Image reconstructions with active illumination in strong-turbulence scenarios with single-frame blind deconvolution approaches

R. Holmes; V. S. Rao Gudimetla

doi:10.1364/AO.58.007823

Applied Optics
Vol. 58,
Issue 28,
pp. 7823-7835
(2019)
•https://doi.org/10.1364/AO.58.007823

Image reconstructions with active illumination in strong-turbulence scenarios with single-frame blind deconvolution approaches

R. Holmes and V. S. Rao Gudimetla

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R. Holmes and V. S. Rao Gudimetla, "Image reconstructions with active illumination in strong-turbulence scenarios with single-frame blind deconvolution approaches," Appl. Opt. 58, 7823-7835 (2019)

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Table of Contents Category
- Imaging Systems, Image Processing, and Displays
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About this Article
History
- Original Manuscript: June 27, 2019
- Revised Manuscript: August 21, 2019
- Manuscript Accepted: August 23, 2019
- Published: September 27, 2019

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Abstract

Image formation over long horizontal or slant paths is of interest in surveillance and remote sensing. Image reconstructions of isolated objects are presented using active illumination in long-path, strong-turbulence conditions using a wave-optics simulation to produce the images. Fast-running reconstruction algorithms are used, including a novel single-frame blind iterative deconvolution algorithm and a generalized expectation maximization algorithm. Significant improvements in image quality and image recognizability can be found for spherical-wave Rytov variances up to 0.4 and for up to 10 atmospheric coherence lengths across the aperture in uniform-turbulence scenarios over a 30 km range. For these conditions, the isoplanatic patch angle is comparable to the diffraction angle, and there are 20 or more isoplanatic patches across the objects considered. The results are compared with idealized atmospheric phase correction with an incoherent beacon. Several image quality metrics are considered. Results for strongest turbulence are explained in terms of a local average of the point spread function and the central limit theorem for cases in which there are many isoplanatic patches across the object.

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Step #	Description
1	Create initial estimate of short-exposure point spread function (PSF) based on estimate of $r_{0}$ , also noise and speckle PSDs, ${PSD}_{noise}$ and ${PSD}_{speckle}$ , respectively
2	Begin single-frame iterative deconvolution through step 15
3	Transform raw measured object and PSF to Fourier domain
4	Construct Wiener filter in Fourier domain: $FT {(PSF)}^{*} / [{\| FT (PSF) \|}^{2} + PSDNoise + PSDSpeckle]$
5	Apply Wiener filter to Fourier transform of object
6	Transform object back to spatial domain
7	Apply support and positivity constraint
8	Erode support based on a threshold of near-zero values of estimated object
9	Dilate support based on sharp gradients in intensity near edge of constraint
10	Re-estimate PSF from $FT (Image 0) / {FT [Image (n)] + PSDNoise}$ at iteration $n$
11	Estimate convergence based on fractional change of object estimate from previous step
12	If fractional change is smallest yet, save image
13	Add in a fraction of the previous image to the current image
14	Recenter working image using centroid
15	Go back to step 3 for up to 50 iterations
16	Sum (incoherently) up to $N$ images ( $N = 20$ in this effort)

Parameter	Rationale
Eq. (1), $λ / (2.5 r_{0})$	Approximate short exposure spot width
Eq. (2), 0.3 STDEV	De-weights shot noise in favor of sensor noise
After Eq. (2), 3%	Provides a reasonable dynamic range for the image in the presence of noise
Eq. (3), $1.5 λ / D_{ap}$	Sets angular scale above which speckle noise is dominant
Eq. (4), 3%	Provides a reasonable dynamic range for the image in the presence of noise
Eq. (8), 0.001	Erodes object support only where intensity is very small
Eq. (9), 0.5	Dilates object support only where intensity is very large near edge
After Eq. (9), every 10 iterations	Avoids excessive random dilation
After Eq. (11c), $0.2 ({0.95}^{n})$	Gives relatively large mixing of current and prior PSF initially, almost no mixing at 50 iterations
Before Eq. (12), termination $metric = 10^{- 3}$	Typical termination metric for such algorithms
Before Eq. (12), 50 iterations	More than 50 usually made little difference

Parameter	Value
Propagation grid size	$1024 \times 1024$
Grid point spacing (mm)	4
Path length (km)	30
# Phase screens	10
Wavelength (nm)	1064
# time steps	up to 20
Object(s)	letter “A”, others
Type of illumination	temporally coherent
Aperture diameter (m)	1.0
Turbulence strength	$σ_{R}^{2} = 10^{- 4} - 1.3$
Turbulence type	Kolmogorov, 5-meter outer scale
Focal plane pixel field of view	133 nrad

Case	$σ_{R}^{2}$	$r_{0}$ (m)	$θ_{0}$ (μrad)	$D_{ap} / r_{0}$	$θ_{0} / (λ / D_{ap})$	$(D_{obj} / R) / θ_{0}$
1	$10^{- 4}$	15.2	161	0.066	151	0.167
2	0.01	0.960	10.2	1.04	9.57	2.58
3	0.1	0.241	2.56	4.14	2.4	10.3
4	0.2	0.159	1.69	6.28	1.59	15.6
5	0.3	0.125	1.32	8.00	1.24	20.1
6	0.4	0.105	1.11	9.51	1.05	23.9
7	0.6	0.083	0.873	12.1	0.820	30.4
8	1.0	0.061	0.643	16.5	0.604	41.4
9	1.3	0.052	0.549	19.3	0.516	48.6

Parameter	Notation	Value	Units
Laser peak power	$P_{L}$	0.5	MW
Laser pulse duration	$Δ t$	10	μs
Laser wavelength	$λ$	1064	nm
Planck’s $constant \times c$	$h c$	$1.98 \times 10^{- 19}$	J-m
Spot FWHM on object	$D_{spt}$	1–10	m
Pixel width on object	$Δ θ_{obj}$	1.6	cm
Range	$R$	30	km
Optical transmission	$T_{opt}$	0.25	N/A
Atm. transmission	$T_{atm}$	0.25	N/A
Object reflectivity	${Re}_{obj}$	0.2	N/A
Quantum efficiency	QE	0.7	N/A
Aperture diameter	$D_{ap}$	1.0	m
Read noise	$σ_{read}$	30	pe

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Applied Optics