Deferred slanted-edge analysis: a unified approach to spatial frequency response measurement on distorted images and color filter array subsets

F. van den Bergh

doi:10.1364/JOSAA.35.000442

Journal of the Optical Society of America A
Vol. 35,
Issue 3,
pp. 442-451
(2018)
•https://doi.org/10.1364/JOSAA.35.000442

Deferred slanted-edge analysis: a unified approach to spatial frequency response measurement on distorted images and color filter array subsets

F. van den Bergh

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F. van den Bergh, "Deferred slanted-edge analysis: a unified approach to spatial frequency response measurement on distorted images and color filter array subsets," J. Opt. Soc. Am. A 35, 442-451 (2018)

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Abstract

The slanted-edge method of spatial frequency response (SFR) measurement is usually applied to grayscale images under the assumption that any distortion of the expected straight edge is negligible. By decoupling the edge orientation and position estimation step from the edge spread function construction step, it is shown in this paper that the slanted-edge method can be extended to allow it to be applied to images suffering from significant geometric distortion, such as produced by equiangular fisheye lenses. This same decoupling also allows the slanted-edge method to be applied directly to Bayer-mosaicked images so that the SFR of the color filter array subsets can be measured directly without the unwanted influence of demosaicking artifacts. Numerical simulation results are presented to demonstrate the efficacy of the proposed deferred slanted-edge method in relation to existing methods.

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Distortion Model	Mapping Function
Equiangular	$r_{d} = \frac{1}{18} (16 \tan^{- 1} \frac{18 r_{u}}{8})$
${Poly}_{1}$	$r_{d} = (- 0.1 r_{u}^{2} + 1.1) r_{u}$
${Poly}_{2}$	$r_{d} = (0.081 r_{u}^{4} - 0.372 r_{u}^{2} + 1.101) r_{u}$

Distortion Model	DSE Mean	DSE Max	Quad Mean	Quad Max
Equiangular	$6.329 e - 6$	$7.772 e - 6$	$1.097 e - 2$	$3.627 e - 2$
${Poly}_{1}$	$6.194 e - 7$	$8.768 e - 7$	$1.851 e - 2$	$6.923 e - 2$
${Poly}_{2}$	$3.661 e - 7$	$1.762 e - 6$	$7.707 e - 2$	$3.049 e - 1$

Distortion Model	Mapping Function
Equiangular	$r_{d} = \frac{1}{18} (16 \tan^{- 1} \frac{18 r_{u}}{8})$
${Poly}_{1}$	$r_{d} = (- 0.1 r_{u}^{2} + 1.1) r_{u}$
${Poly}_{2}$	$r_{d} = (0.081 r_{u}^{4} - 0.372 r_{u}^{2} + 1.101) r_{u}$

Distortion Model	DSE Mean	DSE Max	Quad Mean	Quad Max
Equiangular	$6.329 e - 6$	$7.772 e - 6$	$1.097 e - 2$	$3.627 e - 2$
${Poly}_{1}$	$6.194 e - 7$	$8.768 e - 7$	$1.851 e - 2$	$6.923 e - 2$
${Poly}_{2}$	$3.661 e - 7$	$1.762 e - 6$	$7.707 e - 2$	$3.049 e - 1$

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Journal of the Optical Society of America A