## Abstract

The details of a new design of a fisheye field spectrograph are presented together with performance studies on the prototype. Spectra of different sources together with the microphotometer tracings for the spectra of skylight are given. Details of the calibration are also discussed. The condition for negligible astigmatism, achieved experimentally, has been derived theoretically.

© 1978 Optical Society of America

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### Equations (3)

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(1)
$$\begin{array}{ll}\varphi \left(\u220a\right)\hfill & =\varphi \left(t\right)=\frac{r}{4}\left[\begin{array}{c}-\text{sin}\left(3t\right)+3\phantom{\rule{0.2em}{0ex}}\text{sin}\left(t\right)\\ 3\phantom{\rule{0.2em}{0ex}}\text{cos}\left(t\right)-\text{cos}\left(3t\right)\end{array}\right]\hfill \\ \hfill & =\begin{array}{cc}\left[\begin{array}{c}{\varphi}_{1}\left(t\right)\\ {\varphi}_{2}\left(t\right)\end{array}\right]& t\in \left(0,\frac{\pi}{2}\right),\end{array}\hfill \end{array}$$
(2)
$$\kappa \left(t\right)=\frac{{{\varphi}_{1}}^{\prime}{{\varphi}_{2}}^{\prime \prime}-{{\varphi}_{1}}^{\prime \prime}{{\varphi}_{2}}^{\prime}}{{\Vert {\varphi}^{\prime}\Vert}^{3}}=\frac{{\left(\frac{3r}{2}\right)}^{2}2\phantom{\rule{0.2em}{0ex}}{\text{sin}}^{2}\left(t\right)}{{\left[\frac{3}{2}r\phantom{\rule{0.2em}{0ex}}\text{sin}\left(t\right)\right]}^{3}},$$
(3)
$$\frac{1}{\kappa \left(t\right)}={r}_{m}=\frac{3r}{4}\text{sin}\left(t\right).$$