## Abstract

To reduce the uncorrected higher-order aberrations for holographic
gratings requiring an extreme dispersion, we have modified the Rowland
mounting by moving the recording laser sources away from the
grating. Then, with a multimode deformable plane mirror to record
the grating, the correction of all the aberrations up to the fourth
order inclusive is found sufficient to obtain a high-quality
image. Applied to the FUSE-LYMAN grating, with a groove density of
as much as 5740 grooves/mm, for which a resolution of 30,000 was
required, this new recording device produces a resolution from 139,000
to 222,000 over the spectral range.

© 2000 Optical Society of America

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### Equations (19)

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(1)
$$sin{\mathrm{\beta}}_{0}-sin{\mathrm{\alpha}}_{0}=n{\mathrm{\lambda}}_{0},$$
(2)
$$sinitani+sin{r}_{1}tan{r}_{1}+\left(k{\mathrm{\lambda}}_{1}/{\mathrm{\lambda}}_{0}\right)Q=0,$$
(3)
$$sinitani+sin{r}_{2}tan{r}_{2}+\left(k{\mathrm{\lambda}}_{2}/{\mathrm{\lambda}}_{0}\right)Q=0,$$
(4)
$$Q=sin{\mathrm{\alpha}}_{0}tan{\mathrm{\alpha}}_{0}-sin{\mathrm{\beta}}_{0}tan{\mathrm{\beta}}_{0},$$
(5)
$$sini+sinr=k\mathrm{\lambda}n.$$
(6)
$$\left({cos}^{2}\mathrm{\alpha}/c-cos\mathrm{\alpha}/R\right)-\left({cos}^{2}\mathrm{\beta}/d-cos\mathrm{\beta}/R\right)=0.$$
(7)
$$\left(1/c-cos\mathrm{\alpha}/R\right)-\left(1/d-cos\mathrm{\beta}/R\right)=Q/R.$$
(8)
$$c=N/\left(P{sin}^{2}\mathrm{\beta}-Q{cos}^{2}\mathrm{\beta}\right),d=N/\left(P{sin}^{2}\mathrm{\alpha}-Q{cos}^{2}\mathrm{\alpha}\right),$$
(9)
$$N=R\left({cos}^{2}\mathrm{\alpha}-{cos}^{2}\mathrm{\beta}\right),P=cos\mathrm{\alpha}-cos\mathrm{\beta}.$$
(10)
$$tan\mathrm{\beta}\left(\mathrm{or}tan\mathrm{\alpha}\right)={\left(Q/P\right)}^{1/2}.$$
(11)
$${C}_{1}=\left(k\mathrm{\lambda}/{\mathrm{\lambda}}_{0}\right)\left[sin\mathrm{\alpha}cos\mathrm{\alpha}\left(cos\mathrm{\alpha}-c/R\right)/\left(2{c}^{2}\right)-sin\mathrm{\beta}cos\mathrm{\beta}\left(cos\mathrm{\beta}-d/R\right)/\left(2{d}^{2}\right)\right],$$
(12)
$$R=1750\mathrm{mm},n=5764\mathrm{grooves}/\mathrm{mm},\text{recording laser wavelength}{\mathrm{\lambda}}_{0}=3336\mathit{\AA},\text{working order}k=1,\text{spectral range of}910\u20131030\mathit{\AA},\text{elliptical pupil of}170\times 135\mathrm{mm},\text{needed resolution of}\mathrm{\lambda}/d\mathrm{\lambda}=\mathrm{30,000},\text{abbreviated as}\left[30\right]\text{for simplicity}.$$
(13)
$${\mathrm{\alpha}}_{0}=-72.7101\xb0,{\mathrm{\beta}}_{0}=75.4793\xb0,$$
(14)
$$\mathrm{\alpha}=-78.2082\xb0,$$
(15)
$$c=3014.0909\mathrm{mm},d=1271.4125\mathrm{mm}.$$
(16)
$${C}_{1}=-5.492\times {10}^{-8},{C}_{2}=2.134\times {10}^{-7},{S}_{1}=-2.354\times {10}^{-11},{S}_{2}=1.538\times {10}^{-10},{S}_{3}=-3.081\times {10}^{-11}.$$
(17)
$${i}_{\mathrm{mir}}=9.4\xb0,{d}_{m}=1020\mathrm{mm},$$
(18)
$${A}_{31}=9.325\times {10}^{-7},{A}_{33}=5.166\times {10}^{-7},{A}_{40}=-2.847\times {10}^{-9},{A}_{42}=-3.477\times {10}^{-9},{A}_{44}=-5.345\times {10}^{-10}.$$
(19)
$$-48.4\mathrm{\mu}\mathrm{m}\mathrm{at}910\AA ,-50.5\mathrm{\mu}\mathrm{m}\mathrm{at}970\AA ,-64.4\mathrm{\mu}\mathrm{m}\mathrm{at}1030\AA .$$