## Abstract

We present a configuration for a real-time spatial image processor that is based upon an *imaging* setup in which a grating with Fourier coefficients with tunable phase is attached to the object plane. The illumination that is used for the proposed concept is spatially incoherent. By proper adjusting of the magnification of the imaging system to the spatial period of the grating and the sampling grid of the camera, the aliasing effect due to the digital sampling realizes a nonuniform and tunable spectral distribution (a filter) that is applied over the spectrum of the object. Preliminary numerical and experimental demonstration of the operation principle is provided with a spatial ${\mathrm{LiNbO}}_{3}$ hexagonal grating.

© 2009 Optical Society of America

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### Equations (13)

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(1)
$$\overline{H}(\mu )=H(\mu )\xb7\int [s(x)\xb7g(x)]\mathrm{exp}(2\pi i\mu x)\mathrm{d}x,$$
(2)
$$H(\mu )\approx \mathrm{sinc}\left(\frac{4{W}_{m}{Z}_{i}\mu}{b}\right)\mathrm{.}$$
(3)
$${W}_{m}=\frac{{b}^{2}}{2}(\frac{1}{{Z}_{i}}+\frac{1}{{Z}_{o}}-\frac{1}{F})\mathrm{.}$$
(4)
$$\frac{1}{{Z}_{i}}+\frac{1}{{Z}_{o}}=\frac{1}{F}\mathrm{.}$$
(5)
$$g(x)=\sum _{n}{a}_{n}\mathrm{exp}(2\pi in{\mu}_{0}x)\mathrm{.}$$
(6)
$$\overline{H}(\mu )=\sum _{n}{a}_{n}H(\mu )S(\mu -n{\mu}_{0}),$$
(7)
$${H}_{m}(\mu )=H(\mu )\xb7\text{rect}\left(\frac{\mu -m{\mu}_{0}}{{\mu}_{0}}\right)\mathrm{.}$$
(8)
$$\overline{H}(\mu )=\sum _{n}{a}_{n}{H}_{n}(\mu )S(\mu -n{\mu}_{0})\mathrm{.}$$
(9)
$${\overline{H}}_{d}(\mu )=\overline{H}(\mu )\otimes \sum _{n}\delta (\mu -n{\mu}_{0})\mathrm{.}$$
(10)
$${\overline{H}}_{d}^{(\text{inf})}(\mu )=\sum _{n}{a}_{n}{H}_{n}(\mu )S(\mu )=S(\mu )[\sum _{n}{a}_{n}H(\mu -n{\mu}_{0})]\mathrm{.}$$
(11)
$$f(x)=h(x)\xb7\sum _{n}{a}_{n}\mathrm{exp}(2\pi in{\mu}_{0}x),$$
(12)
$${a}_{n}=\underset{1/{\mu}_{0}}{\int}\left[\frac{f(x)}{h(x)}\right]\mathrm{exp}(-2\pi in{\mu}_{0}x)\mathrm{d}x\mathrm{.}$$
(13)
$$\frac{\lambda F}{2b}M=\frac{35\text{\hspace{0.17em}}\mathrm{\mu m}}{2.5}\mathrm{.}$$