## Abstract

A modification to the usual phase shifting interferometry algorithm permits measurements to be taken fast enough to essentially freeze out vibrations. Only two interferograms are time critical in this 2 + 1 algorithm; the third is null. The implemented system acquires the two time critical interferograms with a 1-millisecond separation on either side of the interline transfer of a standard CCD video camera, resulting in a reduction in sensitivity to vibration of 1–2 orders of magnitude. The required phase shift is achieved via frequency shifting. Laboratory tests comparing this system with a commercial phase shifting package reveal comparable rms errors when vibrations are low; as expected from an analysis of potential phase errors. However, the 2 + 1 system also succeeded when vibrations were large enough to wash out video rate fringes.

© 1990 Optical Society of America

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### Equations (7)

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(1)
$$I(x,y)={I}_{1}+{I}_{2}+2{({I}_{1}{I}_{2})}^{1/2}\hspace{0.17em}\text{cos}[\varphi (x,y)+\alpha (t)],$$
(2)
$$\begin{array}{l}{I}_{A}(x,y)={I}_{1}+{I}_{2}+2{({I}_{1}{I}_{2})}^{1/2}\hspace{0.17em}\text{cos}\varphi ,\\ {I}_{B}(x,y)={I}_{1}+{I}_{2}+2{({I}_{1}{I}_{2})}^{1/2}\hspace{0.17em}\text{cos}(\varphi -\pi /2)\\ ={I}_{1}+{I}_{2}+2{({I}_{1}{I}_{2})}^{1/2}\hspace{0.17em}\text{sin}\varphi .\end{array}$$
(3)
$$\begin{array}{l}{I}_{C}(x,y)=\xbd[{I}_{1}+{I}_{2}+2{({I}_{1}{I}_{2})}^{1/2}\hspace{0.17em}\text{cos}\varphi ]+\xbd[{I}_{1}+{I}_{2}+2{({I}_{1}{I}_{2})}^{1/2}\hspace{0.17em}\text{cos}(\varphi +\pi )]\\ ={I}_{1}+{I}_{2}.\end{array}$$
(4)
$$\text{OPD}(x,y)=\frac{\mathrm{\lambda}}{2\pi}{\text{tan}}^{-1}\frac{{I}_{B}(x,y)-{I}_{C}(x,y)}{{I}_{A}(x,y)-{I}_{C}(x,y)}.$$
(5)
$$2\mathrm{\Delta}\omega =\frac{c\alpha}{\text{OPD}}=2\pi \frac{8{\omega}_{t}r}{\mathrm{\lambda}},$$
(6)
$$\begin{array}{l}{I}_{A}(x,y)={I}_{1}+{I}_{2}+2{({I}_{1}{I}_{2})}^{1/2}\hspace{0.17em}\text{sin}{\varphi}^{\prime},\\ {I}_{B}(x,y)={I}_{1}+{I}_{2}+2{({I}_{1}{I}_{2})}^{1/2}\hspace{0.17em}\text{cos}{\varphi}^{\prime},\end{array}$$
(7)
$$\begin{array}{l}{I}_{C}(x,y)=\xbd[{I}_{1}+{I}_{2}+2{({I}_{1}{I}_{2})}^{1/2}\hspace{0.17em}\text{cos}(\varphi -\pi /2)]+\xbd[{I}_{1}+{I}_{2}+2{({I}_{1}{I}_{2})}^{1/2}\hspace{0.17em}\text{cos}(\varphi +\pi /2)]\\ =({I}_{1}+{I}_{2}).\end{array}$$