The optical path difference W(x,y) between the actual wavefront and its associated reference sphere can be represented as a polynomial series as was indicated by Eq. 1.5. This is an infinite series. But after the eighth order (i+j = 8), the coefficients Wijk are usually insignificant and can be ignored. In Chapter 1 the fourth order terms (where i+j = 4) were discussed. Included here are spherical aberration, coma, and astigmatism. These and higher order terms will be the subject of wavefront sensor measurement in subsequent chapters. This chapter will examine measurements made on the lower order terms in which (i+j) = 0 or 1 or 2. These are piston, tilt, and defocus respectively.
Piston is basically a pedestal shift of the entire wavefront. It does not change the shape of the wavefront, or the resulting point spread (or far-field) pattern. Piston is not something measurable by conventional wavefront sensors, nor is it important that they do so. There is only one scenario where piston plays an extremely important role...optical phased arrays.
Constructing monolithic primary mirrors on the order of 10 meters and larger is prohibitive because of cost, and limits on fabrication technology. Optical phased arrays provide a practical means of building telescope systems with large equivalent apertures. There are two approaches: an array of separate but coupled telescopes, or a segmented primary mirror. The Multi-Mirror Telescope shown in Fig. 3.1 was the pioneer of the first alternative. An embodiment of the latter is the Keck telescope shown in Fig. 3.2.
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