## Abstract

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

© 2009 Optical Society of America

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

*α*for the thermal model is 862, not 169.6 [3].

The reasons that aliasing noise scales with the square of range are correctly described in Subsection 3.B of [1]. However, the scale factor in [1] is incorrect. Aliasing is generated over the entire target area. The scale factor in [1] incorrectly uses one square meter of target area. A target of area ${L}_{\mathit{tgt}}$ ${\mathrm{m}}^{2}$ subtends a solid angle of ${L}_{\mathit{tgt}}\u2215{R}_{\mathit{ng}}^{2}$ square mrad at range ${R}_{\mathit{ng}}$ km. In order to properly scale aliasing noise to detector noise, the aliasing noise term is divided by ${L}_{\mathit{tgt}}\u2215{R}_{\mathit{ng}}^{2}$. That is, the scale factor is ${R}_{\mathit{ng}}^{2}\u2215{L}_{\mathrm{tgt}}$ and not ${R}_{\mathit{ng}}^{2}\u22151$.

In [1], the (${R}_{\mathit{ng}}^{2}$ ${\mathrm{km}}^{2}\u22151\text{\hspace{0.17em}}{\mathrm{m}}^{2}$) scale factor is a units conversion. The problem in Eq. (16) of [1] becomes apparent when applying the aliasing as noise model to small targets. The alias noise scale factor must include target size. Using $1\text{\hspace{0.17em}}{\mathrm{m}}^{2}$ of target area to generate aliasing is arbitrary and incorrect. The whole target area generates aliasing.

${L}_{\mathit{tgt}}$ 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. ${L}_{\mathit{tgt}}$ represents the size of discrimination features. For the billboard example, ${L}_{\mathit{tgt}}$ is letter size.

The second error in [1] is incorrect treatment of the calibration factor *α*. The value 169.6 used in [1] analyses is based on calculating signal to noise at an eye integration time ${t}_{\mathit{\text{eye}}}$ [2]. Equation (15) in [1] applies a $\sqrt{{t}_{\mathit{\text{eye}}}}$ correction factor based on normalizing signal and noise over $1\text{\hspace{0.17em}}\mathrm{s}$. When the $1\text{\hspace{0.17em}}\mathrm{s}$ normalization is used, the value of *α* is 862 [3].

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

**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]