def asphere_sag(test_vector):
"""
Computation of asphere sag equals explicit calculation.
"""
coordinate_system = LocalCoordinates.p(name="root")
radius = 10.0
conic_constant = -1.5
curvature = 1./radius
alpha2 = 1e-3
alpha4 = -1e-6
alpha6 = 1e-8
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 = Asphere.p(coordinate_system, curv=curvature, cc=conic_constant,
coefficients=[alpha2, alpha4, alpha6])
sag = shape.getSag(x_coordinate, y_coordinate)
# comparison with explicitly entered formula
comparison = (curvature*(x_coordinate**2+y_coordinate**2)/
(1.+ np.sqrt(1.-(1.+conic_constant)
*curvature**2
*(x_coordinate**2+y_coordinate**2)))
+alpha2*(x_coordinate**2+y_coordinate**2)
+alpha4*(x_coordinate**2+y_coordinate**2)**2
+alpha6*(x_coordinate**2+y_coordinate**2)**3)
assert np.allclose(sag, comparison)
def asphere_grad(test_vector):
"""
Computation of asphere gradient equals explicit calculation.
Notice grad is calculated in 3 dimensions by grad F = grad(z - f(x, y))
"""
coordinate_system = LocalCoordinates.p(name="root")
radius = 10.0
conic_constant = -1.5
curvature = 1. / radius
alpha2 = 1e-3
alpha4 = -1e-6
alpha6 = 1e-8
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 = Asphere.p(coordinate_system,
curv=curvature,
cc=conic_constant,
coefficients=[alpha2, alpha4, alpha6])
gradient = shape.getGrad(x, y)
comparison = np.zeros_like(gradient)
comparison[0] = (-2 * alpha2 * x - 4 * alpha4 * x * (x**2 + y**2) -
6 * alpha6 * x * (x**2 + y**2)**2 - 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] = (-2 * alpha2 * y - 4 * alpha4 * y * (x**2 + y**2) -
6 * alpha6 * y * (x**2 + y**2)**2 - 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[2, :] = 1.0
assert np.allclose(gradient, comparison)
def initShAsphere(self, curv=0., cc=0., asphereparams=[], **kwargs):
shapeclass = None
if "surface" in kwargs:
shapeclass = kwargs["surface"].shape
curv = shapeclass.curvature.evaluate()
cc = shapeclass.conic.evaluate()
else:
shapeclass = Asphere.p(curv=curv, cc=cc, acoeffs=asphereparams)
self.__obj.addProperty("App::PropertyFloat", "curv", "Shape",
"central curvature").curv = curv
self.__obj.addProperty("App::PropertyFloat", "cc", "Shape",
"conic constant").cc = cc
self.__obj.addProperty(
"App::PropertyFloatList", "asphereparams", "Shape",
"aspherical corrections").asphereparams = asphereparams
self.__obj.shapeclass = shapeclass
decz=-dropletradius),
refname=lccomprism.name) # objectDist
lc2 = s.addLocalCoordinateSystem(
LocalCoordinates.p(name="surf2", decz=dropletradius),
refname=lccomprism.name)
lc3 = s.addLocalCoordinateSystem(
LocalCoordinates.p(name="surf3", decz=0),
refname=lccomprism.name)
lc4 = s.addLocalCoordinateSystem(
LocalCoordinates.p(name="image", decz=-2.*dropletradius),
refname=lccomprism.name)
stopsurf = Surface.p(lc0,
aperture=CircularAperture.p(lc0, maxradius=7*dropletradius))
frontsurf = Surface.p(lc1, shape=Asphere.p(lc1, curv=1./dropletradius),
aperture=CircularAperture.p(lc1, maxradius=dropletradius))
rearsurf = Surface.p(lc2, shape=Asphere.p(lc2, curv=-1./dropletradius),
aperture=CircularAperture.p(lc2, maxradius=dropletradius))
midsurf = Surface.p(lc3, shape=Asphere.p(lc3, curv=0),
aperture=CircularAperture.p(lc3, maxradius=dropletradius))
image = Surface.p(lc4,
aperture=CircularAperture.p(lc4, maxradius=7.*dropletradius))
elem = OpticalElement.p(lc0, name="droplet")
database_basepath = "refractiveindex.info-database/database"
shelf = "3d"
lc1 = s.addLocalCoordinateSystem(LocalCoordinates(name="surf1",
decz=-dropletradius),
refname=lccomprism.name) # objectDist
lc2 = s.addLocalCoordinateSystem(LocalCoordinates(name="surf2",
decz=dropletradius),
refname=lccomprism.name)
lc3 = s.addLocalCoordinateSystem(LocalCoordinates(name="surf3", decz=0),
refname=lccomprism.name)
lc4 = s.addLocalCoordinateSystem(LocalCoordinates(name="image",
decz=-2. * dropletradius),
refname=lccomprism.name)
stopsurf = Surface(lc0,
aperture=CircularAperture(lc0, maxradius=7 * dropletradius))
frontsurf = Surface(lc1,
shape=Asphere(lc1, curv=1. / dropletradius),
aperture=CircularAperture(lc1, maxradius=dropletradius))
rearsurf = Surface(lc2,
shape=Asphere(lc2, curv=-1. / dropletradius),
aperture=CircularAperture(lc2, maxradius=dropletradius))
midsurf = Surface(lc3,
shape=Asphere(lc3, curv=0),
aperture=CircularAperture(lc3, maxradius=dropletradius))
image = Surface(lc4,
aperture=CircularAperture(lc4, maxradius=7. * dropletradius))
elem = OpticalElement(lc0, name="droplet")
database_basepath = "refractiveindex.info-database/database"
shelf = "3d"
def create():
from pyrateoptics.raytracer.surface_shape import Asphere
lc = LocalCoordinates.p(name="global")
a = Asphere.p(lc, curv=0.01, cc=-1.0, coefficients=[1., 2., 3.])
return a