## Abstract

The Fourier transform based interferogram analysis technique of Takeda *et al*. is reviewed, and it is shown that the digitization of the interferogram can act to seriously distort the recovered phase object. An algorithm for dealing with this problem is proposed. The recovered phase object may also be seriously distorted if the response of the recording medium is nonlinear. An algorithm for calibrating the film response is proposed which uses only the data in the interferogram and which can be used to correct the effects of the film nonlinearity. The technique is demonstrated on an experimental inteferogram obtained in a study of laser-produced plasmas.

© 1985 Optical Society of America

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### Equations (6)

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(1)
$$I\left(x,y\right)=B\left(x,y\right)+V\left(x,y\right)\phantom{\rule{0.2em}{0ex}}\text{cos}\left[2\pi \left({\omega}_{0}x+{\nu}_{0}y\right)+\varphi \left(x,y\right)\right],$$
(2)
$$\begin{array}{ll}I\left(x,y\right)=\hfill & B\left(x,y\right)+{V}^{\prime}\left(x,y\right)\phantom{\rule{0.2em}{0ex}}\text{exp}\left[2\pi i\left({\omega}_{0}x+{\nu}_{0}y\right)\right]\hfill \\ \hfill & +{{V}^{\prime}}^{*}\left(x,y\right)\phantom{\rule{0.2em}{0ex}}\text{exp}\left[-2\pi i\left({\omega}_{0}x+{\nu}_{0}y\right)\right],\hfill \end{array}$$
(3)
$$i\left(\omega ,\nu \right)=b\left(\omega ,\nu \right)+{\upsilon}^{\prime}\left(\omega -{\omega}_{0},\nu -{\nu}_{0}\right)+{\upsilon}^{\prime}*\left(\omega +{\omega}_{0},\nu +{\nu}_{0}\right).$$
(4)
$$\text{log}\left[{V}^{\prime}\left(x,y\right)\right]=\text{log}\left[V\left(x,y\right)/2\right]+i\varphi \left(x,y\right).$$
(5)
$${\varphi}^{\prime}\left(x,y\right)=\text{exp}\left[-2\pi i\left(x\delta \omega +y\delta \nu \right)\right]\varphi \left(x,y\right),$$
(6)
$${\varphi}^{\u2033}\left(x,y\right)=\text{exp}\left[2\pi i\left(x\delta {\omega}^{\prime}+y\delta {\nu}^{\prime}\right)\right]{\varphi}^{\prime}\left(x,y\right),$$