forked from Sterncat/opticspy
-
Notifications
You must be signed in to change notification settings - Fork 3
/
interferometer_seidel.py
183 lines (162 loc) · 4.88 KB
/
interferometer_seidel.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
import numpy as __np__
import matplotlib.pyplot as __plt__
import tools as __tools__
def twyman_green(A=0, B=0, C=0, D=0, E=0, F=0, G=0, lambda_1 = 632, PR = 1):
"""
Genertate Twyman_Green Interferogram based on Seidel aberration
=============================================
input
----------------------------------------------
coefficients in wavenumber(ex. D=8 means 8 max error
in defocus aberration)
A: Constant(piston)term
B: Tilt about the y axis
C: Tilt about the x axis
D: Reference sphere change, also called defocus
E: Sagittal astigmatism along the y axis
F: Sagittal coma along the y axis
G: Primary spherical aberration
lambda_1: wavelength in nanometer, default = 632nm
PR: pupil radius, default = 1
output
----------------------------------------------
Interferogram of aberration
"""
lambda_1 = lambda_1*(1e-9)
coefficients = [A,B,C,D,E,F,G]
r = __np__.linspace(-PR, PR, 400)
x, y = __np__.meshgrid(r,r)
rr = __np__.sqrt(x**2 + y**2)
wavemap = lambda n: n*lambda_1*2/PR
[A,B,C,D,E,F,G] = map(wavemap, [A,B,C,D,E,F,G])
OPD = A + \
B * x + \
C * y + \
D * (x**2 + y**2) + \
E * (x**2 + 3 * y**2) + \
F * y * (x**2 + y**2) + \
G * (x**2 + y**2)**2
ph = 2 * __np__.pi/lambda_1 * OPD
I1 = 1
I2 = 1
Ixy = I1 + I2 + 2 * __np__.sqrt(I1*I2) * __np__.cos(ph)
__tools__.makecircle(Ixy, r, PR)
#======================================================
fig = __plt__.figure(figsize=(9, 6), dpi=80)
__plt__.imshow(-Ixy, extent=[-PR,PR,-PR,PR])
__plt__.set_cmap('Greys')
label = ''
def labelgenerate(b):
label = 'Interferogram with '
count = 0
count_1 = 0
labellist = ['A: piston',
'B: Tilt about the y axis',
'C: Tilt about the x axis',
'D: Defocus',
'E: Sagittal astigmatism along the y axis',
'F: Sagittal coma along the y axis',
'G: Primary spherical aberration']
for i in b:
if i != 0:
label = label + str(i) + r'$\lambda$' + ' ' + labellist[count] + '\n'
else:
count_1 = count_1 + 1
count = count + 1
if count_1 == len(b):
label = label + ' ' + 'no aberration'
return label
label = labelgenerate(coefficients)
__plt__.xlabel(label,fontsize=16)
__plt__.title('Twyman Green Interferogram',fontsize=16)
fig.set_tight_layout(True)
__plt__.show()
################################################################
################################################################
def lateral_shear(A=0, B=0, C=0, D=0, E=0, S=0.1, lambda_1 = 632, PR = 1):
"""
Genertate Lateral_Shear Interferogram
=============================================
input
Lateral_Shear(A, B, C, D, E, S, lambda_1 = 632, PR = 1):
----------------------------------------------
coefficients in wavenumber(ex. D=8 means 8 max error
in defocus aberration)
A: Primary spherical aberration
B: Coma
C: Astigmatism
D: Defocus
E: x-Tilt
S: Shear distance(positive)
lambda_1: wavelength in nanometer, default = 632nm
PR: pupil radius, default = 1
output
----------------------------------------------
Lateral Shear interferogram of aberration
"""
lambda_1 = lambda_1*(10**-9)
r = __np__.linspace(-PR, PR, 400)
#r1 = __np__.linspace(-PR-S/2,PR+S/2)
x, y = __np__.meshgrid(r,r)
rr = __np__.sqrt(x**2 + y**2)
coefficients = [A*2,B*2,C*2,D*2,E*2]
def wavenumber(n):
return n*lambda_1*2/PR
[A,B,C,D,E] = map(wavenumber, [A,B,C,D,E])
OPD = 4 * A * (x**2 + y**2) * x * S + \
2 * B * x * y * S + \
C * x * S + \
2 * D * x * S + \
E * y
ph = 2 * __np__.pi / lambda_1 * OPD
I1 = 1
I2 = 1
Ixy = -(I1 + I2 + 2 * __np__.sqrt(I1 * I2) * __np__.cos(ph))
def doublecircle(a, PR, S):
x = int(400+200*S/PR)
y = 400
rec = __np__.zeros((y,x))
for i in range(400):
for j in range(400):
rec[j, i+100*S/PR] = a[j, i]
x1 = __np__.linspace(-PR-S/2, PR+S/2, x)
y1 = __np__.linspace(-PR, PR, y)
max = a.max()
min = a.min()
for i in range(x):
for j in range(y):
a1 = (x1[i] + S/2)**2 + (y1[j])**2
a2 = (x1[i] - S/2)**2 + (y1[j])**2
if a1 > PR**2 and a2 > PR**2:
rec[j,i] = max
elif (a1 > PR**2 and a2 < PR**2) or (a1 < PR**2 and a2 >PR**2):
rec[j,i] = min*2/10
return rec
Ixy_new = doublecircle(Ixy, PR, S)
fig = __plt__.figure(figsize=(9, 6), dpi=80)
__plt__.imshow(Ixy_new, extent=[-PR-S/2,PR+S/2,-PR,PR])
__plt__.set_cmap('Greys')
label = ''
def labelgenerate(b):
label = 'Shear Interferogram with ' + str(S) +' shearing in x' + '\n\n'
count = 0
count_1 = 0
labellist = ['A: Primary spherical aberration',
'B: Coma',
'C: Astigmatism',
'D: Defocus',
'E: x-Tilt']
for i in b:
if i != 0:
label = label + str(i/2) + r'$\lambda$' + ' ' + labellist[count] + '\n'
else:
count_1 = count_1 + 1
count = count + 1
if count_1 == len(b):
label = label + ' ' + 'no aberration'
return label
label = labelgenerate(coefficients)
__plt__.xlabel(label,fontsize=16)
__plt__.title('Lateral Shear Interferogram',fontsize=16)
fig.set_tight_layout(True)
__plt__.show()