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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    ABSTRACT: We introduce a modified current expansion scheme over open surfaces based on the equivalence theorem, which employs closed surfaces, in principle. Weighting the expansion coefficients with a suitable window function compensates for the computed field errors that occur because of the open surfaces. Numerical simulations demonstrate that the equivalent surface currents expanded with low-ordered basis functions on an open surface and weighted by suitable functions can be used to obtain the correct electromagnetic fields in a limited volume near the surface.
    International Workshop on Computational Electromagnetics, Izmir, Turkey; 08/2013
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    • "I i(1–5) represents the phase shifted intensities. The phase can also be determined by the 8-step (n ¼8) algorithm [14], which gives the phase as f 8 i ¼ arctan ÀI i1 À5I i2 þ 11I i3 þ 15I i4 À15I i5 À11I i6 þ 5I i7 þI i8 I i1 À5I i2 À11I i3 þ 15I i4 þ 15I i5 À11I i6 À5I i7 þ I i8 "
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    ABSTRACT: In laser based interferometry, the unambiguous measurement range is limited to half a wavelength. Multiple wavelength or white light interferometer is used to overcome this difficulty. In this paper a white light interferometer with a colour CCD camera is discussed. We access interference intensity information from the three channels of the colour CCD simulating three-wavelength measurement. This makes the data acquisition as simple as in single wavelength interferometry. The unambiguous measurement range however gets limited by the coherence length of the CCD. The usefulness of the proposed method is demonstrated on a micro-sample.
    Optics and Lasers in Engineering 08/2012; 50(8):1084–1088. DOI:10.1016/j.optlaseng.2012.02.002 · 2.24 Impact Factor
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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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    ABSTRACT: CSIRO's Australian Centre for Precision Optics has recently finished the production of a high-precision concave spherical mirror. The specifications were very ambitious: numerical aperture 0.75; asphericity below 5.5 nm rms and 27.3 nm P-V. The available reference transmission sphere had to be calibrated to enable adequate accuracy. Due to the high numerical aperture of the mirror, sub-aperture measurements had to be stitched together to form a complete surface map of the mirror. Phase-shifting interferometry at high numerical aperture suffers from phase-step non-uniformity because of the large off-axis angles. We present what we believe to be a new interpretation of this phenomenon as a focus error, which clarifies where in the interferometer the phase-shift error occurs. We discuss the ball-averaging method for calibrating the reference transmission sphere and present results from the averaging process to ensure an uncertainty commensurate with the certification requirement. For carrying out the sub-aperture measurements, we constructed a two-axis gimbal mount to swivel the mirror around the focus of the test wavefront. If the centers of curvature of the transmission sphere and the mirror coincide, the mirror can be tilted without losing the interferogram. We present a simple and effective alignment method, which can be generally applied to optical tests where the wavefront comes to a focus. The mirror was coated with protected aluminum and tested in its mount. No effect on the sphericity error from the coating was found, and the specifications were exceeded by approximately 30%. We discuss subtleties of the stitching process on curved surfaces and report final results. Bibtex entry for this abstract Preferred format for this abstract (see Preferences) Find Similar Abstracts: Use: Authors Title Abstract Text Return: Query Results Return items starting with number Query Form Database: Astronomy Physics arXiv e-prints
    Proceedings of SPIE - The International Society for Optical Engineering 08/2008; 7064. DOI:10.1117/12.793522 · 0.20 Impact Factor
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