Application of the general image-quality equation to aberrated imagery

Samuel T. Thurman; James R. Fienup

doi:10.1364/AO.49.002132

Applied Optics
Vol. 49,
Issue 11,
pp. 2132-2142
(2010)
•https://doi.org/10.1364/AO.49.002132

Application of the general image-quality equation to aberrated imagery

Samuel T. Thurman and James R. Fienup

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Samuel T. Thurman and James R. Fienup, "Application of the general image-quality equation to aberrated imagery," Appl. Opt. 49, 2132-2142 (2010)

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Abstract

The regression analysis for the general image-quality equation (GIQE) [Appl. Opt. 36, 8322–8328 (1997)] was performed using image data from well-corrected optical systems. We conducted human-subject experiments to examine the use of the GIQE with aberrated imagery. A modified image-quality equation for aberrated imagery is presented based on analysis of the experimental results.

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GIQE Version	$c_{0}$	$c_{1}$	$c_{2}$	$c_{3}$	$c_{4}$
3.0	11.81	$- 3.32$	3.32	$- 1$	$- 1.48$
4.0 with $RER \geq 0.9$	10.251	$- 3.32$	1.559	$- 0.334$	$- 0.656$
4.0 with $RER < 0.9$	10.251	$- 3.16$	2.817	$- 0.334$	$- 0.656$

Term	Minimum	Mean	Maximum
GSD	$0.076 m$	$0.52 m$	$2.03 m$
RER	0.2	0.92	1.3
SNR	2	52.3	130
G	1	10.66	19
H	0.9	1.31	1.9

Parameter	Value
Altitude	$496 km$
Primary mirror diameter, D	$0.60 m$
Obscuration diameter	$0.23 m$
Focal length, f	$8.8 m$
F-number, $FN = f / D$	14.7
Detector-pixel pitch, p	$8.16 μm$
Spectral bandwidth	$0.4 - 1.1 μm$
Mean wavelength, $λ_{0}$	$0.644 μm$
Detector sampling ratio, $Q = λ_{0} FN / p$	1.19
Average number of photoelectrons per pixel, N	162,462
Detector read noise, σ	50 photoelectrons

Parameter	Before Processing	After Processing
GSD	$0.46 m$	$0.46 m$
RER	0.459	0.925
SNR	200	200
G	1	3.42
H	0.876	1.057
GIQE 3.0 NIIRS	5.21	5.93
GIQE 4.0 NIIRS	4.75	5.32

	$SNR = 200$		$SNR = 50$		$SNR = 10$		All SNRs
$Δ NIIRS$ Equation	$μ_{e}$	$σ_{e}$	$μ_{e}$	$σ_{e}$	$μ_{e}$	$σ_{e}$	$μ_{e}$	$σ_{e}$	$R^{2}$	Comment
$1.799 + \log_{2} (RER) - G / SNR - 1.48 H$	0.000	0.108	0.072	0.119	0.244	0.369	0.140	0.274	0.812	GIQE 3.0
$0.238 + \log_{2} (RER) - G / SNR$	0.000	0.110	0.023	0.102	0.154	0.221	0.083	0.173	0.925	GIQE 3.0 w/o H term
$0.884 + 0.951 \log_{2} (RER) - 0.344 G / SNR - 0.656 H$	0.000	0.096	0.085	0.127	0.291	0.366	0.168	0.271	0.815	GIQE 4.0
$0.192 + 0.951 \log_{2} (RER) - 0.344 G / SNR$	0.000	0.096	0.064	0.111	0.251	0.304	0.142	0.228	0.870	GIQE 4.0 w/o H term
$0.195 + \log_{2} (RER)$	0.000	0.100	0.070	0.118	0.246	0.291	0.141	0.220	0.878	$\log_{2} (RER)$ term only
$0.291 + \log_{2} (RER) - 2.229 G / SNR$	0.000	0.130	$- 0.035$	0.122	0.040	0.167	0.011	0.148	0.945	Fitted $G / SNR$ term

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Applied Optics