## Abstract

In our previous paper [Appl. Opt. **55**, 1082
(2016) [CrossRef] ], we presented a
methodology for full control of a polarization state using a pair of
electro-optic modulators. In this erratum, we correct errors in
Eqs. (9b) and (9c) in the original paper.

© 2016 Optical Society of
America

In the original paper [1], the ellipse
shape parameters $(a,\psi ,\chi )$ of a polarization state were expressed by the
parameters for phase retardation $({\u03f5}_{1},{\u03f5}^{\prime})$ and relative transmittance
($\tau $) of electro-optic modulators in
Eqs. (9a)–(9c). However, there were trigonometric function
errors in Eqs. (9b) and (9c). The correct expressions of the two
equations should be

(1)$$\psi =\frac{1}{2}\text{\hspace{0.17em}}\mathrm{arctan}(1-{\tau}^{2}+(1+{\tau}^{2})\mathrm{cos}\text{\hspace{0.17em}}{\u03f5}_{1},2\tau \text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}{\u03f5}^{\prime}\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}{\u03f5}_{1}),$$ (2)$$\chi =\frac{1}{2}\text{\hspace{0.17em}}\mathrm{arccos}\frac{\sqrt{{\{(1-{\tau}^{2})+(1+{\tau}^{2})\mathrm{cos}\text{\hspace{0.17em}}{\u03f5}_{1}\}}^{2}+4{\tau}^{2}\text{\hspace{0.17em}}{\mathrm{sin}}^{2}\text{\hspace{0.17em}}{\u03f5}^{\prime}\text{\hspace{0.17em}}{\mathrm{sin}}^{2}\text{\hspace{0.17em}}{\u03f5}_{1}}}{1+{\tau}^{2}+(1-{\tau}^{2})\mathrm{cos}\text{\hspace{0.17em}}{\u03f5}_{1}}.$$ This correction does not affect the explanation of the theoretical framework in
the main text.

In the sections for experimental results (Section 4) and discussion (Section
5), we sometimes referred to Eqs. (9a)–(9c) for the evaluation
of the experimental results. We actually used the correct versions of the
equations, as shown above. Thus, we do not need to modify the results and
discussion.

## REFERENCE

**1. **J. Kaneshiro, T. M. Watanabe, H. Fujita, and T. Ichimura, “Full control of
polarization state with a pair of electro-optic modulators for
polarization-resolved optical microscopy,”
Appl. Opt. **55**, 1082 (2016). [CrossRef]

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### Equations (2)

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(1)
$$\psi =\frac{1}{2}\text{\hspace{0.17em}}\mathrm{arctan}(1-{\tau}^{2}+(1+{\tau}^{2})\mathrm{cos}\text{\hspace{0.17em}}{\u03f5}_{1},2\tau \text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}{\u03f5}^{\prime}\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}{\u03f5}_{1}),$$
(2)
$$\chi =\frac{1}{2}\text{\hspace{0.17em}}\mathrm{arccos}\frac{\sqrt{{\{(1-{\tau}^{2})+(1+{\tau}^{2})\mathrm{cos}\text{\hspace{0.17em}}{\u03f5}_{1}\}}^{2}+4{\tau}^{2}\text{\hspace{0.17em}}{\mathrm{sin}}^{2}\text{\hspace{0.17em}}{\u03f5}^{\prime}\text{\hspace{0.17em}}{\mathrm{sin}}^{2}\text{\hspace{0.17em}}{\u03f5}_{1}}}{1+{\tau}^{2}+(1-{\tau}^{2})\mathrm{cos}\text{\hspace{0.17em}}{\u03f5}_{1}}.$$