Abstract
We present an erratum to our article [Opt. Express 30(7), 10547 (2022) [CrossRef] ].
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Erratum
There were some errors that occurred while we writing Eq. (16) and incorrect data in our original article [1], which were due to the author forgetting to revise the wrong equation and data in the paper after simulating and drawing conclusions with the correct equation. An incorrect equation, specifically Eq. (16), was given to calculate the center ray position in the y-axis direction on the detector was presented. The corrected equation is:
(1)$$y(\sigma )= {y_{CL}}(\sigma )- ({f + z} )\tan {\varphi _1} = \left[ {f + z - \frac{z}{f}({{l_1} + {l_2}} )} \right]\tan {\varphi _{in}}(\sigma )$$
Accordingly, we also correct the inequality in Eq. (37) by substituting Eq. (16) into Eq. (18):
(2)$$\left\{ {\begin{array}{*{20}{l}} {{l_1} \le \frac{{2{H_G}\sin ({{\alpha_1} - {\alpha_2}} )\cos {\varphi_{in}}({{\sigma_{\min ,\max }}} )- {h_L}\cos ({{\alpha_1} - {\varphi_{in}}({{\sigma_{\min ,\max }}} )} )}}{{2|{\tan {\varphi_{in}}({{\sigma_{\min ,\max }}} )} |}}}\\ {{l_1} + {l_2} \le \frac{{2{H_{CL}}\sin ({{\alpha_1} - {\alpha_2}} )\cos {\varphi_{in}}({{\sigma_{\min ,\max }}} )- {h_L}\cos ({{\alpha_1} - {\varphi_{in}}({{\sigma_{\min ,\max }}} )} )}}{{2|{\tan {\varphi_{in}}({{\sigma_{\min ,\max }}} )} |}}}\\ {\frac{z}{f} \ge \frac{{\sin ({{\alpha_1} - {\alpha_2}} )}}{{\cos {\alpha_1} - \sin {\alpha_1}\tan {\varphi_{in}}({{\sigma_{\min }}} )}}\frac{{na}}{{{h_L}}}}\\ {{\boldsymbol {f + z}} - \frac{{\boldsymbol z}}{{\boldsymbol f}}({{{\boldsymbol l}_{\boldsymbol 1}}{\boldsymbol + }{{\boldsymbol l}_{\boldsymbol 2}}} ){\mathbf \le }\frac{{{\boldsymbol {Na}}}}{{|{{\mathbf {tan}}{{\boldsymbol \varphi }_{{\boldsymbol {in}}}}({{{\boldsymbol \sigma }_{{\mathbf {max}}}}} ){\boldsymbol - }{\mathbf {tan}}{{\boldsymbol \varphi }_{{\boldsymbol {in}}}}({{{\boldsymbol \sigma }_{{\mathbf {min}}}}} )} |}}}\\ {{l_2} + f + z \le \frac{{\frac{{\cos \left( {\theta - \left( {2\frac{{{\sigma_{\min ,\max }} - {\sigma_L}}}{{{\sigma_{\min ,\max }}}} + {\varphi_{in}}^2({{\sigma_{\min ,\max }}} )} \right)\tan \theta } \right)}}{{\cos \theta }} - \frac{{Ma}}{{2m}}}}{{\left|{\tan \left( {\left( {2\frac{{{\sigma_{\min ,\max }} - {\sigma_L}}}{{{\sigma_{\min ,\max }}}} + {\varphi_{in}}^2({{\sigma_{\min ,\max }}} )} \right)\tan \theta } \right)} \right|}}} \end{array}} \right.$$
Additionally, the spacing parameters among the optical elements in Table 2 are corrected as:
Table 2. Key Parameters of the Components Used in the Theoretical Design of the CDSHS
The correct data of the center ray position y(σ) and the height of the interferograms h(σ) in Table 3 are slightly different from those in the original article. The corrected data in Table 3 is:
Table 3. Parameters of Selected Interferograms on the Detector in the Theoretical Design
In the first paragraph below Table 3, the statement should be corrected to:
Figure 6 shows the y-axis coordinates and widths of the interferograms for different wavelengths at the detector plane. As verified using Eq. (21) and Eq. (31), we know that the minimum height of the interferogram h(σmin) 0.13047 mm > 10a = 0.13 mm, and the minimum width of the interference area of the interferogram wA(σmin) 7.2126 mm > 1024a/2 = 6.65 mm.”
The authors regret these mistakes. Reassuringly, the graphs and conclusions were based on correct equations and data, so they remain correct.
Funding
National Natural Science Foundation of China (61505204, 61975255, 6210030850, U2006209); Jilin Province Research Projects in China (20190302047GX, 20200404197YY, 2020SYHZ0040).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
References
1. Q. Chu, X. Li, C. Jirigalantu, J. Sun, J. Chen, Y. Wang, Sun, and Bayanheshig, “Design study of a cross-dispersed spatial heterodyne spectrometer,” Opt. Express 30(7), 10547–10562 (2022). [CrossRef]
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