24 January 2014 Errata: Reanalysis of turbulence effects on short-exposure passive imaging
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Abstract
This article [Opt. Eng.. 50, (1 ), 016001 (2011)] was originally published on 6 January 2011 with errors in Eqs. (51) to (57). They are corrected below.
Tofsted: Errata: Reanalysis of turbulence effects on short-exposure passive imaging

This article [Opt. Eng. 50(1), 016001 (2011)] was originally published on 6 January 2011 with errors in Eqs. (51) to (57). They are corrected below.

The approximation written in Eq. (51) should have included an ω2 dependence inside the exponential:

(51)

MT(Q,X,ω)exp{+(2.1X)5/3N(Q,X)ω2}.

The expression for A in Eq. (54) should have been written using the limits

(54)

A={0.840+0.116Σ(qa),qa=1.35(q+1.50);q>-1.50;0.840+0.280Σ(qc),qc=0.51(q+1.50);q-1.50.

The negative sign in Eq. (56) should have been inside the exponent:

(56)

MS(ω)=M0(ω)MSA(Q,X,ω)=M0(ω)exp{(2.1Xω)5/3[1V(Q,X)ω1/3]}.

A factor of 2π was missing from Eq. (57):

(57)

RX=2πΩ0201ωMX(ω)dω.

The use of V(Q,X) was based on the approximation of Eq. (51) where the primary ω dependence was quadratic. The function was evaluated at the -3dB point of the MS(ω) curve that yielded V>1 under certain conditions. This was incorrectly interpreted as super-resolution behavior. Further research indicates the approximation expression improves performance at low to moderate frequencies but overestimates responses at high frequencies at moderate turbulence levels. In general V is a moderate function of ω, V(Q,X,ω), that falls below unity at high frequencies ω in such a way that diffraction limits are maintained. Enhanced responses (V>1) often appear for Q>1 and ω1/3.

© The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.
David H. Tofsted, "Errata: Reanalysis of turbulence effects on short-exposure passive imaging," Optical Engineering 53(1), 019801 (24 January 2014). https://doi.org/10.1117/1.OE.53.1.019801
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