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Abstract This paper presents a novel method to eliminate cosine error in precision concave and convex surface measurement by integrating a displacement probe in a precision spindle. Cosine error in surface profile measurement comes from an angular misalignment between the measurement axis and the axis of motion and negatively affects the measurement accuracy, especially in optical surface measurements. A corrective multiplier can solve this problem for spherical surface measurement, but cosine error cannot be eliminated in the case of complex optical surface measurement because current tools do not measure such surfaces along the direction normal to the measurement plane. Because the displacement probe is placed on the spindle axis, the spindle error motion will affect the shape precision and surface roughness measurement of optical components such as mirrors and lenses, and the displacement probe will measure a combination of the spindle error motion and the geometry of optical surfaces. Here, the one-dimensional concave, convex, and hollow measurement targets were used, and cosine error was fundamentally eliminated by aligning the probe on the spindle always normal to the measured surface, and compensation was made for the aerostatic bearing spindle rotational error obtained by the reversal method. The results show that this proposed measurement method cannot only eliminate cosine error but also scan the large area quickly and conveniently. In addition, measurement uncertainty and further consideration for future work were discussed.
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Calibration methods for a dual-wavelength interferometer system
Multiple wavelength interferometry has long been considered an option for the measurement of large aspheric slope departures. In particular, a synthetic wavelength offers a variety of approaches by which large phase excursions can be unwrapped. Using multiple wavelengths can create collimation and magnification mismatch errors between the individual wavelengths that arise during beam expansion and propagation. Here, we present and analyze alignment and calibration methods for a dual-wavelength interferometer that can significantly reduce both misalignment errors and chromatic aberrations in the system. To correct for misalignment, a general method is described for the alignment of a dual-wavelength interferometer, including the alignment of lasers, beam expanders, beam splitters for combining beams and for compensating errors in the reference surface, and the fringe imaging system. A Fourier transform test at the detector surface was conducted to validate that there is essentially no magnification difference between two wavelengths resulting from misalignment of optical system. For the chromatic aberration introduced by the optical elements in the system, a ray-trace model of the interferometer has been established, to simulate the chromatic effect that optical elements will have on the measurement results. As an experimental test, we examine an off-axis spherical mirror in a non-null condition using a highly aliased interferogram. The above alignment methods and the results are analyzed based on the simulated system errors. Using this method, we demonstrate a measured surface profile of deviation of λ/25 which is comparable to a direct measurement profile of the surface on axis using a Fizeau interferometer.
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- Award ID(s):
- 1653510
- PAR ID:
- 10087129
- Date Published:
- Journal Name:
- Proc. SPIE 10747, Optical System Alignment, Tolerancing, and Verification XII
- Volume:
- 10747
- Page Range / eLocation ID:
- 6
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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This paper presents a novel method to eliminate cosine error in precision concave and convex surface measurement by integrating a displacement probe in a precision spindle. Cosine error in surface profile measurement comes from an angular misalignment between the measurement axis and the axis of motion and negatively affects the measurement accuracy, especially in optical surface measurements. A corrective multiplier can solve this problem for spherical surface measurement, but cosine error cannot be eliminated in the case of complex optical surface measurement because current tools do not measure such surfaces along the direction normal to the measurement plane. Because the displacement probe is placed on the spindle axis, the spindle error motion will affect the shape precision and surface roughness measurement of optical components such as mirrors and lenses, and the displacement probe will measure a combination of the spindle error motion and the geometry of optical surfaces. Here, the one-dimensional concave, convex, and hollow measurement targets were used, and cosine error was fundamentally eliminated by aligning the probe on the spindle always normal to the measured surface, and compensation was made for the aerostatic bearing spindle rotational error obtained by the reversal method. The results show that this proposed measurement method cannot only eliminate cosine error but also scan the large area quickly and conveniently. In addition, measurement uncertainty and further consideration for future work were discussed.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1117/12.2323127
