Closed-loop laser illumination algorithm using return photon counts

Lanlan Li; Lei Zhou; Ge Ren

doi:10.1364/AO.401524

Applied Optics
Vol. 59,
Issue 30,
pp. 9292-9302
(2020)
•https://doi.org/10.1364/AO.401524

Closed-loop laser illumination algorithm using return photon counts

Lanlan Li, Lei Zhou, and Ge Ren

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Lanlan Li, Lei Zhou, and Ge Ren, "Closed-loop laser illumination algorithm using return photon counts," Appl. Opt. 59, 9292-9302 (2020)

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Related Topics
Table of Contents Category
- Lasers, Optical Amplifiers, and Laser Optics
Optics & Photonics Topics
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The topics in this list come from the Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: June 29, 2020
- Revised Manuscript: September 17, 2020
- Manuscript Accepted: September 18, 2020
- Published: October 13, 2020

Abstract

Boresight and jitter are two fundamental pointing errors of laser illumination systems. A triangular-scanning algorithm is proposed to estimate the direction of the boresight via a three-step maximum boresight estimation and laser beam deflection procedure. On this basis, the closed-loop laser illumination (CLLI) for non-cooperative targets is realized, and the Cramer–Rao lower bounds (CRLB) performance in the lower limit of the pointing error is analyzed. Additionally, a Monte Carlo simulation system is built, and the performance of the CLLI algorithm is analyzed. The simulation results demonstrate that the triangular-scanning algorithm has good performance and can accurately estimate the direction of the boresight to achieve CLLI. Further study shows that the simulation results agree well with theoretical estimations and approximate the CRLB at the lower limit.

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$θ$	Equations
$- π / 4 < θ \leq π / 4$	${\hat{T}}_{x} = b_{3} \sqrt{1 - \frac{b_{3}^{2}}{4 b_{1}^{2}}}$ , ${\hat{T}}_{y} = b_{1} - b_{3} \frac{b_{3}}{2 b_{1}}$
$π / 4 < θ \leq 3 π / 4$	${\hat{T}}_{x} = b_{1} - b_{2} \frac{b_{2}}{2 b_{1}}$ , ${\hat{T}}_{y} = b_{2} \sqrt{1 - \frac{b_{2}^{2}}{4 b_{1}^{2}}}$
$3 π / 4 < θ \leq 5 π / 4$	${\hat{T}}_{x} = - b_{3} \sqrt{1 - \frac{b_{3}^{2}}{4 b_{1}^{2}}}$ , ${\hat{T}}_{y} = b_{1} - b_{3} \frac{b_{3}}{2 b_{1}}$
$5 π / 4 < θ \leq 7 π / 4$	${\hat{T}}_{x} = b_{1} - b_{2} \frac{b_{2}}{2 b_{1}}$ , ${\hat{T}}_{y} = b_{2} \sqrt{1 - \frac{b_{2}^{2}}{4 b_{1}^{2}}} - b_{3}$

	$ρ_{i q}$
$θ$	$X$ Axis	$Y$ Axis
$- π / 4 < θ \leq π / 4$	$ρ_{13} = 0.99$	$ρ_{13} = 0.49$	$\times$	$\times$
$π / 4 < θ \leq 3 π / 4$	$ρ_{12} = 0.53$	$ρ_{12} = - 0.99$	$\times$	$\times$
$3 π / 4 < θ \leq 5 π / 4$	$ρ_{13} = - 0.99$	$ρ_{13} = 0.51$	$\times$	$\times$
$5 π / 4 < θ \leq 7 π / 4$	$ρ_{12} = 0.53$	$ρ_{12} = 0.99$	$ρ_{13} = - 0.47$	$ρ_{23} = 0$

$θ$	Equations
$- π / 4 < θ \leq π / 4$	${\hat{T}}_{x} = b_{3} \sqrt{1 - \frac{b_{3}^{2}}{4 b_{1}^{2}}}$ , ${\hat{T}}_{y} = b_{1} - b_{3} \frac{b_{3}}{2 b_{1}}$
$π / 4 < θ \leq 3 π / 4$	${\hat{T}}_{x} = b_{1} - b_{2} \frac{b_{2}}{2 b_{1}}$ , ${\hat{T}}_{y} = b_{2} \sqrt{1 - \frac{b_{2}^{2}}{4 b_{1}^{2}}}$
$3 π / 4 < θ \leq 5 π / 4$	${\hat{T}}_{x} = - b_{3} \sqrt{1 - \frac{b_{3}^{2}}{4 b_{1}^{2}}}$ , ${\hat{T}}_{y} = b_{1} - b_{3} \frac{b_{3}}{2 b_{1}}$
$5 π / 4 < θ \leq 7 π / 4$	${\hat{T}}_{x} = b_{1} - b_{2} \frac{b_{2}}{2 b_{1}}$ , ${\hat{T}}_{y} = b_{2} \sqrt{1 - \frac{b_{2}^{2}}{4 b_{1}^{2}}} - b_{3}$

	$ρ_{i q}$
$θ$	$X$ Axis	$Y$ Axis
$- π / 4 < θ \leq π / 4$	$ρ_{13} = 0.99$	$ρ_{13} = 0.49$	$\times$	$\times$
$π / 4 < θ \leq 3 π / 4$	$ρ_{12} = 0.53$	$ρ_{12} = - 0.99$	$\times$	$\times$
$3 π / 4 < θ \leq 5 π / 4$	$ρ_{13} = - 0.99$	$ρ_{13} = 0.51$	$\times$	$\times$
$5 π / 4 < θ \leq 7 π / 4$	$ρ_{12} = 0.53$	$ρ_{12} = 0.99$	$ρ_{13} = - 0.47$	$ρ_{23} = 0$

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Applied Optics