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Abstract
This errata corrects typos found in the derived transfer functions in [Opt. Express 23, 11394 (2015) [CrossRef] ].
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The absorption transfer function, originally reported in Eq. (7) in [1], should be
$$H_{\mathrm{abs}}(\mathbf{u}) ={-}\left[ \iint S(\mathbf{u}^{\prime})P^*(\mathbf{u}^{\prime})P(\mathbf{u}^{\prime}+\mathbf{u})\textrm{d}^2\mathbf{u}^{\prime}+ \iint S(\mathbf{u}^{\prime})P(\mathbf{u}^{\prime})P^*(\mathbf{u}^{\prime}-\mathbf{u})\textrm{d}^2\mathbf{u}^{\prime}\right].$$
The phase transfer function, originally reported in Eq. (8) in [1], should be $$H_{\mathrm{ph}}(\mathbf{u}) = \mathrm{i}\left[ \iint S(\mathbf{u}^{\prime})P^*(\mathbf{u}^{\prime})P(\mathbf{u}^{\prime}+\mathbf{u})\textrm{d}^2\mathbf{u}^{\prime}- \iint S(\mathbf{u}^{\prime})P(\mathbf{u}^{\prime})P^*(\mathbf{u}^{\prime}-\mathbf{u})\textrm{d}^2\mathbf{u}^{\prime}\right].$$
References
1. L. Tian and L. Waller, “Quantitative differential phase contrast imaging in an led array microscope,” Opt. Express 23(9), 11394–11403 (2015). [CrossRef]