Adjustment on the received optical power of a ground-based optical instrument by a corner cube retroreflector with a curved front-face

Zhou Hui; Li Song; Yuwei Chen

doi:10.1364/AO.412481

Applied Optics
Vol. 60,
Issue 2,
pp. 405-412
(2021)
•https://doi.org/10.1364/AO.412481

Adjustment on the received optical power of a ground-based optical instrument by a corner cube retroreflector with a curved front-face

Zhou Hui, Li Song, and Yuwei Chen

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Zhou Hui, Li Song, and Yuwei Chen, "Adjustment on the received optical power of a ground-based optical instrument by a corner cube retroreflector with a curved front-face," Appl. Opt. 60, 405-412 (2021)

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Abstract

The dihedral angle errors (DAEs) and flatness errors of a nonideal corner cube retroreflector (CCR) determine a ground-based optical instrument’s received optical power. The smaller tolerance of the dihedral angle with lower divergence is theoretically beneficial to improving the received optical power but could increase the difficulty in the fabrication and bring about a higher manufacturing cost. We propose a new method that is just dependent on the curvature radius of the front-face (CROF) of the CCR to compensate for the divergence of the output beam from the CCR caused by the DAEs. We build up a mathematical model of the received optical power based on the far-field diffraction pattern (FFDP) of the CCR and the layout of the optical instrument and investigate the effects of the DAEs and the CROF on the FFDP and the received optical power for both the coated and uncoated CCRs. Meanwhile, we present a fitting equation between the compensative CROF and the DAEs based on the principle of maximizing the received optical power. The results demonstrate that the compensative CROF has no dependence on whether the reflecting-faces of the CCR are coated or not and is inversely proportional to the absolute value of DAEs. The received optical power is promptly enhanced by utilizing the compensative CROF. Therefore, it is more feasible to improve the received optical power of the ground-based optical instrument by manipulating the CROF of the CCR rather than the DAEs.

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Corrections

Zhou Hui, Li Song, and Yuwei Chen, "Adjustment on the received optical power of a ground-based optical instrument by a corner cube retroreflector with a curved front-face: publisher’s note," Appl. Opt. 61, 7132-7132 (2022)
https://opg.optica.org/ao/abstract.cfm?uri=ao-61-24-7132

3 August 2022: Corrections were made to the body of the paper.

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Reflection Sequence	Linear Polarization		Circular Polarization
Reflection Sequence	Vertical	Horizontal	Left-Handed
123	$E_{s} = - 0.2150 + 0.9035 i$	$E_{s} = 0.2474 - 0.0854 i$	$E_{s} = - 0.0916 + 0.8138 i$
123	$E_{p} = - 0.2474 + 0.0854 i$	$E_{p} = - 0.7268 - 0.5782 i$	$E_{p} = 0.2340 - 0.4535 i$
132	$E_{s} = - 0.5988 - 0.2078 i$	$E_{s} = - 0.4690 - 0.5562 i$	$E_{s} = - 0.0302 - 0.4785 i$
132	$E_{p} = 0.0257 - 0.7271 i$	$E_{p} = - 0.3429 + 0.5331 i$	$E_{p} = - 0.3587 - 0.7566 i$
213	$E_{s} = - 0.5988 - 0.2078 i$	$E_{s} = - 0.0257 + 0.7271 i$	$E_{s} = - 0.9375 - 0.1651 i$
213	$E_{p} = 0.4690 + 0.5562 i$	$E_{p} = - 0.3429 + 0.5331 i$	$E_{p} = - 0.0453 + 0.1508 i$
231	$E_{s} = - 0.5988 - 0.2078 i$	$E_{s} = 0.0257 - 0.7271 i$	$E_{s} = 0.0907 - 0.1287 i$
231	$E_{p} = - 0.4690 - 0.5562 i$	$E_{p} = - 0.3429 + 0.5331 i$	$E_{p} = - 0.7086 - 0.6358 i$
312	$E_{s} = - 0.5988 - 0.2078 i$	$E_{s} = 0.4690 + 0.5562 i$	$E_{s} = - 0.8167 + 0.1847 i$
312	$E_{p} = - 0.0257 + 0.7271 i$	$E_{p} = - 0.3429 + 0.5331 i$	$E_{p} = - 0.3951 + 0.2716 i$
321	$E_{s} = - 0.2150 + 0.9035 i$	$E_{s} = - 0.2474 + 0.0854 i$	$E_{s} = - 0.2124 + 0.4640 i$
321	$E_{p} = 0.2474 - 0.0854 i$	$E_{p} = - 0.7268 - 0.5782 i$	$E_{p} = 0.5838 - 0.5743 i$

Coefficient Matrix	Elements
Coefficient Matrix	$a_{ij}$				$b_{ij}$				$c_{ij}$
$A_{1}$	10.06	8.48	0.02	0.01	0.90	0.98	4.44	6.34	−0.54	2.51	0.69	0.64
$A_{2}$	5.20	3.58	0.03	0.01	0.78	0.98	4.25	6.24	0.16	2.96	1.24	0.43
$A_{3}$	0.03	0.01	0.01	0.01	0.95	2.00	3.98	7.74	0.53	1.72	1.97	−3.12
$A_{4}$	0.05	0.02	0.01	0.01	0.86	2.00	2.95	6.19	−2.09	−0.97	0.34	−1.19

Reflection Sequence	Linear Polarization		Circular Polarization
Reflection Sequence	Vertical	Horizontal	Left-Handed
123	$E_{s} = - 0.2150 + 0.9035 i$	$E_{s} = 0.2474 - 0.0854 i$	$E_{s} = - 0.0916 + 0.8138 i$
123	$E_{p} = - 0.2474 + 0.0854 i$	$E_{p} = - 0.7268 - 0.5782 i$	$E_{p} = 0.2340 - 0.4535 i$
132	$E_{s} = - 0.5988 - 0.2078 i$	$E_{s} = - 0.4690 - 0.5562 i$	$E_{s} = - 0.0302 - 0.4785 i$
132	$E_{p} = 0.0257 - 0.7271 i$	$E_{p} = - 0.3429 + 0.5331 i$	$E_{p} = - 0.3587 - 0.7566 i$
213	$E_{s} = - 0.5988 - 0.2078 i$	$E_{s} = - 0.0257 + 0.7271 i$	$E_{s} = - 0.9375 - 0.1651 i$
213	$E_{p} = 0.4690 + 0.5562 i$	$E_{p} = - 0.3429 + 0.5331 i$	$E_{p} = - 0.0453 + 0.1508 i$
231	$E_{s} = - 0.5988 - 0.2078 i$	$E_{s} = 0.0257 - 0.7271 i$	$E_{s} = 0.0907 - 0.1287 i$
231	$E_{p} = - 0.4690 - 0.5562 i$	$E_{p} = - 0.3429 + 0.5331 i$	$E_{p} = - 0.7086 - 0.6358 i$
312	$E_{s} = - 0.5988 - 0.2078 i$	$E_{s} = 0.4690 + 0.5562 i$	$E_{s} = - 0.8167 + 0.1847 i$
312	$E_{p} = - 0.0257 + 0.7271 i$	$E_{p} = - 0.3429 + 0.5331 i$	$E_{p} = - 0.3951 + 0.2716 i$
321	$E_{s} = - 0.2150 + 0.9035 i$	$E_{s} = - 0.2474 + 0.0854 i$	$E_{s} = - 0.2124 + 0.4640 i$
321	$E_{p} = 0.2474 - 0.0854 i$	$E_{p} = - 0.7268 - 0.5782 i$	$E_{p} = 0.5838 - 0.5743 i$

Coefficient Matrix	Elements
Coefficient Matrix	$a_{ij}$				$b_{ij}$				$c_{ij}$
$A_{1}$	10.06	8.48	0.02	0.01	0.90	0.98	4.44	6.34	−0.54	2.51	0.69	0.64
$A_{2}$	5.20	3.58	0.03	0.01	0.78	0.98	4.25	6.24	0.16	2.96	1.24	0.43
$A_{3}$	0.03	0.01	0.01	0.01	0.95	2.00	3.98	7.74	0.53	1.72	1.97	−3.12
$A_{4}$	0.05	0.02	0.01	0.01	0.86	2.00	2.95	6.19	−2.09	−0.97	0.34	−1.19

Abstract

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Figures (8)

Tables (2)

Equations (10)

Applied Optics