-
Notifications
You must be signed in to change notification settings - Fork 1
/
ISMLMC.py
371 lines (306 loc) · 16.9 KB
/
ISMLMC.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
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
# ISMLMC.py
#====FOREWORD====#
"""
This software is a minimum working example of the Integrating Sphere
Monte Carlo method as described in the accompanying paper by Cook et al.
This program was written for Python 3.6.3.
This software is being provided "as is", without any express or implied warranty. In
particular, the authors do not make any representation or warranty of any kind concerning the
merchantability of this software or its fitness for any particular purpose.
"""
#========#
from math import *
from random import uniform
import MLMC
N = 100000 # number of photons in simulation
#====Sample Definition====#
n = [1.37,1.37,1.37] # refractive index of sample
g = [0.9,0,0.7] # anisotropy factor of sample
mu_a = [1,1,2] # absorption coefficient of sample in 1/cm
mu_s_ = [10,10,3] # reduced scattering coefficient of sample in 1/cm
t = [0.1,0.1,0.2] # thickness of sample in cm
mu_s = [0 for _ in range(len(mu_s_))]
mu_t = [0 for _ in range(len(mu_s_))]
for i in range(len(mu_s_)):
if g[i] == 1: mu_s[i] = mu_s_[i] # scattering coefficient of sample in 1/cm
else: mu_s[i] = mu_s_[i]/(1-g[i]) #
mu_t[i] = mu_a[i] + mu_s[i] # total interaction coefficient of sample in 1/cm
#========#
#====Sphere Parameters====#
R = False # boolean to determine if the reflection sphere is present or not
R_D = 8.382 # diameter of sphere in cm
R_pw = 0.85 # reflectance of reflection sphere
R_fs = 0.1 # sample port fraction of reflection sphere
R_fp = 0.05 # source port fraction of reflection sphere
R_fd = 0.05 # detector fraction of reflection sphere
R_f = R_fs + R_fp + R_fd # total port fraction of reflection sphere
R_angle = pi/10 # angle threshold for specular reflection if no Rsphere is present
specular_included = False # boolean to determine if specular reflection is included or not
T = False # boolean to determine if the transmission sphere is present or not
T_D = 8.382 # diameter of sphere in cm
T_pw = 0.85 # reflectance of transmission sphere
T_fs = 0.1 # sample port fraction of transmission sphere
T_fp = 0.05 # optional port fraction of transmission sphere
T_fd = 0.05 # detector fraction of transmission sphere
T_f = T_fs + T_fp + T_fd # total port fraction of transmission sphere
T_angle = pi/10 # angle threshold for direct transmission if no Tsphere is present
#========#
#====Physics Functions====#
# Snell's law
def multilayer_snell(ni, nt, mu_x, mu_y, mu_z):
ti = acos(abs(mu_z))
tt = asin((ni*sin(ti))/nt)
return mu_x*ni/nt, mu_y*ni/nt, (mu_z/abs(mu_z))*cos(tt)
# function used for determining reflection/transmission
def fresnel_snell(ni,nt,mu_z):
if abs(mu_z) > 0.99999: R = ((nt-ni)/(nt+ni))**2
else:
ti = acos(abs(mu_z))
# if ni*sin(ti)/nt >=1 then total internal reflection occurs, and thus R = 1
if (ni*sin(ti))/nt >=1.: R= 1.
else:
tt = asin((ni*sin(ti))/nt)
R = 0.5 * ( (sin(ti-tt)**2)/(sin(ti+tt)**2) + (tan(ti-tt)**2)/(tan(ti+tt)**2) )
return R
# determine if a photon incident on the sample begins to propagate or is reflected
def incident_reflection(mu_z, n, mu_s, layer):
# check if the incident layer is glass
if mu_s[layer] == 0.0:
n1 = 1.
n2 = n[layer]
n3 = n[layer+1] if mu_z > 0 else n[layer-1]
r1 = fresnel_snell(n1, n2, mu_z)
r2 = fresnel_snell(n2, n3, mu_z)
R = r1 + ((1-r1)**2)*r2/(1-r1*r2)
return uniform(0,1) < R
else: return uniform(0,1) < fresnel_snell(1., n[layer], mu_z)
# if a photon is inside a sphere, this function determines if it is re-incident on the sample
# returns True if re-incident and False if not
def reincidence(pw, fs, f):
return uniform(0,1) < (pw*fs)/(1-pw*(1-f))
#========#
def ISMLMC(N, n, g, t, mu_a, mu_s, mu_t, R, R_pw, R_fs, R_fp, R_fd, R_f, R_angle, \
specular_included, T, T_pw, T_fs, T_fp, T_fd, T_f, T_angle):
A = 0 # total number of absorbed photons
R_diffuse = 0 # total number of diffusely reflected/backscattered photons
R_specular = 0 # total number of specularly reflected photons
T_diffuse = 0 # total number of diffusely transmitted photons
T_direct = 0 # total number of directly transmitted photons
t_tot = sum(t);
for i in range(N):
w = 1 # initial weight of photon
x, y, z = 0, 0, 0 # initial position of photon
# determine inital direction for photon
if specular_included: mu_x, mu_y, mu_z = sqrt(1-0.99**2), 0, 0.99
else: mu_x, mu_y, mu_z = 0, 0, 1
# keep track of what sphere the photon is in
# r for reflection sphere, t for transmission sphere
sample_side = 'r'
while w > 0:
# determine if the photon is incidently reflected from the sample
layer = 0 if mu_z > 0 else len(n) - 1
incident_reflect = incident_reflection(mu_z, n, mu_s, layer)
# check if the photon was incidently reflected and where
if incident_reflect and sample_side == 'r':
# the photon is incidently reflected off of the 'top' surface
# check if a reflection sphere is present
if R: # reflection sphere present
# check to see if the photon leaves directly through the source port
if abs(mu_z) >= sqrt(1-R_fp):
# score the photon as specular reflection and stop propagating
R_specular += w
w = 0
break
# if the photon doesn't leave directly through the source port,
# check to see if it is re-incident on the sample
elif reincidence(R_pw,R_fs,R_f):
# photon is re-incident on the sample; sample a random angle of
# reincidence, reset its position, and continue propagating
mu_z = uniform(0,1)
phi = 2*pi*uniform(0,1)
mu_x = cos(phi)*sqrt(1-mu_z**2)
mu_y = sin(phi)*sqrt(1-mu_z**2)
x, y, z = 0, 0, 0
continue
else:
# the photon neither leaves through the source port, nor is re-incident
# score the photon as diffuse reflection and stop propagating
R_diffuse += w
w = 0
break
else: # there is no reflection sphere
# calculate an effective source port fraction from the angle threshold
fp = 0.5*(1-cos(2*R_angle))
# check if the photon leaves in a direction within
# this effective source port fraction
if abs(mu_z) >= sqrt(1-fp): # photon is within angle threshold, score as
R_specular += w # specular reflection and stop propagating
w = 0
break
else: # photon is NOT within angle threshold, since there is no sphere
# present, score it as diffuse reflection and stop propagating
R_diffuse += w
w = 0
break
elif incident_reflect and sample_side == 't':
# the photon is incidently reflected off of the 'bottom' surface
# check if a transmission sphere is present
if T: # transmission sphere present
# check to see if the photon leaves directly through the optional port
if abs(mu_z) >= sqrt(1-T_fp):
# score the photon as direct transmission and stop propagating
T_direct += w
w = 0
break
# if the photon doesn't leave directly through the optional port,
# check to see if it is re-incident on the sample
elif reincidence(T_pw,T_fs,T_f):
# photon is re-incident on the sample; sample a random angle of
# reincidence, reset its position, and continue propagating
mu_z = -1*uniform(0,1)
phi = 2*pi*uniform(0,1)
mu_x = cos(phi)*sqrt(1-mu_z**2)
mu_y = sin(phi)*sqrt(1-mu_z**2)
x, y, z = 0, 0, t_tot
continue
else:
# the photon neither leaves through the optional port, nor is re-incident
# score the photon as diffuse transmission and stop propagating
T_diffuse += w
w = 0
break
else: # there is no transmission sphere
# calculate an effective optional port fraction from the angle threshold
fp = 0.5*(1-cos(2*T_angle))
# check if the photon leaves in a direction within
# this effective optional port fraction
if abs(mu_z) >= sqrt(1-fp): # photon is within angle threshold, score as
T_direct += w # direct transmission and stop propagating
w = 0
break
else: # photon is NOT within angle threshold, since there is no sphere
# present, score it as diffuse transmission and stop propagating
T_diffuse += w
w = 0
break
else: # the photon is not incidently reflected and may begin propagating
# incident refraction by Snell's Law
mu_x, mu_y, mu_z = multilayer_snell(1., n[layer], mu_x, mu_y, mu_z)
# Monte Carlo Photon Transport
Absorbed, Reflected, Transmitted, mu_x, mu_y, mu_z = \
MLMC.MC(n, mu_a, mu_s, mu_t, g, t, w, x, y, z, mu_x, mu_y, mu_z)
# partial absorption
A += Absorbed
# check to see what happened to the photon
if Reflected: # the photon was reflected/backscattered
w = Reflected
sample_side = 'r'
# check if a reflection sphere is present
if R: # reflection sphere present
# check to see if the photon leaves directly through the source port
if abs(mu_z) >= sqrt(1-R_fp):
# score the photon as specular reflection and stop propagating
R_specular += w
w = 0
break
# if the photon doesn't leave directly through the
# source port, check to see if it is re-incident on the sample
elif reincidence(R_pw,R_fs,R_f):
# photon is re-incident on the sample; sample a random angle of
# reincidence, reset its position, and continue propagating
mu_z = uniform(0,1)
phi = 2*pi*uniform(0,1)
mu_x = cos(phi)*sqrt(1-mu_z**2)
mu_y = sin(phi)*sqrt(1-mu_z**2)
x, y, z = 0, 0, 0
continue
else: # the photon neither leaves through the source port, nor is
# re-incident, score the photon as diffuse reflection
# and stop propagating
R_diffuse += w
w = 0
break
else: # there is no reflection sphere
# calculate an effective source port fraction from the angle threshold
fp = 0.5*(1-cos(2*R_angle))
# check if the photon leaves in a direction within
# this effective source port fraction
if abs(mu_z) >= sqrt(1-fp):
# photon is within angle threshold, score as
# specular reflection and stop propagating
R_specular += w
w = 0
break
else: # photon is NOT within angle threshold, since there is no sphere
# present, score it as diffuse reflection and stop propagating
R_diffuse += w
w = 0
break
elif Transmitted: # the photon transmitted through the sample
w = Transmitted
sample_side = 't'
# check if a transmission sphere is present
if T: # transmission sphere present
# check to see if the photon leaves directly through the optional port
if abs(mu_z) >= sqrt(1-T_fp):
# score the photon as direct transmission and stop propagating
T_direct += w
w = 0
break
# if the photon doesn't leave directly through the
# optional port, check to see if it is re-incident on the sample
elif reincidence(T_pw,T_fs,T_f):
# photon is re-incident on the sample; sample a random angle of
# reincidence, reset its position, and continue propagating
mu_z = -1*uniform(0,1)
phi = 2*pi*uniform(0,1)
mu_x = cos(phi)*sqrt(1-mu_z**2)
mu_y = sin(phi)*sqrt(1-mu_z**2)
x, y, z = 0, 0, t_tot
continue
else: # the photon neither leaves through the optional port,
# nor is re-incident, score the photon as diffuse
# transmission and stop propagating
T_diffuse += w
w = 0
break
else: # there is no transmission sphere
# calculate an effective optional port
# fraction from the angle threshold
fp = 0.5*(1-cos(2*T_angle))
# check if the photon leaves in a direction within this
# effective optional port fraction
if abs(mu_z) >= sqrt(1-fp):
# photon is within angle threshold, score as direct
# transmission and stop propagating
T_direct += w
w = 0
break
else: # photon is NOT within angle threshold, since there is no sphere
# present, score it as diffuse transmission and stop propagating
T_diffuse += w
w = 0
break
else: # the photon was wholly absorbed
w = 0
break
# convert values to percents and return them
return A/N, R_diffuse/N, R_specular/N, T_diffuse/N, T_direct/N
#========#
if __name__ == '__main__':
A, R_diffuse, R_specular, T_diffuse, T_direct = ISMLMC(N, n, g, t, mu_a, mu_s, \
mu_t, R, R_pw, R_fs, R_fp, R_fd, R_f, R_angle, \
specular_included, T, T_pw, T_fs, T_fp, T_fd, T_f, T_angle)
# after all of the photons have propagated, round values and report results
sigfigs = len(str(N))
Absorptance = round(A, sigfigs)
diffuse_Reflectance = round(R_diffuse, sigfigs)
specular_Reflectance = round(R_specular, sigfigs)
diffuse_Transmittance = round(T_diffuse, sigfigs)
direct_Transmittance = round(T_direct, sigfigs)
total_Reflectance = diffuse_Reflectance + specular_Reflectance
total_Transmittance = diffuse_Transmittance + direct_Transmittance
print("""Absorptance: %f\nDiffuse Reflectance: %f\nSpecular Reflectance: %f\nDiffuse \
Transmittance: %f\nDirect Transmittance: %f\nTotal Reflectance: %f\nTotal Transmittance: \
%f""" %(Absorptance, diffuse_Reflectance, specular_Reflectance, diffuse_Transmittance, \
direct_Transmittance, total_Reflectance, total_Transmittance))