## Abstract

Generally, speckles impair the reconstruction of digital and optical holograms of diffusely scattering objects. With the help of an iterative method, it is possible to introduce diffusers in digital holography that do not suffer from this disadvantage. Optically obtained speckle-free reconstructions of digital holograms are presented.

© 1989 Optical Society of America

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### Equations (11)

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(1)
$$\mid f(\mathbf{x}){\mid}^{2}\approx i(\mathbf{x})$$
(2)
$$\mathrm{\Delta}\mathbf{F}=\mathrm{\Delta}\mathbf{I}/2.$$
(3)
$$f({\mathbf{m}}_{f})\stackrel{\text{DFT}}{\leftrightarrow}F({\mathbf{k}}_{f}),$$
(4)
$$\delta \mathbf{u}=\left(\frac{1}{{M}_{f}\delta x},\frac{1}{{N}_{f}\delta y}\right).$$
(5)
$$H(\mathbf{k})=\text{RE}[G(\mathbf{k})]+B=\mid F(\mathbf{k})\mid \text{cos}[2\pi \mathbf{k}{\mathbf{m}}_{0}/M-\mathrm{\Phi}(\mathbf{k})]+B,$$
(6)
$$H(\mathbf{u})=H(\mathbf{k})*\text{rect}(\mathbf{u},\delta \mathbf{u})$$
(7)
$$\text{rect}(\mathbf{u},\mathbf{a})~\text{rect}(u/a)\text{rect}(v/b),$$
(8)
$$\text{rect}(u/a)=\{\begin{array}{ll}1\hfill & \mid u\mid \le a/2\hfill \\ 0\hfill & \text{else}\hfill \end{array}$$
(9)
$$\begin{array}{l}h(\mathbf{x})=\text{FT}[H(\mathbf{u})]=\text{FT}[H(\mathbf{k})]\text{sinc}(\mathbf{x},\delta {\mathbf{u}}^{-1})=(\{\xbdf(\mathbf{x}-{\mathbf{x}}_{0})\\ +\hspace{0.17em}\xbd{f}^{*}[-(\mathbf{x}+{\mathbf{x}}_{0})]+B\hspace{0.17em}\text{sinc}(\mathbf{x},\delta \mathbf{x})\}\\ *\hspace{0.17em}\text{comb}(\mathbf{x},\delta {\mathbf{u}}^{-1}))\text{sinc}(\mathbf{x},\delta {\mathbf{u}}^{-1}),\end{array}$$
(10)
$$\text{sinc}(\mathbf{x},\mathbf{a})~\frac{\text{sin}(\pi x/a)}{\pi x/a}\frac{\text{sin}(\pi y/b)}{\pi y/b}$$
(11)
$${h}_{l}(\mathbf{x})=[h(\mathbf{x})\text{comb}(\mathbf{x},\delta \mathbf{x})]*\text{sinc}(\mathbf{x},\delta \mathbf{x}/l)$$