class Aimy(BaseLogger):
"""
Should take care about ray aiming (approximatively and real).
Should generate aiming matrices and raybundles according to
aiming specifications and field specifications.
"""
def __init__(self,
s,
seq,
wave=standard_wavelength,
num_pupil_points=100,
stopsize=10,
pilotbundle_solution=-1,
pilotbundle_generation="complex",
pilotbundle_delta_angle=1 * degree,
pilotbundle_delta_size=0.1,
pilotbundle_sampling_points=3,
name=""):
# TODO: reduce arguments by summarizing pilotbundle
# parameters into class
super(Aimy, self).__init__(name=name)
self.field_raster = RectGrid()
self.pupil_raster = RectGrid()
self.stopsize = stopsize
self.num_pupil_points = num_pupil_points
self.wave = wave
self.pilotbundle_solution = pilotbundle_solution
self.pilotbundle_generation = pilotbundle_generation
self.pilotbundle_delta_angle = pilotbundle_delta_angle
self.pilotbundle_delta_size = pilotbundle_delta_size
self.pilotbundle_sampling_points = pilotbundle_sampling_points
self.update(s, seq)
def setKind(self):
self.kind = "aimy"
def extract_abcd(self, xyuv):
"""
Extracts sub matrices from a general linear transfer matrix.
"""
self.debug(str(xyuv.shape))
a_xyuv = xyuv[0:2, 0:2]
b_xyuv = xyuv[0:2, 2:4] # take only real part of the k vectors
c_xyuv = xyuv[2:4, 0:2]
d_xyuv = xyuv[2:4, 2:4]
return (a_xyuv, b_xyuv, c_xyuv, d_xyuv)
def update(self, system, seq):
"""
Update the matrices from object to stop and
from stop to image for a specific system and a
specific sequence.
"""
obj_dx = self.pilotbundle_delta_size # pilot bundle properties
obj_dphi = self.pilotbundle_delta_angle # pilot bundle properties
first_element_seq_name = seq[0]
(first_element_name, first_element_seq) = first_element_seq_name
(objsurfname, _) = first_element_seq[0]
self.objectsurface = system.elements[first_element_name].\
surfaces[objsurfname]
self.start_material = system.material_background
# TODO: pilotray starts always in background (how about immersion?)
# if mat is None: ....
if self.pilotbundle_generation.lower() == "real":
self.info("call real sampled pilotbundle")
pilotbundles = build_pilotbundle(
self.objectsurface,
self.start_material, (obj_dx, obj_dx), (obj_dphi, obj_dphi),
num_sampling_points=self.pilotbundle_sampling_points)
# TODO: wavelength?
elif self.pilotbundle_generation.lower() == "complex":
self.info("call complex sampled pilotbundle")
pilotbundles = build_pilotbundle_complex(
self.objectsurface,
self.start_material, (obj_dx, obj_dx), (obj_dphi, obj_dphi),
num_sampling_points=self.pilotbundle_sampling_points)
self.info("choose " + str(self.pilotbundle_solution) + " raybundle")
self.pilotbundle = pilotbundles[self.pilotbundle_solution]
# one of the last two
(self.m_obj_stop,
self.m_stop_img) =\
system.extractXYUV(
self.pilotbundle,
seq,
pilotbundle_generation=self.pilotbundle_generation)
self.info("show linear matrices")
self.info(
"obj -> stop:\n" +
np.array_str(self.m_obj_stop, precision=10, suppress_small=True))
self.info(
"stop -> img:\n" +
np.array_str(self.m_stop_img, precision=10, suppress_small=True))
def aim_core_angle_known(self, theta2d):
"""
Calculates different start positions for the rays
when direction vector is known.
"""
(thetax, thetay) = theta2d
rmx = rodrigues(thetax, [0, 1, 0])
rmy = rodrigues(thetay, [1, 0, 0])
rmfinal = np.dot(rmy, rmx)
dpilot_global = self.pilotbundle.returnKtoD()[0, :, 0]
kpilot_global = self.pilotbundle.k[0, :, 0]
dpilot_object = self.objectsurface.rootcoordinatesystem.\
returnGlobalToLocalDirections(dpilot_global)[:, np.newaxis]
kpilot_object = self.objectsurface.rootcoordinatesystem.\
returnGlobalToLocalDirections(kpilot_global)[:, np.newaxis]
kpilot_object = np.repeat(kpilot_object, self.num_pupil_points, axis=1)
dvec = np.dot(rmfinal, dpilot_object)
kvec = returnDtoK(dvec) # TODO: implement fake implementation
dk_vec = kvec - kpilot_object
dk_obj = dk_vec[0:2, :]
(a_obj_stop, b_obj_stop, _, _) = self.extract_abcd(self.m_obj_stop)
a_obj_stop_inv = np.linalg.inv(a_obj_stop)
(xraster, yraster) = self.pupil_raster.getGrid(self.num_pupil_points)
dr_stop = (np.vstack((xraster, yraster)) * self.stopsize)
intermediate = np.dot(b_obj_stop, dk_obj)
dr_obj = np.dot(a_obj_stop_inv, dr_stop - intermediate)
return (dr_obj, dk_obj)
def aim_core_k_known(self, dk_obj):
"""
Calculates different start position and angles when
k-vector is known.
"""
(a_obj_stop, b_obj_stop, _, _) = self.extract_abcd(self.m_obj_stop)
a_obj_stop_inv = np.linalg.inv(a_obj_stop)
(xraster, yraster) = self.pupil_raster.getGrid(self.num_pupil_points)
(num_points, ) = xraster.shape
dr_stop = (np.vstack((xraster, yraster)) * self.stopsize)
dk_obj2 = np.repeat(dk_obj[:, np.newaxis], num_points, axis=1)
intermediate = np.dot(b_obj_stop, dk_obj2)
dr_obj = np.dot(a_obj_stop_inv, dr_stop - intermediate)
return (dr_obj, dk_obj2)
def aim_core_r_known(self, delta_xy):
"""
Calculates different start position and angles when
position at stop is known.
"""
(a_obj_stop, b_obj_stop, _, _) = self.extract_abcd(self.m_obj_stop)
self.debug(str(b_obj_stop.shape))
b_obj_stop_inv = np.linalg.inv(b_obj_stop)
(xraster, yraster) = self.pupil_raster.getGrid(self.num_pupil_points)
(num_points, ) = xraster.shape
dr_stop = (np.vstack((xraster, yraster)) * self.stopsize)
dr_obj = np.repeat(delta_xy[:, np.newaxis], num_points, axis=1)
dk_obj = np.dot(b_obj_stop_inv, dr_stop - np.dot(a_obj_stop, dr_obj))
# TODO: in general some direction vector is derived
# TODO: this must been mapped to a k vector
# TODO: what about anamorphic systems?
return (dr_obj, dk_obj)
def aim(self, delta_xy, fieldtype="angle"):
"""
Generates bundles.
"""
if fieldtype == "angle":
(dr_obj, dk_obj) = self.aim_core_angle_known(delta_xy)
elif fieldtype == "objectheight":
(dr_obj, dk_obj) = self.aim_core_r_known(delta_xy)
elif fieldtype == "kvector":
# (dr_obj, dk_obj) = self.aim_core_k_known(delta_xy)
raise NotImplementedError()
else:
raise NotImplementedError()
(_, num_points) = np.shape(dr_obj)
dr_obj3d = np.vstack((dr_obj, np.zeros(num_points)))
dk_obj3d = np.vstack((dk_obj, np.zeros(num_points)))
xp_objsurf = self.objectsurface.rootcoordinatesystem.\
returnGlobalToLocalPoints(self.pilotbundle.x[0, :, 0])
xp_objsurf = np.repeat(xp_objsurf[:, np.newaxis], num_points, axis=1)
dx3d = np.dot(self.objectsurface.rootcoordinatesystem.localbasis.T,
dr_obj3d)
xparabasal = xp_objsurf + dx3d
kp_objsurf = self.objectsurface.rootcoordinatesystem.\
returnGlobalToLocalDirections(self.pilotbundle.k[0, :, 0])
kp_objsurf = np.repeat(kp_objsurf[:, np.newaxis], num_points, axis=1)
dk3d = np.dot(self.objectsurface.rootcoordinatesystem.localbasis.T,
dk_obj3d)
# FIXME: k coordinate system for which dispersion relation is respected
# modified k in general violates dispersion relation
kparabasal = kp_objsurf + dk3d
efield_obj = self.pilotbundle.Efield[0, :, 0]
efield_parabasal = np.repeat(efield_obj[:, np.newaxis],
num_points,
axis=1)
# Eparabasal introduces anisotropy in aiming through
# rotationally symmetric system since copy of Eparabasal (above)
# is not in the right direction for the
# dispersion relation (i.e. in isotropic media k perp E which is not
# fulfilled); solution: use k, insert into propagator (svdmatrix),
# calculate E by (u, sigma, v) = np.linalg.svd(propagator) where E is
# some linearcombination of all u which belong to sigma = 0 values.
# This is necessary to get the right ray direction also in isotropic
# case
# Outstanding problems:
# * Only vacuum considered (attach to material!)
# [i.e. svdmatrix should come from material]
# * Selection of E depends only on smallest eigenvalue
# (this is the "I don't care about polarization variant")
# => Later the user should choose the polarization in an stable
# reproducible way (i.e. sorting by scalar products)
(_, nlength) = kparabasal.shape
kronecker = np.repeat(np.identity(3)[np.newaxis, :, :],
nlength,
axis=0)
svdmatrix = -kronecker * np.sum(kparabasal * kparabasal,
axis=0)[:, np.newaxis, np.newaxis] +\
np.einsum("i...,j...", kparabasal, kparabasal) +\
kronecker # epstensor
# svdmatrix = -delta_ij (k*k) + k_i k_j + delta
(unitary_arrays, singular_values, _) = np.linalg.svd(svdmatrix)
smallest_absolute_values = np.argsort(np.abs(singular_values),
axis=1).T[0]
for i in range(nlength):
efield_parabasal[:, i] =\
unitary_arrays[i, :, smallest_absolute_values[i]]
# Aimy: returns only linearized results which are not exact
return RayBundle(xparabasal,
kparabasal,
efield_parabasal,
wave=self.wave)
class Aimy(BaseLogger):
"""
Should take care about ray aiming (approximatively and real).
Should generate aiming matrices and raybundles according to
aiming specifications and field specifications.
"""
def __init__(self,
s,
seq,
wave=standard_wavelength,
num_pupil_points=100,
stopsize=10,
name="",
kind="aimy",
**kwargs):
super(Aimy, self).__init__(name=name, kind=kind, **kwargs)
self.field_raster = RectGrid()
self.pupil_raster = RectGrid()
self.stopsize = stopsize
self.num_pupil_points = num_pupil_points
self.wave = wave
self.update(s, seq)
def extractABCD(self, xyuv):
self.info(str(xyuv.shape))
Axyuv = xyuv[0:2, 0:2]
Bxyuv = xyuv[0:2, 2:4] # take only real part of the k vectors
Cxyuv = xyuv[2:4, 0:2]
Dxyuv = xyuv[2:4, 2:4]
return (Axyuv, Bxyuv, Cxyuv, Dxyuv)
def update(self, s, seq):
obj_dx = 0.1 # pilot bundle properties
obj_dphi = 1. * degree # pilot bundle properties
first_element_seq_name = seq[0]
(first_element_name, first_element_seq) = first_element_seq_name
(objsurfname, objsurfoptions) = first_element_seq[0]
self.objectsurface = s.elements[first_element_name].surfaces[
objsurfname]
self.start_material = s.material_background
# TODO: pilotray starts always in background (how about immersion?)
# if mat is None: ....
#build_pilotbundle(
# self.objectsurface,
# self.start_material,
# (obj_dx, obj_dx),
# (obj_dphi, obj_dphi),
# num_sampling_points=3) # TODO: wavelength?
self.info("call complex sampled pilotbundle")
pilotbundles = build_pilotbundle_complex(self.objectsurface,
self.start_material,
(obj_dx, obj_dx),
(obj_dphi, obj_dphi),
num_sampling_points=3)
self.info("choose last raybundle (hard coded)")
self.pilotbundle = pilotbundles[-1]
# TODO: one solution selected hard coded
(self.m_obj_stop,
self.m_stop_img) = s.extractXYUV(self.pilotbundle, seq)
self.info("show linear matrices")
self.info(
np.array_str(self.m_obj_stop, precision=5, suppress_small=True))
self.info(
np.array_str(self.m_stop_img, precision=5, suppress_small=True))
def aim_core_angle_known(self, theta2d):
"""
knows about xyuv matrices
"""
(thetax, thetay) = theta2d
rmx = rodrigues(thetax, [0, 1, 0])
rmy = rodrigues(thetay, [1, 0, 0])
rmfinal = np.dot(rmy, rmx)
dpilot_global = self.pilotbundle.returnKtoD()[0, :, 0]
kpilot_global = self.pilotbundle.k[0, :, 0]
dpilot_object = self.objectsurface.rootcoordinatesystem.returnGlobalToLocalDirections(
dpilot_global)[:, np.newaxis]
kpilot_object = self.objectsurface.rootcoordinatesystem.returnGlobalToLocalDirections(
kpilot_global)[:, np.newaxis]
kpilot_object = np.repeat(kpilot_object, self.num_pupil_points, axis=1)
d = np.dot(rmfinal, dpilot_object)
k = returnDtoK(d) # TODO: implement fake implementation
dk = k - kpilot_object
dk_obj = dk[0:2, :]
(A_obj_stop, B_obj_stop, C_obj_stop,
D_obj_stop) = self.extractABCD(self.m_obj_stop)
A_obj_stop_inv = np.linalg.inv(A_obj_stop)
(xp, yp) = self.pupil_raster.getGrid(self.num_pupil_points)
dr_stop = (np.vstack((xp, yp)) * self.stopsize)
intermediate = np.dot(B_obj_stop, dk_obj)
dr_obj = np.dot(A_obj_stop_inv, dr_stop - intermediate)
return (dr_obj, dk_obj)
def aim_core_k_known(self, dk_obj):
"""
knows about xyuv matrices
"""
(A_obj_stop, B_obj_stop, C_obj_stop,
D_obj_stop) = self.extractABCD(self.m_obj_stop)
A_obj_stop_inv = np.linalg.inv(A_obj_stop)
(xp, yp) = self.pupil_raster.getGrid(self.num_pupil_points)
dr_stop = (np.vstack((xp, yp)) * self.stopsize)
dk_obj2 = np.repeat(dk_obj[:, np.newaxis],
self.num_pupil_points,
axis=1)
intermediate = np.dot(B_obj_stop, dk_obj2)
dr_obj = np.dot(A_obj_stop_inv, dr_stop - intermediate)
return (dr_obj, dk_obj2)
def aim_core_r_known(self, delta_xy):
(A_obj_stop, B_obj_stop, C_obj_stop,
D_obj_stop) = self.extractABCD(self.m_obj_stop)
self.info(str(B_obj_stop.shape))
B_obj_stop_inv = np.linalg.inv(B_obj_stop)
(xp, yp) = self.pupil_raster.getGrid(self.num_pupil_points)
dr_stop = (np.vstack((xp, yp)) * self.stopsize)
dr_obj = np.repeat(delta_xy[:, np.newaxis],
self.num_pupil_points,
axis=1)
dk_obj = np.dot(B_obj_stop_inv, dr_stop - np.dot(A_obj_stop, dr_obj))
# TODO: in general some direction vector is derived
# TODO: this must been mapped to a k vector
# TODO: what about anamorphic systems?
return (dr_obj, dk_obj)
def aim(self, delta_xy, fieldtype="angle"):
"""
Generates bundles.
"""
if fieldtype == "angle":
(dr_obj, dk_obj) = self.aim_core_angle_known(delta_xy)
elif fieldtype == "objectheight":
(dr_obj, dk_obj) = self.aim_core_r_known(delta_xy)
elif fieldtype == "kvector":
# (dr_obj, dk_obj) = self.aim_core_k_known(delta_xy)
raise NotImplementedError()
else:
raise NotImplementedError()
(dim, num_points) = np.shape(dr_obj)
dr_obj3d = np.vstack((dr_obj, np.zeros(num_points)))
dk_obj3d = np.vstack((dk_obj, np.zeros(num_points)))
xp_objsurf = self.objectsurface.rootcoordinatesystem.returnGlobalToLocalPoints(
self.pilotbundle.x[0, :, 0])
xp_objsurf = np.repeat(xp_objsurf[:, np.newaxis], num_points, axis=1)
dx3d = np.dot(self.objectsurface.rootcoordinatesystem.localbasis.T,
dr_obj3d)
xparabasal = xp_objsurf + dx3d
kp_objsurf = self.objectsurface.rootcoordinatesystem.returnGlobalToLocalDirections(
self.pilotbundle.k[0, :, 0])
kp_objsurf = np.repeat(kp_objsurf[:, np.newaxis], num_points, axis=1)
dk3d = np.dot(self.objectsurface.rootcoordinatesystem.localbasis.T,
dk_obj3d)
# TODO: k coordinate system for which dispersion relation is respected
kparabasal = kp_objsurf + dk3d
E_obj = self.pilotbundle.Efield[0, :, 0]
Eparabasal = np.repeat(E_obj[:, np.newaxis], num_points, axis=1)
# Aimy: returns only linearized results which are not exact
return RayBundle(xparabasal, kparabasal, Eparabasal, wave=self.wave)
class Aimy(BaseLogger):
"""
Should take care about ray aiming (approximatively and real).
Should generate aiming matrices and raybundles according to
aiming specifications and field specifications.
"""
def __init__(self,
s,
seq,
wave=standard_wavelength,
num_pupil_points=100,
stopsize=10,
pilotbundle_solution=-1,
pilotbundle_generation="complex",
pilotbundle_delta_angle=1 * degree,
pilotbundle_delta_size=0.1,
pilotbundle_sampling_points=3,
name=""):
super(Aimy, self).__init__(name=name)
self.field_raster = RectGrid()
self.pupil_raster = RectGrid()
self.stopsize = stopsize
self.num_pupil_points = num_pupil_points
self.wave = wave
self.pilotbundle_solution = pilotbundle_solution
self.pilotbundle_generation = pilotbundle_generation
self.pilotbundle_delta_angle = pilotbundle_delta_angle
self.pilotbundle_delta_size = pilotbundle_delta_size
self.pilotbundle_sampling_points = pilotbundle_sampling_points
self.update(s, seq)
def setKind(self):
self.kind = "aimy"
def extractABCD(self, xyuv):
self.debug(str(xyuv.shape))
Axyuv = xyuv[0:2, 0:2]
Bxyuv = xyuv[0:2, 2:4] # take only real part of the k vectors
Cxyuv = xyuv[2:4, 0:2]
Dxyuv = xyuv[2:4, 2:4]
return (Axyuv, Bxyuv, Cxyuv, Dxyuv)
def update(self, s, seq):
obj_dx = self.pilotbundle_delta_size # pilot bundle properties
obj_dphi = self.pilotbundle_delta_angle # pilot bundle properties
first_element_seq_name = seq[0]
(first_element_name, first_element_seq) = first_element_seq_name
(objsurfname, objsurfoptions) = first_element_seq[0]
self.objectsurface = s.elements[first_element_name].surfaces[
objsurfname]
self.start_material = s.material_background
# TODO: pilotray starts always in background (how about immersion?)
# if mat is None: ....
if self.pilotbundle_generation.lower() == "real":
self.info("call real sampled pilotbundle")
pilotbundles = build_pilotbundle(
self.objectsurface,
self.start_material, (obj_dx, obj_dx), (obj_dphi, obj_dphi),
num_sampling_points=self.pilotbundle_sampling_points)
# TODO: wavelength?
elif self.pilotbundle_generation.lower() == "complex":
self.info("call complex sampled pilotbundle")
pilotbundles = build_pilotbundle_complex(
self.objectsurface,
self.start_material, (obj_dx, obj_dx), (obj_dphi, obj_dphi),
num_sampling_points=self.pilotbundle_sampling_points)
self.info("choose " + str(self.pilotbundle_solution) + " raybundle")
self.pilotbundle = pilotbundles[self.pilotbundle_solution]
# one of the last two
(self.m_obj_stop, self.m_stop_img) = s.extractXYUV(
self.pilotbundle,
seq,
pilotbundle_generation=self.pilotbundle_generation)
self.info("show linear matrices")
self.info(
"obj -> stop:\n" +
np.array_str(self.m_obj_stop, precision=10, suppress_small=True))
self.info(
"stop -> img:\n" +
np.array_str(self.m_stop_img, precision=10, suppress_small=True))
def aim_core_angle_known(self, theta2d):
"""
knows about xyuv matrices
"""
(thetax, thetay) = theta2d
rmx = rodrigues(thetax, [0, 1, 0])
rmy = rodrigues(thetay, [1, 0, 0])
rmfinal = np.dot(rmy, rmx)
dpilot_global = self.pilotbundle.returnKtoD()[0, :, 0]
kpilot_global = self.pilotbundle.k[0, :, 0]
dpilot_object = self.objectsurface.rootcoordinatesystem.returnGlobalToLocalDirections(
dpilot_global)[:, np.newaxis]
kpilot_object = self.objectsurface.rootcoordinatesystem.returnGlobalToLocalDirections(
kpilot_global)[:, np.newaxis]
kpilot_object = np.repeat(kpilot_object, self.num_pupil_points, axis=1)
d = np.dot(rmfinal, dpilot_object)
k = returnDtoK(d) # TODO: implement fake implementation
dk = k - kpilot_object
dk_obj = dk[0:2, :]
(A_obj_stop, B_obj_stop, C_obj_stop,
D_obj_stop) = self.extractABCD(self.m_obj_stop)
A_obj_stop_inv = np.linalg.inv(A_obj_stop)
(xp, yp) = self.pupil_raster.getGrid(self.num_pupil_points)
dr_stop = (np.vstack((xp, yp)) * self.stopsize)
intermediate = np.dot(B_obj_stop, dk_obj)
dr_obj = np.dot(A_obj_stop_inv, dr_stop - intermediate)
return (dr_obj, dk_obj)
def aim_core_k_known(self, dk_obj):
"""
knows about xyuv matrices
"""
(A_obj_stop, B_obj_stop, C_obj_stop,
D_obj_stop) = self.extractABCD(self.m_obj_stop)
A_obj_stop_inv = np.linalg.inv(A_obj_stop)
(xp, yp) = self.pupil_raster.getGrid(self.num_pupil_points)
(num_points, ) = xp.shape
dr_stop = (np.vstack((xp, yp)) * self.stopsize)
dk_obj2 = np.repeat(dk_obj[:, np.newaxis], num_points, axis=1)
intermediate = np.dot(B_obj_stop, dk_obj2)
dr_obj = np.dot(A_obj_stop_inv, dr_stop - intermediate)
return (dr_obj, dk_obj2)
def aim_core_r_known(self, delta_xy):
(A_obj_stop, B_obj_stop, C_obj_stop,
D_obj_stop) = self.extractABCD(self.m_obj_stop)
self.debug(str(B_obj_stop.shape))
B_obj_stop_inv = np.linalg.inv(B_obj_stop)
(xp, yp) = self.pupil_raster.getGrid(self.num_pupil_points)
(num_points, ) = xp.shape
dr_stop = (np.vstack((xp, yp)) * self.stopsize)
dr_obj = np.repeat(delta_xy[:, np.newaxis], num_points, axis=1)
dk_obj = np.dot(B_obj_stop_inv, dr_stop - np.dot(A_obj_stop, dr_obj))
# TODO: in general some direction vector is derived
# TODO: this must been mapped to a k vector
# TODO: what about anamorphic systems?
return (dr_obj, dk_obj)
def aim(self, delta_xy, fieldtype="angle"):
"""
Generates bundles.
"""
if fieldtype == "angle":
(dr_obj, dk_obj) = self.aim_core_angle_known(delta_xy)
elif fieldtype == "objectheight":
(dr_obj, dk_obj) = self.aim_core_r_known(delta_xy)
elif fieldtype == "kvector":
# (dr_obj, dk_obj) = self.aim_core_k_known(delta_xy)
raise NotImplementedError()
else:
raise NotImplementedError()
(dim, num_points) = np.shape(dr_obj)
dr_obj3d = np.vstack((dr_obj, np.zeros(num_points)))
dk_obj3d = np.vstack((dk_obj, np.zeros(num_points)))
xp_objsurf = self.objectsurface.rootcoordinatesystem.returnGlobalToLocalPoints(
self.pilotbundle.x[0, :, 0])
xp_objsurf = np.repeat(xp_objsurf[:, np.newaxis], num_points, axis=1)
dx3d = np.dot(self.objectsurface.rootcoordinatesystem.localbasis.T,
dr_obj3d)
xparabasal = xp_objsurf + dx3d
kp_objsurf = self.objectsurface.rootcoordinatesystem.returnGlobalToLocalDirections(
self.pilotbundle.k[0, :, 0])
kp_objsurf = np.repeat(kp_objsurf[:, np.newaxis], num_points, axis=1)
dk3d = np.dot(self.objectsurface.rootcoordinatesystem.localbasis.T,
dk_obj3d)
# FIXME: k coordinate system for which dispersion relation is respected
# modified k in general violates dispersion relation
kparabasal = kp_objsurf + dk3d
self.debug("E pilotbundle")
self.debug(str(self.pilotbundle.Efield.shape))
self.debug(str(self.pilotbundle.Efield))
E_obj = self.pilotbundle.Efield[0, :, 0]
self.debug("E_obj")
self.debug(str(E_obj))
Eparabasal = np.repeat(E_obj[:, np.newaxis], num_points, axis=1)
self.debug(str(np.sum(kparabasal * Eparabasal, axis=0)))
# FIXME: Efield introduces anisotropy in aiming through
# rotationally symmetric system
# since copy of Eparabasal is not in the right direction for the
# dispersion relation (i.e. in isotropic media k perp E which is not
# fulfilled); solution: use k, insert into propagator, calculate
# E by (u, sigma, v) = np.linalg.svd(propagator) where E is
# linearcombination of all u which belong to sigma = 0 values.
# This is necessary to get the right ray direction also in isotropic
# case
# Aimy: returns only linearized results which are not exact
return RayBundle(xparabasal, kparabasal, Eparabasal, wave=self.wave)
class Aimy(BaseLogger):
"""
Should take care about ray aiming (approximatively and real).
Should generate aiming matrices and raybundles according to
aiming specifications and field specifications.
"""
def __init__(self, s, seq,
wave=standard_wavelength,
num_pupil_points=100,
stopsize=10,
pilotbundle_solution=-1,
pilotbundle_generation="complex",
pilotbundle_delta_angle=1*degree,
pilotbundle_delta_size=0.1,
pilotbundle_sampling_points=3,
name="", kind="aimy", **kwargs):
super(Aimy, self).__init__(name=name, kind=kind, **kwargs)
self.field_raster = RectGrid()
self.pupil_raster = RectGrid()
self.stopsize = stopsize
self.num_pupil_points = num_pupil_points
self.wave = wave
self.pilotbundle_solution = pilotbundle_solution
self.pilotbundle_generation = pilotbundle_generation
self.pilotbundle_delta_angle = pilotbundle_delta_angle
self.pilotbundle_delta_size = pilotbundle_delta_size
self.pilotbundle_sampling_points = pilotbundle_sampling_points
self.update(s, seq)
def extractABCD(self, xyuv):
self.debug(str(xyuv.shape))
Axyuv = xyuv[0:2, 0:2]
Bxyuv = xyuv[0:2, 2:4] # take only real part of the k vectors
Cxyuv = xyuv[2:4, 0:2]
Dxyuv = xyuv[2:4, 2:4]
return (Axyuv, Bxyuv, Cxyuv, Dxyuv)
def update(self, s, seq):
obj_dx = self.pilotbundle_delta_size # pilot bundle properties
obj_dphi = self.pilotbundle_delta_angle # pilot bundle properties
first_element_seq_name = seq[0]
(first_element_name, first_element_seq) = first_element_seq_name
(objsurfname, objsurfoptions) = first_element_seq[0]
self.objectsurface = s.elements[first_element_name].surfaces[objsurfname]
self.start_material = s.material_background
# TODO: pilotray starts always in background (how about immersion?)
# if mat is None: ....
if self.pilotbundle_generation.lower() == "real":
self.info("call real sampled pilotbundle")
pilotbundles = build_pilotbundle(
self.objectsurface,
self.start_material,
(obj_dx, obj_dx),
(obj_dphi, obj_dphi),
num_sampling_points=self.pilotbundle_sampling_points)
# TODO: wavelength?
elif self.pilotbundle_generation.lower() == "complex":
self.info("call complex sampled pilotbundle")
pilotbundles = build_pilotbundle_complex(
self.objectsurface,
self.start_material,
(obj_dx, obj_dx),
(obj_dphi, obj_dphi),
num_sampling_points=self.pilotbundle_sampling_points)
self.info("choose " + str(self.pilotbundle_solution) + " raybundle")
self.pilotbundle = pilotbundles[self.pilotbundle_solution]
# one of the last two
(self.m_obj_stop, self.m_stop_img) = s.extractXYUV(self.pilotbundle,
seq,
pilotbundle_generation=self.pilotbundle_generation)
self.info("show linear matrices")
self.info("obj -> stop:\n" + np.array_str(self.m_obj_stop, precision=10, suppress_small=True))
self.info("stop -> img:\n" + np.array_str(self.m_stop_img, precision=10, suppress_small=True))
def aim_core_angle_known(self, theta2d):
"""
knows about xyuv matrices
"""
(thetax, thetay) = theta2d
rmx = rodrigues(thetax, [0, 1, 0])
rmy = rodrigues(thetay, [1, 0, 0])
rmfinal = np.dot(rmy, rmx)
dpilot_global = self.pilotbundle.returnKtoD()[0, :, 0]
kpilot_global = self.pilotbundle.k[0, :, 0]
dpilot_object = self.objectsurface.rootcoordinatesystem.returnGlobalToLocalDirections(dpilot_global)[:, np.newaxis]
kpilot_object = self.objectsurface.rootcoordinatesystem.returnGlobalToLocalDirections(kpilot_global)[:, np.newaxis]
kpilot_object = np.repeat(kpilot_object, self.num_pupil_points, axis=1)
d = np.dot(rmfinal, dpilot_object)
k = returnDtoK(d) # TODO: implement fake implementation
dk = k - kpilot_object
dk_obj = dk[0:2, :]
(A_obj_stop, B_obj_stop, C_obj_stop, D_obj_stop) = self.extractABCD(self.m_obj_stop)
A_obj_stop_inv = np.linalg.inv(A_obj_stop)
(xp, yp) = self.pupil_raster.getGrid(self.num_pupil_points)
dr_stop = (np.vstack((xp, yp))*self.stopsize)
intermediate = np.dot(B_obj_stop, dk_obj)
dr_obj = np.dot(A_obj_stop_inv, dr_stop - intermediate)
return (dr_obj, dk_obj)
def aim_core_k_known(self, dk_obj):
"""
knows about xyuv matrices
"""
(A_obj_stop,
B_obj_stop,
C_obj_stop,
D_obj_stop) = self.extractABCD(self.m_obj_stop)
A_obj_stop_inv = np.linalg.inv(A_obj_stop)
(xp, yp) = self.pupil_raster.getGrid(self.num_pupil_points)
(num_points,) = xp.shape
dr_stop = (np.vstack((xp, yp))*self.stopsize)
dk_obj2 = np.repeat(dk_obj[:, np.newaxis], num_points, axis=1)
intermediate = np.dot(B_obj_stop, dk_obj2)
dr_obj = np.dot(A_obj_stop_inv, dr_stop - intermediate)
return (dr_obj, dk_obj2)
def aim_core_r_known(self, delta_xy):
(A_obj_stop,
B_obj_stop,
C_obj_stop,
D_obj_stop) = self.extractABCD(self.m_obj_stop)
self.debug(str(B_obj_stop.shape))
B_obj_stop_inv = np.linalg.inv(B_obj_stop)
(xp, yp) = self.pupil_raster.getGrid(self.num_pupil_points)
(num_points,) = xp.shape
dr_stop = (np.vstack((xp, yp))*self.stopsize)
dr_obj = np.repeat(delta_xy[:, np.newaxis], num_points, axis=1)
dk_obj = np.dot(B_obj_stop_inv, dr_stop - np.dot(A_obj_stop, dr_obj))
# TODO: in general some direction vector is derived
# TODO: this must been mapped to a k vector
# TODO: what about anamorphic systems?
return (dr_obj, dk_obj)
def aim(self, delta_xy, fieldtype="angle"):
"""
Generates bundles.
"""
if fieldtype == "angle":
(dr_obj, dk_obj) = self.aim_core_angle_known(delta_xy)
elif fieldtype == "objectheight":
(dr_obj, dk_obj) = self.aim_core_r_known(delta_xy)
elif fieldtype == "kvector":
# (dr_obj, dk_obj) = self.aim_core_k_known(delta_xy)
raise NotImplementedError()
else:
raise NotImplementedError()
(dim, num_points) = np.shape(dr_obj)
dr_obj3d = np.vstack((dr_obj, np.zeros(num_points)))
dk_obj3d = np.vstack((dk_obj, np.zeros(num_points)))
xp_objsurf = self.objectsurface.rootcoordinatesystem.returnGlobalToLocalPoints(self.pilotbundle.x[0, :, 0])
xp_objsurf = np.repeat(xp_objsurf[:, np.newaxis], num_points, axis=1)
dx3d = np.dot(self.objectsurface.rootcoordinatesystem.localbasis.T, dr_obj3d)
xparabasal = xp_objsurf + dx3d
kp_objsurf = self.objectsurface.rootcoordinatesystem.returnGlobalToLocalDirections(self.pilotbundle.k[0, :, 0])
kp_objsurf = np.repeat(kp_objsurf[:, np.newaxis], num_points, axis=1)
dk3d = np.dot(self.objectsurface.rootcoordinatesystem.localbasis.T, dk_obj3d)
# FIXME: k coordinate system for which dispersion relation is respected
# modified k in general violates dispersion relation
kparabasal = kp_objsurf + dk3d
self.debug("E pilotbundle")
self.debug(str(self.pilotbundle.Efield.shape))
self.debug(str(self.pilotbundle.Efield))
E_obj = self.pilotbundle.Efield[0, :, 0]
self.debug("E_obj")
self.debug(str(E_obj))
Eparabasal = np.repeat(E_obj[:, np.newaxis], num_points, axis=1)
self.debug(str(np.sum(kparabasal*Eparabasal, axis=0)))
# FIXME: Efield introduces anisotropy in aiming through
# rotationally symmetric system
# since copy of Eparabasal is not in the right direction for the
# dispersion relation (i.e. in isotropic media k perp E which is not
# fulfilled); solution: use k, insert into propagator, calculate
# E by (u, sigma, v) = np.linalg.svd(propagator) where E is
# linearcombination of all u which belong to sigma = 0 values.
# This is necessary to get the right ray direction also in isotropic
# case
# Aimy: returns only linearized results which are not exact
return RayBundle(xparabasal, kparabasal, Eparabasal, wave=self.wave)