Optical Shop Testing

Chapter 2.9.1 - Analysis of Interferograms of Arbitrary Wavefronts

2.9.1.   Analysis of Interferograms of Arbitrary Wavefronts

The problem of determining the shape of a wavefront with arbitrary shape from a
single Twyman–Green interferogram has been considered very generally and briefly
by many authors, for example, by Berggren (1970) and more completely by Rimmer
et al. (1972). The procedure consists in measuring the positions of the fringes at many
points over the interferograms and taking readings of the position (x, y) and the order
of interference m. Since the measurements are taken at a limited number of points, an
interpolation procedure must be adopted. The interpolation may be performed by the
use of splines or a least squares procedure with polynomial fitting as described in
detail in Chapter 16.

If the wavefront is smooth enough, it is very convenient to express the final
wavefront W(x, y) in terms of a linear combination of Zernike polynomials. Then
the process of removing or adding defocussing or tilts becomes much simpler.
With the final results, it is an extremely simple matter to plot level maps of the
wavefront. Further details can be found in the book by Malacara, Servın and
Malacara (2005).

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