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On the generality of the Talbot condition for inducing self-imaging effects on periodic objects: erratum

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Abstract

Corrections to Eqs. (12) and (15) in our recent publication [Opt. Lett. 41, 340 (2016) [CrossRef]  ] are presented in this erratum.

© 2016 Optical Society of America

Regrettably, errors have been found in Eqs. (12) and (15) and Table 1 of our previous paper [1]. However, these typographic errors can be easily identified, and they do not affect the central results of the work.

Tables Icon

Table 1. Values of s in the Fundamental Range [1,2q1] for Different Values of p and q=2

From [2], Eq. (12) can be corrected as follows:

Gn;p,q=1qeiπ(p4pq([1p]q)2n2+12(1(qp))).

The error is in the order of the factors p and q in the Jacobi symbol (written as (pq), instead of (qp), in our previous paper), as in this case, q is an even integer and thus cannot occupy the bottom position in the symbol.

Equation (15) is obtained directly from manipulating Eq. (12). The typographic error in Eq. (12) affects only the constant c (which makes no fundamental difference to the findings reported in our previous work). Equation (15) can be corrected as follows:

s=p([1p]q)2,m=q,c=p41(qp)2.

Finally, the first row of Table 1, which contains the values of the parameter s for several values of the parameter p and q=2, presents errors. The corrected row is provided here.

This erratum is provided for completeness and to avoid possible confusion.

REFERENCES

1. L. Romero Cortés, H. Guillet de Chatellus, and J. Azaña, Opt. Lett. 41, 340 (2016). [CrossRef]  

2. S. Matsutani and Y. Ônishi, Found. Phys. Lett. 16, 325 (2003). [CrossRef]  

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Tables (1)

Tables Icon

Table 1. Values of s in the Fundamental Range [ 1 , 2 q 1 ] for Different Values of p and q = 2

Equations (2)

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G n ; p , q = 1 q e i π ( p 4 p q ( [ 1 p ] q ) 2 n 2 + 1 2 ( 1 ( q p ) ) ) .
s = p ( [ 1 p ] q ) 2 , m = q , c = p 4 1 ( q p ) 2 .
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