularGrad(zcCol, xSensor, ySensor, zobsR, "dx")
dZidy[ii, :, :] = ZernikeAnnularGrad(zcCol, xSensor, ySensor, zobsR, "dy")
# Set the specific Zk cofficient back to 0 to avoid interfering
# other Zk's calculation
zcCol[ii] = 0
# Calculate Mij matrix, need to check the stability of integration
# and symmetry later
Mij = np.zeros([numTerms, numTerms])
for ii in range(numTerms):
for jj in range(numTerms):
Mij[ii, jj] = np.sum(I0*(dZidx[ii, :, :].squeeze()*dZidx[jj, :, :].squeeze() +
dZidy[ii, :, :].squeeze()*dZidy[jj, :, :].squeeze()))
Mij = dOmega/(apertureDiameter/2.)**2 * Mij
# Calculate dz
focalLength = self._inst.getFocalLength()
offset = self._inst.getDefocalDisOffset()
dz = 2*focalLength*(focalLength-offset)/offset
# Define zc
zc = np.zeros(numTerms)
# Consider specific Zk terms only
idx = (self.getZernikeTerms() - 1).tolist()
# Solve the equation: M*W = F => W = M^(-1)*F
zc_tmp = np.linalg.lstsq(Mij[:, idx][idx], F[idx], rcond=None)[0]/dz
zc[idx] = zc_tmp
# Estimate the wavefront surface based on z4 - z22
# z0 - z3 are set to be 0 instead
West = ZernikeAnnularEval(np.concatenate(([0, 0, 0], zc[3:])),
xSensor, ySensor, zobsR)
return zc, West
def _createSignal(self, I1, I2, cliplevel):
"""Calculate the wavefront singal for "fft" to use in solving the
Poisson's equation.
Need to discuss the method to define threshold and discuss to use
np.median() instead.
Need to discuss why the calculation of I0 is different from "exp".
Parameters
----------
I1 : Image
Intra- or extra-focal image.
I2 : Image
Intra- or extra-focal image.
cliplevel : float
Parameter to determine the threshold of calculating I0.
Returns
-------
numpy.ndarray
Approximated wavefront signal.
"""
# Check the condition of images
I1image, I2image = self._checkImageDim(I1, I2)
# Wavefront signal S=-(1/I0)*(dI/dz) is approximated to be
# -(1/delta z)*(I1-I2)/(I1+I2)
num = I1image - I2image
den = I1image + I2image
# Define the effective minimum central signal element by the threshold
# ( I0=(I1+I2)/2 )
# Calculate the threshold
pixelList = den * self.cMask
pixelList = pixelList[pixelList != 0]
low = pixelList.min()
high = pixelList.max()
medianThreshold = (high-low)/2. + low
# Define the effective minimum central signal element
den[den < medianThreshold*cliplevel] = 1.5*medianThreshold
# Calculate delta z = f(f-l)/l, f: focal length, l: defocus distance of
# the image planes
focalLength = self._inst.getFocalLength()
offset = self._inst.getDefocalDisOffset()
deltaZ = focalLength*(focalLength-offset)/offset
# Calculate the wavefront signal. Enforce the element outside the mask
# to be 0.
den[den == 0] = np.inf
# Calculate the wavefront signal
S = num/den/deltaZ
# Extend the dimension of signal to the order of 2 for "fft" to use
padDim = self.getFftDimension()
Sout = padArray(S, padDim)*self.cMaskPad
return Sout
def _getdIandI(self, I1, I2):
"""Calculate the central image and differential image to be used in the
serial expansion method.
It is noted that the images are assumed to be co-center already. And
the intra-/ extra-focal image can overlap with one another after the
rotation of 180 degree.
Parameters
----------
I1 : Image
Intra- or extra-focal image.
I2 : Image
Intra- or extra-focal image.
Returns
-------
numpy.ndarray
Image data of I0.
numpy.ndarray
Differential image (dI) of I0.
"""
# Check the condition of images
I1image, I2image = self._checkImageDim(I1, I2)
# Calculate the central image and differential iamge
I0 = (I1image+I2image)/2
dI = I2image-I1image
return I0, dI
def _checkImageDim(self, I1, I2):
"""Check the dimension of images.
It is noted that the I2 image is rotated by 180 degree.
Parameters
----------
I1 : Image
Intra- or extra-focal image.
I2 : Image
Intra- or extra-focal image.
Returns
-------
numpy.ndarray
I1 defocal image.
numpy.ndarray
I2 defocal image. It is noted that the I2 image is rotated by 180
degree.
Raises
------
Exception
Check the dimension of images is n by n or not.
Exception
Check two defocal images have the same size or not.
"""
# Check the condition of images
m1, n1 = I1.getImg().shape
m2, n2 = I2.getImg().shape
if (m1 != n1 or m2 != n2):
raise Exception("Image is not square.")
if (m1 != m2 or n1 != n2):
raise Exception("Images do not have the same size.")
# Define I1
I1image = I1.getImg()
# Rotate the image by 180 degree through rotating two times of 90
# degree
I2image = np.rot90(I2.getImg(), k=2)
return I1image, I2image
def _makeMasterMask(self, I1, I2, poissonSolver=None):
"""Calculate the common mask of defocal images.
Parameters
----------
I1 : Image
Intra- or extra-focal image.
I2 : Image
Intra- or extra-focal image.
poissonSolver : str, optional
Algorithm to solve the Poisson's equation. If the "fft" is used,
the mask dimension will be extended to the order of 2 for the "fft"
to use. (the default is None.)
"""
# Get the overlap region of mask for intra- and extra-focal images.
# This is to avoid the anormalous signal due to difference in
# vignetting.
self.pMask = I1.getPaddedMask() * I2.getPaddedMask()
self.cMask = I1.getNonPaddedMask() * I2.getNonPaddedMask()
# Change the dimension of image for fft to use
if (poissonSolver == "fft"):
padDim = self.getFftDimension()
self.pMaskPad = padArray(self.pMask, padDim)
self.cMaskPad = padArray(self.cMask, padDim)
def _applyI1I2pMask(self, I1, I2):
"""Correct the defocal images if I1 and I2 are belong to different
sources.
(There is a problem for this actually. If I1 and I2 come from different
sources, what should the correction of TIE be? At this moment, the
fieldX and fieldY of I1 and I2 should be different. And the sources are
different also.)
Parameters
----------
I1 : Image
Intra- or extra-focal image.
I2 : Image
Intra- or extra-focal image.
Returns
-------
numpy.ndarray
Corrected I1 image.
numpy.ndarray
Corrected I2 image.
"""
# Get the overlap region of images and do the normalization.
if (I1.fieldX != I2.fieldX or I1.fieldY != I2.fieldY):
# Get the overlap region of image
I1.updateImage(I1.getImg()*self.pMask)
# Rotate the image by 180 degree through rotating two times of 90
# degree
I2.updateImage(I2.getImg()*np.rot90(self.pMask, 2))
# Do the normalization of image.
I1.updateImage(I1.getImg()/np.sum(I1.getImg()))
I2.updateImage(I2.getImg()/np.sum(I2.getImg()))
# Return the correct images. It is noted that there is no need of
# vignetting correction.
# This is after masking already in _singleItr() or itr0().
return I1, I2
def _reset(self, I1, I2):
"""Reset the iteration time of outer loop and defocal images.
Parameters
----------
I1 : Image
Intra- or extra-focal image.
I2 : Image
Intra- or extra-focal image.
"""
# Reset the current iteration time to 0
self.currentItr = 0
# Show the reset information
if (self.debugLevel >= 3):
print("Resetting images: I1 and I2")
# Determine to reset the images or not based on the existence of
# the attribute: Image.image0. Only after the first run of
# inner loop, this attribute will exist.
try:
# Reset the images to the first beginning
I1.updateImage(I1.getImgInit().copy())
I2.updateImage(I2.getImgInit().copy())
# Show the information of resetting image
if (self.debugLevel >= 3):
print("Resetting images in inside.")
except AttributeError:
# Show the information of no image0
if (self.debugLevel >= 3):
print("Image0 = None. This is the first time to run the code.")
pass
def outZer4Up(self, unit="nm", filename=None, showPlot=False):
"""Put the coefficients of normal/ annular Zernike polynomials on
terminal or file ande show the image if it is needed.
Parameters
----------
unit : str, optional
Unit of the coefficients of normal/ annular Zernike polynomials. It
can be m, nm, or um. (the default is "nm".)
filename : str, optional
Name of output file. (the default is None.)
showPlot : bool, optional
Decide to show the plot or not. (the default is False.)
"""
# List of Zn,m
Znm = ["Z0,0", "Z1,1", "Z1,-1", "Z2,0", "Z2,-2", "Z2,2", "Z3,-1",
"Z3,1", "Z3,-3", "Z3,3", "Z4,0", "Z4,2", "Z4,-2", "Z4,4",
"Z4,-4", "Z5,1", "Z5,-1", "Z5,3", "Z5,-3", "Z5,5", "Z5,-5",
"Z6,0"]
# Decide the format of z based on the input unit (m, nm, or um)
if (unit == "m"):
z = self.zer4UpNm*1e-9
elif (unit == "nm"):
z = self.zer4UpNm
elif (unit == "um"):
z = self.zer4UpNm*1e-3
else:
print("Unknown unit: %s" % unit)
print("Unit options are: m, nm, um")
return
# Write the coefficients into a file if needed.
if (filename is not None):
f = open(filename, "w")
else:
f = sys.stdout
for ii in range(4, len(z)+4):
f.write("Z%d (%s)\t %8.3f\n" % (ii, Znm[ii-1], z[ii-4]))
# Close the file
if (filename is not None):
f.close()
# Show the plot
if (showPlot):
plt.figure()
x = range(4, len(z) + 4)
plt.plot(x, z, marker="o", color="r", markersize=10)
plt.xlabel("Zernike Index")
plt.ylabel("Zernike coefficient (%s)" % unit)
plt.grid()
plt.show()
class Algorithm(object):
def __init__(self, algoDir):
"""Initialize the Algorithm class.
Algorithm used to solve the transport of intensity equation to get
normal/ annular Zernike polynomials.
Parameters
----------
algoDir : str
Algorithm configuration directory.
"""
self.algoDir = algoDir
self.algoParamFile = ParamReader()
self._inst = Instrument("")
# Show the calculation message based on this value
# 0 means no message will be showed
self.debugLevel = 0
# Image has the problem or not from the over-compensation
self.caustic = False
# Record the Zk coefficients in each outer-loop iteration
# The actual total outer-loop iteration time is Num_of_outer_itr + 1
self.converge = np.array([])
# Current number of outer-loop iteration
self.currentItr = 0
# Record the coefficients of normal/ annular Zernike polynomials after
# z4 in unit of nm
self.zer4UpNm = np.array([])
# Converged wavefront.
self.wcomp = np.array([])
# Calculated wavefront in previous outer-loop iteration.
self.West = np.array([])
# Converged Zk coefficients
self.zcomp = np.array([])
# Calculated Zk coefficients in previous outer-loop iteration
self.zc = np.array([])
# Padded mask for use at the offset planes
self.pMask = None
# Non-padded mask corresponding to aperture
self.cMask = None
# Change the dimension of mask for fft to use
self.pMaskPad = None
self.cMaskPad = None
def reset(self):
"""Reset the calculation for the new input images with the same
algorithm settings."""
self.caustic = False
self.converge = np.zeros(self.converge.shape)
self.currentItr = 0
self.zer4UpNm = np.zeros(self.zer4UpNm.shape)
self.wcomp = np.zeros(self.wcomp.shape)
self.West = np.zeros(self.West.shape)
self.zcomp = np.zeros(self.zcomp.shape)
self.zc = np.zeros(self.zc.shape)
self.pMask = None
self.cMask = None
self.pMaskPad = None
self.cMaskPad = None
def config(self, algoName, inst, debugLevel=0):
"""Configure the algorithm to solve TIE.
Parameters
----------
algoName : str
Algorithm configuration file to solve the Poisson's equation in the
transport of intensity equation (TIE). It can be "fft" or "exp"
here.
inst : Instrument
Instrument to use.
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.)
"""
algoParamFilePath = os.path.join(self.algoDir, "%s.yaml" % algoName)
self.algoParamFile.setFilePath(algoParamFilePath)
self._inst = inst
self.debugLevel = debugLevel
self.caustic = False
numTerms = self.getNumOfZernikes()
outerItr = self.getNumOfOuterItr()
self.converge = np.zeros((numTerms, outerItr + 1))
self.currentItr = 0
self.zer4UpNm = np.zeros(numTerms - 3)
# Wavefront related parameters
dimOfDonut = self._inst.getDimOfDonutOnSensor()
self.wcomp = np.zeros((dimOfDonut, dimOfDonut))
self.West = self.wcomp.copy()
# Used in model basis ("zer").
self.zcomp = np.zeros(numTerms)
self.zc = self.zcomp.copy()
# Mask related variables
self.pMask = None
self.cMask = None
self.pMaskPad = None
self.cMaskPad = None
def setDebugLevel(self, debugLevel):
"""Set the debug level.
If the value is higher, the information shows more. It can be 0, 1, 2,
or 3.
Parameters
----------
debugLevel : int
Show the information under the running.
"""
self.debugLevel = int(debugLevel)
def getDebugLevel(self):
"""Get the debug level.
If the value is higher, the information shows more. It can be 0, 1, 2,
or 3.
Returns
-------
int
Debug level.
"""
return self.debugLevel
def getZer4UpInNm(self):
"""Get the coefficients of Zernike polynomials of z4-zn in nm.
Returns
-------
numpy.ndarray
Zernike polynomials of z4-zn in nm.
"""
return self.zer4UpNm
def getPoissonSolverName(self):
"""Get the method name to solve the Poisson equation.
Returns
-------
str
Method name to solve the Poisson equation.
"""
return self.algoParamFile.getSetting("poissonSolver")
def getNumOfZernikes(self):
"""Get the maximum number of Zernike polynomials supported.
Returns
-------
int
Maximum number of Zernike polynomials supported.
"""
return int(self.algoParamFile.getSetting("numOfZernikes"))
def getZernikeTerms(self):
"""Get the Zernike terms in using.
Returns
-------
list[int]
Zernike terms in using.
"""
numTerms = self.getNumOfZernikes()
return list(range(numTerms))
def getObsOfZernikes(self):
"""Get the obscuration of annular Zernike polynomials.
Returns
-------
float
Obscuration of annular Zernike polynomials
"""
zobsR = self.algoParamFile.getSetting("obsOfZernikes")
if zobsR == 1:
zobsR = self._inst.getObscuration()
return float(zobsR)
def getNumOfOuterItr(self):
"""Get the number of outer loop iteration.
Returns
-------
int
Number of outer loop iteration.
"""
return int(self.algoParamFile.getSetting("numOfOuterItr"))
def getNumOfInnerItr(self):
"""Get the number of inner loop iteration.
This is for the fast Fourier transform (FFT) solver only.
Returns
-------
int
Number of inner loop iteration.
"""
return int(self.algoParamFile.getSetting("numOfInnerItr"))
def getFeedbackGain(self):
"""Get the gain value used in the outer loop iteration.
Returns
-------
float
Gain value used in the outer loop iteration.
"""
return self.algoParamFile.getSetting("feedbackGain")
def getOffAxisPolyOrder(self):
"""Get the number of polynomial order supported in off-axis correction.
Returns
-------
int
Number of polynomial order supported in off-axis correction.
"""
return int(self.algoParamFile.getSetting("offAxisPolyOrder"))
def getCompensatorMode(self):
"""Get the method name to compensate the wavefront by wavefront error.
Returns
-------
str
Method name to compensate the wavefront by wavefront error.
"""
return self.algoParamFile.getSetting("compensatorMode")
def getCompSequence(self):
"""Get the compensated sequence of Zernike order for each iteration.
Returns
-------
numpy.ndarray[int]
Compensated sequence of Zernike order for each iteration.
"""
compSequenceFromFile = self.algoParamFile.getSetting("compSequence")
compSequence = np.array(compSequenceFromFile, dtype=int)
# If outerItr is large, and compSequence is too small,
# the rest in compSequence will be filled.
# This is used in the "zer" method.
outerItr = self.getNumOfOuterItr()
compSequence = self._extend1dArray(compSequence, outerItr)
compSequence = compSequence.astype(int)
return compSequence
def _extend1dArray(self, origArray, targetLength):
"""Extend the 1D original array to the taget length.
The extended value will be the final element of original array. Nothing
will be done if the input array is not 1D or its length is less than
the target.
Parameters
----------
origArray : numpy.ndarray
Original array with 1 dimension.
targetLength : int
Target length of new extended array.
Returns
-------
numpy.ndarray
Extended 1D array.
"""
if (len(origArray) < targetLength) and (origArray.ndim == 1):
leftOver = np.ones(targetLength - len(origArray))
extendArray = np.append(origArray, origArray[-1] * leftOver)
else:
extendArray = origArray
return extendArray
def getBoundaryThickness(self):
"""Get the boundary thickness that the computation mask extends beyond
the pupil mask.
It is noted that in Fast Fourier transform (FFT) algorithm, it is also
the width of Neuman boundary where the derivative of the wavefront is
set to zero
Returns
-------
int
Boundary thickness.
"""
return int(self.algoParamFile.getSetting("boundaryThickness"))
def getFftDimension(self):
"""Get the FFT pad dimension in pixel.
This is for the fast Fourier transform (FFT) solver only.
Returns
-------
int
FFT pad dimention.
"""
fftDim = int(self.algoParamFile.getSetting("fftDimension"))
# Make sure the dimension is the order of multiple of 2
if fftDim == 999:
dimToFit = self._inst.getDimOfDonutOnSensor()
else:
dimToFit = fftDim
padDim = int(2 ** np.ceil(np.log2(dimToFit)))
return padDim
def getSignalClipSequence(self):
"""Get the signal clip sequence.
The number of values should be the number of compensation plus 1.
This is for the fast Fourier transform (FFT) solver only.
Returns
-------
numpy.ndarray
Signal clip sequence.
"""
sumclipSequenceFromFile = self.algoParamFile.getSetting("signalClipSequence")
sumclipSequence = np.array(sumclipSequenceFromFile)
# If outerItr is large, and sumclipSequence is too small, the rest in
# sumclipSequence will be filled.
# This is used in the "zer" method.
targetLength = self.getNumOfOuterItr() + 1
sumclipSequence = self._extend1dArray(sumclipSequence, targetLength)
return sumclipSequence
def getMaskScalingFactor(self):
"""Get the mask scaling factor for fast beam.
Returns
-------
float
Mask scaling factor for fast beam.
"""
# m = R'*f/(l*R), R': radius of the no-aberration image
focalLength = self._inst.getFocalLength()
marginalFL = self._inst.getMarginalFocalLength()
maskScalingFactor = focalLength / marginalFL
return maskScalingFactor
def getWavefrontMapEsti(self):
"""Get the estimated wavefront map.
Returns
-------
numpy.ndarray
Estimated wavefront map.
"""
return self._getWavefrontMapWithMaskApplied(self.wcomp)
def getWavefrontMapResidual(self):
"""Get the residual wavefront map.
Returns
-------
numpy.ndarray
Residual wavefront map.
"""
return self._getWavefrontMapWithMaskApplied(self.West)
def _getWavefrontMapWithMaskApplied(self, wfMap):
"""Get the wavefront map with mask applied.
Parameters
----------
wfMap : numpy.ndarray
Wavefront map.
Returns
-------
numpy.ndarray
Wavefront map with mask applied.
"""
self._checkNotItr0()
wfMapWithMask = wfMap.copy()
wfMapWithMask[self.pMask == 0] = np.nan
return wfMapWithMask
def _checkNotItr0(self):
"""Check not in the iteration 0.
TIE: Transport of intensity equation.
Raises
------
RuntimeError
Need to solve the TIE first.
"""
if self.currentItr == 0:
raise RuntimeError("Need to solve the TIE first.")
def itr0(self, I1, I2, model):
"""Calculate the wavefront and coefficients of normal/ annular Zernike
polynomials in the first iteration time.
Parameters
----------
I1 : CompensableImage
Intra- or extra-focal image.
I2 : CompensableImage
Intra- or extra-focal image.
model : str
Optical model. It can be "paraxial", "onAxis", or "offAxis".
"""
# Reset the iteration time of outer loop and decide to reset the
# defocal images or not
self._reset(I1, I2)
# Solve the transport of intensity equation (TIE)
self._singleItr(I1, I2, model)
def runIt(self, I1, I2, model, tol=1e-3):
"""Calculate the wavefront error by solving the transport of intensity
equation (TIE).
The inner (for fft algorithm) and outer loops are used. The inner loop
is to solve the Poisson's equation. The outer loop is to compensate the
intra- and extra-focal images to mitigate the calculation of wavefront
(e.g. S = -1/(delta Z) * (I1 - I2)/ (I1 + I2)).
Parameters
----------
I1 : CompensableImage
Intra- or extra-focal image.
I2 : CompensableImage
Intra- or extra-focal image.
model : str
Optical model. It can be "paraxial", "onAxis", or "offAxis".
tol : float, optional
Tolerance of difference of coefficients of Zk polynomials compared
with the previours iteration. (the default is 1e-3.)
"""
# To have the iteration time initiated from global variable is to
# distinguish the manually and automatically iteration processes.
itr = self.currentItr
while itr <= self.getNumOfOuterItr():
stopItr = self._singleItr(I1, I2, model, tol)
# Stop the iteration of outer loop if converged
if stopItr:
break
itr += 1
def nextItr(self, I1, I2, model, nItr=1):
"""Run the outer loop iteration with the specific time defined in nItr.
Parameters
----------
I1 : CompensableImage
Intra- or extra-focal image.
I2 : CompensableImage
Intra- or extra-focal image.
model : str
Optical model. It can be "paraxial", "onAxis", or "offAxis".
nItr : int, optional
Outer loop iteration time. (the default is 1.)
"""
# Do the iteration
ii = 0
while ii < nItr:
self._singleItr(I1, I2, model)
ii += 1
def _singleItr(self, I1, I2, model, tol=1e-3):
"""Run the outer-loop with single iteration to solve the transport of
intensity equation (TIE).
This is to compensate the approximation of wavefront:
S = -1/(delta Z) * (I1 - I2)/ (I1 + I2)).
Parameters
----------
I1 : CompensableImage
Intra- or extra-focal image.
I2 : CompensableImage
Intra- or extra-focal image.
model : str
Optical model. It can be "paraxial", "onAxis", or "offAxis".
tol : float, optional
Tolerance of difference of coefficients of Zk polynomials compared
with the previours iteration. (the default is 1e-3.)
Returns
-------
bool
Status of iteration.
"""
# Use the zonal mode ("zer")
compMode = self.getCompensatorMode()
# Define the gain of feedbackGain
feedbackGain = self.getFeedbackGain()
# Set the pre-condition
if self.currentItr == 0:
# Check this is the first time of running iteration or not
if I1.getImgInit() is None or I2.getImgInit() is None:
# Check the image dimension
if I1.getImg().shape != I2.getImg().shape:
print(
"Error: The intra and extra image stamps need to be of same size."
)
sys.exit()
# Calculate the pupil mask (binary matrix) and related
# parameters
boundaryT = self.getBoundaryThickness()
I1.makeMask(self._inst, model, boundaryT, 1)
I2.makeMask(self._inst, model, boundaryT, 1)
self._makeMasterMask(I1, I2, self.getPoissonSolverName())
# Load the offAxis correction coefficients
if model == "offAxis":
offAxisPolyOrder = self.getOffAxisPolyOrder()
I1.setOffAxisCorr(self._inst, offAxisPolyOrder)
I2.setOffAxisCorr(self._inst, offAxisPolyOrder)
# Cocenter the images to the center referenced to fieldX and
# fieldY. Need to check the availability of this.
I1.imageCoCenter(self._inst, debugLevel=self.debugLevel)
I2.imageCoCenter(self._inst, debugLevel=self.debugLevel)
# Update the self-initial image
I1.updateImgInit()
I2.updateImgInit()
# Initialize the variables used in the iteration.
self.zcomp = np.zeros(self.getNumOfZernikes())
self.zc = self.zcomp.copy()
dimOfDonut = self._inst.getDimOfDonutOnSensor()
self.wcomp = np.zeros((dimOfDonut, dimOfDonut))
self.West = self.wcomp.copy()
self.caustic = False
# Rename this index (currentItr) for the simplification
jj = self.currentItr
# Solve the transport of intensity equation (TIE)
if not self.caustic:
# Reset the images before the compensation
I1.updateImage(I1.getImgInit().copy())
I2.updateImage(I2.getImgInit().copy())
if compMode == "zer":
# Zk coefficient from the previous iteration
ztmp = self.zc.copy()
# Do the feedback of Zk from the lower terms first based on the
# sequence defined in compSequence
if jj != 0:
compSequence = self.getCompSequence()
ztmp[int(compSequence[jj - 1]) :] = 0
# Add partial feedback of residual estimated wavefront in Zk
self.zcomp = self.zcomp + ztmp * feedbackGain
# Remove the image distortion by forwarding the image to pupil
I1.compensate(self._inst, self, self.zcomp, model)
I2.compensate(self._inst, self, self.zcomp, model)
# Check the image condition. If there is the problem, done with
# this _singleItr().
if (I1.isCaustic() is True) or (I2.isCaustic() is True):
self.converge[:, jj] = self.converge[:, jj - 1]
self.caustic = True
return
# Correct the defocal images if I1 and I2 are belong to different
# sources, which is determined by the (fieldX, field Y)
I1, I2 = self._applyI1I2pMask(I1, I2)
# Solve the Poisson's equation
self.zc, self.West = self._solvePoissonEq(I1, I2, jj)
# Record/ calculate the Zk coefficient and wavefront
if compMode == "zer":
self.converge[:, jj] = self.zcomp + self.zc
xoSensor, yoSensor = self._inst.getSensorCoorAnnular()
self.wcomp = self.West + ZernikeAnnularEval(
np.concatenate(([0, 0, 0], self.zcomp[3:])),
xoSensor,
yoSensor,
self.getObsOfZernikes(),
)
else:
# Once we run into caustic, stop here, results may be close to real
# aberration.
# Continuation may lead to disatrous results.
self.converge[:, jj] = self.converge[:, jj - 1]
# Record the coefficients of normal/ annular Zernike polynomials after
# z4 in unit of nm
self.zer4UpNm = self.converge[3:, jj] * 1e9
# Status of iteration
stopItr = False
# Calculate the difference
if jj > 0:
diffZk = (
np.sum(np.abs(self.converge[:, jj] - self.converge[:, jj - 1])) * 1e9
)
# Check the Status of iteration
if diffZk < tol:
stopItr = True
# Update the current iteration time
self.currentItr += 1
# Show the Zk coefficients in interger in each iteration
if self.debugLevel >= 2:
print("itr = %d, z4-z%d" % (jj, self.getNumOfZernikes()))
print(np.rint(self.zer4UpNm))
return stopItr
def _solvePoissonEq(self, I1, I2, iOutItr=0):
"""Solve the Poisson's equation by Fourier transform (differential) or
serial expansion (integration).
There is no convergence for fft actually. Need to add the difference
comparison and X-alpha method. Need to discuss further for this.
Parameters
----------
I1 : CompensableImage
Intra- or extra-focal image.
I2 : CompensableImage
Intra- or extra-focal image.
iOutItr : int, optional
ith number of outer loop iteration which is important in "fft"
algorithm. (the default is 0.)
Returns
-------
numpy.ndarray
Coefficients of normal/ annular Zernike polynomials.
numpy.ndarray
Estimated wavefront.
"""
# Calculate the aperature pixel size
apertureDiameter = self._inst.getApertureDiameter()
sensorFactor = self._inst.getSensorFactor()
dimOfDonut = self._inst.getDimOfDonutOnSensor()
aperturePixelSize = apertureDiameter * sensorFactor / dimOfDonut
# Calculate the differential Omega
dOmega = aperturePixelSize ** 2
# Solve the Poisson's equation based on the type of algorithm
numTerms = self.getNumOfZernikes()
zobsR = self.getObsOfZernikes()
PoissonSolver = self.getPoissonSolverName()
if PoissonSolver == "fft":
# Use the differential method by fft to solve the Poisson's
# equation
# Parameter to determine the threshold of calculating I0.
sumclipSequence = self.getSignalClipSequence()
cliplevel = sumclipSequence[iOutItr]
# Generate the v, u-coordinates on pupil plane
padDim = self.getFftDimension()
v, u = np.mgrid[
-0.5
/ aperturePixelSize : 0.5
/ aperturePixelSize : 1.0
/ padDim
/ aperturePixelSize,
-0.5
/ aperturePixelSize : 0.5
/ aperturePixelSize : 1.0
/ padDim
/ aperturePixelSize,
]
# Show the threshold and pupil coordinate information
if self.debugLevel >= 3:
print("iOuter=%d, cliplevel=%4.2f" % (iOutItr, cliplevel))
print(v.shape)
# Calculate the const of fft:
# FT{Delta W} = -4*pi^2*(u^2+v^2) * FT{W}
u2v2 = -4 * (np.pi ** 2) * (u * u + v * v)
# Set origin to Inf to result in 0 at origin after filtering
ctrIdx = int(np.floor(padDim / 2.0))
u2v2[ctrIdx, ctrIdx] = np.inf
# Calculate the wavefront signal
Sini = self._createSignal(I1, I2, cliplevel)
# Find the just-outside and just-inside indices of a ring in pixels
# This is for the use in setting dWdn = 0
boundaryT = self.getBoundaryThickness()
struct = generate_binary_structure(2, 1)
struct = iterate_structure(struct, boundaryT)
ApringOut = np.logical_xor(
binary_dilation(self.pMask, structure=struct), self.pMask
).astype(int)
ApringIn = np.logical_xor(
binary_erosion(self.pMask, structure=struct), self.pMask
).astype(int)
bordery, borderx = np.nonzero(ApringOut)
# Put the signal in boundary (since there's no existing Sestimate,
# S just equals self.S as the initial condition of SCF
S = Sini.copy()
for jj in range(self.getNumOfInnerItr()):
# Calculate FT{S}
SFFT = np.fft.fftshift(np.fft.fft2(np.fft.fftshift(S)))
# Calculate W by W=IFT{ FT{S}/(-4*pi^2*(u^2+v^2)) }
W = np.fft.fftshift(
np.fft.irfft2(np.fft.fftshift(SFFT / u2v2), s=S.shape)
)
# Estimate the wavefront (includes zeroing offset & masking to
# the aperture size)
# Take the estimated wavefront
West = extractArray(W, dimOfDonut)
# Calculate the offset
offset = West[self.pMask == 1].mean()
West = West - offset
West[self.pMask == 0] = 0
# Set dWestimate/dn = 0 around boundary
WestdWdn0 = West.copy()
# Do a 3x3 average around each border pixel, including only
# those pixels inside the aperture
for ii in range(len(borderx)):
reg = West[
borderx[ii] - boundaryT : borderx[ii] + boundaryT + 1,
bordery[ii] - boundaryT : bordery[ii] + boundaryT + 1,
]
intersectIdx = ApringIn[
borderx[ii] - boundaryT : borderx[ii] + boundaryT + 1,
bordery[ii] - boundaryT : bordery[ii] + boundaryT + 1,
]
WestdWdn0[borderx[ii], bordery[ii]] = reg[
np.nonzero(intersectIdx)
].mean()
# Take Laplacian to find sensor signal estimate (Delta W = S)
del2W = laplace(WestdWdn0) / dOmega
# Extend the dimension of signal to the order of 2 for "fft" to
# use
Sest = padArray(del2W, padDim)
# Put signal back inside boundary, leaving the rest of
# Sestimate
Sest[self.pMaskPad == 1] = Sini[self.pMaskPad == 1]
# Need to recheck this condition
S = Sest
# Calculate the coefficient of normal/ annular Zernike polynomials
if self.getCompensatorMode() == "zer":
xSensor, ySensor = self._inst.getSensorCoor()
zc = ZernikeMaskedFit(
West, xSensor, ySensor, numTerms, self.pMask, zobsR
)
else:
zc = np.zeros(numTerms)
elif PoissonSolver == "exp":
# Use the integration method by serial expansion to solve the
# Poisson's equation
# Calculate I0 and dI
I0, dI = self._getdIandI(I1, I2)
# Get the x, y coordinate in mask. The element outside mask is 0.
xSensor, ySensor = self._inst.getSensorCoor()
xSensor = xSensor * self.cMask
ySensor = ySensor * self.cMask
# Create the F matrix and Zernike-related matrixes
F = np.zeros(numTerms)
dZidx = np.zeros((numTerms, dimOfDonut, dimOfDonut))
dZidy = dZidx.copy()
zcCol = np.zeros(numTerms)
for ii in range(int(numTerms)):
# Calculate the matrix for each Zk related component
# Set the specific Zk cofficient to be 1 for the calculation
zcCol[ii] = 1
F[ii] = (
np.sum(dI * ZernikeAnnularEval(zcCol, xSensor, ySensor, zobsR))
* dOmega
)
dZidx[ii, :, :] = ZernikeAnnularGrad(
zcCol, xSensor, ySensor, zobsR, "dx"
)
dZidy[ii, :, :] = ZernikeAnnularGrad(
zcCol, xSensor, ySensor, zobsR, "dy"
)
# Set the specific Zk cofficient back to 0 to avoid interfering
# other Zk's calculation
zcCol[ii] = 0
# Calculate Mij matrix, need to check the stability of integration
# and symmetry later
Mij = np.zeros([numTerms, numTerms])
for ii in range(numTerms):
for jj in range(numTerms):
Mij[ii, jj] = np.sum(
I0
* (
dZidx[ii, :, :].squeeze() * dZidx[jj, :, :].squeeze()
+ dZidy[ii, :, :].squeeze() * dZidy[jj, :, :].squeeze()
)
)
Mij = dOmega / (apertureDiameter / 2.0) ** 2 * Mij
# Calculate dz
focalLength = self._inst.getFocalLength()
offset = self._inst.getDefocalDisOffset()
dz = 2 * focalLength * (focalLength - offset) / offset
# Define zc
zc = np.zeros(numTerms)
# Consider specific Zk terms only
idx = self.getZernikeTerms()
# Solve the equation: M*W = F => W = M^(-1)*F
zc_tmp = np.linalg.lstsq(Mij[:, idx][idx], F[idx], rcond=None)[0] / dz
zc[idx] = zc_tmp
# Estimate the wavefront surface based on z4 - z22
# z0 - z3 are set to be 0 instead
West = ZernikeAnnularEval(
np.concatenate(([0, 0, 0], zc[3:])), xSensor, ySensor, zobsR
)
return zc, West
def _createSignal(self, I1, I2, cliplevel):
"""Calculate the wavefront singal for "fft" to use in solving the
Poisson's equation.
Need to discuss the method to define threshold and discuss to use
np.median() instead.
Need to discuss why the calculation of I0 is different from "exp".
Parameters
----------
I1 : CompensableImage
Intra- or extra-focal image.
I2 : CompensableImage
Intra- or extra-focal image.
cliplevel : float
Parameter to determine the threshold of calculating I0.
Returns
-------
numpy.ndarray
Approximated wavefront signal.
"""
# Check the condition of images
I1image, I2image = self._checkImageDim(I1, I2)
# Wavefront signal S=-(1/I0)*(dI/dz) is approximated to be
# -(1/delta z)*(I1-I2)/(I1+I2)
num = I1image - I2image
den = I1image + I2image
# Define the effective minimum central signal element by the threshold
# ( I0=(I1+I2)/2 )
# Calculate the threshold
pixelList = den * self.cMask
pixelList = pixelList[pixelList != 0]
low = pixelList.min()
high = pixelList.max()
medianThreshold = (high - low) / 2.0 + low
# Define the effective minimum central signal element
den[den < medianThreshold * cliplevel] = 1.5 * medianThreshold
# Calculate delta z = f(f-l)/l, f: focal length, l: defocus distance of
# the image planes
focalLength = self._inst.getFocalLength()
offset = self._inst.getDefocalDisOffset()
deltaZ = focalLength * (focalLength - offset) / offset
# Calculate the wavefront signal. Enforce the element outside the mask
# to be 0.
den[den == 0] = np.inf
# Calculate the wavefront signal
S = num / den / deltaZ
# Extend the dimension of signal to the order of 2 for "fft" to use
padDim = self.getFftDimension()
Sout = padArray(S, padDim) * self.cMaskPad
return Sout
def _getdIandI(self, I1, I2):
"""Calculate the central image and differential image to be used in the
serial expansion method.
It is noted that the images are assumed to be co-center already. And
the intra-/ extra-focal image can overlap with one another after the
rotation of 180 degree.
Parameters
----------
I1 : CompensableImage
Intra- or extra-focal image.
I2 : CompensableImage
Intra- or extra-focal image.
Returns
-------
numpy.ndarray
Image data of I0.
numpy.ndarray
Differential image (dI) of I0.
"""
# Check the condition of images
I1image, I2image = self._checkImageDim(I1, I2)
# Calculate the central image and differential iamge
I0 = (I1image + I2image) / 2
dI = I2image - I1image
return I0, dI
def _checkImageDim(self, I1, I2):
"""Check the dimension of images.
It is noted that the I2 image is rotated by 180 degree.
Parameters
----------
I1 : CompensableImage
Intra- or extra-focal image.
I2 : CompensableImage
Intra- or extra-focal image.
Returns
-------
numpy.ndarray
I1 defocal image.
numpy.ndarray
I2 defocal image. It is noted that the I2 image is rotated by 180
degree.
Raises
------
Exception
Check the dimension of images is n by n or not.
Exception
Check two defocal images have the same size or not.
"""
# Check the condition of images
m1, n1 = I1.getImg().shape
m2, n2 = I2.getImg().shape
if m1 != n1 or m2 != n2:
raise Exception("Image is not square.")
if m1 != m2 or n1 != n2:
raise Exception("Images do not have the same size.")
# Define I1
I1image = I1.getImg()
# Rotate the image by 180 degree through rotating two times of 90
# degree
I2image = np.rot90(I2.getImg(), k=2)
return I1image, I2image
def _makeMasterMask(self, I1, I2, poissonSolver=None):
"""Calculate the common mask of defocal images.
Parameters
----------
I1 : CompensableImage
Intra- or extra-focal image.
I2 : CompensableImage
Intra- or extra-focal image.
poissonSolver : str, optional
Algorithm to solve the Poisson's equation. If the "fft" is used,
the mask dimension will be extended to the order of 2 for the "fft"
to use. (the default is None.)
"""
# Get the overlap region of mask for intra- and extra-focal images.
# This is to avoid the anormalous signal due to difference in
# vignetting.
self.pMask = I1.getPaddedMask() * I2.getPaddedMask()
self.cMask = I1.getNonPaddedMask() * I2.getNonPaddedMask()
# Change the dimension of image for fft to use
if poissonSolver == "fft":
padDim = self.getFftDimension()
self.pMaskPad = padArray(self.pMask, padDim)
self.cMaskPad = padArray(self.cMask, padDim)
def _applyI1I2pMask(self, I1, I2):
"""Correct the defocal images if I1 and I2 are belong to different
sources.
(There is a problem for this actually. If I1 and I2 come from different
sources, what should the correction of TIE be? At this moment, the
fieldX and fieldY of I1 and I2 should be different. And the sources are
different also.)
Parameters
----------
I1 : CompensableImage
Intra- or extra-focal image.
I2 : CompensableImage
Intra- or extra-focal image.
Returns
-------
numpy.ndarray
Corrected I1 image.
numpy.ndarray
Corrected I2 image.
"""
# Get the overlap region of images and do the normalization.
if I1.getFieldXY() != I2.getFieldXY():
# Get the overlap region of image
I1.updateImage(I1.getImg() * self.pMask)
# Rotate the pMask by 180 degree through rotating two times of 90
# degree because I2 has been rotated by 180 degree already.
I2.updateImage(I2.getImg() * np.rot90(self.pMask, 2))
# Do the normalization of image.
I1.updateImage(I1.getImg() / np.sum(I1.getImg()))
I2.updateImage(I2.getImg() / np.sum(I2.getImg()))
# Return the correct images. It is noted that there is no need of
# vignetting correction.
# This is after masking already in _singleItr() or itr0().
return I1, I2
def _reset(self, I1, I2):
"""Reset the iteration time of outer loop and defocal images.
Parameters
----------
I1 : CompensableImage
Intra- or extra-focal image.
I2 : CompensableImage
Intra- or extra-focal image.
"""
# Reset the current iteration time to 0
self.currentItr = 0
# Show the reset information
if self.debugLevel >= 3:
print("Resetting images: I1 and I2")
# Determine to reset the images or not based on the existence of
# the attribute: Image.image0. Only after the first run of
# inner loop, this attribute will exist.
try:
# Reset the images to the first beginning
I1.updateImage(I1.getImgInit().copy())
I2.updateImage(I2.getImgInit().copy())
# Show the information of resetting image
if self.debugLevel >= 3:
print("Resetting images in inside.")
except AttributeError:
# Show the information of no image0
if self.debugLevel >= 3:
print("Image0 = None. This is the first time to run the code.")
pass
def outZer4Up(self, unit="nm", filename=None, showPlot=False):
"""Put the coefficients of normal/ annular Zernike polynomials on
terminal or file ande show the image if it is needed.
Parameters
----------
unit : str, optional
Unit of the coefficients of normal/ annular Zernike polynomials. It
can be m, nm, or um. (the default is "nm".)
filename : str, optional
Name of output file. (the default is None.)
showPlot : bool, optional
Decide to show the plot or not. (the default is False.)
"""
# List of Zn,m
Znm = [
"Z0,0",
"Z1,1",
"Z1,-1",
"Z2,0",
"Z2,-2",
"Z2,2",
"Z3,-1",
"Z3,1",
"Z3,-3",
"Z3,3",
"Z4,0",
"Z4,2",
"Z4,-2",
"Z4,4",
"Z4,-4",
"Z5,1",
"Z5,-1",
"Z5,3",
"Z5,-3",
"Z5,5",
"Z5,-5",
"Z6,0",
]
# Decide the format of z based on the input unit (m, nm, or um)
if unit == "m":
z = self.zer4UpNm * 1e-9
elif unit == "nm":
z = self.zer4UpNm
elif unit == "um":
z = self.zer4UpNm * 1e-3
else:
print("Unknown unit: %s" % unit)
print("Unit options are: m, nm, um")
return
# Write the coefficients into a file if needed.
if filename is not None:
f = open(filename, "w")
else:
f = sys.stdout
for ii in range(4, len(z) + 4):
f.write("Z%d (%s)\t %8.3f\n" % (ii, Znm[ii - 1], z[ii - 4]))
# Close the file
if filename is not None:
f.close()
# Show the plot
if showPlot:
zkIdx = range(4, len(z) + 4)
plotZernike(zkIdx, z, unit)