def conic_sag(test_vector):
"""
Computation of conic sag equals explicit calculation.
"""
coordinate_system = LocalCoordinates(name="root")
radius = 10.0
conic_constant = -1.5
curvature = 1. / radius
maxradius = (math.sqrt(1. / ((1 + conic_constant) * curvature**2))
if conic_constant > -1 else abs(radius))
values = (2 * test_vector - 1.) * maxradius
x_coordinate = values[0]
y_coordinate = values[1]
shape = Conic(coordinate_system, curv=curvature, cc=conic_constant)
sag = shape.getSag(x_coordinate, y_coordinate)
# comparison with explicitly entered formula
assert np.allclose(
sag, (curvature * (x_coordinate**2 + y_coordinate**2) /
(1. + np.sqrt(1. - (1. + conic_constant) * curvature**2 *
(x_coordinate**2 + y_coordinate**2)))))
def initShConic(self, curv=0., cc=0., **kwargs):
shapeclass = None
if kwargs.has_key("surface"):
shapeclass = kwargs["surface"].shape
curv = shapeclass.curvature.evaluate()
cc = shapeclass.conic.evaluate()
else:
shapeclass = Conic(self.__obj.LocalCoordinatesLink.getLC(), curv=curv, cc=cc)
self.__obj.addProperty("App::PropertyFloat", "curv", "Shape", "central curvature").curv = curv
self.__obj.addProperty("App::PropertyFloat", "cc", "Shape", "conic constant").cc = cc
self.__obj.shapeclass = shapeclass
def conic_grad(test_vector):
"""
Computation of conic grad equals explicit calculation.
"""
coordinate_system = LocalCoordinates(name="root")
radius = 10.0
conic_constant = -1.5
curvature = 1. / radius
maxradius = (math.sqrt(1. / ((1 + conic_constant) * curvature**2))
if conic_constant > -1 else abs(radius))
values = (2 * test_vector - 1.) * maxradius
x = values[0]
y = values[1]
shape = Conic(coordinate_system, curv=curvature, cc=conic_constant)
gradient = shape.getGrad(x, y)
comparison = np.zeros_like(gradient)
comparison[2, :] = 1.
comparison[0] = (-curvature**3 * x * (conic_constant + 1) * (x**2 + y**2) /
(np.sqrt(-curvature**2 * (conic_constant + 1) *
(x**2 + y**2) + 1) *
(np.sqrt(-curvature**2 * (conic_constant + 1) *
(x**2 + y**2) + 1) + 1)**2) -
2 * curvature * x / (np.sqrt(-curvature**2 *
(conic_constant + 1) *
(x**2 + y**2) + 1) + 1))
comparison[1] = (-curvature**3 * y * (conic_constant + 1) * (x**2 + y**2) /
(np.sqrt(-curvature**2 * (conic_constant + 1) *
(x**2 + y**2) + 1) *
(np.sqrt(-curvature**2 * (conic_constant + 1) *
(x**2 + y**2) + 1) + 1)**2) -
2 * curvature * y / (np.sqrt(-curvature**2 *
(conic_constant + 1) *
(x**2 + y**2) + 1) + 1))
comparison = comparison * gradient[
2] # comparison and gradient are calculated differently
assert np.allclose(gradient, comparison)
def initShExplicit(self, **kwargs):
# this function offers the flexibility to use function objects with tunable parameters
# TODO: implement
self.__obj.shapeclass = Conic(curv=0, cc=0)
(si * 4.529e-12, -2.085)]),
apert=CircularAperture(lcS2, 40.0))
D2Psurf = Surface(lcD2prime)
D3surf = Surface(lcD3)
#S3surf = Surface(lcS3, shape=Conic(lcS3, curv=si*1./108.187, cc=0.0001), apert=CircularAperture(lcS3, 100.0))
S3surf = Surface(lcS3,
shape=Biconic(lcS3,
curvy=si * 1. / 108.187,
curvx=si * 1. / 73.105,
coefficients=[(0., 0.), (-si * 5.542e-7, -0.08),
(-si * 8.176e-11, -1.379)]),
apert=CircularAperture(lcS3, 40.0))
D3Psurf = Surface(lcD3prime)
D4surf = Surface(lcD4)
S4surf = Surface(lcS4,
shape=Conic(lcS4, curv=1. / 77.772),
apert=CircularAperture(lcS4, 40.0))
D4Psurf = Surface(lcD4prime)
imgsurf = Surface(lcimage)
elem = OpticalElement(lc0, name="HUD")
elem.addMaterial("air", air)
elem.addMaterial("glass", glass)
elem.addSurface("object", objsurf, (None, None))
elem.addSurface("d1", D1surf, (None, None))
elem.addSurface("s1", S1surf, (None, "glass"))
elem.addSurface("d1p", D1Psurf, ("glass", "glass"))
elem.addSurface("d2", D2surf, ("glass", "glass"))
elem.addSurface("s2", S2surf, ("glass", "glass"))
wavelength = 0.5876e-3
# definition of optical system
s = OpticalSystem()
lc0 = s.addLocalCoordinateSystem(LocalCoordinates(name="stop", decz=0.0),
refname=s.rootcoordinatesystem.name)
lc1 = s.addLocalCoordinateSystem(LocalCoordinates(name="surf1", decz=5.0),
refname=lc0.name) # objectDist
lc2 = s.addLocalCoordinateSystem(LocalCoordinates(name="surf2", decz=20.0),
refname=lc1.name)
lc3 = s.addLocalCoordinateSystem(LocalCoordinates(name="image", decz=100.0),
refname=lc2.name)
stopsurf = Surface(lc0)
frontsurf = Surface(lc1, shape=Conic(lc1), apert=CircularAperture(lc1, 12.7))
backsurf = Surface(lc2,
shape=Asphere(lc2,
curv=-1. / 50.0,
cc=-1.,
coefficients=[0.0, 0.0, 0.0]),
apert=CircularAperture(lc2, 12.7))
image = Surface(lc3)
elem = OpticalElement(lc0, name="asphereelement")
bk7 = ConstantIndexGlass(lc1, n=1.5168)
elem.addMaterial("BK7", bk7)
elem.addSurface("stop", stopsurf, (None, None))