Window function influence on phase error in phase-shifting algorithms

Applied Optics (Impact Factor: 1.78). 10/1996; 35(28):5642-9. DOI: 10.1364/AO.35.005642
Source: PubMed


We present five different eight-point phase-shifting algorithms, each with a different window function. The window function plays a crucial role in determining the phase (wavefront) because it significantly influences phase error. We begin with a simple eight-point algorithm that uses a rectangular window function. We then present alternative algorithms with triangular and bell-shaped window functions that were derived from a new error-reducing multiple-averaging technique. The algorithms with simple (rectangular and triangular) window functions show a large phase error, whereas the algorithms with bell-shaped window functions are considerably less sensitive to different phase-error sources. We demonstrate that the shape of the window function significantly influences phase error.

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    • "This paper proposes to apply well-known window functions, such as " generalized cosine windows " (which are commonly used in signal processing applications [3] and in other branches of science [4]) to overcome the errors introduced by truncating equivalent surface currents at the edges of open surfaces. A higher-order generalized cosine window function is defined by [5] win "
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    • "An analytical approach to optimizing the phase shift (calculating an area-weighted average on the sphere section covered by our numerical aperture) yielded a best setting of ≅ 103º for the maximum phase shift. We then used a highly errorresistant 8-sample phase-shifting formula, first given in Ref. [15] as the " 8Bell-7 " formula, to take all measurements for the calibration and the mirror certification. "
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