Comprehensive polychromatic integral diffraction efficiency sensitivity to tilt error for multilayer diffractive optical elements with oblique incidence

Liangliang Yang; Chenglin Liu; Renjia Guo; Yongbing Zhao

doi:10.1364/AO.382110

Applied Optics
Vol. 59,
Issue 2,
pp. 508-514
(2020)
•https://doi.org/10.1364/AO.382110

Comprehensive polychromatic integral diffraction efficiency sensitivity to tilt error for multilayer diffractive optical elements with oblique incidence

Liangliang Yang, Chenglin Liu, Renjia Guo, and Yongbing Zhao

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Liangliang Yang, Chenglin Liu, Renjia Guo, and Yongbing Zhao, "Comprehensive polychromatic integral diffraction efficiency sensitivity to tilt error for multilayer diffractive optical elements with oblique incidence," Appl. Opt. 59, 508-514 (2020)

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Abstract

Oblique incidence is the general working state for multilayer diffractive optical elements (MLDOEs) in an imaging optical system. The polychromatic integral diffraction efficiency (PIDE) is very sensitive to the incident angle. Therefore, it is necessary to analyze the effect of tilt error on diffraction efficiency/PIDE with oblique incidence. The theoretical model of the relationship between the diffraction efficiency and tilt error with oblique incidence is presented, and the effect of tilt error on diffraction efficiency/PIDE is analyzed. The analysis model of comprehensive PIDE for a certain range of incident angles and the tilt error for MLDOEs is established. The simulation results showed that the comprehensive PIDE is sensitive to tilt angle with oblique incidence, and the tolerance of the tilt error angle can be determined by the comprehensive PIDE. The tilt error tolerance is furthermore investigated with decenter error based on the maximum of comprehensive PIDE. The method and results can be used to guide the tolerance formulation of tilt error for MLDOEs in hybrid optical systems.

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	Tilt Error/°
Wavelength/µm	0	5	10	20
0.435	100%	99.51%	91.12%	14.42%
0.598	100%	99.69%	95.21%	41.73%
0.4–0.7	99.25%	98.88%	93.25%	33.14%

	Tilt Error/°
$θ /^{\circ}$	0	5	10	15	20
0	99.25%	98.88%	93.25%	71.66%	33.14%
5	99.21%	94.08%	67.64%	24.90%	2.98%
10	98.59%	86.51%	37.55%	3.14%	2.09%
15	95.63%	78.70%	15.10%	3.11%	1.90%
20	86.58%	72.43%	3.99%	2.05%	0.63%

	$θ_{max} /^{\circ}$
${\bar{η}}_{c} / %$	0	5	10	15	20
98	6.74°	3.96°	2.92°	2.61°	2.56°
95	9.16°	6.10°	4.51°	3.79°	3.51°
90	11.17°	7.98°	6.03°	4.99°	4.55°
85	12.51°	9.27°	7.13°	5.88°	5.17°

	$θ /^{\circ}$
	0		10
PIDE/%	500 µm	200 µm	500 µm	200 µm
98	1.26	0.63	0.62	0.25
95	5.16	2.58	2.56	1.03
90	9.27	4.64	4.64	1.86
85	12.50	6.25	6.25	2.51

	Tilt Error/°
Wavelength/µm	0	5	10	20
0.435	100%	99.51%	91.12%	14.42%
0.598	100%	99.69%	95.21%	41.73%
0.4–0.7	99.25%	98.88%	93.25%	33.14%

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Applied Optics