Revised formulas to estimate diffraction effects in radiometry for
point and extended sources are derived. They are found to work as
well as or better than previous formulas. In some instances the
formulas can be written in closed form; otherwise their evaluation
entails performing simple integrations as indicated. Formulas have
been found for nonlimiting apertures, large defining apertures, and
pinhole apertures. Examples of all three types of application are
presented.
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Found by use of relation (38), for a
point source and for the extended source in the Fresnel approximation,
by use of relation (34), and as found in more-detailed numerical
approximations.
Table 3
Geometry Parameters and F1 for Nine Examples of Limiting Aperturesa
Results are presented as found for
relations (20), (39), (37), and numerical results carried
out in the Fresnel approximation.
Table 4
F1 for Two Apertures Found from
Simplified Formulas Discussed in the Text and Detailed Calculations
Using the Fresnel Approximation for Two Different Pinhole Apertures
R
λ (μm)
F
1
, R = 52 μm
F
1
, R = 101 μm
This Study
Fresnel
This Study
Fresnel
5
0.848
0.847
0.921
0.920
10
0.650
0.648
0.843
0.841
15
0.449
0.449
0.742
0.740
20
0.305
0.305
0.637
0.635
25
0.214
0.214
0.530
0.529
30
0.157
0.157
0.433
0.433
Tables (4)
Table 1
Parameters That Specify the Geometries Used in Ref.
8
Geometry
Values of These Parameters
rs (mm)
ds (mm)
R (mm)
rd (mm)
dd (mm)
1
0.5
500
3.5
1.25
500
2
0.5
500
7.5
1.25
500
3
0.5
850
3.5
1.60
400
4
0.5
500
3.5
1.25
850
5
0.5
650
3.5
1.25
700
6
0.5
800
3.5
1.25
550
7
0.5
950
3.5
1.25
400
Table 2
F2 for Geometries Indicated in
Table 1 at λ = 0.58 μma
Found by use of relation (38), for a
point source and for the extended source in the Fresnel approximation,
by use of relation (34), and as found in more-detailed numerical
approximations.
Table 3
Geometry Parameters and F1 for Nine Examples of Limiting Aperturesa
Results are presented as found for
relations (20), (39), (37), and numerical results carried
out in the Fresnel approximation.
Table 4
F1 for Two Apertures Found from
Simplified Formulas Discussed in the Text and Detailed Calculations
Using the Fresnel Approximation for Two Different Pinhole Apertures
R