103 lines
4.1 KiB
Python
103 lines
4.1 KiB
Python
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from sympy.core.evalf import N
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from sympy.core.numbers import (Float, I, oo, pi)
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from sympy.core.symbol import symbols
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from sympy.functions.elementary.miscellaneous import sqrt
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from sympy.functions.elementary.trigonometric import atan2
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from sympy.matrices.dense import Matrix
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from sympy.polys.polytools import factor
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from sympy.physics.optics import (BeamParameter, CurvedMirror,
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CurvedRefraction, FlatMirror, FlatRefraction, FreeSpace, GeometricRay,
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RayTransferMatrix, ThinLens, conjugate_gauss_beams,
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gaussian_conj, geometric_conj_ab, geometric_conj_af, geometric_conj_bf,
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rayleigh2waist, waist2rayleigh)
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def streq(a, b):
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return str(a) == str(b)
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def test_gauss_opt():
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mat = RayTransferMatrix(1, 2, 3, 4)
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assert mat == Matrix([[1, 2], [3, 4]])
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assert mat == RayTransferMatrix( Matrix([[1, 2], [3, 4]]) )
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assert [mat.A, mat.B, mat.C, mat.D] == [1, 2, 3, 4]
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d, f, h, n1, n2, R = symbols('d f h n1 n2 R')
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lens = ThinLens(f)
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assert lens == Matrix([[ 1, 0], [-1/f, 1]])
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assert lens.C == -1/f
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assert FreeSpace(d) == Matrix([[ 1, d], [0, 1]])
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assert FlatRefraction(n1, n2) == Matrix([[1, 0], [0, n1/n2]])
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assert CurvedRefraction(
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R, n1, n2) == Matrix([[1, 0], [(n1 - n2)/(R*n2), n1/n2]])
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assert FlatMirror() == Matrix([[1, 0], [0, 1]])
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assert CurvedMirror(R) == Matrix([[ 1, 0], [-2/R, 1]])
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assert ThinLens(f) == Matrix([[ 1, 0], [-1/f, 1]])
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mul = CurvedMirror(R)*FreeSpace(d)
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mul_mat = Matrix([[ 1, 0], [-2/R, 1]])*Matrix([[ 1, d], [0, 1]])
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assert mul.A == mul_mat[0, 0]
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assert mul.B == mul_mat[0, 1]
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assert mul.C == mul_mat[1, 0]
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assert mul.D == mul_mat[1, 1]
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angle = symbols('angle')
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assert GeometricRay(h, angle) == Matrix([[ h], [angle]])
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assert FreeSpace(
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d)*GeometricRay(h, angle) == Matrix([[angle*d + h], [angle]])
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assert GeometricRay( Matrix( ((h,), (angle,)) ) ) == Matrix([[h], [angle]])
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assert (FreeSpace(d)*GeometricRay(h, angle)).height == angle*d + h
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assert (FreeSpace(d)*GeometricRay(h, angle)).angle == angle
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p = BeamParameter(530e-9, 1, w=1e-3)
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assert streq(p.q, 1 + 1.88679245283019*I*pi)
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assert streq(N(p.q), 1.0 + 5.92753330865999*I)
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assert streq(N(p.w_0), Float(0.00100000000000000))
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assert streq(N(p.z_r), Float(5.92753330865999))
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fs = FreeSpace(10)
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p1 = fs*p
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assert streq(N(p.w), Float(0.00101413072159615))
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assert streq(N(p1.w), Float(0.00210803120913829))
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w, wavelen = symbols('w wavelen')
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assert waist2rayleigh(w, wavelen) == pi*w**2/wavelen
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z_r, wavelen = symbols('z_r wavelen')
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assert rayleigh2waist(z_r, wavelen) == sqrt(wavelen*z_r)/sqrt(pi)
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a, b, f = symbols('a b f')
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assert geometric_conj_ab(a, b) == a*b/(a + b)
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assert geometric_conj_af(a, f) == a*f/(a - f)
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assert geometric_conj_bf(b, f) == b*f/(b - f)
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assert geometric_conj_ab(oo, b) == b
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assert geometric_conj_ab(a, oo) == a
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s_in, z_r_in, f = symbols('s_in z_r_in f')
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assert gaussian_conj(
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s_in, z_r_in, f)[0] == 1/(-1/(s_in + z_r_in**2/(-f + s_in)) + 1/f)
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assert gaussian_conj(
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s_in, z_r_in, f)[1] == z_r_in/(1 - s_in**2/f**2 + z_r_in**2/f**2)
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assert gaussian_conj(
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s_in, z_r_in, f)[2] == 1/sqrt(1 - s_in**2/f**2 + z_r_in**2/f**2)
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l, w_i, w_o, f = symbols('l w_i w_o f')
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assert conjugate_gauss_beams(l, w_i, w_o, f=f)[0] == f*(
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-sqrt(w_i**2/w_o**2 - pi**2*w_i**4/(f**2*l**2)) + 1)
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assert factor(conjugate_gauss_beams(l, w_i, w_o, f=f)[1]) == f*w_o**2*(
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w_i**2/w_o**2 - sqrt(w_i**2/w_o**2 - pi**2*w_i**4/(f**2*l**2)))/w_i**2
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assert conjugate_gauss_beams(l, w_i, w_o, f=f)[2] == f
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z, l, w_0 = symbols('z l w_0', positive=True)
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p = BeamParameter(l, z, w=w_0)
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assert p.radius == z*(pi**2*w_0**4/(l**2*z**2) + 1)
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assert p.w == w_0*sqrt(l**2*z**2/(pi**2*w_0**4) + 1)
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assert p.w_0 == w_0
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assert p.divergence == l/(pi*w_0)
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assert p.gouy == atan2(z, pi*w_0**2/l)
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assert p.waist_approximation_limit == 2*l/pi
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p = BeamParameter(530e-9, 1, w=1e-3, n=2)
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assert streq(p.q, 1 + 3.77358490566038*I*pi)
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assert streq(N(p.z_r), Float(11.8550666173200))
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assert streq(N(p.w_0), Float(0.00100000000000000))
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