Abstract

In this paper, we demonstrate the development of a point-cloud metrology method for the noncontact, high resolution, high precision testing of freeform surfaces. The method leverages swept source optical coherence tomography together with a common-path setup in the sample arm configured to mitigate the axial jitter caused by scanning and environmental perturbations. The lateral x-y scanning field was also rigorously evaluated for the sampling step, linearity, straightness, and orthogonality. Based on the finely engineered system hardware, a comprehensive system model was developed capable of characterizing the vertical displacement sensitivity and lateral scanning noise. The model enables predicting the point-cloud surface-metrology uncertainty map of any freeform surface and guiding the selection of optimum experimental conditions. A system was then assembled and experimentally evaluated first with flat and spherical standards to demonstrate the measurement uncertainty. Results of measuring an Alvarez freeform surface with 400-µm peak-to-valley sag show 93 nm (< λ/14) precision and 128 nm (< λ/10) root-mean-square residual from the nominal shape. The high resolution measurements also reveal mid spatial frequency structures on the test part.

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

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References

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2018 (1)

2017 (3)

J. Reimers, A. Bauer, K. P. Thompson, and J. P. Rolland, “Freeform spectrometer enabling increased compactness,” Light Sci. Appl. 6(7), e17026 (2017).
[Crossref]

S. Wills, “Freeform optics: notes from the revolution,” Opt. Photonics News 28(7), 34–41 (2017).
[Crossref]

K. Liang and M. A. Alonso, “Understanding the effects of groove structures on the MTF,” Opt. Express 25(16), 18827–18841 (2017).
[Crossref] [PubMed]

2016 (2)

2015 (4)

2014 (5)

2013 (4)

I. Kaya and J. P. Rolland, “Hybrid RBF and local ϕ-polynomial freeform surfaces,” Adv. Opt. Technol. 2(1), 81–88 (2013).

P. Meemon, J. Yao, K. S. Lee, K. P. Thompson, M. Ponting, E. Baer, and J. P. Rolland, “Optical coherence tomography enabling non destructive metrology of layered polymeric GRIN material,” Sci. Rep. 3(1), 1709 (2013).
[Crossref]

Y. Zhou, Y. S. Ghim, A. Fard, and A. Davies, “Application of the random ball test for calibrating slope-dependent errors in profilometry measurements,” Appl. Opt. 52(24), 5925–5931 (2013).
[Crossref] [PubMed]

J. Yao, P. Meemon, K. S. Lee, and J. P. Rolland, “Nondestructive metrology by optical coherence tomography empowering manufacturing iterations of layered polymeric optical materials,” Opt. Eng. 52(11), 112111 (2013).
[Crossref]

2012 (3)

P. J. Smilie, B. S. Dutterer, J. L. Lineberger, M. A. Davies, and T. J. Suleski, “Design and characterization of an infrared Alvarez lens,” Opt. Eng. 51(1), 013006 (2012).
[Crossref]

C. Faber, E. Olesch, R. Krobot, and G. Häusler, “Deflectometry challenges interferometry – the competition gets tougher!” Proc. SPIE 8493, 84930R (2012).
[Crossref]

K. P. Thompson and J. P. Rolland, “A revolution in imaging optical design,” Opt. Photonics News 23(6), 30–35 (2012).
[Crossref]

2011 (1)

2010 (3)

2009 (2)

2007 (2)

E. Savio, L. De Chiffre, and R. Schmitt, “Metrology of freeform shaped parts,” CIRP Annals - Manufacturing Technology 56(2), 810–835 (2007).
[Crossref]

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys. 3(2), 129–134 (2007).
[Crossref] [PubMed]

2006 (1)

2005 (2)

2004 (1)

M. C. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE 5457, 366 (2004).
[Crossref]

2003 (2)

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14(5), 38–43 (2003).
[Crossref]

M. Choma, M. Sarunic, C. Yang, and J. Izatt, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Express 11(18), 2183–2189 (2003).
[Crossref] [PubMed]

2000 (1)

F. A. Potra and S. J. Wright, “Interior-point methods,” J. Comput. Appl. Math. 124(1–2), 281–302 (2000).
[Crossref]

1997 (1)

D. Perard and J. Beyerer, “Three-dimensional measurement of specular free-form surfaces with a structured-lighting reflection technique,” Proc. SPIE 3204, 74–80 (1997).
[Crossref]

1992 (1)

M. A. Browne, O. Akinyemi, and A. Boyde, “Confocal surface profiling utilizing chromatic aberration,” Scanning 14(3), 145–153 (1992).
[Crossref]

1991 (1)

1988 (1)

1963 (1)

Akcay, A. C.

Akinyemi, O.

M. A. Browne, O. Akinyemi, and A. Boyde, “Confocal surface profiling utilizing chromatic aberration,” Scanning 14(3), 145–153 (1992).
[Crossref]

Alonso, M. A.

Angel, R. P.

Baer, E.

P. Meemon, J. Yao, K. S. Lee, K. P. Thompson, M. Ponting, E. Baer, and J. P. Rolland, “Optical coherence tomography enabling non destructive metrology of layered polymeric GRIN material,” Sci. Rep. 3(1), 1709 (2013).
[Crossref]

Baer, G.

Bauer, A.

J. Reimers, A. Bauer, K. P. Thompson, and J. P. Rolland, “Freeform spectrometer enabling increased compactness,” Light Sci. Appl. 6(7), e17026 (2017).
[Crossref]

A. Bauer and J. P. Rolland, “Visual space assessment of two all-reflective, freeform, optical see-through head-worn displays,” Opt. Express 22(11), 13155–13163 (2014).
[Crossref] [PubMed]

Beyerer, J.

D. Perard and J. Beyerer, “Three-dimensional measurement of specular free-form surfaces with a structured-lighting reflection technique,” Proc. SPIE 3204, 74–80 (1997).
[Crossref]

Boppart, S. A.

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys. 3(2), 129–134 (2007).
[Crossref] [PubMed]

Bothe, T.

T. Bothe, W. Li, C. von Kopylow, and W. P. O. Juptner, “High-resolution 3D shape measurement on specular surfaces by fringe reflection,” Proc. SPIE5457, 411 (2004).
[Crossref]

Boyde, A.

M. A. Browne, O. Akinyemi, and A. Boyde, “Confocal surface profiling utilizing chromatic aberration,” Scanning 14(3), 145–153 (1992).
[Crossref]

Browne, M. A.

M. A. Browne, O. Akinyemi, and A. Boyde, “Confocal surface profiling utilizing chromatic aberration,” Scanning 14(3), 145–153 (1992).
[Crossref]

Brunelle, M.

K. Medicus, J. D. Nelson, and M. Brunelle, “The need for fiducials on freeform optical surfaces,” Proc. SPIE 9582, 958204 (2015).

Burge, J. H.

Carney, P. S.

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys. 3(2), 129–134 (2007).
[Crossref] [PubMed]

Chen, M.

Chen, S.

Cheng, D.

Cheng, H.

Cho, S. W.

Choi, S.

Choma, M.

Chun, S. K.

Cirucci, N.

J. Huang, J. Yao, N. Cirucci, T. Ivanov, and J. P. Rolland, “Performance analysis of optical coherence tomography in the context of a thickness estimation task,” J. Biomed. Opt. 20(12), 121306 (2015).
[PubMed]

Clarkson, E.

Dai, Y.

Dallas, W.

Davies, A.

Davies, M. A.

P. J. Smilie, B. S. Dutterer, J. L. Lineberger, M. A. Davies, and T. J. Suleski, “Design and characterization of an infrared Alvarez lens,” Opt. Eng. 51(1), 013006 (2012).
[Crossref]

De Chiffre, L.

E. Savio, L. De Chiffre, and R. Schmitt, “Metrology of freeform shaped parts,” CIRP Annals - Manufacturing Technology 56(2), 810–835 (2007).
[Crossref]

Delemos, T.

Dumas, P.

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14(5), 38–43 (2003).
[Crossref]

Dutterer, B. S.

P. J. Smilie, B. S. Dutterer, J. L. Lineberger, M. A. Davies, and T. J. Suleski, “Design and characterization of an infrared Alvarez lens,” Opt. Eng. 51(1), 013006 (2012).
[Crossref]

Faber, C.

C. Faber, E. Olesch, R. Krobot, and G. Häusler, “Deflectometry challenges interferometry – the competition gets tougher!” Proc. SPIE 8493, 84930R (2012).
[Crossref]

Falaggis, K.

Fard, A.

Fleig, J.

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14(5), 38–43 (2003).
[Crossref]

Forbes, G.

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14(5), 38–43 (2003).
[Crossref]

Fuerschbach, K.

Gan, X.

Ghim, Y. S.

Gu, M.

Hao, Q.

Hausler, G.

M. C. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE 5457, 366 (2004).
[Crossref]

Häusler, G.

C. Faber, E. Olesch, R. Krobot, and G. Häusler, “Deflectometry challenges interferometry – the competition gets tougher!” Proc. SPIE 8493, 84930R (2012).
[Crossref]

Hu, Y.

Huang, J.

Ivanov, T.

J. Huang, J. Yao, N. Cirucci, T. Ivanov, and J. P. Rolland, “Performance analysis of optical coherence tomography in the context of a thickness estimation task,” J. Biomed. Opt. 20(12), 121306 (2015).
[PubMed]

Izatt, J.

Jang, H.

Jin, G.

Juptner, W. P. O.

T. Bothe, W. Li, C. von Kopylow, and W. P. O. Juptner, “High-resolution 3D shape measurement on specular surfaces by fringe reflection,” Proc. SPIE5457, 411 (2004).
[Crossref]

Kaminski, J.

M. C. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE 5457, 366 (2004).
[Crossref]

Kaya, I.

I. Kaya and J. P. Rolland, “Hybrid RBF and local ϕ-polynomial freeform surfaces,” Adv. Opt. Technol. 2(1), 81–88 (2013).

Kim, C. S.

Knauer, M. C.

M. C. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE 5457, 366 (2004).
[Crossref]

Koliopoulos, C. L.

Krobot, R.

C. Faber, E. Olesch, R. Krobot, and G. Häusler, “Deflectometry challenges interferometry – the competition gets tougher!” Proc. SPIE 8493, 84930R (2012).
[Crossref]

Kuhn, W. P.

Kurokawa, T.

Lawrence, G. N.

Lee, K. S.

P. Meemon, J. Yao, K. S. Lee, K. P. Thompson, M. Ponting, E. Baer, and J. P. Rolland, “Optical coherence tomography enabling non destructive metrology of layered polymeric GRIN material,” Sci. Rep. 3(1), 1709 (2013).
[Crossref]

J. Yao, P. Meemon, K. S. Lee, and J. P. Rolland, “Nondestructive metrology by optical coherence tomography empowering manufacturing iterations of layered polymeric optical materials,” Opt. Eng. 52(11), 112111 (2013).
[Crossref]

S. Murali, P. Meemon, K. S. Lee, W. P. Kuhn, K. P. Thompson, and J. P. Rolland, “Assessment of a liquid lens enabled in vivo optical coherence microscope,” Appl. Opt. 49(16), D145–D156 (2010).
[Crossref] [PubMed]

K. S. Lee, A. C. Akcay, T. Delemos, E. Clarkson, and J. P. Rolland, “Dispersion control with a Fourier-domain optical delay line in a fiber-optic imaging interferometer,” Appl. Opt. 44(19), 4009–4022 (2005).
[Crossref] [PubMed]

Lee, Y. W.

Li, S.

Li, T.

Li, W.

T. Bothe, W. Li, C. von Kopylow, and W. P. O. Juptner, “High-resolution 3D shape measurement on specular surfaces by fringe reflection,” Proc. SPIE5457, 411 (2004).
[Crossref]

Liang, K.

Lineberger, J. L.

P. J. Smilie, B. S. Dutterer, J. L. Lineberger, M. A. Davies, and T. J. Suleski, “Design and characterization of an infrared Alvarez lens,” Opt. Eng. 51(1), 013006 (2012).
[Crossref]

Liu, Y. M.

Ma, B.

Marcos, S.

Marks, D. L.

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys. 3(2), 129–134 (2007).
[Crossref] [PubMed]

Medicus, K.

K. Medicus, J. D. Nelson, and M. Brunelle, “The need for fiducials on freeform optical surfaces,” Proc. SPIE 9582, 958204 (2015).

Meemon, P.

Milster, T. D.

Moteki, D.

Murali, S.

Murphy, P.

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14(5), 38–43 (2003).
[Crossref]

Nelson, J. D.

K. Medicus, J. D. Nelson, and M. Brunelle, “The need for fiducials on freeform optical surfaces,” Proc. SPIE 9582, 958204 (2015).

Offner, A.

Olesch, E.

C. Faber, E. Olesch, R. Krobot, and G. Häusler, “Deflectometry challenges interferometry – the competition gets tougher!” Proc. SPIE 8493, 84930R (2012).
[Crossref]

Ortiz, S.

Osten, W.

Park, N. S.

Parks, R. E.

Perard, D.

D. Perard and J. Beyerer, “Three-dimensional measurement of specular free-form surfaces with a structured-lighting reflection technique,” Proc. SPIE 3204, 74–80 (1997).
[Crossref]

Ponting, M.

Potra, F. A.

F. A. Potra and S. J. Wright, “Interior-point methods,” J. Comput. Appl. Math. 124(1–2), 281–302 (2000).
[Crossref]

Pruss, C.

Ralston, T. S.

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys. 3(2), 129–134 (2007).
[Crossref] [PubMed]

Reimers, J.

J. Reimers, A. Bauer, K. P. Thompson, and J. P. Rolland, “Freeform spectrometer enabling increased compactness,” Light Sci. Appl. 6(7), e17026 (2017).
[Crossref]

Remon, L.

Rhee, H. G.

Rolland, J. P.

J. Reimers, A. Bauer, K. P. Thompson, and J. P. Rolland, “Freeform spectrometer enabling increased compactness,” Light Sci. Appl. 6(7), e17026 (2017).
[Crossref]

J. Yao, K. P. Thompson, B. Ma, M. Ponting, and J. P. Rolland, “Volumetric rendering and metrology of spherical gradient refractive index lens imaged by angular scan optical coherence tomography system,” Opt. Express 24(17), 19388–19404 (2016).
[Crossref] [PubMed]

J. Yao, J. Huang, P. Meemon, M. Ponting, and J. P. Rolland, “Simultaneous estimation of thickness and refractive index of layered gradient refractive index optics using a hybrid confocal-scan swept-source optical coherence tomography system,” Opt. Express 23(23), 30149–30164 (2015).
[Crossref] [PubMed]

J. Huang, J. Yao, N. Cirucci, T. Ivanov, and J. P. Rolland, “Performance analysis of optical coherence tomography in the context of a thickness estimation task,” J. Biomed. Opt. 20(12), 121306 (2015).
[PubMed]

J. Yao, P. Meemon, M. Ponting, and J. P. Rolland, “Angular scan optical coherence tomography imaging and metrology of spherical gradient refractive index preforms,” Opt. Express 23(5), 6428–6443 (2015).
[Crossref] [PubMed]

A. Bauer and J. P. Rolland, “Visual space assessment of two all-reflective, freeform, optical see-through head-worn displays,” Opt. Express 22(11), 13155–13163 (2014).
[Crossref] [PubMed]

K. Fuerschbach, K. P. Thompson, and J. P. Rolland, “Interferometric measurement of a concave, φ-polynomial, Zernike mirror,” Opt. Lett. 39(1), 18–21 (2014).
[Crossref] [PubMed]

I. Kaya and J. P. Rolland, “Hybrid RBF and local ϕ-polynomial freeform surfaces,” Adv. Opt. Technol. 2(1), 81–88 (2013).

J. Yao, P. Meemon, K. S. Lee, and J. P. Rolland, “Nondestructive metrology by optical coherence tomography empowering manufacturing iterations of layered polymeric optical materials,” Opt. Eng. 52(11), 112111 (2013).
[Crossref]

P. Meemon, J. Yao, K. S. Lee, K. P. Thompson, M. Ponting, E. Baer, and J. P. Rolland, “Optical coherence tomography enabling non destructive metrology of layered polymeric GRIN material,” Sci. Rep. 3(1), 1709 (2013).
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K. P. Thompson and J. P. Rolland, “A revolution in imaging optical design,” Opt. Photonics News 23(6), 30–35 (2012).
[Crossref]

K. Fuerschbach, J. P. Rolland, and K. P. Thompson, “A new family of optical systems employing φ-polynomial surfaces,” Opt. Express 19(22), 21919–21928 (2011).
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S. Murali, P. Meemon, K. S. Lee, W. P. Kuhn, K. P. Thompson, and J. P. Rolland, “Assessment of a liquid lens enabled in vivo optical coherence microscope,” Appl. Opt. 49(16), D145–D156 (2010).
[Crossref] [PubMed]

K. S. Lee, A. C. Akcay, T. Delemos, E. Clarkson, and J. P. Rolland, “Dispersion control with a Fourier-domain optical delay line in a fiber-optic imaging interferometer,” Appl. Opt. 44(19), 4009–4022 (2005).
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Song, W.

Su, P.

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P. J. Smilie, B. S. Dutterer, J. L. Lineberger, M. A. Davies, and T. J. Suleski, “Design and characterization of an infrared Alvarez lens,” Opt. Eng. 51(1), 013006 (2012).
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Tsutsumi, H.

H. Takeuchi, K. Yosizumi, and H. Tsutsumi, “Ultrahigh accurate 3-D profilometer using atomic force probe of measuring nanometer,” Proc. ASPE Winter Topical Meeting on Free-form optics: Design, Fabrication, Metrology and Assembly, 102–107 (2004).

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T. Bothe, W. Li, C. von Kopylow, and W. P. O. Juptner, “High-resolution 3D shape measurement on specular surfaces by fringe reflection,” Proc. SPIE5457, 411 (2004).
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F. A. Potra and S. J. Wright, “Interior-point methods,” J. Comput. Appl. Math. 124(1–2), 281–302 (2000).
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J. Yao, K. P. Thompson, B. Ma, M. Ponting, and J. P. Rolland, “Volumetric rendering and metrology of spherical gradient refractive index lens imaged by angular scan optical coherence tomography system,” Opt. Express 24(17), 19388–19404 (2016).
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J. Huang, J. Yao, N. Cirucci, T. Ivanov, and J. P. Rolland, “Performance analysis of optical coherence tomography in the context of a thickness estimation task,” J. Biomed. Opt. 20(12), 121306 (2015).
[PubMed]

J. Yao, P. Meemon, M. Ponting, and J. P. Rolland, “Angular scan optical coherence tomography imaging and metrology of spherical gradient refractive index preforms,” Opt. Express 23(5), 6428–6443 (2015).
[Crossref] [PubMed]

J. Yao, J. Huang, P. Meemon, M. Ponting, and J. P. Rolland, “Simultaneous estimation of thickness and refractive index of layered gradient refractive index optics using a hybrid confocal-scan swept-source optical coherence tomography system,” Opt. Express 23(23), 30149–30164 (2015).
[Crossref] [PubMed]

J. Yao, P. Meemon, K. S. Lee, and J. P. Rolland, “Nondestructive metrology by optical coherence tomography empowering manufacturing iterations of layered polymeric optical materials,” Opt. Eng. 52(11), 112111 (2013).
[Crossref]

P. Meemon, J. Yao, K. S. Lee, K. P. Thompson, M. Ponting, E. Baer, and J. P. Rolland, “Optical coherence tomography enabling non destructive metrology of layered polymeric GRIN material,” Sci. Rep. 3(1), 1709 (2013).
[Crossref]

Yosizumi, K.

H. Takeuchi, K. Yosizumi, and H. Tsutsumi, “Ultrahigh accurate 3-D profilometer using atomic force probe of measuring nanometer,” Proc. ASPE Winter Topical Meeting on Free-form optics: Design, Fabrication, Metrology and Assembly, 102–107 (2004).

Zhou, Y.

Adv. Opt. Technol. (1)

I. Kaya and J. P. Rolland, “Hybrid RBF and local ϕ-polynomial freeform surfaces,” Adv. Opt. Technol. 2(1), 81–88 (2013).

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K. S. Lee, A. C. Akcay, T. Delemos, E. Clarkson, and J. P. Rolland, “Dispersion control with a Fourier-domain optical delay line in a fiber-optic imaging interferometer,” Appl. Opt. 44(19), 4009–4022 (2005).
[Crossref] [PubMed]

S. Murali, P. Meemon, K. S. Lee, W. P. Kuhn, K. P. Thompson, and J. P. Rolland, “Assessment of a liquid lens enabled in vivo optical coherence microscope,” Appl. Opt. 49(16), D145–D156 (2010).
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Y. Zhou, Y. S. Ghim, A. Fard, and A. Davies, “Application of the random ball test for calibrating slope-dependent errors in profilometry measurements,” Appl. Opt. 52(24), 5925–5931 (2013).
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E. Savio, L. De Chiffre, and R. Schmitt, “Metrology of freeform shaped parts,” CIRP Annals - Manufacturing Technology 56(2), 810–835 (2007).
[Crossref]

J. Biomed. Opt. (1)

J. Huang, J. Yao, N. Cirucci, T. Ivanov, and J. P. Rolland, “Performance analysis of optical coherence tomography in the context of a thickness estimation task,” J. Biomed. Opt. 20(12), 121306 (2015).
[PubMed]

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F. A. Potra and S. J. Wright, “Interior-point methods,” J. Comput. Appl. Math. 124(1–2), 281–302 (2000).
[Crossref]

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

Light Sci. Appl. (1)

J. Reimers, A. Bauer, K. P. Thompson, and J. P. Rolland, “Freeform spectrometer enabling increased compactness,” Light Sci. Appl. 6(7), e17026 (2017).
[Crossref]

Nat. Phys. (1)

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys. 3(2), 129–134 (2007).
[Crossref] [PubMed]

Opt. Eng. (2)

P. J. Smilie, B. S. Dutterer, J. L. Lineberger, M. A. Davies, and T. J. Suleski, “Design and characterization of an infrared Alvarez lens,” Opt. Eng. 51(1), 013006 (2012).
[Crossref]

J. Yao, P. Meemon, K. S. Lee, and J. P. Rolland, “Nondestructive metrology by optical coherence tomography empowering manufacturing iterations of layered polymeric optical materials,” Opt. Eng. 52(11), 112111 (2013).
[Crossref]

Opt. Express (11)

J. Yao, P. Meemon, M. Ponting, and J. P. Rolland, “Angular scan optical coherence tomography imaging and metrology of spherical gradient refractive index preforms,” Opt. Express 23(5), 6428–6443 (2015).
[Crossref] [PubMed]

J. Yao, J. Huang, P. Meemon, M. Ponting, and J. P. Rolland, “Simultaneous estimation of thickness and refractive index of layered gradient refractive index optics using a hybrid confocal-scan swept-source optical coherence tomography system,” Opt. Express 23(23), 30149–30164 (2015).
[Crossref] [PubMed]

J. Yao, K. P. Thompson, B. Ma, M. Ponting, and J. P. Rolland, “Volumetric rendering and metrology of spherical gradient refractive index lens imaged by angular scan optical coherence tomography system,” Opt. Express 24(17), 19388–19404 (2016).
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M. Choma, M. Sarunic, C. Yang, and J. Izatt, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Express 11(18), 2183–2189 (2003).
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G. Baer, J. Schindler, C. Pruss, J. Siepmann, and W. Osten, “Calibration of a non-null test interferometer for the measurement of aspheres and free-form surfaces,” Opt. Express 22(25), 31200–31211 (2014).
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A. Bauer and J. P. Rolland, “Visual space assessment of two all-reflective, freeform, optical see-through head-worn displays,” Opt. Express 22(11), 13155–13163 (2014).
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D. Cheng, Y. Wang, C. Xu, W. Song, and G. Jin, “Design of an ultra-thin near-eye display with geometrical waveguide and freeform optics,” Opt. Express 22(17), 20705–20719 (2014).
[Crossref] [PubMed]

K. Fuerschbach, J. P. Rolland, and K. P. Thompson, “A new family of optical systems employing φ-polynomial surfaces,” Opt. Express 19(22), 21919–21928 (2011).
[Crossref] [PubMed]

Y. S. Ghim, H. G. Rhee, A. Davies, H. S. Yang, and Y. W. Lee, “3D surface mapping of freeform optics using wavelength scanning lateral shearing interferometry,” Opt. Express 22(5), 5098–5105 (2014).
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K. Liang and M. A. Alonso, “Understanding the effects of groove structures on the MTF,” Opt. Express 25(16), 18827–18841 (2017).
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S. K. Chun, H. Jang, S. W. Cho, N. S. Park, and C. S. Kim, “Unfolding displacement measurement method for the aliasing interferometer signal of a wavelength-comb-swept laser,” Opt. Express 26(5), 5789–5799 (2018).
[Crossref] [PubMed]

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Opt. Photonics News (3)

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14(5), 38–43 (2003).
[Crossref]

K. P. Thompson and J. P. Rolland, “A revolution in imaging optical design,” Opt. Photonics News 23(6), 30–35 (2012).
[Crossref]

S. Wills, “Freeform optics: notes from the revolution,” Opt. Photonics News 28(7), 34–41 (2017).
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Proc. SPIE (4)

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P. Meemon, J. Yao, K. S. Lee, K. P. Thompson, M. Ponting, E. Baer, and J. P. Rolland, “Optical coherence tomography enabling non destructive metrology of layered polymeric GRIN material,” Sci. Rep. 3(1), 1709 (2013).
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H. Takeuchi, K. Yosizumi, and H. Tsutsumi, “Ultrahigh accurate 3-D profilometer using atomic force probe of measuring nanometer,” Proc. ASPE Winter Topical Meeting on Free-form optics: Design, Fabrication, Metrology and Assembly, 102–107 (2004).

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[Crossref]

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Figures (16)

Fig. 1
Fig. 1 SS-OCT freeform-metrology system layout. CL: collimating lens; OL: objective lens; PC: polarization controller; FC: fiber circulator; VNDF: variable neutral density filter; MTS: motorized translation stage; BP: balanced photodetector.
Fig. 2
Fig. 2 A photograph and a cross-sectional schematic of a common path setup of the reference flat and test sample simultaneously mounted on x-y motorized translation stages.
Fig. 3
Fig. 3 (a) A raw gray-scale x-y plane image of a dot grid target acquired by the SS-OCT freeform-metrology system. (b) A corresponding image after applying a centroiding algorithm to image (a), which shows the detected centroids (blue crosshairs) of the dots overlaying the dot grid (shown as enhanced red dots). (c) and (d) are enlarged views of the yellow boxes inside (a) and (b), respectively.
Fig. 4
Fig. 4 The nominal physical x coordinates of the centroids vs. (a) the detected x pixel numbers of the centroids averaged column-wise, (c) the linear fitting residuals of x dot grid lines averaged over all rows, and (e) the computed x pixel resolutions averaged column-wise. The nominal physical y coordinates of the centroids vs. (b) the detected y pixel numbers of the centroids averaged row-wise, (d) the linear fitting residuals of y dot grid lines averaged over all columns, and (f) the computed y pixel resolutions averaged row-wise.
Fig. 5
Fig. 5 Data processing procedures for SS-OCT freeform metrology.
Fig. 6
Fig. 6 (a) Experimentally measured decay of sensitivity (with error bars) in SS-OCT across 5 mm depth range. (b) Consistency of the measured depth with the ground truth. (c) Increased measurement uncertainty as a function of the increasing measured depth.
Fig. 7
Fig. 7 (a) Theoretical and experimentally-measured (with error bars) signal decay in SS-OCT with the increased distance up to 1 mm from the optical flat to the focus of the objective lens. (b) Increased measurement uncertainty in locating the sample surface placed at 50 µm depth with the increased defocus distance (i.e., signal decay).
Fig. 8
Fig. 8 Illustration of the geometry of the light cones incident and reflected by a surface with an inclination angle α. (a) and (b) are x-z and x-y cross-sectional views of the geometry, respectively. (c) and (d) illustrate two different cases in the calculation of the back-reflected signal re-collected by the SS-OCT system, depending on the surface inclination angle α. The shaded areas in all graphs represent the portion of back-reflected light captured by the objective lens.
Fig. 9
Fig. 9 (a) Theoretical signal decay in SS-OCT with increased slope of the test surface. (b) Simulated increased measurement uncertainty in locating the sample surface placed at 50 µm depth and at focus with the increased slope of the test surface.
Fig. 10
Fig. 10 (a) Contour plot of the mean surface measurement uncertainty as a function of the z locations of the zero-optical-delay plane and focal plane. The orange star denotes the valley of the plot. (b) illustrates the location of the z = 0 reference plane with respect to the Caliball. (c) Simulated surface uncertainty map under the specific focus and sample depth conditions denoted by the orange star in (a).
Fig. 11
Fig. 11 (a) Contour plot of the mean surface measurement uncertainty as a function of the z locations of the zero-optical-delay plane and focal plane. The orange star denotes the valley of the plot. (b) illustrates the location of the z = 0 reference plane with respect to the Alvarez surface. (c) Simulated surface uncertainty map under the specific focus and sample depth conditions denoted by the orange star in (a).
Fig. 12
Fig. 12 Using the common path setup schematically shown in (a), the surface profile of a λ/20 plane mirror measured by the SS-OCT system is shown in (b). A laser Fizeau interferometry test result of the same mirror is shown in (c).
Fig. 13
Fig. 13 An R = 12.7 mm Caliball is measured by the SS-OCT metrology system using the common path setup schematically shown in (a). Within the imaging ROI of 1.85 mm radius, the residual profile of the Caliball after subtracting out its nominal form is shown in (b). The standard deviation profile across five repeated measurements is shown in (c). (d) The standard deviation map in (c) is azimuthally averaged in 60 µm wide annuli and plotted as a function of the mean slope of the analysis annuli to demonstrate slope-dependent measurement precision (blue dots), which agrees with simulation results (black curve).
Fig. 14
Fig. 14 (a) Two snapshots of the 3D views of an Alvarez freeform surface with a surface sag of ~400 µm PV. (b) The slope map of the Alvarez surface computed from its nominal equation. (c) A photograph of the Alvarez surface with clocking marks on the edge.
Fig. 15
Fig. 15 (a) and (b) are two SS-OCT measurements of the residual profiles of the Alvarez surface after subtracting out its nominal form. (a) and (b) were acquired with a reverse in the orthogonal fast and slow scanning axes. (c) The standard deviation profile across 10 SS-OCT measurements of the Alvarez surface.
Fig. 16
Fig. 16 (a) and (b) are two measured residual profiles of the Alvarez surface by a precision tactile commercial profilometer. (a) and (b) were acquired with a reverse in the fast and slow scanning axes.

Tables (2)

Tables Icon

Table 1 List of criteria and formulas used to evaluate the lateral scanning field from the imaging of the grid target

Tables Icon

Table 2 Zernike fitting coefficients of the Alvarez surface profile: nominal form vs. SS-OCT measurements

Equations (14)

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

D 1 (i) = { x 1 (i) , y 1 (i) , z 1 (i) } T = R z (α) R y (β) R x (γ) D 0 (i) +T( x t , y t , z t ),
R z (α)=[ cosα sinα 0 sinα cosα 0 0 0 1 ], R y (β)=[ cosβ 0 sinβ 0 1 0 sinβ 0 cosβ ], R x (γ)=[ 1 0 0 0 cosγ sinγ 0 sinγ cosγ ],T( x t , y t , z t )=[ x t y t z t ] [ 1,1....1 ] 1×Q .
I(r,z')= c w 2 (z') e 2 r 2 w 2 (z') ,
w(z')= w 0 1+ ( z' z R ) 2 .
z'=tan( 2α )rcosφ+ f cos( 2α ) ,
I(r,φ)= c w 0 2 [ 1+ ( tan( 2α ) z R rcosφ f z R cos( 2α ) ) 2 ] e 2 r 2 w 0 2 [ 1+ ( tan( 2α ) z R rcosφ f z R cos( 2α ) ) 2 ] .
P in = (σ) I(r,φ)rdrdφ .
( rcosφ a ) 2 + ( rsinφ b ) 2 =1,
( rcosφd ) 2 + ( rsinφ ) 2 = r 0 2 ,
a=f tan(2α+θ)tan(2αθ) 2 ,
b=f tanθ cos2α ,
d=f tan(2α+θ)+tan(2αθ) 2 .
P in ={ 2 0 ϕ i dφ 0 ab a 2 sin 2 φ+ b 2 cos 2 φ I(r,φ)rdr +2 ϕ i π dφ 0 dcosφ+ r 0 2 d 2 sin 2 φ I(r,φ)rdr ,ifd r 0 2 0 ϕ i dφ dcosφ r 0 2 d 2 sin 2 φ ab a 2 sin 2 φ+ b 2 cos 2 φ I(r,φ)rdr +2 ϕ i sin 1 ( r 0 d ) dφ dcosφ r 0 2 d 2 sin 2 φ dcosφ+ r 0 2 d 2 sin 2 φ I(r,φ)rdr ,ifd> r 0
z(x,y)=0.000566( x 3 + y 3 )(mm).

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