def create_lens(power=0., bending=0., th=None, sd=1., med=None):
if med is None:
med = Glass()
rndx = med.rindex('d')
cv1 = power / (2 * (rndx - 1))
cv2 = -power / (2 * (rndx - 1))
s1 = Surface(profile=Spherical(c=cv1), max_ap=sd, delta_n=(rndx - 1))
s2 = Surface(profile=Spherical(c=cv2), max_ap=sd, delta_n=(1 - rndx))
if th is None:
th = sd / 5
g = Gap(t=th, med=med)
le = Element(s1, s2, g, sd=sd)
return [[s1, g, None, rndx, 1], [s2, None, None, 1, 1]], [le]
def create_mirror(c=0.0,
r=None,
cc=0.0,
ec=None,
power=None,
profile=None,
sd=None,
**kwargs):
'''Create a sequence and element for a mirror.
Args:
c: vertex curvature
r: vertex radius of curvature
cc: conic constant
ec: 1 + cc
power: optical power of the mirror
sd: semi-diameter
profile: Spherical or Conic
'''
delta_n = kwargs['delta_n'] if 'delta_n' in kwargs else -2
if power:
cv = power / delta_n
elif r:
cv = 1.0 / r
else:
cv = c
if ec:
k = ec - 1.0
else:
k = cc
if profile is Spherical:
prf = Spherical(c=cv)
elif profile is Conic:
prf = Conic(c=cv, cc=k)
else:
if k == 0.0:
prf = Spherical(c=cv)
else:
prf = Conic(c=cv, cc=k)
m = Surface(profile=prf,
interact_mode='reflect',
max_ap=sd,
delta_n=delta_n,
**kwargs)
me = Mirror(m, sd=sd)
return [[m, None, None, 1, -1]], [me]
def test_concave_sphere(self):
r3 = 10
s3 = Spherical(r=-r3)
# test for p0 ray, (0, 0, 0), (0, 0, 1)
p0_truth = 1.0, np.array([0., 0., 0.])
p0s3_dir = s3.intersect(self.p0, self.dir0, self.eps, self.z_dir)
p0s3_tnp = s3.intersect_tangent_plane(self.p0, self.dir0,
self.eps, self.z_dir)
assert ((p0s3_dir[0], p0s3_dir[1].all()) ==
(p0s3_tnp[0], p0s3_tnp[1].all()))
p0s3 = p0s3_dir
assert ((p0s3[0], p0s3[1].all()) == (p0_truth[0], p0_truth[1].all()))
# test for p1 ray, (0, 1, 0), (0, 0, 1)
sag3 = r3 - sqrt(r3*r3 - 1.0)
p1_truth = 1-sag3, np.array([0., 1., -sag3])
p1s3_tnp = s3.intersect_tangent_plane(self.p1, self.dir0,
self.eps, self.z_dir)
p1s3_dir = s3.intersect(self.p1, self.dir0, self.eps, self.z_dir)
assert ((p1s3_dir[0], p1s3_dir[1].all()) ==
(p1s3_tnp[0], p1s3_tnp[1].all()))
p1s3 = p1s3_dir
assert p1s3[0] == approx(p1_truth[0], rel=1e-14, abs=1e-14)
assert p1s3[1].all() == p1_truth[1].all()
dir_p1s3 = s3.normal(p1s3[1])
dir_p1s3_truth = normalize(p1_truth[1] - np.array([0, 0, -r3]))
assert dir_p1s3.all() == dir_p1s3_truth.all()
def test_dbgauss_s1(self):
r1 = 56.20238
c1 = 1/r1
y0 = 25.0
s1 = Spherical(c=c1)
p1 = np.array([0., y0, 0.])
sag1 = r1 - sqrt(r1*r1 - y0*y0)
# test for p0 ray, (0, 0, 0), (0, 0, 1)
p0_truth = 1.0, np.array([0., 0., 0.])
p0s1 = s1.intersect(self.p0, self.dir0, self.eps, self.z_dir)
assert ((p0s1[0], p0s1[1].all()) ==
(p0_truth[0], p0_truth[1].all()))
self.assertEqual(p0s1[0], 1.0)
npt.assert_allclose(p0s1[1], np.array([0., 0., 0.]),
rtol=1e-14, atol=1e-14)
# test for p1 ray, (0, 1, 0), (0, 0, 1)
p1_truth = 5.866433424372758, np.array([0., y0, sag1])
p1s1 = s1.intersect(p1, self.dir0, self.eps, self.z_dir)
assert p1s1[0] == approx(p1_truth[0], rel=1e-14, abs=1e-14)
npt.assert_allclose(p1s1[1], p1_truth[1], rtol=1e-14)
dir_p1s1 = s1.normal(p1s1[1])
dir_p1s1_truth = -normalize(p1_truth[1] - np.array([0, 0, r1]))
assert dir_p1s1.all() == dir_p1s1_truth.all()
npt.assert_allclose(dir_p1s1, dir_p1s1_truth, rtol=1e-14)
def test_planar_sphere(self):
s1 = Spherical(c=0.0)
p_truth = 1.0, np.array([0., 0., 0.])
# test for p0 ray, (0, 0, 0), (0, 0, 1)
p0s1 = s1.intersect(self.p0, self.dir0, self.eps, self.z_dir)
assert (p0s1[0], p0s1[1].all()) == (p_truth[0], p_truth[1].all())
# test for p1 ray, (0, 1, 0), (0, 0, 1)
p1s1 = s1.intersect(self.p1, self.dir0, self.eps, self.z_dir)
assert ((p1s1[0], p1s1[1].all()) ==
(p_truth[0], np.array([0., 1., 0.]).all()))
def create_mirror(c=0.0,
r=None,
cc=0.0,
ec=None,
power=None,
profile=None,
sd=None,
**kwargs):
delta_n = kwargs['delta_n'] if 'delta_n' in kwargs else -2
if power:
cv = power / delta_n
elif r:
cv = 1.0 / r
else:
cv = c
if ec:
k = ec - 1.0
else:
k = cc
if profile is Spherical:
prf = Spherical(c=cv)
elif profile is Conic:
prf = Conic(c=cv, cc=k)
else:
if k == 0.0:
prf = Spherical(c=cv)
else:
prf = Conic(c=cv, cc=k)
m = Surface(profile=prf,
interact_mode='reflect',
max_ap=sd,
delta_n=delta_n,
**kwargs)
me = Mirror(m, sd=sd)
return [[m, None, None, 1, -1]], [me]
def test_convex_sphere(self):
r2 = 10
c2 = 1/r2
s2 = Spherical(c=c2)
# test for p0 ray, (0, 0, 0), (0, 0, 1)
p0_truth = 1.0, np.array([0., 0., 0.])
p0s2_dir = s2.intersect(self.p0, self.dir0, self.eps, self.z_dir)
p0s2_tnp = s2.intersect_tangent_plane(self.p0, self.dir0,
self.eps, self.z_dir)
assert ((p0s2_dir[0], p0s2_dir[1].all()) ==
(p0s2_tnp[0], p0s2_tnp[1].all()))
p0s2 = p0s2_dir
assert ((p0s2[0], p0s2[1].all()) == (p0_truth[0], p0_truth[1].all()))
# A spherical EvenPolynomial will use iteration to find the
# intersection. Use this case to further check results
sa2 = EvenPolynomial(c=c2)
p0sa2 = sa2.intersect(self.p0, self.dir0, self.eps, self.z_dir)
assert ((p0sa2[0], p0sa2[1].all()) ==
(p0_truth[0], p0_truth[1].all()))
assert (p0s2_dir[0], p0s2_dir[1].all()) == (p0sa2[0], p0sa2[1].all())
# test for p1 ray, (0, 1, 0), (0, 0, 1)
sag2 = r2 - sqrt(r2*r2 - 1.0)
p1_truth = 1+sag2, np.array([0., 1., sag2])
p1s2_dir = s2.intersect(self.p1, self.dir0, self.eps, self.z_dir)
p1s2_tnp = s2.intersect_tangent_plane(self.p1, self.dir0,
self.eps, self.z_dir)
assert ((p1s2_dir[0], p1s2_dir[1].all()) ==
(p1s2_tnp[0], p1s2_tnp[1].all()))
p1s2 = p1s2_dir
assert ((p1s2[0], p1s2[1].all()) ==
(p1_truth[0], p1_truth[1].all()))
dir_p1s2 = s2.normal(p1s2[1])
dir_p1s2_truth = -normalize(p1_truth[1] - np.array([0, 0, r2]))
assert dir_p1s2.all() == dir_p1s2_truth.all()