## Abstract

Infrared spectral features have proved useful in the identification of threat objects. Dual-band focal-plane arrays (FPAs) have been developed in which each pixel consists of superimposed midwave and long-wave photodetectors [Dyer and Tidrow, *Conference on Infrared Detectors and Focal Plane Arrays* (SPIE, Bellingham, Wash., 1999), pp. 434–440]. Combining dual-band FPAs with imaging spectrometers capable of interband hyperspectral resolution greatly improves spatial target discrimination. The computed-tomography imaging spectrometer (CTIS) [Descour and Dereniak, Appl. Opt. **34**, 4817–4826 (1995)] has proved effective in producing hyperspectral images in a single spectral region. Coupling the CTIS with a dual-band detector can produce two hyperspectral data cubes simultaneously. We describe the design of two-dimensional, surface-relief, computer-generated hologram dispersers that permit image information in these two bands simultaneously.

© 2003 Optical Society of America

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### Equations (8)

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(1)
$${\mathrm{\varphi}}_{\mathrm{pixel}}\left(\mathrm{\lambda}\right)=\frac{2\mathrm{\pi}}{\mathrm{\lambda}}\left[n\left(\mathrm{\lambda}\right)-1\right]{d}_{\mathrm{pixel}},$$
(2)
$${t}_{0}\left(r,s,\mathrm{\lambda}\right)=\left[\left(\sum _{n=-N/2}^{N/2-1}\sum _{m=-M/2}^{M/2-1}exp\left[i{\mathrm{\Phi}}_{\mathit{mn}}\left(\mathrm{\lambda}\right)\right]\mathrm{\delta}\left(r-\mathit{nd}\right)\times \mathrm{\delta}\left(s-\mathit{md}\right)\right)**\mathrm{rect}\left(\frac{r}{d},\frac{s}{d}\right)\right],$$
(3)
$$t\left(r,s,\mathrm{\lambda}\right)=\left[{t}_{0}\left(r,s,\mathrm{\lambda}\right)**\frac{1}{\mathit{NMd}}\mathrm{comb}\left(\frac{r}{\mathit{Nd}},\frac{s}{\mathit{Md}}\right)\right]\times \mathrm{rect}\left(\frac{r}{\mathit{RNd}},\frac{s}{\mathit{SMd}}\right),$$
(4)
$$\mathrm{comb}\left(x\right)=\sum _{n=-\infty}^{\infty}\mathrm{\delta}\left(x-n\right).$$
(5)
$$U\left(x,y,\mathrm{\lambda}\right)\propto {\mathit{RSMNd}}^{2}\mathrm{sinc}\left(\frac{\mathit{RNdx}}{\mathrm{\lambda}f},\frac{\mathit{SMdy}}{\mathrm{\lambda}f}\right)**\times \left[\left(\left\{\sum _{n=-N/2}^{N/2-1}\sum _{m=M/2}^{M/2-1}exp\left[i{\mathrm{\Phi}}_{\mathit{mn}}\left(\mathrm{\lambda}\right)\right]exp\times \left[-\mathrm{i}2\mathrm{\pi}d\left(\frac{\mathit{nx}+\mathit{my}}{\mathrm{\lambda}f}\right)\right]\right\}\times {d}^{2}\mathrm{sinc}\left(\frac{\mathit{dx}}{\mathrm{\lambda}f},\frac{\mathit{dy}}{\mathrm{\lambda}f}\right)\right)\times \mathrm{comb}\left(\frac{\mathit{Ndx}}{\mathrm{\lambda}f},\frac{\mathit{Mdy}}{\mathrm{\lambda}f}\right)\right],$$
(6)
$$\mathrm{MSE}\left(\mathrm{\lambda}\right)=\frac{1}{256}\sum _{m=-8}^{7}\sum _{n=-8}^{7}{\left[\mathrm{\eta}_{\mathit{mn}}{}^{d}\left(\mathrm{\lambda}\right)-\mathrm{\eta}_{\mathit{mn}}{}^{a}\left(\mathrm{\lambda}\right)\right]}^{2},$$
(7)
$${\mathrm{\eta}}_{\mathrm{total}}\left(\mathrm{\lambda}\right)=\sum _{\begin{array}{c}m,n\\ \mathrm{desired}\end{array}}\mathrm{\eta}_{m,n}{}^{a}\left(\mathrm{\lambda}\right).$$
(8)
$${\mathrm{IEFOM}}_{\mathrm{MWIR}}=\sum _{\mathrm{\lambda}=3\mathrm{\mu}\mathrm{m}}^{5\mathrm{\mu}\mathrm{m}}\left\{\frac{1}{K-1}\times \sum _{\begin{array}{c}\mathrm{specified}\\ m,n\end{array}}{\left[\mathrm{\eta}_{\mathit{mn}}{}^{a}\left(\mathrm{\lambda}\right)-{\overline{\mathrm{\eta}}}_{\mathrm{MWIR}}\right]}^{2}\right\},{\mathrm{IEFOM}}_{\mathrm{LWIR}}=\sum _{\mathrm{\lambda}=8\mathrm{\mu}\mathrm{m}}^{12\mathrm{\mu}\mathrm{m}}\left\{\frac{1}{K-1}\times \sum _{\begin{array}{c}\mathrm{specified}\\ m,n\end{array}}{\left[\mathrm{\eta}_{\mathit{mn}}{}^{a}\left(\mathrm{\lambda}\right)-{\overline{\mathrm{\eta}}}_{\mathrm{LWIR}}\right]}^{2}\right\},$$