## Abstract

We used a numerical minimization method to design a Rowland holographic spherical grating that is recorded with two stigmatic laser sources. The method aims at simultaneously reducing all aberrations up to fourth order over a significant spectral range. In the context of a high spectral resolution, far-ultraviolet spectrograph, an original solution is found that implies a nonclassical recording geometry with one virtual source. This solution satisfies the requirement of a resolving power of ~ 30 000 with the unquestionable advantage of manufacturing and testing simplicity. Finally, another example, which is obtained in a different context, shows that the properties of this recording geometry probably have a general applicability.

© 1992 Optical Society of America

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### Equations (12)

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(1)
$$F=\u3008AP\u3009+\u3008PB\u3009+nm\mathrm{\lambda}.$$
(2)
$$n{\mathrm{\lambda}}_{0}=(\u3008CP\u3009-\u3008DP\u3009)-(\u3008CO\u3009-\u3008DO\u3009),$$
(3)
$${(x-R)}^{2}+{y}^{2}+{z}^{2}={R}^{2}.$$
(4)
$$x(y,z)=1/2R{y}^{2}+1/2R{z}^{2}+1/8{R}^{3}{y}^{4}+1/4{R}^{3}{y}^{2}{z}^{2}+1/8{R}^{3}{z}^{4}.$$
(5)
$$F(y,z)={F}_{00}+{F}_{10}+1/2{y}^{2}{F}_{20}+1/2{z}^{2}{F}_{02}+1/2{y}^{3}{F}_{30}+1/2y{z}^{2}{F}_{12}+1/8{y}^{4}{F}_{40}+1/4{y}^{2}{z}^{2}{F}_{22}+1/8{z}^{4}{F}_{04}.$$
(6)
$${F}_{ij}={M}_{ij}+(m\mathrm{\lambda}/{\mathrm{\lambda}}_{0}){H}_{ij}.$$
(7)
$$\text{sin}\hspace{0.17em}\mathrm{\alpha}+\text{sin}\hspace{0.17em}\mathrm{\beta}=(m\mathrm{\lambda}/{\mathrm{\lambda}}_{0})(\text{sin}\hspace{0.17em}\mathrm{\delta}-\text{sin}\hspace{0.17em}\mathrm{\gamma}).$$
(8)
$$N=(\text{sin}\hspace{0.17em}\mathrm{\delta}-\text{sin}\hspace{0.17em}\mathrm{\gamma})/{\mathrm{\lambda}}_{0}.$$
(9)
$$\begin{array}{l}\mathrm{\delta}y=\frac{(Rb-y\hspace{0.17em}\text{sin}\hspace{0.17em}\mathrm{\beta})}{Rb\hspace{0.17em}\text{cos}\hspace{0.17em}\mathrm{\beta}}\left[(Rb-y\hspace{0.17em}\text{sin}\hspace{0.17em}\mathrm{\beta})\frac{\partial F}{\partial y}-y\hspace{0.17em}\text{sin}\hspace{0.17em}\mathrm{\beta}\frac{\partial F}{\partial z}\right],\\ \partial z=(Rb-y\hspace{0.17em}\text{sin}\hspace{0.17em}\mathrm{\beta})\frac{\partial F}{\partial z}.\end{array}$$
(10)
$$\mathrm{\Phi}=\mathrm{\Sigma}\hspace{0.17em}{w}_{i}\mathrm{\Sigma}\hspace{0.17em}{(\mathrm{\delta}y+f\mathrm{\delta}z)}^{2}.$$
(11)
$${M}_{02}=1/R[1/\text{cos}\hspace{0.17em}\mathrm{\alpha}+1/\text{cos}\hspace{0.17em}\mathrm{\beta}-\text{cos}\hspace{0.17em}\mathrm{\alpha}-\text{cos}\hspace{0.17em}\mathrm{\beta}],$$
(12)
$$\mathrm{\beta}=ASN(Nm\mathrm{\lambda}-\text{sin}\hspace{0.17em}\mathrm{\alpha}).$$