def setUp(self):
"""
Prepare an assembly with two subassemblies: one assembly representing
a spherical lens behind a flat screen, and one asssembly representing a
perfect mirror.
The mirror will be placed at the two subassemblies' focus, so a paraxial
ray will come back on the other side of the optical axis.
Reference:
In [1], the lensmaker equation
"""
# focal length = 1, thickness = 1/6
R = 1./6.
back_surf = Surface(HemisphereGM(R), opt.RefractiveHomogenous(1., 1.5),
location=N.r_[0., 0., -R/2.])
front_surf = Surface(HemisphereGM(R), opt.RefractiveHomogenous(1., 1.5),
location=N.r_[0., 0., R/2.], rotation=rotx(N.pi/2.)[:3,:3])
front_lens = AssembledObject(surfs=[back_surf, front_surf])
back_surf = Surface(FlatGeometryManager(), opt.RefractiveHomogenous(1., 1.5),
location=N.r_[0., 0., -0.01])
front_surf = Surface(FlatGeometryManager(), opt.RefractiveHomogenous(1., 1.5),
location=N.r_[0., 0., 0.01])
glass_screen = AssembledObject(surfs=[back_surf, front_surf],
transform=translate(0., 0., 0.5))
lens_assembly = Assembly(objects=[glass_screen, front_lens])
lens_assembly.set_transform(translate(0., 0., 1.))
full_assembly = Assembly(objects=[rect_one_sided_mirror(1., 1., 0.)],
subassemblies = [lens_assembly])
self.engine = TracerEngine(full_assembly)
def setUp(self):
self.assembly = Assembly()
surface1 = Surface(FlatGeometryManager(),
opt.RefractiveHomogenous(1., 1.5),
location=N.array([0, 0, -1.]))
surface2 = Surface(FlatGeometryManager(),
opt.RefractiveHomogenous(1., 1.5),
location=N.array([0, 0, 1.]))
object1 = AssembledObject(surfs=[surface1, surface2])
boundary = BoundarySphere(location=N.r_[0, 0., 3], radius=3.)
surface3 = Surface(CutSphereGM(2., boundary), opt.perfect_mirror)
object2 = AssembledObject(surfs=[surface3],
transform=translate(0., 0., 2.))
self.assembly = Assembly(objects=[object1, object2])
x = 1. / (math.sqrt(2))
dir = N.c_[[0, 1., 0.], [0, x, x], [0, 0, 1.]]
position = N.c_[[0, 0, 2.], [0, 0, 2.], [0, 0., 2.]]
self._bund = RayBundle(position,
dir,
ref_index=N.ones(3),
energy=N.ones(3))
self.engine = TracerEngine(self.assembly)
def test_transformed(self):
"""A transformed triangle excludes rays correctly"""
frame = np.dot(translate(0, -1, 0.5), rotx(np.pi/4.))
prm = self.tri.find_intersections(frame, self.bund)
np.testing.assert_array_equal(np.isfinite(prm),
np.r_[False, False, True, False, False, True])
def setUp(self):
dir = N.c_[[1, 1, -1], [-1, 1, -1], [-1, -1, -1], [1, -1, -1]] / math.sqrt(3)
position = N.c_[[0,0,1], [1,-1,1], [1,1,1], [-1,1,1]]
self._bund = RayBundle(position, dir)
self.gm = FlatGeometryManager()
frame = SP.translate(1., 0., 0.)
self.prm = self.gm.find_intersections(frame, self._bund)
def setUp(self):
dir = N.c_[[1, 1, -1], [-1, 1, -1], [-1, -1, -1],
[1, -1, -1]] / math.sqrt(3)
position = N.c_[[0, 0, 1], [1, -1, 1], [1, 1, 1], [-1, 1, 1]]
self._bund = RayBundle(position, dir)
self.gm = FlatGeometryManager()
frame = SP.translate(1., 0., 0.)
self.prm = self.gm.find_intersections(frame, self._bund)
def test_paraxial_ray(self):
"""A paraxial ray reaches the focus"""
rb = RayBundle(N.c_[[0., 0.001, 1.]], N.c_[[0., 0., -1.]],
energy=N.r_[1.], ref_index=N.r_[1.])
screen = rect_one_sided_mirror(5, 5)
f = self.lens.focal_length()
screen.set_transform(translate(0, 0, -f))
e = TracerEngine(Assembly([self.lens, screen]))
vert, _ = e.ray_tracer(rb, 3, 1e-6)
self.failUnlessAlmostEqual(vert[1,2], 0, 4)
def test_paraxial_ray(self):
"""A paraxial ray reaches the focus of a planoconvex lens"""
rb = RayBundle(N.c_[[0., 0.001, 1.]], N.c_[[0., 0., -1.]],
energy=N.r_[1.], ref_index=N.r_[1.])
screen = rect_one_sided_mirror(5, 5)
f = self.lens.focal_length()
screen.set_transform(translate(0, 0, -f))
e = TracerEngine(Assembly([self.lens, screen]))
vert, _ = e.ray_tracer(rb, 3, 1e-6)
self.failUnlessAlmostEqual(vert[1,2], 0, 4)
def setUp(self):
"""
Prepare an assembly with two subassemblies: one assembly representing
a spherical lens behind a flat screen, and one asssembly representing a
perfect mirror.
The mirror will be placed at the two subassemblies' focus, so a paraxial
ray will come back on the other side of the optical axis.
Reference:
In [1], the lensmaker equation
"""
# focal length = 1, thickness = 1/6
R = 1. / 6.
back_surf = Surface(HemisphereGM(R),
opt.RefractiveHomogenous(1., 1.5),
location=N.r_[0., 0., -R / 2.])
front_surf = Surface(HemisphereGM(R),
opt.RefractiveHomogenous(1., 1.5),
location=N.r_[0., 0., R / 2.],
rotation=rotx(N.pi / 2.)[:3, :3])
front_lens = AssembledObject(surfs=[back_surf, front_surf])
back_surf = Surface(RoundPlateGM(R),
opt.RefractiveHomogenous(1., 1.5),
location=N.r_[0., 0., -0.01])
front_surf = Surface(RoundPlateGM(R),
opt.RefractiveHomogenous(1., 1.5),
location=N.r_[0., 0., 0.01])
glass_screen = AssembledObject(surfs=[back_surf, front_surf],
transform=translate(0., 0., 0.5))
lens_assembly = Assembly(objects=[glass_screen, front_lens])
lens_assembly.set_transform(translate(0., 0., 1.))
full_assembly = Assembly(objects=[rect_one_sided_mirror(1., 1., 0.)],
subassemblies=[lens_assembly])
self.engine = TracerEngine(full_assembly)
def setUp(self):
self.assembly = Assembly()
surface1 = Surface(FlatGeometryManager(), opt.perfect_mirror)
self.object1 = AssembledObject()
self.object1.add_surface(surface1)
boundary = BoundarySphere(location=N.r_[0,0.,3], radius=3.)
surface3 = Surface(CutSphereGM(2., boundary), opt.perfect_mirror)
self.object2 = AssembledObject()
self.object2.add_surface(surface3)
self.transform1 = generate_transform(N.r_[1.,0,0], N.pi/4, N.c_[[0,0,-1.]])
self.transform2 = translate(0., 0., 2.)
self.assembly.add_object(self.object1, self.transform1)
self.assembly.add_object(self.object2, self.transform2)
def setUp(self):
self.assembly = Assembly()
surface1 = Surface(FlatGeometryManager(), opt.perfect_mirror)
self.object1 = AssembledObject()
self.object1.add_surface(surface1)
boundary = BoundarySphere(location=N.r_[0, 0., 3], radius=3.)
surface3 = Surface(CutSphereGM(2., boundary), opt.perfect_mirror)
self.object2 = AssembledObject()
self.object2.add_surface(surface3)
self.transform1 = generate_transform(N.r_[1., 0, 0], N.pi / 4,
N.c_[[0, 0, -1.]])
self.transform2 = translate(0., 0., 2.)
self.assembly.add_object(self.object1, self.transform1)
self.assembly.add_object(self.object2, self.transform2)
def test_image_size(self):
"""Image size of an object imaged by a biconcave lens matches theory"""
origin = N.c_[[0., 0.001, 1.]]
direct = -origin/N.linalg.norm(origin)
rb = RayBundle(origin, direct, energy=N.r_[1.], ref_index=N.r_[1.])
# Magnification, see [1] p. 26.
f = self.lens.focal_length()
m = f/(origin[2] + f)
# Image location, [ibid]:
loc = origin[2]*m
screen = rect_one_sided_mirror(5, 5)
screen.set_transform(translate(0, 0, -loc))
e = TracerEngine(Assembly([self.lens, screen]))
vert, _ = e.ray_tracer(rb, 3, 1e-6)
self.failUnlessAlmostEqual(vert[1,2], -m*origin[1], 4)
def test_image_size(self):
"""Image size of an object imaged by a biconcave lens matches theory"""
origin = N.c_[[0., 0.001, 1.]]
direct = -origin / N.linalg.norm(origin)
rb = RayBundle(origin, direct, energy=N.r_[1.], ref_index=N.r_[1.])
# Magnification, see [1] p. 26.
f = self.lens.focal_length()
m = f / (origin[2] + f)
# Image location, [ibid]:
loc = origin[2] * m
screen = rect_one_sided_mirror(5, 5)
screen.set_transform(translate(0, 0, -loc))
e = TracerEngine(Assembly([self.lens, screen]))
vert, _ = e.ray_tracer(rb, 3, 1e-6)
self.failUnlessAlmostEqual(vert[1, 2], -m * origin[1], 4)
def setUp(self):
self.assembly = Assembly()
surface1 = Surface(FlatGeometryManager(),
opt.RefractiveHomogenous(1., 1.5),
location=N.array([0,0,-1.]))
surface2 = Surface(FlatGeometryManager(),
opt.RefractiveHomogenous(1., 1.5),
location=N.array([0,0,1.]))
object1 = AssembledObject(surfs=[surface1, surface2])
boundary = BoundarySphere(location=N.r_[0,0.,3], radius=3.)
surface3 = Surface(CutSphereGM(2., boundary), opt.perfect_mirror)
object2 = AssembledObject(surfs=[surface3],
transform=translate(0., 0., 2.))
self.assembly = Assembly(objects=[object1, object2])
x = 1./(math.sqrt(2))
dir = N.c_[[0,1.,0.],[0,x,x],[0,0,1.]]
position = N.c_[[0,0,2.],[0,0,2.],[0,0.,2.]]
self._bund = RayBundle(position, dir, ref_index=N.ones(3), energy=N.ones(3))
self.engine = TracerEngine(self.assembly)
