Abstract

This document provides a correction to the derivation of the distributions of the scattered fields presented in Optica 7, 63 (2020) [CrossRef]   and discusses the implications this correction has on the rest of the paper.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. C. A. Metzler, F. Heide, P. Rangarajan, M. M. Balaji, A. Viswanath, A. Veeraraghavan, and R. G. Baraniuk, “Deep-inverse correlography: towards real-time high-resolution non-line-of-sight imaging,” Optica 7, 63–71 (2020).
    [Crossref]
  2. J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications, 2nd ed. (Roberts and Company Publishers, 2020).
  3. N. O’Donoughue and J. M. Moura, “On the product of independent complex Gaussians,” IEEE Trans. Signal Process. 60, 1050–1063 (2011).
    [Crossref]
  4. J. R. Fienup, “Emerging systems and technologies,” in The Infrared and Electro-Optical Systems Handbook, Atmospheric propagation of radiation (Infrared Information Analysis Center, 1993), Vol. 8, Chap. 1.5.
  5. P. Welch, “The use of fast fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms,” IEEE Trans. Audio Electroacoust. 15, 70–73 (1967).
    [Crossref]

2020 (1)

2011 (1)

N. O’Donoughue and J. M. Moura, “On the product of independent complex Gaussians,” IEEE Trans. Signal Process. 60, 1050–1063 (2011).
[Crossref]

1967 (1)

P. Welch, “The use of fast fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms,” IEEE Trans. Audio Electroacoust. 15, 70–73 (1967).
[Crossref]

Balaji, M. M.

Baraniuk, R. G.

Fienup, J. R.

J. R. Fienup, “Emerging systems and technologies,” in The Infrared and Electro-Optical Systems Handbook, Atmospheric propagation of radiation (Infrared Information Analysis Center, 1993), Vol. 8, Chap. 1.5.

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications, 2nd ed. (Roberts and Company Publishers, 2020).

Heide, F.

Metzler, C. A.

Moura, J. M.

N. O’Donoughue and J. M. Moura, “On the product of independent complex Gaussians,” IEEE Trans. Signal Process. 60, 1050–1063 (2011).
[Crossref]

O’Donoughue, N.

N. O’Donoughue and J. M. Moura, “On the product of independent complex Gaussians,” IEEE Trans. Signal Process. 60, 1050–1063 (2011).
[Crossref]

Rangarajan, P.

Veeraraghavan, A.

Viswanath, A.

Welch, P.

P. Welch, “The use of fast fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms,” IEEE Trans. Audio Electroacoust. 15, 70–73 (1967).
[Crossref]

IEEE Trans. Audio Electroacoust. (1)

P. Welch, “The use of fast fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms,” IEEE Trans. Audio Electroacoust. 15, 70–73 (1967).
[Crossref]

IEEE Trans. Signal Process. (1)

N. O’Donoughue and J. M. Moura, “On the product of independent complex Gaussians,” IEEE Trans. Signal Process. 60, 1050–1063 (2011).
[Crossref]

Optica (1)

Other (2)

J. R. Fienup, “Emerging systems and technologies,” in The Infrared and Electro-Optical Systems Handbook, Atmospheric propagation of radiation (Infrared Information Analysis Center, 1993), Vol. 8, Chap. 1.5.

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications, 2nd ed. (Roberts and Company Publishers, 2020).

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Equations (13)

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E V S i n ( x V S ) = 1.
E V S o u t ( x V S ) C N ( 0 , σ E V S o u t 2 ) ,
E O i n p 2 F ( p 1 E V S o u t ) ,
E O o u t ( x O ) = g O ( x O ) E O i n ( x O ) ,
r σ O i n 2 δ ( Δ x O ) .
E V D i n p 4 F ( p 3 E O o u t ) ,
I ( x D ) = | g D ( x D ) E V D i n ( x D ) | 2 = | g D ( x D ) | 2 | E V D i n ( x D ) | 2 ,
I ( x D ) = | g D ( x D ) | 2 | F ( E ~ O o u t ) | 2 ,
R I ( x D , Δ x D ) R β ( Δ x D ) R E ( Δ x D ) .
F ( R I ) ( Δ x ) F ( R β ) ( Δ x ) F ( R E ) ( Δ x ) ,
F ( R I ) ( Δ x ) c 2 F ( R E ) ( Δ x ) + c 1 δ ( Δ x ) F ( R E ) ( Δ x ) , c 3 + c 1 F ( R E ) ( Δ x ) .
E [ | ( f f ) | 2 ] ( Δ x ) = x 1 x 2 E [ z ¯ 1 ( x 1 + Δ x ) z 1 ( x 1 ) z 1 ( x 2 + Δ x ) z ¯ 1 ( x 2 ) ] E [ z ¯ 2 ( x 1 + Δ x ) z 2 ( x 1 ) z 2 ( x 2 + Δ x ) z ¯ 2 ( x 2 ) ] d x 1 d x 2 .
E [ | ( f f ) | 2 ] ( Δ x ) = x 1 x 2 [ r ( x 1 ) r ( x 2 ) δ ( Δ x ) + r ( x 1 ) r ( x 2 ) δ ( Δ x ) δ ( x 2 x 1 ) + r ( x 1 + Δ x ) r ( x 1 ) δ ( x 2 x 1 ) δ ( Δ x ) + r ( x 1 + Δ x ) r ( x 1 ) δ ( x 2 x 1 ) ] d x 1 d x 2 = δ ( Δ x ) x 1 x 2 [ r ( x 1 ) r ( x 2 ) + r ( x 1 ) r ( x 2 ) δ ( x 2 x 1 ) + r ( x 1 + Δ x ) r ( x 1 ) δ ( x 2 x 1 ) ] d x 1 d x 2 + x 1 x 2 r ( x 1 + Δ x ) r ( x 1 ) δ ( x 2 x 1 ) d x 1 d x 2 = δ ( Δ x ) W + r r ( Δ x ) ,