Comparison of models for multiplexed holograms

Raymond K. Kostuk

doi:10.1364/AO.28.000771

Applied Optics
Vol. 28,
Issue 4,
pp. 771-777
(1989)
•https://doi.org/10.1364/AO.28.000771

Comparison of models for multiplexed holograms

Raymond K. Kostuk

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Raymond K. Kostuk, "Comparison of models for multiplexed holograms," Appl. Opt. 28, 771-777 (1989)

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Abstract

Three models for multiplexed transmission gratings are compared. The underlying assumptions for each model are changed to allow an examination of the effects of generating higher diffraction orders and coupling between diffraction orders on the efficiency and SNR of these gratings. The influence of grating thickness, grating number, and object beam angle is also examined.

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Model	Assumptions
A	Linear response of recoding material Coupling between diffraction orders through intermodulation gratings Coupling between reconstruction beam and intermodulation grating One diffraction order from each grating Phase grating TE reconstruction beam polarization
B	Linear response of recording material Coupling between reconstruction beam and intermodulation grating One diffraction order from each grating Phase grating TE reconstruction beam polarization
C	Linear response of recording material Coupling between reconstruction beam and intermodulation grating Five diffraction orders from each grating Phase grating TE reconstruction beam polarization

B	Model A η_T;SNR	Model B η_T;SNR	Model C η_T;SNR
1	67.5;8.4	82.8;8.4	71.2;2.6
2	80.8;16.7	90.5;16.2	83.1;4.9
5	91.7;42.0	95.5;39.6	92.3;12.7
10	95.4;83.1	97.5;70.9	95.6;25.6
15	96.6;113.6	98.2;106	96.9;35.5
20	97.4;150	98.6;141	97.6;47.4

Primary orders	d (μm); n₁; Δθ 15; 0.005; 0.1°	d (μm); n₁; Δθ 15; 0.005; 1.0°	d (μm); n₁; Δθ 30; 0.0026; 0.10	d (μm); n₁; Δθ 60; 0.0013; 0.10
+2	1.2 × 10⁻⁵	1.3 × 10⁻⁵	8.0 × 10⁻⁷	3 × 10⁻⁶
+1	9.2 × 10⁻²	9.5 × 10⁻²	9.3 × 10⁻²	9.2 × 10⁻²
−1	1.4 × 10⁻⁴	1.5 × 10⁻⁴	8.0 × 10⁻⁶	3.5 × 10⁻⁵
−2	6.1 × 10⁻⁹	6.4 × 10⁻⁹	1.8 × 10⁻¹¹	3.1 × 10⁻¹⁰
Intermodulation Orders

+2	7.7 × 10⁻⁷	2.5 × 10⁻¹⁰	8.6 × 10⁻⁷	8.7 × 10⁻⁷
+1	9.1 × 10⁻⁴	2.6 × 10⁻⁵	9.1 × 10⁻⁴	9.1 × 10⁻⁴
−1	9.0 × 10⁻⁴	2.8 × 10⁻⁵	9.1 × 10⁻⁴	9.1 × 10⁻⁴
−2	7.7 × 10⁻⁷	3.1 × 10⁻¹⁰	8.6 × 10⁻⁷	8.7 × 10⁻⁷

Model	Assumptions
A	Linear response of recoding material Coupling between diffraction orders through intermodulation gratings Coupling between reconstruction beam and intermodulation grating One diffraction order from each grating Phase grating TE reconstruction beam polarization
B	Linear response of recording material Coupling between reconstruction beam and intermodulation grating One diffraction order from each grating Phase grating TE reconstruction beam polarization
C	Linear response of recording material Coupling between reconstruction beam and intermodulation grating Five diffraction orders from each grating Phase grating TE reconstruction beam polarization

B	Model A η_T;SNR	Model B η_T;SNR	Model C η_T;SNR
1	67.5;8.4	82.8;8.4	71.2;2.6
2	80.8;16.7	90.5;16.2	83.1;4.9
5	91.7;42.0	95.5;39.6	92.3;12.7
10	95.4;83.1	97.5;70.9	95.6;25.6
15	96.6;113.6	98.2;106	96.9;35.5
20	97.4;150	98.6;141	97.6;47.4

Abstract

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Applied Optics