Performance measurement techniques for simple Fourier transform lenses

David Casasent; Thanh Luu

doi:10.1364/AO.17.002973

Applied Optics
Vol. 17,
Issue 18,
pp. 2973-2980
(1978)
•https://doi.org/10.1364/AO.17.002973

Performance measurement techniques for simple Fourier transform lenses

David Casasent and Thanh Luu

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David Casasent and Thanh Luu, "Performance measurement techniques for simple Fourier transform lenses," Appl. Opt. 17, 2973-2980 (1978)

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Abstract

The use of simple off-the-shelf lenses as Fourier transform elements in an optical computer is considered. Several schemes for measuring those lens parameters that determine the performance of such simple lenses as Fourier transform elements are provided with emphasis on lens phase errors. It is assumed that no lens design data are available for the lens under test.

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Displacement along x Axis in mm
Displacement along y Axis in mm		−40	−30	−20	−10	+10	+20	+30	+40
	+30			−0.42	−0.26	−0.14	−0.36
	+20	−0.68	−0.4	−0.18	−0.08	−0.10	−0.24	−0.5	−0.8
	+10			−0.26	−0.12	−0.08	−0.2
	0	−0.74	−0.46	−0.24	−0.06	−0.06	−0.18	−0.36	−0.68
	−10		−0.22	−0.22	−0.08	−0.08	−0.28
	−20	+0.76	+0.46	+0.26	+0.10	−0.24	−0.44	−0.6	−0.72
	−30			−0.36	−0.16	−0.18	−0.32

Fourier Plane Position of Microscope (mm)	Input Plane Position of Slits in mm											Corresponding Input Spatial Frequency (cy/mm)
Fourier Plane Position of Microscope (mm)	−25	−20	−15	−10	−5	0	5	10	15	20	25	Corresponding Input Spatial Frequency (cy/mm)
+25	−0.32	−0.18	−0.01	0.13	0.28	0.36	0.19	0.07	−0.05	−0.16	−0.30	51.8
+20	−0.29	−0.14	0	0.09	0.23	0.27	0.13	0.07	−0.02	−0.10	−0.24	41.4
+15	−0.17	−0.09	0	0.06	0.16	0.16	0.08	0.04	−0.04	0.08	0.16	31.1
+10	−0.17	−0.07	−0.02	0.08	0.08	0.10	0.10	0.04	0	−0.04	0.10	20.7
+ 5	−0.08	−0.04	0.02	0.02	0.08	0.06	0.04	0.02	−0.02	−0.04	−0.08	10.4
0	−0.06	−0.02	0	0.02	0.04	0.04	0.04	0	0	−0.04	−0.06	0
− 5	−0.07	−0.03	0.01	0.04	0.10	0.08	0.04	−0.01	−0.03	−0.05	−0.11	−10.4
−10	−0.09	−0.05	0.03	0.03	0.11	0.14	0.09	0.03	−0.03	−0.09	−0.18	−20.7
−15	−0.15	−0.06	0	0.08	0.13	0.21	0.15	0.06	−0.02	−0.15	−0.25	−31.1
−20	−0.22	−0.08	0	0.11	0.21	0.32	0.19	0.09	−0.08	−0.20	−0.35	−41.4
−25	−0.32	−0.13	0.02	0.16	0.31	0.43	0.27	0.10	−0.09	−0.25	−0.50	−51.8

Displacement along x Axis in mm
Displacement along y Axis in mm		−40	−30	−20	−10	+10	+20	+30	+40
	+30			−0.42	−0.26	−0.14	−0.36
	+20	−0.68	−0.4	−0.18	−0.08	−0.10	−0.24	−0.5	−0.8
	+10			−0.26	−0.12	−0.08	−0.2
	0	−0.74	−0.46	−0.24	−0.06	−0.06	−0.18	−0.36	−0.68
	−10		−0.22	−0.22	−0.08	−0.08	−0.28
	−20	+0.76	+0.46	+0.26	+0.10	−0.24	−0.44	−0.6	−0.72
	−30			−0.36	−0.16	−0.18	−0.32

Fourier Plane Position of Microscope (mm)	Input Plane Position of Slits in mm											Corresponding Input Spatial Frequency (cy/mm)
Fourier Plane Position of Microscope (mm)	−25	−20	−15	−10	−5	0	5	10	15	20	25	Corresponding Input Spatial Frequency (cy/mm)
+25	−0.32	−0.18	−0.01	0.13	0.28	0.36	0.19	0.07	−0.05	−0.16	−0.30	51.8
+20	−0.29	−0.14	0	0.09	0.23	0.27	0.13	0.07	−0.02	−0.10	−0.24	41.4
+15	−0.17	−0.09	0	0.06	0.16	0.16	0.08	0.04	−0.04	0.08	0.16	31.1
+10	−0.17	−0.07	−0.02	0.08	0.08	0.10	0.10	0.04	0	−0.04	0.10	20.7
+ 5	−0.08	−0.04	0.02	0.02	0.08	0.06	0.04	0.02	−0.02	−0.04	−0.08	10.4
0	−0.06	−0.02	0	0.02	0.04	0.04	0.04	0	0	−0.04	−0.06	0
− 5	−0.07	−0.03	0.01	0.04	0.10	0.08	0.04	−0.01	−0.03	−0.05	−0.11	−10.4
−10	−0.09	−0.05	0.03	0.03	0.11	0.14	0.09	0.03	−0.03	−0.09	−0.18	−20.7
−15	−0.15	−0.06	0	0.08	0.13	0.21	0.15	0.06	−0.02	−0.15	−0.25	−31.1
−20	−0.22	−0.08	0	0.11	0.21	0.32	0.19	0.09	−0.08	−0.20	−0.35	−41.4
−25	−0.32	−0.13	0.02	0.16	0.31	0.43	0.27	0.10	−0.09	−0.25	−0.50	−51.8

Abstract

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Tables (2)

Equations (11)

Applied Optics