Investigation of depth-resolved nanoscale structural changes in regulated cell proliferation and chromatin decondensation: erratum

Abstract

We correct minor errors in two equations reported in our paper [Biomed. Opt. Express 4, 596–613 (2013)]; an additional factor of two was mistakenly incorporated in Eqs. (3) and (4). We give the correct equations below. All the simulations and experiments in the previous paper were performed using the correct equations, and therefore, remain the same.

We correct Eqs. (3) and (4) in our previous paper [1] by removing the factor of two that was mistakenly incorporated in both of them. The correct versions of Eqs. (3) and (4) respectively are,

$$p\left(z_{\text{opl}}\right)=2\text{Γ}\otimes \left[\left(R_r+R_s\right)\delta (0)+2r_r{ℱ}^{-1}\left(\underset{0}{\overset{Z}{{\displaystyle \int }}}{r}_s\left(z^{\text{'}}\right)\cos \left(4\pi \frac{K}{2}n(z^{\text{'}})z^{\text{'}}\right)d{z}^{\text{'}}\right)\right]\left(z_{opl}\right),$$ (3)

and,

$$\delta p\left(z_{\text{opl}}\right)=\frac{{\lambda }_0}{2\pi }\arctan \left(\frac{\text{Im}\left(p\left(z_{\text{opl}}\right)\right)}{\text{Re}(p(z_{\text{opl}}))}\right) ,z_{opl}\ne 0.$$ (4)

In Eq. (3), the convolution argument has been changed from 2z_opl to z_opl, and in Eq. (4), the factor of two has been removed from the denominator. The reason for the deletion, also explained in our original paper [1], is that the factor of two is implicitly incorporated within the spatial frequency K = (k_s – k _i)/2π = 2(k/2π) z = (k/π) z, under the normal illumination and collection geometry for the common-path setup, thereby allowing us to directly perform the Fourier transform at the optical depth location of z_opl. The simulation and experimental results reported in the paper remain unaltered, as they were performed using the correct equations.