The sample object
Scott Prahl
Aug 2021
[1]:
import iadpython
Object creation
The Sample object contains all the information needed to calculate the reflected and transmitted light for a 1D air-slide-sample-slide-air sandwich.
If glass slides are not present, then they can be set to have an index of refraction equal to 1 (that of the air).
The default object created by Sample() is absorbing-only, 1mm thick, with an index of refraction of 1.
[2]:
s = iadpython.Sample()
print(s)
Intrinsic Properties
albedo = 0.000
optical thickness = 1.000
anisotropy = 0.000
thickness = 1.000 mm
sample index = 1.000
top slide index = 1.000
bottom slide index= 1.000
cos(theta incident) = 1.000
quadrature points = 4
Derived quantities
mu_a = 1.000 1/mm
mu_s = 0.000 1/mm
mu_s*(1-g) = 0.000 1/mm
theta incident = 0.0°
cos(theta critical) = 0.0000
theta critical = 90.0°
The correct values can be used when the sample object is created.
[7]:
a = 0.8 # albedo
b = 2.0 # optical thickness
g = 0.9 # scattering anisotropy
d = 2.0 # physical thickness of the sample
s = iadpython.Sample(a=a,b=b,g=g,d=d)
print(s)
Intrinsic Properties
albedo = 0.800
optical thickness = 2.000
anisotropy = 0.900
thickness = 2.000 mm
sample index = 1.000
top slide index = 1.000
bottom slide index= 1.000
cos(theta incident) = 1.000
quadrature points = 4
Derived quantities
mu_a = 0.200 1/mm
mu_s = 0.800 1/mm
mu_s*(1-g) = 0.080 1/mm
theta incident = 0.0°
cos(theta critical) = 0.0000
theta critical = 90.0°
Or all the values can be changed.
[45]:
s = iadpython.Sample()
s.a = 0.99 # albedo
s.b = 2.0 # optical thickness
s.g = 0.9 # scattering anisotropy
s.d = 2.0 # physical thickness of the sample
s.quad_pts=8
s.n = 1.3
s.n_above = 1.532
s.n_below = 1.532
print(s)
Intrinsic Properties
albedo = 0.990
optical thickness = 2.000
anisotropy = 0.900
thickness = 2.000 mm
sample index = 1.300
top slide index = 1.532
bottom slide index= 1.532
cos(theta incident) = 1.000
quadrature points = 8
Derived quantities
mu_a = 0.010 1/mm
mu_s = 0.990 1/mm
mu_s*(1-g) = 0.099 1/mm
theta incident = 0.0°
cos(theta critical) = 0.6390
theta critical = 50.3°
Calculated values
The scattering and absorption coeffients easily obtained.
[27]:
print('The scattering coefficient is %.3f [1/mm]' % s.mu_s())
print('The absorption coefficient is %.3f [1/mm]' % s.mu_a())
print('The reduced scattering coefficient is %.3f [1/mm]' % s.mu_sp())
The scattering coefficient is 0.990 [1/mm]
The absorption coefficient is 0.010 [1/mm]
The reduced scattering coefficient is 0.099 [1/mm]
The quadrature angles and weight might also be found.
[34]:
s.update_quadrature()
print(" i mu weight 2*mu*w")
for i,mu in enumerate(s.nu):
two_mu_w = s.twonuw[i]
w = two_mu_w / 2 / mu
print("%2d %.5f %.5f %.5f" % (i, mu, w, two_mu_w))
i mu weight 2*mu*w
0 0.04859 0.12172 0.01183
1 0.23096 0.22820 0.10541
2 0.46890 0.22820 0.21401
3 0.65126 0.12172 0.15855
4 0.72644 0.06617 0.09614
5 0.82275 0.11651 0.19173
6 0.93627 0.09870 0.18482
7 1.00000 0.01876 0.03752
The reflection and transmission matrices for this sample for light from the bottom and light from the top are identical (and they should be because of the symmetry).
[44]:
R03, R30, T03, T30 = s.rt_matrices()
print("Reflected light for light incident from the top")
s.wrmatrix(R03)
print("Reflected light for light incident from the bottom")
s.wrmatrix(R30)
print("\n**************\nTransmitted light for light incident from the top")
s.wrmatrix(T03)
print("Transmitted light for light incident from the bottom")
s.wrmatrix(T30)
Reflected light for light incident from the top
cos_theta | 0.04436 0.21087 0.42810 0.59461 0.67095 0.78680 0.92334 1.00000 | flux
----------+-------------------------------------------------------------------------+---------
0.04436 | ***** 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 | 1.00000
0.21087 | 0.00000 11.38065 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 | 1.00000
0.42810 | 0.00000 0.00000 5.60563 0.00000 0.00000 0.00000 0.00000 0.00000 | 1.00000
0.59461 | 0.00000 0.00000 0.00000 7.56644 0.00000 0.00000 0.00000 0.00000 | 1.00000
0.67095 | 0.00000 0.00000 0.00000 0.00000 2.84086 0.35528 0.22764 0.15525 | 0.43869
0.78680 | 0.00000 0.00000 0.00000 0.00000 0.35528 0.66950 0.19884 0.14898 | 0.23591
0.92334 | 0.00000 0.00000 0.00000 0.00000 0.22764 0.19884 0.37339 0.12491 | 0.15567
1.00000 | 0.00000 0.00000 0.00000 0.00000 0.15525 0.14898 0.12491 1.22254 | 0.13200
----------+-------------------------------------------------------------------------+---------
flux | 1.00000 1.00000 1.00000 1.00000 0.43869 0.23591 0.15567 0.13200 | 0.23486
Reflected light for light incident from the bottom
cos_theta | 0.04436 0.21087 0.42810 0.59461 0.67095 0.78680 0.92334 1.00000 | flux
----------+-------------------------------------------------------------------------+---------
0.04436 | ***** 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 | 1.00000
0.21087 | 0.00000 11.38065 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 | 1.00000
0.42810 | 0.00000 0.00000 5.60563 0.00000 0.00000 0.00000 0.00000 0.00000 | 1.00000
0.59461 | 0.00000 0.00000 0.00000 7.56644 0.00000 0.00000 0.00000 0.00000 | 1.00000
0.67095 | 0.00000 0.00000 0.00000 0.00000 2.36601 0.43778 0.28194 0.19267 | 0.41976
0.78680 | 0.00000 0.00000 0.00000 0.00000 0.43778 0.55633 0.25015 0.18750 | 0.23275
0.92334 | 0.00000 0.00000 0.00000 0.00000 0.28194 0.25015 0.28414 0.18337 | 0.15585
1.00000 | 0.00000 0.00000 0.00000 0.00000 0.19267 0.18750 0.18337 0.64415 | 0.13120
----------+-------------------------------------------------------------------------+---------
flux | 1.00000 1.00000 1.00000 1.00000 0.41976 0.23275 0.15585 0.13120 | 0.23027
**************
Transmitted light for light incident from the top
cos_theta | 0.04436 0.21087 0.42810 0.59461 0.67095 0.78680 0.92334 1.00000 | flux
----------+-------------------------------------------------------------------------+---------
0.04436 | 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 | 0.00000
0.21087 | 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 | 0.00000
0.42810 | 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 | 0.00000
0.59461 | 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 | 0.00000
0.67095 | 0.00000 0.00000 0.00000 0.00000 1.82457 0.82078 0.51591 0.28526 | 0.50187
0.78680 | 0.00000 0.00000 0.00000 0.00000 0.79244 1.90450 0.77877 0.47102 | 0.69665
0.92334 | 0.00000 0.00000 0.00000 0.00000 0.49524 0.77295 2.32938 1.31302 | 0.79331
1.00000 | 0.00000 0.00000 0.00000 0.00000 0.27476 0.46781 1.31224 8.98364 | 0.82563
----------+-------------------------------------------------------------------------+---------
flux | 0.00000 0.00000 0.00000 0.00000 0.49062 0.69825 0.79677 0.82763 | 0.70714
Transmitted light for light incident from the bottom
cos_theta | 0.04436 0.21087 0.42810 0.59461 0.67095 0.78680 0.92334 1.00000 | flux
----------+-------------------------------------------------------------------------+---------
0.04436 | 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 | 0.00000
0.21087 | 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 | 0.00000
0.42810 | 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 | 0.00000
0.59461 | 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 | 0.00000
0.67095 | 0.00000 0.00000 0.00000 0.00000 1.82457 0.79244 0.49524 0.27476 | 0.49062
0.78680 | 0.00000 0.00000 0.00000 0.00000 0.82078 1.90450 0.77295 0.46781 | 0.69825
0.92334 | 0.00000 0.00000 0.00000 0.00000 0.51591 0.77877 2.32938 1.31224 | 0.79677
1.00000 | 0.00000 0.00000 0.00000 0.00000 0.28526 0.47102 1.31302 8.98364 | 0.82763
----------+-------------------------------------------------------------------------+---------
flux | 0.00000 0.00000 0.00000 0.00000 0.50187 0.69665 0.79331 0.82563 | 0.70714
Now, break symmetry and recalculate to see that that matrices for light
[53]:
s = iadpython.Sample()
s.a = 0.90 # albedo
s.b = 1.0 # optical thickness
s.g = 0.0 # scattering anisotropy
s.d = 2.0 # physical thickness of the sample
s.quad_pts=8
s.n = 1.33
s.n_above = 1.532
s.n_below = 1.0
print(s)
R03, R30, T03, T30 = s.rt_matrices()
print("Reflected light for light incident from the top")
s.wrmatrix(R03)
print("Reflected light for light incident from the bottom")
s.wrmatrix(R30)
print("\n**************\nTransmitted light for light incident from the top")
s.wrmatrix(T03)
print("Transmitted light for light incident from the bottom")
s.wrmatrix(T30)
Intrinsic Properties
albedo = 0.900
optical thickness = 1.000
anisotropy = 0.000
thickness = 2.000 mm
sample index = 1.330
top slide index = 1.532
bottom slide index= 1.000
cos(theta incident) = 1.000
quadrature points = 8
Derived quantities
mu_a = 0.050 1/mm
mu_s = 0.450 1/mm
mu_s*(1-g) = 0.450 1/mm
theta incident = 0.0°
cos(theta critical) = 0.6593
theta critical = 48.8°
Reflected light for light incident from the top
cos_theta | 0.04578 0.21758 0.44172 0.61352 0.68948 0.79881 0.92766 1.00000 | flux
----------+-------------------------------------------------------------------------+---------
0.04578 | 95.25256 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 | 1.00000
0.21758 | -0.00000 10.68963 -0.00000 -0.00000 0.00000 0.00000 0.00000 0.00000 | 1.00000
0.44172 | 0.00000 0.00000 5.26527 0.00000 0.00000 0.00000 0.00000 0.00000 | 1.00000
0.61352 | 0.00000 0.00000 0.00000 7.10701 0.00000 0.00000 0.00000 0.00000 | 1.00000
0.68948 | -0.00000 -0.00000 -0.00000 -0.00000 2.81749 0.35725 0.33522 0.32080 | 0.45065
0.79881 | -0.00000 -0.00000 -0.00000 -0.00000 0.35725 0.76189 0.37167 0.35576 | 0.29040
0.92766 | -0.00000 -0.00000 -0.00000 -0.00000 0.33522 0.37167 0.60179 0.33436 | 0.25258
1.00000 | -0.00000 -0.00000 -0.00000 -0.00000 0.32080 0.35576 0.33436 1.52141 | 0.24269
----------+-------------------------------------------------------------------------+---------
flux | 1.00000 1.00000 1.00000 1.00000 0.45065 0.29040 0.25258 0.24269 | 0.30226
Reflected light for light incident from the bottom
cos_theta | 0.04578 0.21758 0.44172 0.61352 0.68948 0.79881 0.92766 1.00000 | flux
----------+-------------------------------------------------------------------------+---------
0.04578 | 95.25256 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 | 1.00000
0.21758 | 0.00000 10.68963 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 | 1.00000
0.44172 | 0.00000 0.00000 5.26527 0.00000 0.00000 0.00000 0.00000 0.00000 | 1.00000
0.61352 | 0.00000 0.00000 0.00000 7.10701 0.00000 0.00000 0.00000 0.00000 | 1.00000
0.68948 | 0.00000 0.00000 0.00000 0.00000 2.39508 0.40407 0.37627 0.36010 | 0.42700
0.79881 | 0.00000 0.00000 0.00000 0.00000 0.40407 0.64436 0.40471 0.38740 | 0.27863
0.92766 | 0.00000 0.00000 0.00000 0.00000 0.37627 0.40471 0.50556 0.36130 | 0.24496
1.00000 | 0.00000 0.00000 0.00000 0.00000 0.36010 0.38740 0.36130 0.96565 | 0.23538
----------+-------------------------------------------------------------------------+---------
flux | 1.00000 1.00000 1.00000 1.00000 0.42700 0.27863 0.24496 0.23538 | 0.29018
**************
Transmitted light for light incident from the top
cos_theta | 0.04578 0.21758 0.44172 0.61352 0.68948 0.79881 0.92766 1.00000 | flux
----------+-------------------------------------------------------------------------+---------
0.04578 | 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 | 0.00000
0.21758 | 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 | 0.00000
0.44172 | 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 | 0.00000
0.61352 | 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 | 0.00000
0.68948 | -0.00000 -0.00000 -0.00000 -0.00000 1.66974 0.34862 0.33139 0.31913 | 0.32908
0.79881 | -0.00000 -0.00000 -0.00000 -0.00000 0.33805 1.58114 0.35835 0.34503 | 0.45828
0.92766 | -0.00000 -0.00000 -0.00000 -0.00000 0.31880 0.35551 1.85951 0.32490 | 0.50850
1.00000 | -0.00000 -0.00000 -0.00000 -0.00000 0.30702 0.34231 0.32491 8.36577 | 0.52794
----------+-------------------------------------------------------------------------+---------
flux | -0.00000 -0.00000 -0.00000 -0.00000 0.32371 0.45867 0.51040 0.52977 | 0.45832
Transmitted light for light incident from the bottom
cos_theta | 0.04578 0.21758 0.44172 0.61352 0.68948 0.79881 0.92766 1.00000 | flux
----------+-------------------------------------------------------------------------+---------
0.04578 | 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 | 0.00000
0.21758 | 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 | 0.00000
0.44172 | 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 | 0.00000
0.61352 | 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 | 0.00000
0.68948 | 0.00000 0.00000 0.00000 0.00000 1.66974 0.33805 0.31880 0.30702 | 0.32371
0.79881 | 0.00000 0.00000 0.00000 0.00000 0.34862 1.58114 0.35551 0.34231 | 0.45867
0.92766 | 0.00000 0.00000 0.00000 0.00000 0.33139 0.35835 1.85951 0.32491 | 0.51040
1.00000 | 0.00000 0.00000 0.00000 0.00000 0.31913 0.34503 0.32490 8.36577 | 0.52977
----------+-------------------------------------------------------------------------+---------
flux | 0.00000 0.00000 0.00000 0.00000 0.32908 0.45828 0.50850 0.52794 | 0.45832
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