Abstract

The vibration modulated stitching interferometry acquires many subaperture phases timely forming the high overlapping density subapertures for asphere phase stitching. The large number of overlapping subapertures had been proven effective in suppressing the reference error. In this research, we propose a pixel-by-pixel reference calibration method by using the averaged difference between the stitched phase and compensated phase within the overlapping subapertures. The measurement for both tested optics and calibration of the reference optics are accomplished in a single phase stitching process. The requirement for a high-quality reference optics or dedicated reference calibration procedure for subaperture stitching interferometry is therefore significantly eliminated. Both the simulation and experimental results shows the feasibility of the proposed method for high frequency reference error and most of the form error in the third order Zernike aberrations.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  4. U. Griesmann, Q. Wang, J. Soons, and R. Carakos, “A simple ball averager for reference sphere calibrations,” Proc. SPIE 5869, 58690S (2005).
    [Crossref]
  5. P. Zhou and J. H. Burge, “Limits for interferometer calibration using the random ball test,” Proc. SPIE 7426, 74260U (2009).
    [Crossref]
  6. P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, and S. O’Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J (2006).
    [Crossref]
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    [Crossref] [PubMed]
  10. J. Xue, L. Huang, B. Gao, K. Kaznatcheev, and M. Idir, “One-dimensional stitching interferometry assisted by a triple-beam interferometer,” Opt. Express 25(8), 9393–9405 (2017).
    [Crossref] [PubMed]
  11. S. Chen, S. Xue, Y. Dai, and S. Li, “Subaperture stitching test of convex aspheres by using the reconfigurable optical null,” Opt. Laser Technol. 91, 175–184 (2017).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  14. C. W. Liang, H. S. Chang, P. C. Lin, C. C. Lee, and Y. C. Chen, “Vibration modulated subaperture stitching interferometry,” Opt. Express 21(15), 18255–18260 (2013).
    [Crossref] [PubMed]
  15. H. S. Chang, C. W. Liang, P. C. Lin, and Y. C. Chen, “Measurement improvement by high overlapping density subaperture stitching interferometry,” Appl. Opt. 53(29), H102–H108 (2014).
    [Crossref] [PubMed]
  16. P. C. Lin, H. S. Chang, Y. C. Chen, and C. W. Liang, “Interferometer reference error suppression by the high-overlapping-density phase-stitching algorithm,” Appl. Opt. 53(29), H220–H226 (2014).
    [Crossref] [PubMed]

2017 (2)

J. Xue, L. Huang, B. Gao, K. Kaznatcheev, and M. Idir, “One-dimensional stitching interferometry assisted by a triple-beam interferometer,” Opt. Express 25(8), 9393–9405 (2017).
[Crossref] [PubMed]

S. Chen, S. Xue, Y. Dai, and S. Li, “Subaperture stitching test of convex aspheres by using the reconfigurable optical null,” Opt. Laser Technol. 91, 175–184 (2017).
[Crossref]

2015 (2)

2014 (3)

2013 (2)

2012 (1)

2009 (1)

P. Zhou and J. H. Burge, “Limits for interferometer calibration using the random ball test,” Proc. SPIE 7426, 74260U (2009).
[Crossref]

2006 (1)

P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, and S. O’Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J (2006).
[Crossref]

2005 (1)

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, “A simple ball averager for reference sphere calibrations,” Proc. SPIE 5869, 58690S (2005).
[Crossref]

1998 (1)

R. E. Parks, C. J. Evans, and L. Shao, “Calibration of interferometer transmission spheres,” in Optical Fabrication and Testing Workshop OSA Technical Digest Series 12, 80–83 (1998).

1990 (1)

Burge, J. H.

G. A. Smith and J. H. Burge, “Subaperture stitching tolerancing for annular ring geometry,” Appl. Opt. 54(27), 8080–8086 (2015).
[Crossref] [PubMed]

P. Zhou and J. H. Burge, “Limits for interferometer calibration using the random ball test,” Proc. SPIE 7426, 74260U (2009).
[Crossref]

Carakos, R.

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, “A simple ball averager for reference sphere calibrations,” Proc. SPIE 5869, 58690S (2005).
[Crossref]

Chang, H. S.

Chen, S.

Chen, Y. C.

Creath, K.

Dai, Y.

DeVries, G.

P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, and S. O’Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J (2006).
[Crossref]

Ehret, G.

Evans, C. J.

R. E. Parks, C. J. Evans, and L. Shao, “Calibration of interferometer transmission spheres,” in Optical Fabrication and Testing Workshop OSA Technical Digest Series 12, 80–83 (1998).

Fleig, J.

P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, and S. O’Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J (2006).
[Crossref]

Forbes, G.

P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, and S. O’Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J (2006).
[Crossref]

Gao, B.

Griesmann, U.

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, “A simple ball averager for reference sphere calibrations,” Proc. SPIE 5869, 58690S (2005).
[Crossref]

Huang, L.

Idir, M.

Kaznatcheev, K.

Knell, H.

Laubach, S.

Lee, C. C.

Lee, C. M.

Lehmann, P.

Li, S.

Liang, C. W.

Liao, W.

Lin, P. C.

Miladinovic, D.

P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, and S. O’Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J (2006).
[Crossref]

Murphy, P.

P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, and S. O’Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J (2006).
[Crossref]

O’Donohue, S.

P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, and S. O’Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J (2006).
[Crossref]

Parks, R. E.

R. E. Parks, C. J. Evans, and L. Shao, “Calibration of interferometer transmission spheres,” in Optical Fabrication and Testing Workshop OSA Technical Digest Series 12, 80–83 (1998).

Shao, L.

R. E. Parks, C. J. Evans, and L. Shao, “Calibration of interferometer transmission spheres,” in Optical Fabrication and Testing Workshop OSA Technical Digest Series 12, 80–83 (1998).

Smith, G. A.

Soons, J.

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, “A simple ball averager for reference sphere calibrations,” Proc. SPIE 5869, 58690S (2005).
[Crossref]

Wang, Q.

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, “A simple ball averager for reference sphere calibrations,” Proc. SPIE 5869, 58690S (2005).
[Crossref]

Wyant, J. C.

Xue, J.

Xue, S.

S. Chen, S. Xue, Y. Dai, and S. Li, “Subaperture stitching test of convex aspheres by using the reconfigurable optical null,” Opt. Laser Technol. 91, 175–184 (2017).
[Crossref]

S. Chen, S. Xue, Y. Dai, and S. Li, “Subaperture stitching test of large steep convex spheres,” Opt. Express 23(22), 29047–29058 (2015).
[Crossref] [PubMed]

Zhou, P.

P. Zhou and J. H. Burge, “Limits for interferometer calibration using the random ball test,” Proc. SPIE 7426, 74260U (2009).
[Crossref]

Appl. Opt. (6)

in Optical Fabrication and Testing Workshop OSA Technical Digest Series (1)

R. E. Parks, C. J. Evans, and L. Shao, “Calibration of interferometer transmission spheres,” in Optical Fabrication and Testing Workshop OSA Technical Digest Series 12, 80–83 (1998).

Opt. Express (4)

Opt. Laser Technol. (1)

S. Chen, S. Xue, Y. Dai, and S. Li, “Subaperture stitching test of convex aspheres by using the reconfigurable optical null,” Opt. Laser Technol. 91, 175–184 (2017).
[Crossref]

Proc. SPIE (3)

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, “A simple ball averager for reference sphere calibrations,” Proc. SPIE 5869, 58690S (2005).
[Crossref]

P. Zhou and J. H. Burge, “Limits for interferometer calibration using the random ball test,” Proc. SPIE 7426, 74260U (2009).
[Crossref]

P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, and S. O’Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J (2006).
[Crossref]

Other (1)

A. E. Jensen, “Absolute calibration method for laser Twyman-Green wavefront testing interferometers,” Paper ThG19, Fall OSA Meeting (October 1973), Rochester, N.Y. (abstract only).

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Figures (7)

Fig. 1
Fig. 1 Two reference locations, the blue triangle dot and red cross dot, are spread on the tested optics forming the averaging paths for constructing the reference phase, as presented by the dashed blue circles and dashed red circles on the tested optics coordinate, respectively.
Fig. 2
Fig. 2 The simulation results of the reference phase reconstruction presented with five third-order Zernike aberrations.
Fig. 3
Fig. 3 For the zero-degree astigmatism, (a) If the overlap is sheared in the tangential direction, the tangential tilt aberration presents in the overlapped region. (b)If the overlap is sheared in the sagittal direction, the sagittal tilt aberration presents in the overlapped region.
Fig. 4
Fig. 4 The experimental configuration: (a) the subaperture lattice; (b) the number of overlapped subapertures at each pixel.
Fig. 5
Fig. 5 Experimental results: (a) the stitched phase; (b) the stitching quality map.
Fig. 6
Fig. 6 The reference phase measured by (a) the random ball test by 100 measurements; (b) the HOD-SSI with 346 subapertures stitching; (c) the difference between both methods.
Fig. 7
Fig. 7 The RMS σ of the the proposed method have the relation with the number of measurements N as σ = a + b / N . measurement in (a) linear scale; (b) log-log scale with the constant a omitted.

Equations (10)

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S i = k 1 = 2 N i k 2 = 1 k 1 1 [ ( ϕ i , k 1 + n = 1 4 C i , k 1 , n ) ( ϕ i , k 2 + n = 1 4 C i , k 2 , n ) ] 2 ,
Φ i = ϕ ^ i , k ¯ = 1 N i k = 1 N i ( ϕ i , k + n = 1 4 C i , k , n ) ,
σ i = 1 N i k = 1 N i ( ϕ ^ i , k ϕ ^ i , k ¯ ) 2 ,
W M = W R E F W T ,
lim N ( 1 N j = 1 N W T j ) 0 ,
ϕ i , k = T i ( R j , k + n = 1 4 C i , k , n ) ,
R j , k = δ i + Φ i ϕ ^ i , k ,
R j , k = δ i + γ i , k ,
R j = δ i ¯ + γ i , k ¯ ,
S i = k 1 = 2 N i k 2 = 1 k 1 1 (R j 1 , k 1 -R j 1 , k 2 + n = 1 4 C i , k 1 k 2 , n ) 2 ,

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