Application of Apodization to Increase Two-Point Resolution by the Sparrow Criterion. II. Incoherent Illumination

Richard Barakat; Elgie Levin

doi:10.1364/JOSA.53.000274

Journal of the Optical Society of America
Vol. 53,
Issue 2,
pp. 274-282
(1963)
•https://doi.org/10.1364/JOSA.53.000274

Application of Apodization to Increase Two-Point Resolution by the Sparrow Criterion. II. Incoherent Illumination

Richard Barakat and Elgie Levin

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Richard Barakat and Elgie Levin, "Application of Apodization to Increase Two-Point Resolution by the Sparrow Criterion. II. Incoherent Illumination," J. Opt. Soc. Am. 53, 274-282 (1963)

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Abstract

An apodization scheme (due to Luneberg) for increasing the incoherent Sparrow resolution limit is formulated via the calculus of variations. The determination of the required pupil function (amplitude distribution over the exit pupil) necessitates the solution of an homogeneous Fredholm integral equation. The four pupil-function parameters are evaluated by solving a set of four simultaneous nonlinear equations. Both slit and circular apertures are studied in detail.

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Equations (80)

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δ₀	T₀	T₁	T₂	T₃
2.976	1.41	0	0	0
2.90	1.42	−0.260	−1.22	1.41
2.80	1.46	−0.613	−2.72	3.01
2.60	1.67	−1.62	−6.36	6.24
2.40	2.10	−2.80	−9.64	8.30
2.20	2.80	−4.06	−12.16	9.10
2.00	3.82	−5.47	−14.13	9.10

δ₀	T₀	T₁	T₂	T₃
2.606	0.707	0	0	0
2.50	0.711	−0.086	0.327	−0.311
2.40	0.726	−0.196	0.700	−0.624
2.30	0.753	−0.338	1.13	−0.938
2.20	0.798	−0.511	1.59	−1.23
2.10	0.865	−0.713	2.06	−1.48
2.00	0.958	−0.940	2.51	−1.68
1.90	1.08	−1.19	2.94	−1.82
1.80	1.24	−1.46	3.34	−1.90
1.60	1.70	−2.10	4.06	−1.96
1.40	2.42	−2.95	4.77	−1.93
1.20	3.54	−4.17	5.55	−1.85

δ₀	T₀	T₁	T₂	T₃
2.976	1.41	0	0	0
2.90	1.42	−0.260	−1.22	1.41
2.80	1.46	−0.613	−2.72	3.01
2.60	1.67	−1.62	−6.36	6.24
2.40	2.10	−2.80	−9.64	8.30
2.20	2.80	−4.06	−12.16	9.10
2.00	3.82	−5.47	−14.13	9.10

δ₀	T₀	T₁	T₂	T₃
2.606	0.707	0	0	0
2.50	0.711	−0.086	0.327	−0.311
2.40	0.726	−0.196	0.700	−0.624
2.30	0.753	−0.338	1.13	−0.938
2.20	0.798	−0.511	1.59	−1.23
2.10	0.865	−0.713	2.06	−1.48
2.00	0.958	−0.940	2.51	−1.68
1.90	1.08	−1.19	2.94	−1.82
1.80	1.24	−1.46	3.34	−1.90
1.60	1.70	−2.10	4.06	−1.96
1.40	2.42	−2.95	4.77	−1.93
1.20	3.54	−4.17	5.55	−1.85

Abstract

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Tables (2)

Equations (80)

Journal of the Optical Society of America