## Abstract

In a conventional grating spectrograph consisting of a single entrance slit, a grating, and a multichannel (imaging) detector, considerable light throughput advantage can be realized by replacement of the single entrance slit with a mask. This replacement can yield a signal-to-noise ratio increase because of increased light collection over an extended area of the mask when compared with a single slit. The mask produces a spectrum on the detector, which is the convolution of the mask pattern and the spectral distribution of the light source. To retrieve the spectrum, the spectrum has to be inverted. In special cases in which emission spectra are superimposed on weak backgrounds, the signal-to-noise advantage is preserved through the inversion process. Thus this technique is valuable in the observation of light sources that are produced by atomic or molecular emissions such as aurora, airglow, some interstellar emission, or laboratory spectra. Considerable signal-to-noise advantages can also be realized when the background noise of the imaging detector is not negligible. The spectral mixing of the light from the mask on the detector causes high photon fluxes on the detector, which tend to swamp the detector noise. This is a particularly important advantage in the application of CCD’s as detectors because they can have significant background noise. The technique was demonstrated by computer simulations and laboratory tests.

© 1993 Optical Society of America

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### Equations (17)

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(1)
$$\begin{array}{cccccccc}{X}_{1}& 1& 1& 1& 0& 1& 0& 0\\ {X}_{2}& 0& 1& 1& 1& 0& 1& 0\\ {X}_{3}& 0& 0& 1& 1& 1& 0& 1\\ {X}_{4}& 1& 0& 0& 1& 1& 1& 0\\ {X}_{5}& 0& 1& 0& 0& 1& 1& 1\\ {X}_{6}& 1& 0& 1& 0& 0& 1& 1\\ {X}_{7}& 1& 1& 0& 1& 0& 0& 1\\ \hspace{0.17em}& {S}_{1}& {S}_{2}& {S}_{3}& {S}_{4}& {S}_{5}& {S}_{6}& {S}_{7}\end{array}$$
(2)
$${S}_{j}=\sum _{i=1}^{n}{a}_{ij}{I}_{i}.$$
(3)
$${X}_{i}=\frac{2}{n+1}\sum _{j=1}^{n}2({a}_{ij}-0.5){S}_{j}.$$
(4)
$${S}_{j}=\sum _{i=1}^{n}{a}_{ij}{I}_{i}+{e}_{j}.$$
(5)
$${X}_{i}={I}_{i}+\frac{2}{n+1}\sum _{j=1}^{n}2({a}_{ij}-0.5){e}_{j}$$
(6)
$${X}_{i}-{I}_{i}=\frac{2}{n+1}\sum _{j=1}^{n}2({a}_{ij}-0.5){e}_{j}.$$
(7)
$$E={[{({X}_{i}-{I}_{i})}^{2}]}^{1/2}=\frac{2}{n+1}{\left(\sum _{j=1}^{n}\overline{{{e}_{j}}^{2}}\right)}^{1/2},$$
(8)
$${E}_{q}=\frac{2}{n+1}{\left(\frac{n+1}{2}\sum _{i=1}^{n}{I}_{i}\right)}^{1/2}.$$
(9)
$${E}_{q}=\frac{2}{n+1}{\left(\frac{n+1}{2}\sum _{j=1}^{n}{I}_{c}\right)}^{1/2}={\left(\frac{2n}{n+1}{I}_{c}\right)}^{1/2}.$$
(10)
$${E}_{q}=\frac{2}{n+1}{\left(\frac{n+1}{2}{I}_{s}\right)}^{1/2}={\left(\frac{2}{n+1}{I}_{s}\right)}^{1/2}.$$
(11)
$${E}_{{d}_{c}}=\frac{2}{n+1}{\left(\sum _{j=1}^{n}{{d}_{c}}^{2}\right)}^{1/2}=2\frac{\sqrt{n}}{n+1}{d}_{c}.$$
(12)
$$\mathrm{\eta}=\mathrm{\u220a}\mathrm{\psi},$$
(13)
$$\Vert \mathcal{G}(\mathrm{\eta}-\mathrm{\u220a}\mathrm{\psi})\Vert ,$$
(14)
$${g}_{ii}=\frac{1}{{\mathrm{\sigma}}_{i}}.$$
(15)
$$\mathrm{\psi}={({\tilde{\mathrm{\u220a}}}^{t}\tilde{\mathrm{\u220a}})}^{-1}{\tilde{\mathrm{\u220a}}}^{t}\tilde{\mathrm{\eta}},$$
(16)
$$\tilde{\mathrm{\u220a}}=\mathcal{G}\mathrm{\u220a},$$
(17)
$$\tilde{\mathrm{\eta}}=\mathcal{G}\mathrm{\eta}.$$