## Abstract

Filtering off noise from fringe patterns is important for the processing and analysis of interferometric fringe patterns. Spin filters proposed by the author have been proven to be effective in filtering off noise without blurring and distortion to fringe patterns with small fringe curvature. But spin filters still have problems processing fringe patterns with large fringe curvature. We develop a new spin filtering with curve windows that is suitable for all kinds of fringe pattern regardless of fringe curvature. The experimental results show that the new spin filtering provides optimal results in filtering off noise without distortion of the fringe features, regardless of fringe curvature.

© 2002 Optical Society of America

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### Equations (7)

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(1)
$$g\left(i,j\right)=\mathit{ai}+\mathit{bj}+c,$$
(2)
$$\mathrm{\theta}=\mathrm{arctan}\frac{a}{b}=\mathrm{arctan}\frac{{\displaystyle \sum _{i,j}}{f}_{\mathit{ij}}i}{{\displaystyle \sum _{i,j}}{f}_{\mathit{ij}}j},$$
(3)
$${x}_{i+1}={x}_{i}+cos{\mathrm{\theta}}_{i},{y}_{i+1}={y}_{i}+sin{\mathrm{\theta}}_{i},$$
(4)
$${x}_{-i-1}={x}_{-i}+cos{\mathrm{\theta}}_{-i},{y}_{-i-1}={y}_{-i}+sin{\mathrm{\theta}}_{-i}.$$
(5)
$$I\left(x,y\right)={I}_{0}\left(x,y\right)+{I}_{1}\left(x,y\right)cos\left[\mathrm{\varphi}\left(x,y\right)\right]+{I}_{n}\left(x,y\right),$$
(6)
$$I\left(x,y\right)=128exp\left(\frac{-{r}^{2}}{{256}^{2}}\right)+60exp\left(\frac{-{r}^{2}}{{256}^{2}}\right)cos\left[\left(\frac{1000r-{r}^{2}}{2500}\right)\mathrm{\pi}\right]+{I}_{n}\left(x,y\right),$$
(7)
$$\mathrm{\varphi}\left(x,y\right)=\mathrm{arccos}\left[I\left(x,y\right)-{I}_{0}\left(x,y\right)/{I}_{1}\left(x,y\right)\right],$$