Predicting range performance of sampled imagers by treating aliased signal as target-dependent noise: erratum

doi:10.1364/JOSAA.26.002418

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

Editor: Stephen A. Burns
Vol. 26, Iss. 11 — Nov. 1, 2009
pp: 2418–2418

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Predicting range performance of sampled imagers by treating aliased signal as target-dependent noise: erratum

Richard H. Vollmerhausen, Ronald G. Driggers, and David L. Wilson »View Author Affiliations

JOSA A, Vol. 26, Issue 11, pp. 2418-2418 (2009)
http://dx.doi.org/10.1364/JOSAA.26.002418

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Abstract

This erratum is to correct errors made in our paper [ J. Opt. Soc. Am. A 25, 2055 (2008) ].

We would like to correct two errors in Eq. (16) of [1

R. H. Vollmerhausen, R. G. Driggers, and D. L. Wilson, “Predicting range performance of sampled imagers by treating aliased signal as target-dependent noise,” J. Opt. Soc. Am. A 25, 2055–2065 (2008). [CrossRef]

]. The correct equation is

{CTF}_{sys} (ξ) = \frac{CTF (\frac{ξ}{smag})}{H_{sys} (ξ)} {(1 + \frac{α^{2} Γ_{\det}^{2} Q (ξ, η)}{{SCN}^{2}} + \frac{α^{2} t_{eye} T_{con}^{2} R_{ng}^{2} Q_{a} (ξ, η)}{L_{tgt} {SCN}^{2}})}^{1 ∕ 2} .

In the corrected equation,

L_{tgt}

is the presented area of the target in square meters

(m^{2})

. For the experimental target set used in [1

R. H. Vollmerhausen, R. G. Driggers, and D. L. Wilson, “Predicting range performance of sampled imagers by treating aliased signal as target-dependent noise,” J. Opt. Soc. Am. A 25, 2055–2065 (2008). [CrossRef]

],

L_{tgt}

is

9.7 m^{2}

[2

R. H. Vollmerhausen, E. Jacobs, and R. G. Driggers, “New metric for predicting target acquisition performance,” Opt. Eng. (Bellingham) 43, 2806–2818 (2004). [CrossRef]

]. Also, the value of α for the thermal model is 862, not 169.6 [3

R. H. Vollmerhausen, “Representing the observer in electro-optical target acquisition models,” Opt. Express 17, 17253–17268 (2009). [CrossRef] [PubMed]

].

The reasons that aliasing noise scales with the square of range are correctly described in Subsection 3.B of [1

R. H. Vollmerhausen, R. G. Driggers, and D. L. Wilson, “Predicting range performance of sampled imagers by treating aliased signal as target-dependent noise,” J. Opt. Soc. Am. A 25, 2055–2065 (2008). [CrossRef]

]. However, the scale factor in [1

R. H. Vollmerhausen, R. G. Driggers, and D. L. Wilson, “Predicting range performance of sampled imagers by treating aliased signal as target-dependent noise,” J. Opt. Soc. Am. A 25, 2055–2065 (2008). [CrossRef]

] is incorrect. Aliasing is generated over the entire target area. The scale factor in [1

R. H. Vollmerhausen, R. G. Driggers, and D. L. Wilson, “Predicting range performance of sampled imagers by treating aliased signal as target-dependent noise,” J. Opt. Soc. Am. A 25, 2055–2065 (2008). [CrossRef]

] incorrectly uses one square meter of target area. A target of area

L_{tgt}

m^{2}

subtends a solid angle of

L_{tgt} ∕ R_{ng}^{2}

square mrad at range

R_{ng}

km. In order to properly scale aliasing noise to detector noise, the aliasing noise term is divided by

L_{tgt} ∕ R_{ng}^{2}

. That is, the scale factor is

R_{ng}^{2} ∕ L_{tgt}

and not

R_{ng}^{2} ∕ 1

.

In [1

R. H. Vollmerhausen, R. G. Driggers, and D. L. Wilson, “Predicting range performance of sampled imagers by treating aliased signal as target-dependent noise,” J. Opt. Soc. Am. A 25, 2055–2065 (2008). [CrossRef]

], the (

R_{ng}^{2}

{km}^{2} ∕ 1 m^{2}

) scale factor is a units conversion. The problem in Eq. (16) of [1

R. H. Vollmerhausen, R. G. Driggers, and D. L. Wilson, “Predicting range performance of sampled imagers by treating aliased signal as target-dependent noise,” J. Opt. Soc. Am. A 25, 2055–2065 (2008). [CrossRef]

] becomes apparent when applying the aliasing as noise model to small targets. The alias noise scale factor must include target size. Using

1 m^{2}

of target area to generate aliasing is arbitrary and incorrect. The whole target area generates aliasing.

L_{tgt}

actually represents the scale of the spatial features used to discriminate the target. For example, consider two billboards. One billboard is twice the size of the other. However, the words on both billboards are the same size and font. The large billboard cannot be read at twice the distance of the small billboard.

L_{tgt}

represents the size of discrimination features. For the billboard example,

L_{tgt}

is letter size.

The second error in [1

R. H. Vollmerhausen, R. G. Driggers, and D. L. Wilson, “Predicting range performance of sampled imagers by treating aliased signal as target-dependent noise,” J. Opt. Soc. Am. A 25, 2055–2065 (2008). [CrossRef]

] is incorrect treatment of the calibration factor α. The value 169.6 used in [1

R. H. Vollmerhausen, R. G. Driggers, and D. L. Wilson, “Predicting range performance of sampled imagers by treating aliased signal as target-dependent noise,” J. Opt. Soc. Am. A 25, 2055–2065 (2008). [CrossRef]

] analyses is based on calculating signal to noise at an eye integration time

t_{eye}

[2

R. H. Vollmerhausen, E. Jacobs, and R. G. Driggers, “New metric for predicting target acquisition performance,” Opt. Eng. (Bellingham) 43, 2806–2818 (2004). [CrossRef]

]. Equation (15) in [1

R. H. Vollmerhausen, R. G. Driggers, and D. L. Wilson, “Predicting range performance of sampled imagers by treating aliased signal as target-dependent noise,” J. Opt. Soc. Am. A 25, 2055–2065 (2008). [CrossRef]

] applies a

\sqrt{t_{eye}}

correction factor based on normalizing signal and noise over

1 s

. When the

1 s

normalization is used, the value of α is 862 [3

R. H. Vollmerhausen, “Representing the observer in electro-optical target acquisition models,” Opt. Express 17, 17253–17268 (2009). [CrossRef] [PubMed]

].

The two corrections increase the alias noise term by 60% and improve the fit between model and data. In Table 3 of [1

R. H. Vollmerhausen, R. G. Driggers, and D. L. Wilson, “Predicting range performance of sampled imagers by treating aliased signal as target-dependent noise,” J. Opt. Soc. Am. A 25, 2055–2065 (2008). [CrossRef]

], the coefficient of determination (COD) for experiments 21, 25, and 36 are 0.92, 0.90, and 0.92, respectively. With the corrections, COD are 0.98, 0.92, and 0.94, respectively. The corrections improve the predictive accuracy of the model.

References and links

1.	R. H. Vollmerhausen, R. G. Driggers, and D. L. Wilson, “Predicting range performance of sampled imagers by treating aliased signal as target-dependent noise,” J. Opt. Soc. Am. A 25, 2055–2065 (2008). [CrossRef]
2.	R. H. Vollmerhausen, E. Jacobs, and R. G. Driggers, “New metric for predicting target acquisition performance,” Opt. Eng. (Bellingham) 43, 2806–2818 (2004). [CrossRef]
3.	R. H. Vollmerhausen, “Representing the observer in electro-optical target acquisition models,” Opt. Express 17, 17253–17268 (2009). [CrossRef] [PubMed]

OCIS Codes
(110.3000) Imaging systems : Image quality assessment
(110.3080) Imaging systems : Infrared imaging
(280.4991) Remote sensing and sensors : Passive remote sensing

History
Original Manuscript: October 6, 2009
Manuscript Accepted: October 6, 2009
Published: October 21, 2009

Citation
Richard H. Vollmerhausen, Ronald G. Driggers, and David L. Wilson, "Predicting range performance of sampled imagers by treating aliased signal as target-dependent noise: erratum," J. Opt. Soc. Am. A 26, 2418-2418 (2009)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-26-11-2418

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References

R. H. Vollmerhausen, R. G. Driggers, and D. L. Wilson, “Predicting range performance of sampled imagers by treating aliased signal as target-dependent noise,” J. Opt. Soc. Am. A 25, 2055-2065 (2008). [CrossRef]
R. H. Vollmerhausen, E. Jacobs, and R. G. Driggers, “New metric for predicting target acquisition performance,” Opt. Eng. (Bellingham) 43, 2806-2818 (2004). [CrossRef]
R. H. Vollmerhausen, “Representing the observer in electro-optical target acquisition models,” Opt. Express 17, 17253-17268 (2009). [CrossRef] [PubMed]

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Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

Predicting range performance of sampled imagers by treating aliased signal as target-dependent noise: erratum

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