Abstract

The newest experimental validation report of the coverage for the rotationally non-symmetric departure of a freeform surface in adaptive interferometry is about 20 µm. A compact adaptive interferometer is introduced to test unknown freeform surfaces with larger departure. The cascaded DMs (woofer and tweeter) can effectively double the measurable rotationally non-symmetric departure, to ∼80 µm using current DM technology. With a constrained decoupling control algorithm, the woofer and tweeter can averagely share the aberrations without coupling. DM surface monitoring is addressed by a time-division-monitoring (TDM) technique, which avoids separate monitoring devices and configurations and thus makes a compact configuration. Measurements of two different surfaces are presented: a nearly flat freeform with ∼40 um departure, and an off-axis paraboloid with ∼50 um of asymmetric departure.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (4)

2018 (5)

2017 (2)

S. Chen, X. Shuai, 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]

U. Bitenc, “Software compensation method for achieving high stability of Alpao deformable mirrors,” Opt. Express 25(4), 4368–4381 (2017).
[Crossref]

2016 (1)

2015 (1)

2014 (2)

2013 (2)

2012 (1)

2011 (1)

2010 (2)

M. Tricard, A. Kulawiec, M. Bauer, G. Devries, J. Fleig, G. Forbes, D. Miladinovich, and P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Ann. 59(1), 547–550 (2010).
[Crossref]

C. Li, N. Sredar, K. M. Ivers, H. Queener, and J. Porter, “A correction algorithm to simultaneously control dual deformable mirrors in a woofer-tweeter adaptive optics system,” Opt. Express 18(16), 16671–16684 (2010).
[Crossref]

2009 (3)

2008 (1)

2007 (3)

2005 (1)

2004 (1)

C. Pruss and A. H. J. Tiziani, “Dynamic null lens for aspheric testing using a membrane mirror,” Opt. Commun. 233(1-3), 15–19 (2004).
[Crossref]

2003 (1)

H. Liu, Q. Zhu, and Q. Hao, “Design of novel part-compensating lens used in aspheric testing,” Proc. SPIE 5253, 480–484 (2003).
[Crossref]

1998 (1)

Anderson, A.

Bai, J.

Bauer, M.

M. Tricard, A. Kulawiec, M. Bauer, G. Devries, J. Fleig, G. Forbes, D. Miladinovich, and P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Ann. 59(1), 547–550 (2010).
[Crossref]

Beresnev, L.

Bitenc, U.

Booth, M.

Burns, S. A.

Carhart, G.

Chaudhuri, R.

Chen, D.

Chen, S.

Choi, H.

Choi, S. S.

Chong, S.

Dai, Y.

S. Chen, X. Shuai, 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]

Deng, W.

Devries, G.

M. Tricard, A. Kulawiec, M. Bauer, G. Devries, J. Fleig, G. Forbes, D. Miladinovich, and P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Ann. 59(1), 547–550 (2010).
[Crossref]

Dong, L.

Fan, Z.

Fleig, J.

M. Tricard, A. Kulawiec, M. Bauer, G. Devries, J. Fleig, G. Forbes, D. Miladinovich, and P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Ann. 59(1), 547–550 (2010).
[Crossref]

Forbes, G.

M. Tricard, A. Kulawiec, M. Bauer, G. Devries, J. Fleig, G. Forbes, D. Miladinovich, and P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Ann. 59(1), 547–550 (2010).
[Crossref]

Fuerschbach, K.

Ge, B.

Graves, L. R.

Greivenkamp, J. E.

J. J. Sullivan and J. E. Greivenkamp, “Design of partial nulls for testing of fast aspheric surfaces,” Proc. SPIE 6671, 66710W (2007).
[Crossref]

Gudimetla, V. S. R.

Guo, H.

Hao, Q.

H. Liu, Q. Zhu, and Q. Hao, “Design of novel part-compensating lens used in aspheric testing,” Proc. SPIE 5253, 480–484 (2003).
[Crossref]

He, T.

Hofer, H.

Huang, L.

Ivers, K. M.

Jiang, W.

Jones, S. M.

Kawata, S.

Kim, D. W.

Kulawiec, A.

M. Tricard, A. Kulawiec, M. Bauer, G. Devries, J. Fleig, G. Forbes, D. Miladinovich, and P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Ann. 59(1), 547–550 (2010).
[Crossref]

Lei, X.

Li, C.

Li, D.

Li, J.

Li, S.

S. Chen, X. Shuai, 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]

Liu, D.

Liu, G.

Liu, H.

H. Liu, Q. Zhu, and Q. Hao, “Design of novel part-compensating lens used in aspheric testing,” Proc. SPIE 5253, 480–484 (2003).
[Crossref]

Liu, W.

Liu, Y.

Miladinovich, D.

M. Tricard, A. Kulawiec, M. Bauer, G. Devries, J. Fleig, G. Forbes, D. Miladinovich, and P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Ann. 59(1), 547–550 (2010).
[Crossref]

Murphy, P.

M. Tricard, A. Kulawiec, M. Bauer, G. Devries, J. Fleig, G. Forbes, D. Miladinovich, and P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Ann. 59(1), 547–550 (2010).
[Crossref]

Oliver, S. S.

Ota, T.

Papa, J.

Peng, J.

Porter, J.

Pruss, C.

C. Pruss and A. H. J. Tiziani, “Dynamic null lens for aspheric testing using a membrane mirror,” Opt. Commun. 233(1-3), 15–19 (2004).
[Crossref]

Qi, X.

Queener, H.

Rao, C.

Riker, J.

Roberts, L. C. J.

Rolland, J. P.

Shen, Y.

Shi, T.

Shuai, X.

S. Chen, X. Shuai, 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]

Sivokon, V. P.

Sredar, N.

Sullivan, J. J.

J. J. Sullivan and J. E. Greivenkamp, “Design of partial nulls for testing of fast aspheric surfaces,” Proc. SPIE 6671, 66710W (2007).
[Crossref]

Sun, H. B.

Thompson, K. P.

Tian, C.

D. Liu, C. Tian, and Y. Zhuo, “Non-null interferometric aspheric testing with partial null lens and reverse optimization,” Proc. SPIE 7426, 74260M (2009).
[Crossref]

Tie, G.

Tiziani, A. H. J.

C. Pruss and A. H. J. Tiziani, “Dynamic null lens for aspheric testing using a membrane mirror,” Opt. Commun. 233(1-3), 15–19 (2004).
[Crossref]

Tricard, M.

M. Tricard, A. Kulawiec, M. Bauer, G. Devries, J. Fleig, G. Forbes, D. Miladinovich, and P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Ann. 59(1), 547–550 (2010).
[Crossref]

Vorontsov, M.

Vorontsov, M. A.

Wang, S.

Werner, J. S.

Weyrauch, T.

Wilson, T.

Xu, B.

Xue, S.

Yan, H.

Yang, H.

Yang, P.

Yang, Y.

Yu, B.

Zawadzki, R. J.

Zhang, L.

Zhang, Y.

Zhao, W.

Zhou, S.

Zhu, Q.

H. Liu, Q. Zhu, and Q. Hao, “Design of novel part-compensating lens used in aspheric testing,” Proc. SPIE 5253, 480–484 (2003).
[Crossref]

Zhuo, Y.

D. Liu, C. Tian, and Y. Zhuo, “Non-null interferometric aspheric testing with partial null lens and reverse optimization,” Proc. SPIE 7426, 74260M (2009).
[Crossref]

Zou, W.

Appl. Opt. (4)

Chin. Opt. Lett. (2)

CIRP Ann. (1)

M. Tricard, A. Kulawiec, M. Bauer, G. Devries, J. Fleig, G. Forbes, D. Miladinovich, and P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Ann. 59(1), 547–550 (2010).
[Crossref]

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

C. Pruss and A. H. J. Tiziani, “Dynamic null lens for aspheric testing using a membrane mirror,” Opt. Commun. 233(1-3), 15–19 (2004).
[Crossref]

Opt. Express (13)

S. Xue, S. Chen, and G. Tie, “Adaptive null interferometric test using spatial light modulator for free-form surfaces,” Opt. Express 27(6), 8414–8428 (2019).
[Crossref]

S. Xue, W. Deng, and S. Chen, “Intelligence enhancement of the adaptive wavefront interferometer,” Opt. Express 27(8), 11084–11102 (2019).
[Crossref]

C. Li, N. Sredar, K. M. Ivers, H. Queener, and J. Porter, “A correction algorithm to simultaneously control dual deformable mirrors in a woofer-tweeter adaptive optics system,” Opt. Express 18(16), 16671–16684 (2010).
[Crossref]

W. Zou and S. A. Burns, “High-accuracy wavefront control for retinal imaging with Adaptive-Influence-Matrix Adaptive Optics,” Opt. Express 17(22), 20167 (2009).
[Crossref]

J. Peng, D. Chen, and H. Guo, “Variable optical null based on a yawing CGH for measuring steep acylindrical surface,” Opt. Express 26(16), 20306–20318 (2018).
[Crossref]

S. Xue, S. Chen, and Z. Fan, “Adaptive wavefront interferometry for unknown free-form surfaces,” Opt. Express 26(17), 21910–21928 (2018).
[Crossref]

S. Xue, S. Chen, and G. Tie, “Near-null interferometry using an aspheric null lens generating a broad range of variable spherical aberration for flexible test of aspheres,” Opt. Express 26(24), 31172–31189 (2018).
[Crossref]

H. Hofer, N. Sredar, H. Queener, C. Li, and J. Porter, “Wavefront sensorless adaptive optics ophthalmoscopy in the human eye,” Opt. Express 19(15), 14160–14171 (2011).
[Crossref]

X. Lei, S. Wang, H. Yan, W. Liu, L. Dong, P. Yang, and B. Xu, “Double-deformable-mirror adaptive optics system for laser beam cleanup using blind optimization,” Opt. Express 20(20), 22143–22157 (2012).
[Crossref]

W. Liu, L. Dong, P. Yang, X. Lei, H. Yan, and B. Xu, “A Zernike mode decomposition decoupling control algorithm for dual deformable mirrors adaptive optics system,” Opt. Express 21(20), 23885–23895 (2013).
[Crossref]

U. Bitenc, “Software compensation method for achieving high stability of Alpao deformable mirrors,” Opt. Express 25(4), 4368–4381 (2017).
[Crossref]

L. Zhang, D. Liu, T. Shi, Y. Yang, S. Chong, B. Ge, Y. Shen, and J. Bai, “Aspheric subaperture stitching based on system modeling,” Opt. Express 23(15), 19176–19188 (2015).
[Crossref]

L. Zhang, S. Zhou, D. Li, Y. Liu, T. He, B. Yu, and J. Li, “Pure adaptive interferometer for free form surfaces metrology,” Opt. Express 26(7), 7888 (2018).
[Crossref]

Opt. Laser Technol. (1)

S. Chen, X. Shuai, 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]

Opt. Lett. (5)

Proc. SPIE (3)

H. Liu, Q. Zhu, and Q. Hao, “Design of novel part-compensating lens used in aspheric testing,” Proc. SPIE 5253, 480–484 (2003).
[Crossref]

J. J. Sullivan and J. E. Greivenkamp, “Design of partial nulls for testing of fast aspheric surfaces,” Proc. SPIE 6671, 66710W (2007).
[Crossref]

D. Liu, C. Tian, and Y. Zhuo, “Non-null interferometric aspheric testing with partial null lens and reverse optimization,” Proc. SPIE 7426, 74260M (2009).
[Crossref]

Other (1)

Alpao corporation, “Deformable Mirror datasheet,” https://www.alpao.com/adaptive-optics/deformable-mirrors.html (2019).

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Figures (10)

Fig. 1.
Fig. 1. System layout of the compact interferometer.
Fig. 2.
Fig. 2. TDM process for DMs monitoring (a) woofer monitoring, (b) middle process, (c) tweeter monitoring.
Fig. 3.
Fig. 3. (a) Wavefront coupling illustration, (b)-(d) traditional decoupling, (e)-(g) desired decoupling.
Fig. 4.
Fig. 4. Flow chart of cascaded DMs decoupling with sharing in adaptive interferometer.
Fig. 5.
Fig. 5. Interferograms in the whole experiment process, (a) uncompensated interferogram, (b) interferogram segmentation, (c)-(f) are interferograms in the process of SPGD decoupling, (h) and (j) are the fringes characterizing the woofer and tweeter surfaces after decoupling, (i) and (k) are those after aberration sharing step, which come from (h) and (j), respectively, (g) is the final interferogram characterizing tested freeform surface.
Fig. 6.
Fig. 6. The performance comparison in the first step between woofer only, tweeter only, woofer-tweeter without decoupling and woofer-tweeter with decoupling, (a) the residual pixel number of unresolvable regions in the mentioned four cases with iterations, (b) the resulted interferograms in the four cases.
Fig. 7.
Fig. 7. DM surfaces stability in different initial stroke in five minutes at 25 °C,(a)-(c) are three repetitive experimental results of the woofer, (d)-(f) are three repetitive experimental results of the tweeter.
Fig. 8.
Fig. 8. Final surface figure map and contour line, (a) surface figure map by our adaptive interferometer, (b) contour lines comparison with Taylor Hobson profilometer. (c) and (d) are surface figure maps tested in the other two repetitive experiments.
Fig. 9.
Fig. 9. Test result of the off-axis paraboloidal mirror, (a) the interferogram variation process, (b) the interferograms and corresponding surface sag of the woofer, (c) the interferograms and corresponding surface sag of the tweeter, (d) the surface figure map by the adaptive interferometer, (e) surface figure error, (f) surface figure error by Zygo interferometer, (g) the difference of (e) and (f) with mapping.
Fig. 10.
Fig. 10. Multiple DCD design for large departure test with general commercial interferometers.

Tables (2)

Tables Icon

Table 1. The specific error values

Tables Icon

Table 2. Correction capacity comparison in different aberrations form

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

J i  = N ( I u n r e s o v i )
δ J i = J ( V w i + δ V w i ; V t i + δ V t i ) J ( V w i ; V t i ) ,
{ V w i + 1 = V w i γ w δ J δ V w i V t i + 1 = V t i γ t δ J δ V t i ,
{ A w = B w V w A t = B t V t .
{ A w = [ a w 2 , a w 3 , , a w q , 0 , 0 , , 0 ] T A t = [ 0 , 0 , , 0 , a t ( q + 1 ) , a t ( q + 2 ) , , a t 37 ] T ,
δ J i = J ( A w i + δ A w i ; A t i + δ A t i ) J ( A w i ; A t i ) ,
{ A w i + 1 = A w i  -  γ w δ J δ A w i A t i + 1 = A t i  -  γ t δ J δ A t i ,
{ A w = [ a w 2 , a w 3 , , a w q , 0 , 0 , , 0 ] A t = [ a t 2 , a t 3 , , a t q , a t ( q + 1 ) , , a t 37 ] .
{ A w i + 1 = A w i  +  γ w δ J δ A w i A t i + 1 = A t i γ t δ J δ A t i  =  A t i γ w δ J δ A w i .
J i  = PV ( I i )  +  | PV ( A w i Z ) PV ( A t i Z ) | ,