## Abstract

Quantitative analysis of 3-D phase objects by moire deflectometry is suggested. The method is based on measuring the deflection of rays from a collimated light beam due to gradients in the refractive index. To analyze asymmetric density fields it is necessary to obtain data of deflections at sufficient angular viewing angles about the test section and to mathematically invert the data. The moire deflectometry inversion procedure is shown to be simpler than interferometry inversion since no numerical differentiation of the measured data has to be performed. The method is demonstrated by mapping a temperature field generated above the top of two heated cylinders.

© 1984 Optical Society of America

Full Article |

PDF Article
### Equations (7)

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

(1)
$${p}^{\prime}=\frac{p}{2\hspace{0.17em}\text{sin}(\alpha /2)}.$$
(2)
$$\phi \simeq \frac{1}{{n}_{\infty}}{\int}_{-\infty}^{\infty}\left[\frac{\partial n(x,y,z)}{\partial {y}^{\prime}}\right]d{x}^{\prime},$$
(3)
$$N(r,\psi )=n(r,\psi )-{n}_{\infty}.$$
(4)
$$F({y}^{\prime},\theta )={\int}_{-\infty}^{\infty}{\int}_{-\infty}^{\infty}N(r,\psi )\delta [{y}^{\prime}-r\hspace{0.17em}\text{sin}(\psi -\theta )]dxdy,$$
(5)
$$N(r,\psi )=\frac{1}{2{\pi}^{2}}{\int}_{-\pi /2}^{\pi /2}d\theta {\int}_{-\infty}^{\infty}\frac{(\partial F/\partial {y}^{\prime})d{y}^{\prime}}{r\hspace{0.17em}\text{sin}(\psi -\theta )-{y}^{\prime}}.$$
(6)
$$\begin{array}{l}\frac{\partial F}{\partial {y}^{\prime}}=\frac{\partial}{\partial {y}^{\prime}}\int [n(x,y,z)-{n}_{\infty}]d{x}^{\prime}\\ =\int \frac{\partial [n(x,y,z)-{n}_{\infty}]}{\partial {y}^{\prime}}d{x}^{\prime},\end{array}$$
(7)
$$\phi =\alpha h/\mathrm{\Delta},$$