Abstract

The ideal mapping geometry in a Fizeau interferometer is to map equal height increments on a flat object and equal angle increments on a spherical surface to equal heights on the detector. So the initial intent of the optical design of Fizeau transmission spheres (TSs) is to provide Rθ mapping geometry for equal angle increments. The corresponding unequal heights mapping will introduce retrace error as coma when linear carrier fringes exist. On the contrary, equal heights mapping with Rsinθ mapping geometry will avoid linear carrier fringes induced coma error. These two different mapping geometries conflict especially for the TS with a small f-number. In this paper, we will first explore the design and the performance of the f/0.75  TS according to the two different mapping geometries, and then evaluate the mapping geometry for the commercial ZYGO f/0.75  TS, and give some engineering notes for the designers, the metrologists, and the fabricators in the optical laboratory.

© 2018 Optical Society of America

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References

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2017 (1)

W. Peng, C. Ho, W. Lin, Z. Yu, C. Huang, C. Kuo, and W. Hsu, “Design, tolerance analysis, fabrication, and testing of a 6-in. dual-wavelength transmission sphere for a Fizeau interferometers,” Opt. Eng. 56, 035105 (2017).
[Crossref]

2015 (2)

P. de Groot, T. Dresel, and B. Truax, “Axial alignment for high-precision interferometric measurements of steeply-curved spheres,” Surf. Topogr. Prop. 3, 044004 (2015).
[Crossref]

Q. Yuan, Z. Gao, and D. Zhu, “Applying slope constrained Qbfs aspheres for aspherictiy redistribution in the design of infrared transmission spheres,” Appl. Opt. 54, 6857–6864 (2015).
[Crossref]

2011 (2)

2010 (1)

J. H. Burge, C. Zhao, and P. Zhou, “Imaging issues for interferometry with CGH null correctors,” Proc. SPIE 7739, 77390T (2010).
[Crossref]

2009 (1)

2008 (1)

M. Novak, C. Zhao, and J. H. Burge, “Distortion mapping correction in aspheric null testing,” Proc. SPIE 7063, 706313 (2008).
[Crossref]

Burge, J. H.

J. H. Burge, C. Zhao, and P. Zhou, “Imaging issues for interferometry with CGH null correctors,” Proc. SPIE 7739, 77390T (2010).
[Crossref]

M. Novak, C. Zhao, and J. H. Burge, “Distortion mapping correction in aspheric null testing,” Proc. SPIE 7063, 706313 (2008).
[Crossref]

Chen, C.

de Groot, P.

P. de Groot, T. Dresel, and B. Truax, “Axial alignment for high-precision interferometric measurements of steeply-curved spheres,” Surf. Topogr. Prop. 3, 044004 (2015).
[Crossref]

Dresel, T.

P. de Groot, T. Dresel, and B. Truax, “Axial alignment for high-precision interferometric measurements of steeply-curved spheres,” Surf. Topogr. Prop. 3, 044004 (2015).
[Crossref]

Gao, Z.

Geary, J. M.

J. M. Geary, Optical Testing: A Practical Introduction for Scientists, Engineers, Optical Designers, Students and Optical Workshop Personnel (Willmann-Bell, 2008).

Ho, C.

W. Peng, C. Ho, W. Lin, Z. Yu, C. Huang, C. Kuo, and W. Hsu, “Design, tolerance analysis, fabrication, and testing of a 6-in. dual-wavelength transmission sphere for a Fizeau interferometers,” Opt. Eng. 56, 035105 (2017).
[Crossref]

Holmes, M. L.

D. M. Sykora and M. L. Holmes, “Dynamic measurements using a Fizeau interferometer,” Proc. SPIE 8082, 80821R (2011).
[Crossref]

Hsu, W.

W. Peng, C. Ho, W. Lin, Z. Yu, C. Huang, C. Kuo, and W. Hsu, “Design, tolerance analysis, fabrication, and testing of a 6-in. dual-wavelength transmission sphere for a Fizeau interferometers,” Opt. Eng. 56, 035105 (2017).
[Crossref]

Huang, C.

W. Peng, C. Ho, W. Lin, Z. Yu, C. Huang, C. Kuo, and W. Hsu, “Design, tolerance analysis, fabrication, and testing of a 6-in. dual-wavelength transmission sphere for a Fizeau interferometers,” Opt. Eng. 56, 035105 (2017).
[Crossref]

Kuechel, M.

D. M. Sykora and M. Kuechel, “In situ calibration of interferometers,” U.S. patent9234739 B2 (12January, 2016).

Kuo, C.

W. Peng, C. Ho, W. Lin, Z. Yu, C. Huang, C. Kuo, and W. Hsu, “Design, tolerance analysis, fabrication, and testing of a 6-in. dual-wavelength transmission sphere for a Fizeau interferometers,” Opt. Eng. 56, 035105 (2017).
[Crossref]

Lin, W.

W. Peng, C. Ho, W. Lin, Z. Yu, C. Huang, C. Kuo, and W. Hsu, “Design, tolerance analysis, fabrication, and testing of a 6-in. dual-wavelength transmission sphere for a Fizeau interferometers,” Opt. Eng. 56, 035105 (2017).
[Crossref]

Novak, M.

M. Novak, C. Zhao, and J. H. Burge, “Distortion mapping correction in aspheric null testing,” Proc. SPIE 7063, 706313 (2008).
[Crossref]

Peng, W.

W. Peng, C. Ho, W. Lin, Z. Yu, C. Huang, C. Kuo, and W. Hsu, “Design, tolerance analysis, fabrication, and testing of a 6-in. dual-wavelength transmission sphere for a Fizeau interferometers,” Opt. Eng. 56, 035105 (2017).
[Crossref]

Reardon, P. J.

Robinson, B. M.

Sykora, D. M.

D. M. Sykora and M. L. Holmes, “Dynamic measurements using a Fizeau interferometer,” Proc. SPIE 8082, 80821R (2011).
[Crossref]

D. M. Sykora and M. Kuechel, “In situ calibration of interferometers,” U.S. patent9234739 B2 (12January, 2016).

Truax, B.

P. de Groot, T. Dresel, and B. Truax, “Axial alignment for high-precision interferometric measurements of steeply-curved spheres,” Surf. Topogr. Prop. 3, 044004 (2015).
[Crossref]

Wang, D.

Yang, Y.

Yu, Z.

W. Peng, C. Ho, W. Lin, Z. Yu, C. Huang, C. Kuo, and W. Hsu, “Design, tolerance analysis, fabrication, and testing of a 6-in. dual-wavelength transmission sphere for a Fizeau interferometers,” Opt. Eng. 56, 035105 (2017).
[Crossref]

Yuan, Q.

Zhao, C.

J. H. Burge, C. Zhao, and P. Zhou, “Imaging issues for interferometry with CGH null correctors,” Proc. SPIE 7739, 77390T (2010).
[Crossref]

M. Novak, C. Zhao, and J. H. Burge, “Distortion mapping correction in aspheric null testing,” Proc. SPIE 7063, 706313 (2008).
[Crossref]

Zhou, P.

J. H. Burge, C. Zhao, and P. Zhou, “Imaging issues for interferometry with CGH null correctors,” Proc. SPIE 7739, 77390T (2010).
[Crossref]

Zhu, D.

Zhuo, Y.

Appl. Opt. (3)

Opt. Eng. (1)

W. Peng, C. Ho, W. Lin, Z. Yu, C. Huang, C. Kuo, and W. Hsu, “Design, tolerance analysis, fabrication, and testing of a 6-in. dual-wavelength transmission sphere for a Fizeau interferometers,” Opt. Eng. 56, 035105 (2017).
[Crossref]

Proc. SPIE (3)

J. H. Burge, C. Zhao, and P. Zhou, “Imaging issues for interferometry with CGH null correctors,” Proc. SPIE 7739, 77390T (2010).
[Crossref]

D. M. Sykora and M. L. Holmes, “Dynamic measurements using a Fizeau interferometer,” Proc. SPIE 8082, 80821R (2011).
[Crossref]

M. Novak, C. Zhao, and J. H. Burge, “Distortion mapping correction in aspheric null testing,” Proc. SPIE 7063, 706313 (2008).
[Crossref]

Surf. Topogr. Prop. (1)

P. de Groot, T. Dresel, and B. Truax, “Axial alignment for high-precision interferometric measurements of steeply-curved spheres,” Surf. Topogr. Prop. 3, 044004 (2015).
[Crossref]

Other (2)

D. M. Sykora and M. Kuechel, “In situ calibration of interferometers,” U.S. patent9234739 B2 (12January, 2016).

J. M. Geary, Optical Testing: A Practical Introduction for Scientists, Engineers, Optical Designers, Students and Optical Workshop Personnel (Willmann-Bell, 2008).

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Figures (5)

Fig. 1.
Fig. 1. Imaging bundle of the Fizeau interferometer: (a) test a plane surface, (b) test a spherical surface.
Fig. 2.
Fig. 2. Illumination bundle of the Fizeau f/0.75 TS: (a) the optical layout, (b) footprint diagram on the entrance pupil and on the reference surface with Rsinθ mapping geometry, (c) footprint diagram on the reference surface with R-θ mapping geometry.
Fig. 3.
Fig. 3. OPD error results in the interferometer model: OPD error for a circular carrier with eight fringes using the TS with (a) Rsinθ mapping geometry and (b) R-θ mapping geometry; OPD error for a linear carrier with eight fringes using the TS with (c) Rsinθ mapping geometry and (d) R-θ mapping geometry; PV value of OPD error varied with linear carrier fringes using the TS with (e) Rsinθ mapping geometry and (f) R-θ mapping geometry.
Fig. 4.
Fig. 4. Mapping distortion analysis of the ZYGO f/0.75  TS: (a) a photograph of fiducial mask, (b) optical layout for TS mapping distortion measurement, (c) image of the distorted grid on the diffuser, (d) distorted grid for ideal Rsinθ mapping geometry, (e) distorted grid for ideal Rθ mapping geometry, and (f) footprint spacing comparison.
Fig. 5.
Fig. 5. OPD error results due to eight carrier fringes using the ZYGO f/0.75  TS: (a) circular carrier, and (b) linear carrier.

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