Deep convolutional neural networks-based scatterer density and resolution estimators in optical coherence tomography: erratum

Abstract

Errata are presented to correct the inconsistencies between the values and their units displayed in the figures and the texts in our published manuscript [Biomed. Opt. Express 13, 168 (2022) 10.1364/BOE.443343 ]. The errors were caused by the unit presentation of the original manuscript, and hence, it does not affect the main results and the conclusion.

In the vertical axes of Figs. 4, 5, and 8(b) of our published manuscript [1], the unit was $\mu {\mathrm{m}}^{-3}$ but numbers were in ${\mathrm{pix}}^{-3}$ . The unit displays of the color scale of the second row of Fig. 7 was $\mu {\mathrm{m}}^{-3}$ but the numbers were in ${\mathrm{pix}}^{-3}$ . The correct figures were obtained by correcting the numbers as follows.

Fig. 4.

The numbers of the vertical axis of (b) have been corrected to be consistent with the displayed unit.

Fig. 5.

The numbers of the right vertical axes have been corrected to be consistent with the displayed unit.

Fig. 8.

The numbers of the vertical axes have been corrected to be consistent with the displayed unit.

Fig. 7.

The numbers in the color scale of the second row were corrected.

The same inconsistency about the values and the units have been found in the texts and are corrected as follows.

The first sentence of the second paragraph of Section 3.1 is corrected as follows: The root mean square errors (RMSEs) of the estimations are 0.113 scatterers/ ${\mathrm{pix}}^3$ for the scatterer density, 3.06 scatterers for the ENS, 1.78 $\mu$ m for the lateral, 1.88 $\mu$ m for the axial resolutions, and 1.82 dB for the SNR.

The third, forth, and sixth paragraphs of Section 3.2.1 were corrected as follows.

Third paragraph: The estimated scatterer densities have a linear relationship with the concentration. The average slopes of the three measurements (three phantoms) are 0.5622 (for −0 dB attenuation), 0.5436 (−5.4 dB), and 0.5577 (−11.76 dB) ${\mathrm{pix}}^{-3}/\mathrm{\%}$ (v/v) , or equally, 0.0204 (−0 dB), 0.0197 (−5.4 dB), and 0.0202 (−11.76 dB) $\mu {\mathrm{m}}^{-3}/\mathrm{\%}$ (v/v) for the high-NA objective, and 0.5560 (−0 dB), 0.5587 (−5.4 dB), and 0.5415 (−11.76 dB) ${\mathrm{pix}}^{-3}/\mathrm{\%}$ (v/v) , or equally, 0.0202 (−0 dB), 0.0203 (−5.4 dB), and 0.0197 (−11.76 dB) $\mu {\mathrm{m}}^{-3}/\mathrm{\%}$ (v/v) for the low-NA objective.

Fourth paragraph: We can compute the scatterer size from these slopes as discussed in detail in Section 4.1. The intercepts of plots are found not to be zero, although the ideal intercept is zero. The intercepts are 0.0447 (for −0 dB attenuation) and 0.0436 (for −5.4 dB and −11.76 dB) $\mu {\mathrm{m}}^{-3}$ , or equally, 1.23 (−0 dB) and 1.20 (for −5.4 dB and −11.76 dB) ${\mathrm{pix}}^{-3}$ for the high-NA objective, and 0.0458 (−0 dB), 0.0447 (−5.4 dB), and 0.0454 (−11.76 dB) $\mu {\mathrm{m}}^{-3}$ , or equally, 1.26 (−0 dB), 1.23 (−5.4 dB), and 1.25 (−11.76 dB) ${\mathrm{pix}}^{-3}$ for the low-NA objective. This issue is discussed in Section 4.4.

The last sentence of the sixth paragraph: The mean scatterer densities in the Intralipid region are 0.050 scatterers/ $\mu {\mathrm{m}}^3$ (1.37 scatterers/ ${\mathrm{pix}}^3$ ) and 0.049 scatterers/ $\mu {\mathrm{m}}^3$ (1.35 scatterers/ ${\mathrm{pix}}^3$ ) for the high- and low-NA objectives, respectively, i.e., the difference is only 1.5%.

The first sentence of the second paragraph of Section 4.1 is corrected as follows: In our Intralipid phantom measurements (Section 3.2.1), the slope of the relation between the scatterer density and $\sigma$ is found to be 0.0201 $\pm$ 0.0003 $\mu {\mathrm{m}}^{-3}/\mathrm{\%}$ (v/v) (0.5533 $\pm$ 0.0086 ${\mathrm{pix}}^{-3}/\mathrm{\%}$ (v/v)), or equivalently 2.01 $\pm$ 0.03 $\mu {\mathrm{m}}^{-3}$ /(v/v ratio) (55.33 $\pm$ 0.86 ${\mathrm{pix}}^{-3}$ /(v/v ratio)) (mean $\pm$ standard deviation over three attenuations and two NAs).

Disclosures

Seesan, Abd El-Sadek, Mukherjee, Zhu, Oikawa: Yokogawa Electric Corp. (F), Sky technology (F), Nikon (F), Kao Corp. (F), Topcon (F). Miyazawa: Yokogawa Electric Corp. (F), Sky technology (F, E), Nikon (F), Kao Corp. (F), Topcon (F). Shen, Matsusaka: None. Makita, Yasuno: Yokogawa Electric Corp. (F), Sky technology (F), Nikon (F), Kao Corp. (F), Topcon (F), Tomey Corp (P). Buranasiri: None.