Simulation of anisoplanatic lucky look imaging and statistics through optical turbulence using numerical wave propagation

Michael A. Rucci; Michael A. Rucci; Russell C. Hardie; Richard K. Martin

doi:10.1364/AO.427716

Applied Optics
Vol. 60,
Issue 25,
pp. G19-G29
(2021)
•https://doi.org/10.1364/AO.427716

Simulation of anisoplanatic lucky look imaging and statistics through optical turbulence using numerical wave propagation

Michael A. Rucci, Russell C. Hardie, and Richard K. Martin

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Michael A. Rucci, Russell C. Hardie, and Richard K. Martin, "Simulation of anisoplanatic lucky look imaging and statistics through optical turbulence using numerical wave propagation," Appl. Opt. 60, G19-G29 (2021)

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About this Article
History
- Original Manuscript: April 13, 2021
- Revised Manuscript: May 25, 2021
- Manuscript Accepted: May 25, 2021
- Published: June 11, 2021

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Abstract

This paper investigates anisoplanatic numerical wave simulation in the context of lucky look imaging. We demonstrate that numerical wave propagation can produce root mean square (RMS) wavefront distributions and probability of lucky look (PLL) statistics that are consistent with Kolmogorov theory. However, the simulated RMS statistics are sensitive to the sampling parameters used in the propagation window. To address this, we propose and validate a new sample spacing rule based on the point source bandwidth used in the propagation and the level of atmospheric turbulence. We use the tuned simulator to parameterize the wavefront RMS probability density function as a function of turbulence strength. The fully parameterized RMS distribution model is used to provide a way to accurately predict the PLL for a range of turbulence strengths. We also propose and validate a new parametric average lucky look optical transfer function (OTF) model that could be used to aid in image restoration. Our OTF model blends the theoretical diffraction-limited OTF and the average turbulence short exposure OTF. Finally, we show simulated images for several anisoplanatic imaging scenarios that reveal the spatially varying nature of the RMS values impacting local image quality.

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Corrections

Michael A. Rucci, Russell C. Hardie, and Richard K. Martin, "Simulation of anisoplanatic lucky look imaging and statistics through optical turbulence using numerical wave propagation: erratum," Appl. Opt. 61, 5734-5734 (2022)
https://opg.optica.org/ao/abstract.cfm?uri=ao-61-19-5734

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Parameter	Value
Aperture	$D = 0.2034 m$
Focal length	$l = 1.2 m$
F-number	$f / # = 5.9$
Wavelength	$λ = 0.525 µ m$
Object distance	$L = 7$ km
Nyquist pixel spacing (focal plane)	$δ_{f} = 1.5488 µ m$
Nyquist pixel spacing (object plane)	$δ_{f} = 9.0344 µ m$

$C_{n}^{2} (m^{- 2 / 3})$	$0.284 \times 10^{- 15}$			$0.558 \times 10^{- 15}$			$0.901 \times 10^{- 15}$
$D / r_{0}$	2			3			4
Fried PLL [4]	$0.986 \pm 0.006$			$0.765 \pm 0.005$			$0.334 \pm 0.014$
$a_{g}$	3	4	5	3	4	5	3	4	5
$Δ x_{v}$ (mm)	3.789	3.789	3.789	3.789	3.789	3.789	3.789	3.789	3.789
$N$	256	256	256	256	256	256	256	256	256
PLL	0.992	0.991	0.956	0.815	0.811	0.551	0.434	0.409	0.126
$Δ x_{r_{0}}$ (mm)	5.686	4.325	3.490	5.531	4.235	3.431	5.385	4.148	3.374
$N_{r_{0}}$	256	256	328	256	256	352	256	256	364
PLL	0.988	0.987	0.988	0.746	0.763	0.767	0.301	0.333	0.340
Optimal $Δ \hat{x}$ (mm)	5.668	4.315	3.554	5.507	4.220	3.423	5.354	4.130	3.383
$N_{r_{0}}$	256	256	328	256	256	352	256	256	364
Optimal PLL	0.988	0.988	0.986	0.752	0.764	0.765	0.318	0.339	0.334

	$C_{n}^{2} \times 10^{- 16}$ ( $m^{- 2 / 3}$ )
Parameter	2.838	5.578	9.009
Theoretical $r_{0}$ (m)	0.102	0.068	0.051
Simulation $r_{0}$ (m)	0.104	0.071	0.053
Percent error	2.134	4.313	4.316
Theoretical $θ_{0}$ ( $µ$ rads)	4.568	3.045	2.284
Simulation $θ_{0}$ ( $µ$ rads)	4.746	3.347	2.560
Percent error	3.904	9.910	12.112
Theoretical RMS Z-tilt (pixels)	1.520	2.132	2.709
Simulation RMS Z-tilt (pixels)	1.524	2.105	2.777
Percent error (%)	0.207	−1.272	2.493

Parameter	Value
Aperture	$D = 0.2034 m$
Focal length	$l = 1.2 m$
F-number	$f / # = 5.9$
Wavelength	$λ = 0.525 µ m$
Object distance	$L = 7$ km
Nyquist pixel spacing (focal plane)	$δ_{f} = 1.5488 µ m$
Nyquist pixel spacing (object plane)	$δ_{f} = 9.0344 µ m$

$C_{n}^{2} (m^{- 2 / 3})$	$0.284 \times 10^{- 15}$			$0.558 \times 10^{- 15}$			$0.901 \times 10^{- 15}$
$D / r_{0}$	2			3			4
Fried PLL [4]	$0.986 \pm 0.006$			$0.765 \pm 0.005$			$0.334 \pm 0.014$
$a_{g}$	3	4	5	3	4	5	3	4	5
$Δ x_{v}$ (mm)	3.789	3.789	3.789	3.789	3.789	3.789	3.789	3.789	3.789
$N$	256	256	256	256	256	256	256	256	256
PLL	0.992	0.991	0.956	0.815	0.811	0.551	0.434	0.409	0.126
$Δ x_{r_{0}}$ (mm)	5.686	4.325	3.490	5.531	4.235	3.431	5.385	4.148	3.374
$N_{r_{0}}$	256	256	328	256	256	352	256	256	364
PLL	0.988	0.987	0.988	0.746	0.763	0.767	0.301	0.333	0.340
Optimal $Δ \hat{x}$ (mm)	5.668	4.315	3.554	5.507	4.220	3.423	5.354	4.130	3.383
$N_{r_{0}}$	256	256	328	256	256	352	256	256	364
Optimal PLL	0.988	0.988	0.986	0.752	0.764	0.765	0.318	0.339	0.334

Abstract

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Data Availability

Cited By

Figures (8)

Tables (3)

Equations (33)

Applied Optics