We correct an error in the original manuscript, where an unrecognized assumption was made about the relationship between the out-of-focus light and the in-focus light. We summarize the condition under which the assumption may still hold, and mention alternative methods researchers can use to obtain accurate quantitative sectioning.

© 2015 Optical Society of America

Section 5 in the original manuscript provides two expressions for the normalized modulated images μi:μi=12+m2cos(vxϕi) and μi = gi/iw. By equating the two expressions, one can obtain an estimate for the modulation factor m at each pixel (Eq. (15) in the original paper). However, if one uses the second expression and substitutes the equation for the ith measured image, gi=12d+sif, together with iw = d + f, one obtains the result


That is, the two expressions can be equated only when df — when the out-of-focus light is small in comparison to the in-focus light. This is an implicit assumption that went unrecognized in the original manuscript and will cause serious quantitative error.

The problem is that in the expression for the measurement images,

the amplitude of the modulation m and the brightness of the in-focus signal f are coupled and cannot be separated from one another using the measurement images alone. As a result, a weak modulation factor such as that produced by a blurred illumination pattern will produce the same effect on the measurement as a weak signal from the in-focus plane.

Quantitative results are still possible, but require additional steps. For example, in order to separate the effects of m from f, one can create phantoms of known f such that the two factors m and f can be separated from one another. Care must be taken to ensure that the phantom will have similar optical properties to the sample of interest, and that the various phantoms have known signal f at several different depths within the tissue, so that one can measure the change in modulation m as a function of depth. Another method would be to apply a Monte Carlo simulation of the tissue properties in order to model the modulation depth at the section plane as a function of the modulation depth incident at the surface.

References and links

1. N. Hagen, L. Gao, and T. S. Tkaczyk, “Quantitative sectioning and noise analysis for structured illumination microscopy,” Opt. Express 20(1), 403–413 (2012). [CrossRef]   [PubMed]  


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  1. N. Hagen, L. Gao, and T. S. Tkaczyk, “Quantitative sectioning and noise analysis for structured illumination microscopy,” Opt. Express 20(1), 403–413 (2012).
    [Crossref] [PubMed]

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Equations (2)

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μ i = 1 2 + m 2 cos ( v x ϕ i ) f d + f .
g i = d + f 2 + m f 2 cos ( v x ϕ i ) ,