## Abstract

This paper presents a method for organizing computations in phase-step interferometry for irregular shapes that is straightforward to program. In addition to data files, which are recorded with incremental phase steps between the interfering beams, this method requires a mask file where the valid pixels can be distinguished from invalid pixels. For example, they may lie above a known threshold. By means of a simple edge-following routine, the program moves around the perimeter of the undone portion of the shape, doing the phase calculations and changing the mask pixels to mark them done. This allows the program to move contiguously from pixels that have been done to those that have not. Modulo 2π ambiguities are avoided by computing the phase differences between neighboring pixels and summing them to obtain individual pixel values.

© 1992 Optical Society of America

Full Article |

PDF Article
### Equations (8)

Equations on this page are rendered with MathJax. Learn more.

(1)
$$\mathrm{\theta}=\text{arctan}(n/d),$$
(2)
$$n=A\hspace{0.17em}\text{sin}(\mathrm{\theta}),\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}d=A\hspace{0.17em}\text{cos}(\mathrm{\theta}).$$
(3)
$$A={({n}^{2}+{d}^{2})}^{1/2}.$$
(4)
$$\begin{array}{l}\mathrm{\Delta}{\mathrm{\theta}}_{21}={\mathrm{\theta}}_{2}-{\mathrm{\theta}}_{1}\\ =\text{arctan}[({n}_{2}{d}_{1}-{n}_{1}{d}_{2})/({n}_{1}{n}_{2}+{d}_{1}{d}_{2})].\end{array}$$
(5)
$${\mathrm{\theta}}_{2}={\mathrm{\theta}}_{1}+\mathrm{\Delta}{\mathrm{\theta}}_{21}.$$
(6)
$$\begin{array}{l}\text{to}\hspace{0.17em}\text{ignore}\mid \mathrm{\Delta}\mathrm{\theta}\mid \hspace{0.17em}>\mathrm{\pi}/2,\\ \text{set}\hspace{0.17em}\mathrm{\Delta}\mathrm{\theta}=0\hspace{0.17em}\text{if}\hspace{0.17em}{n}_{1}{n}_{2}+{d}_{1}{d}_{2}<0.\end{array}$$
(7)
$$N=({I}_{3}-{I}_{2})/(\text{sin}\hspace{0.17em}2\mathrm{\pi}/3),$$
(8)
$$D=(2{I}_{1}-{I}_{2}-{I}_{3})/(1-\text{cos}2\mathrm{\pi}/3),$$