## Abstract

The properties of a 4-m plane-grating Czerny–Turner spectrograph have been analyzed by tracing rays through the spectrograph. Contrary to results recently reported by Chandler in this journal, it was found that the optimum position of the grating is near that predicted by the Fastie–Rosendahl analytical expression. It is also shown that the image width can be made small all the way across a 50-cm plate, that the focal curve can be made straight, and that a position of the entrance slit can be found that makes it unnecessary to refocus the spectrograph when the grating is rotated.

© 1969 Optical Society of America

Full Article |

PDF Article
### Equations (23)

Equations on this page are rendered with MathJax. Learn more.

(1)
$${z}_{m}=2(R-g)\hspace{0.17em}({z}_{s}-{z}_{0})/R.$$
(2)
$${x}_{m}={[{R}^{2}-{({z}_{m}-{z}_{0})}^{2}]}^{{\scriptstyle \frac{1}{2}}}.$$
(3)
$$a={[{({x}_{m}-g)}^{2}+{{z}_{m}}^{2}]}^{{\scriptstyle \frac{1}{2}}}.$$
(4)
$$\text{cos}\alpha ={(Ra)}^{-1}[{x}_{m}({x}_{m}-g)+({z}_{m}-{z}_{0}){z}_{m}].$$
(5)
$$\text{sin}\alpha ={(Ra)}^{-1}[{x}_{m}{z}_{m}-({x}_{m}-g)\hspace{0.17em}({z}_{m}-{z}_{0})].$$
(6)
$$l={R}^{-1}[{x}_{m}\hspace{0.17em}\text{cos}\alpha +({z}_{m}-{z}_{0})\hspace{0.17em}\text{sin}\alpha ]$$
(7)
$$m={R}^{-1}[({z}_{m}-{z}_{0})\hspace{0.17em}\text{cos}\alpha -{x}_{m}\hspace{0.17em}\text{sin}\alpha ],$$
(8)
$${x}_{e}={x}_{m}-tl$$
(9)
$${z}_{e}={z}_{m}-tm.$$
(10)
$$t=R\hspace{0.17em}\text{cos}\alpha /2.$$
(11)
$${{z}_{m}}^{\prime}={z}_{m}+\frac{2a}{R}({z}_{s}-{z}_{e}).$$
(12)
$${\overline{z}}_{0}={\overline{z}}_{p}-\frac{R}{2}\frac{{\overline{z}}_{m}}{R-g}.$$
(13)
$${\overline{t}}_{m}=(R\hspace{0.17em}\text{cos}{\overline{\alpha}}_{m})/2;$$
(14)
$${{\overline{z}}_{0}}^{\prime}={\overline{z}}_{0}+{\overline{z}}_{p}-{\overline{z}}_{e}.$$
(15)
$$b={\text{tan}}^{-1}[\mid {z}_{m}\mid /({x}_{m}-g)].$$
(16)
$$c={\text{tan}}^{-1}[{\overline{z}}_{m}/({\overline{x}}_{m}-g)].$$
(18)
$$\text{sin}\gamma =\frac{n{\mathrm{\lambda}}_{m}}{2d\hspace{0.17em}\text{cos}\phi},$$
(19)
$$i=\gamma -\phi ,$$
(20)
$$r=\gamma +\phi .$$
(22)
$$dg=-\hspace{0.17em}(d{k}_{c})\frac{{R}^{2}}{2\sqrt{3}{h}^{2}},$$