Page 130 - Chalcogenide Glasses for Infrared Optics

Characterization of Glass Pr operties 107

the intensity at each angle point. The seven sets of data points are
input to the computer program to calculate the deviation angle. The
increments are equal. The seven sets of data are expressed as seven
quadratic equations with intensity I and angle as the variables:

I = Aθ + Bθ+ C
2
A derivative of intensity with respect to angle is taken and equated
to zero for maximum intensity:

dI Aθ + θ = − B
0
dθ == 2 B or 2 A
With all angle differences the same, the seven equations are
added and subtracted to solve for the angle of maximum intensity.
The solution is a fraction of 1°. The deviation angle as shown in the
diagram is composed of the initial angle, in this case 91, added to
the fraction to become 91.4808. The value is then recorded in the
proper place in the computer program, so the refractive index is
calculated and recorded for that specific wavelength point. An
example of how the method was applied to measure the refractive
index for a new AMI glass, Amtir 4, is shown in Table 4.6. The ori-
entation is designated LD for left and down. Notice that NIR and
numbers 3 to 12 are together. Such data are combined with the
results from the three other orientations (LU, RD, and RU), aver-
8
aged, and then fit by Bill Thompson to a Sellmeier equation or to a
Hertzberger equation.

Mirror normal Prism Normal
75.72893 65.69428 Date Apex Angle NIR
Material Amtir 4 Number Amtir 4 #1 Apex Angle 10.03465 Orientation LD
Wavelength Ref. Angle P Normal A + D Angle Sin A + D 4/10/2006 Sin A Index
1 92.94464 65.69428 27.25036 10.03465 0.45788 0.174244 2.627811
1.064 92.81109 65.69428 27.11681 10.03465 0.455806 0.174244 2.615911
1.25 92.52313 65.69428 26.82885 10.03465 0.451327 0.174244 2.590205
1.5 92.29906 65.69428 26.60478 10.03465 0.447834 0.174244 2.570157
1.75 92.17473 65.69428 26.48045 10.03465 0.445892 0.174244 2.559016
2 92.09728 65.69428 26.403 10.03465 0.444682 0.174244 2.55207
65.69428 10.03465 0 0.174244 0
3 91.91464 65.69428 26.22036 10.03465 0.441825 0.174244 2.535671
4 91.86354 65.69428 26.16926 10.03465 0.441024 0.174244 2.531078
5 91.83104 65.69428 26.13676 10.03465 0.440515 0.174244 2.528156
6 91.80147 65.69428 26.10719 10.03465 0.440052 0.174244 2.525496
7 91.77626 65.69428 26.08198 10.03465 0.439657 0.174244 2.523229
8 91.74275 65.69428 26.04847 10.03465 0.439131 0.174244 2.520213
9 91.71588 65.69428 26.0216 10.03465 0.43871 0.174244 2.517795
10 91.67937 65.69428 25.98509 10.03465 0.438137 0.174244 2.514508
11 91.64149 65.69428 25.94721 10.03465 0.437543 0.174244 2.511097
12 91.59983 65.69428 25.90555 10.03465 0.436889 0.174244 2.507344
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TABLE 4.6 AMI infrared refractive index results for Amtir 4, wavelengths 1 to 12 µm,
prism orientation LD.