def makePixelToTanPixel(bbox, orientation, focalPlaneToPupil, pixelSizeMm):
"""!Make an XYTransform whose forward direction converts PIXEL to TAN_PIXEL for one detector
PIXELS and TAN_PIXELS are defined in @ref afwCameraGeomCoordSys in doc/cameraGeom.dox
@param[in] bbox detector bounding box (an lsst.afw.geom.Box2I)
@param[in] orientation orientation of detector in focal plane (an lsst.afw.cameraGeom.Orientation)
@param[in] focalPlaneToPupil an lsst.afw.math.XYTransform that converts from focal plane (mm)
to pupil coordinates (radians) in the forward direction
@param[in] pixelSizeMm size of the pixel in mm in X and Y (an lsst.afw.geom.Extent2D)
"""
pixelToFocalPlane = orientation.makePixelFpTransform(pixelSizeMm)
pixelToPupil = afwGeom.MultiXYTransform(
(pixelToFocalPlane, focalPlaneToPupil))
# pupilToTanPix is affine and matches pupilToPix at pupil center
# Note: focal plane to pupil is typically a radial transform,
# and linearizing the inverse transform of that may fail,
# so linearize the forward direction instead. (pixelToPupil is pixelToFocalPlane,
# an affine transform, followed by focalPlaneToPupil,
# so the same consideration applies to pixelToPupil)
pixAtPupilCtr = pixelToPupil.reverseTransform(afwGeom.Point2D(0, 0))
tanPixToPupilAffine = pixelToPupil.linearizeForwardTransform(pixAtPupilCtr)
pupilToTanPix = afwGeom.AffineXYTransform(tanPixToPupilAffine.invert())
return afwGeom.MultiXYTransform((pixelToPupil, pupilToTanPix))
def testSimpleCurvedFocalPlane(self):
"""Test a trivial curved focal plane with square pixels
The CCD's lower left pixel is centered on the boresight
pupil center = focal plane center
CCD x is along focal plane x
"""
bbox = afwGeom.Box2I(afwGeom.Point2I(0, 0), afwGeom.Extent2I(1000, 1000))
pixelSizeMm = afwGeom.Extent2D(0.02, 0.02)
plateScale = 25.0 # arcsec/mm
yaw = 0 * afwGeom.degrees
fpPosition = afwGeom.Point2D(0, 0) # focal-plane position of ref position on detector (mm)
refPoint = afwGeom.Point2D(0, 0) # ref position on detector (pos of lower left corner)
orientation = cameraGeom.Orientation(
fpPosition,
refPoint,
yaw,
)
pixelToFocalPlane = orientation.makePixelFpTransform(pixelSizeMm)
plateScaleRad = afwGeom.Angle(plateScale, afwGeom.arcseconds).asRadians()
focalPlaneToPupil = afwGeom.RadialXYTransform((0.0, plateScaleRad, 0.0, 0.001 * plateScaleRad))
pixelToPupil = afwGeom.MultiXYTransform((pixelToFocalPlane, focalPlaneToPupil))
pixelToTanPixel = makePixelToTanPixel(
bbox=bbox,
orientation=orientation,
focalPlaneToPupil=focalPlaneToPupil,
pixelSizeMm=pixelSizeMm,
)
# pupil center should be pixel position 0, 0 and tan pixel position 0, 0
pixAtPupilCtr = pixelToPupil.reverseTransform(afwGeom.Point2D(0, 0))
self.assertPairsNearlyEqual(pixAtPupilCtr, [0, 0])
tanPixAtPupilCr = pixelToTanPixel.forwardTransform(pixAtPupilCtr)
self.assertPairsNearlyEqual(tanPixAtPupilCr, [0, 0])
# build same camera geometry transforms without optical distortion
focalPlaneToPupilNoDistortion = afwGeom.RadialXYTransform((0.0, plateScaleRad))
pixelToPupilNoDistortion = afwGeom.MultiXYTransform(
(pixelToFocalPlane, focalPlaneToPupilNoDistortion))
for x in (100, 200, 1000):
for y in (100, 500, 800):
pixPos = afwGeom.Point2D(x, y)
tanPixPos = pixelToTanPixel.forwardTransform(pixPos)
# pix to tan pix should be radial
self.assertAlmostEqual(
math.atan2(pixPos[1], pixPos[0]),
math.atan2(tanPixPos[1], tanPixPos[0]),
)
# for a given pupil angle (which, together with a pointing, gives a position on the sky):
# - pupil to pixels gives pixPos
# - undistorted pupil to pixels gives tanPixPos
pupilPos = pixelToPupil.forwardTransform(pixPos)
desTanPixPos = pixelToPupilNoDistortion.reverseTransform(pupilPos)
self.assertPairsNearlyEqual(desTanPixPos, tanPixPos)
def testCurvedFocalPlane(self):
"""Test a curved focal plane (with rectangular pixels)
"""
bbox = afwGeom.Box2I(afwGeom.Point2I(0, 0),
afwGeom.Extent2I(1000, 1000))
pixelSizeMm = afwGeom.Extent2D(0.02, 0.03)
plateScale = 25.0 # arcsec/mm
yaw = afwGeom.Angle(20, afwGeom.degrees)
fpPosition = afwGeom.Point2D(
50, 25) # focal-plane position of ref position on detector (mm)
refPoint = afwGeom.Point2D(
-0.5, -0.5) # ref position on detector (pos of lower left corner)
orientation = cameraGeom.Orientation(
fpPosition,
refPoint,
yaw,
)
plateScaleRad = afwGeom.Angle(plateScale,
afwGeom.arcseconds).asRadians()
focalPlaneToPupil = afwGeom.RadialXYTransform(
(0.0, plateScaleRad, 0.0, 0.001 * plateScaleRad))
pixelToTanPixel = makePixelToTanPixel(
bbox=bbox,
orientation=orientation,
focalPlaneToPupil=focalPlaneToPupil,
pixelSizeMm=pixelSizeMm,
plateScale=plateScale,
)
# the center point of the detector should not move
ctrPointPix = afwGeom.Box2D(bbox).getCenter()
ctrPointTanPix = pixelToTanPixel.forwardTransform(ctrPointPix)
for i in range(2):
self.assertAlmostEquals(ctrPointTanPix[i], ctrPointPix[i])
# two points separated by x pixels in tan pixels coordinates
# should be separated x * rad/tanPix in pupil coordinates,
# where rad/tanPix = plate scale in rad/MM * mean pixel size in mm
radPerTanPixel = plateScaleRad * (pixelSizeMm[0] +
pixelSizeMm[1]) / 2.0
pixelToFocalPlane = orientation.makePixelFpTransform(pixelSizeMm)
pixelToPupil = afwGeom.MultiXYTransform(
(pixelToFocalPlane, focalPlaneToPupil))
prevPointPupil = None
prevPointTanPix = None
for pointPix in (
afwGeom.Point2D(0, 0),
afwGeom.Point2D(1000, 2000),
afwGeom.Point2D(-100.5, 27.23),
afwGeom.Point2D(-95.3, 0.0),
):
pointPupil = pixelToPupil.forwardTransform(pointPix)
pointTanPix = pixelToTanPixel.forwardTransform(pointPix)
if prevPointPupil:
pupilSep = numpy.linalg.norm(pointPupil - prevPointPupil)
tanPixSep = numpy.linalg.norm(pointTanPix - prevPointTanPix)
self.assertAlmostEquals(tanPixSep * radPerTanPixel, pupilSep)
prevPointPupil = pointPupil
prevPointTanPix = pointTanPix
def testCurvedFocalPlane(self):
"""Test a curved focal plane (with rectangular pixels)
"""
bbox = afwGeom.Box2I(afwGeom.Point2I(0, 0), afwGeom.Extent2I(1000, 1000))
pixelSizeMm = afwGeom.Extent2D(0.02, 0.03)
plateScale = 25.0 # arcsec/mm
yaw = afwGeom.Angle(20, afwGeom.degrees)
fpPosition = afwGeom.Point2D(50, 25) # focal-plane position of ref position on detector (mm)
refPoint = afwGeom.Point2D(-0.5, -0.5) # ref position on detector (pos of lower left corner)
orientation = cameraGeom.Orientation(
fpPosition,
refPoint,
yaw,
)
pixelToFocalPlane = orientation.makePixelFpTransform(pixelSizeMm)
plateScaleRad = afwGeom.Angle(plateScale, afwGeom.arcseconds).asRadians()
focalPlaneToPupil = afwGeom.RadialXYTransform((0.0, plateScaleRad, 0.0, 0.001 * plateScaleRad))
pixelToPupil = afwGeom.MultiXYTransform((pixelToFocalPlane, focalPlaneToPupil))
pixelToTanPixel = makePixelToTanPixel(
bbox=bbox,
orientation=orientation,
focalPlaneToPupil=focalPlaneToPupil,
pixelSizeMm=pixelSizeMm,
)
# the center point of the pupil frame should not move
pixAtPupilCtr = pixelToPupil.reverseTransform(afwGeom.Point2D(0, 0))
tanPixAtPupilCr = pixelToTanPixel.forwardTransform(pixAtPupilCtr)
self.assertPairsNearlyEqual(pixAtPupilCtr, tanPixAtPupilCr)
# build same camera geometry transforms without optical distortion
focalPlaneToPupilNoDistortion = afwGeom.RadialXYTransform((0.0, plateScaleRad))
pixelToPupilNoDistortion = afwGeom.MultiXYTransform(
(pixelToFocalPlane, focalPlaneToPupilNoDistortion))
for x in (100, 200, 1000):
for y in (100, 500, 800):
pixPos = afwGeom.Point2D(x, y)
tanPixPos = pixelToTanPixel.forwardTransform(pixPos)
# for a given pupil position (which, together with a pointing, gives a position on the sky):
# - pupil to pixels gives pixPos
# - undistorted pupil to pixels gives tanPixPos
pupilPos = pixelToPupil.forwardTransform(pixPos)
desTanPixPos = pixelToPupilNoDistortion.reverseTransform(pupilPos)
self.assertPairsNearlyEqual(desTanPixPos, tanPixPos)
def makePixelToTanPixel(bbox, orientation, focalPlaneToPupil, pixelSizeMm,
plateScale):
"""!Make an XYTransform whose forward direction converts PIXEL to TAN_PIXEL for one detector
PIXELS and TAN_PIXELS are defined in @ref afwCameraGeomCoordSys in doc/cameraGeom.dox
@param[in] bbox detector bounding box (an lsst.afw.geom.Box2I)
@param[in] orientation orientation of detector in focal plane (an lsst.afw.cameraGeom.Orientation)
@param[in] focalPlaneToPupil an lsst.afw.math.XYTransform that converts from focal plane (mm)
to pupil coordinates (radians) in the forward direction
@param[in] pixelSizeMm size of the pixel in mm in X and Y (an lsst.afw.geom.Extent2D)
@param[in] plateScale plate scale of the camera in arcsec/mm (a double)
"""
pixelToFocalPlane = orientation.makePixelFpTransform(pixelSizeMm)
meanPixelSizeMm = (pixelSizeMm[0] + pixelSizeMm[1]) / 2.0
radPerMeanPix = afwGeom.Angle(
plateScale, afwGeom.arcseconds).asRadians() * meanPixelSizeMm
detCtrPix = afwGeom.Box2D(bbox).getCenter()
detCtrTanPix = detCtrPix # by definition
detCtrPupil = focalPlaneToPupil.forwardTransform(
pixelToFocalPlane.forwardTransform(detCtrPix))
pupilTanPixAngRad = -orientation.getYaw().asRadians()
pupilTanPixSin = math.sin(pupilTanPixAngRad)
pupilTanPixCos = math.cos(pupilTanPixAngRad)
tanPixToPupilRotMat = numpy.array((
(pupilTanPixCos, pupilTanPixSin),
(-pupilTanPixSin, pupilTanPixCos),
)) * radPerMeanPix
tanPixToPupilRotTransform = afwGeom.AffineTransform(tanPixToPupilRotMat)
tanPixCtrMinus0Pupil = tanPixToPupilRotTransform(detCtrTanPix)
tanPix0Pupil = numpy.array(detCtrPupil) - numpy.array(tanPixCtrMinus0Pupil)
tanPixToPupilAffine = afwGeom.AffineTransform(tanPixToPupilRotMat,
numpy.array(tanPix0Pupil))
pupilToTanPix = afwGeom.AffineXYTransform(tanPixToPupilAffine.invert())
return afwGeom.MultiXYTransform(
(pixelToFocalPlane, focalPlaneToPupil, pupilToTanPix))