Abstract

Freeform optics have emerged as promising components in diverse applications due to the potential for superior optical performance. There are many research fields in the area ranging from fabrication to measurement, with metrology being one of the most challenging tasks. In this paper, we describe a new variant of lateral shearing interferometer with a tunable laser source that enables 3D surface profile measurements of freeform optics with high speed, high vertical resolution, large departure, and large field-of-view. We have verified the proposed technique by comparing our measurement result with that of an existing technique and measuring a representative freeform optic.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. Savio, L. D. Chiffre, R. Schmitt, “Metrology of freeform shaped parts,” Annals of the CIRP 56(2), 810–835 (2007).
    [CrossRef]
  2. R. Henselmans, L. A. Cacace, G. F. Y. Kramer, P. C. J. N. Rosielle, M. Steinbuch, “The NANOMEFOS non-contact measurement machine for freeform optics,” Precis. Eng. 35(4), 607–624 (2011).
    [CrossRef]
  3. C. Faber, E. Olesch, R. Krobot, and G. Häusler, “Deflectometry challenges interferometry – the competition gets tougher!,” Proc. SPIE 8493, 0R-1-0R-15(2013).
  4. G. Häusler, C. Faber, E. Olesch, and S. Ettl, “Deflectometry vs. Interferometry,” Proc. SPIE 8788, 1C–1-1C–11(2013).
  5. M. V. R. K. Murty, “The use of a single plane parallel plate as a lateral shearing interferometer with a visible gas laser source,” Appl. Opt. 3(4), 531–534 (1964).
    [CrossRef]
  6. J. C. Wyant, “Double frequency grating lateral shear interferometer,” Appl. Opt. 12(9), 2057–2060 (1973).
    [CrossRef] [PubMed]
  7. M. P. Rimmer, “Method for evaluating lateral shearing interferograms,” Appl. Opt. 13(3), 623–629 (1974).
    [CrossRef] [PubMed]
  8. M. P. Rimmer, J. C. Wyant, “Evaluation of large aberrations using a lateral-shear interferometer having variable shear,” Appl. Opt. 14(1), 142–150 (1975).
    [CrossRef] [PubMed]
  9. S. Okuda, T. Nomura, K. Kamiya, H. Miyashiro, K. Yoshikawa, H. Tashiro, “High-precision analysis of a lateral shearing interferogram by use of the integration method and polynomials,” Appl. Opt. 39(28), 5179–5186 (2000).
    [CrossRef] [PubMed]
  10. H.-H. Lee, J.-H. You, S.-H. Park, “Phase-shifting lateral shearing interferometer with two pairs of wedge plates,” Opt. Lett. 28(22), 2243–2245 (2003).
    [CrossRef] [PubMed]
  11. P. Liang, J. Ding, Z. Jin, C.-S. Guo, H.-T. Wang, “Two-dimensional wave-front reconstruction from lateral shearing interferograms,” Opt. Express 14(2), 625–634 (2006).
    [CrossRef] [PubMed]
  12. S. Ettl, J. Kaminski, M. C. Knauer, G. Häusler, “Shape reconstruction from gradient data,” Appl. Opt. 47(12), 2091–2097 (2008).
    [CrossRef] [PubMed]
  13. F. Dai, F. Tang, X. Wang, O. Sasaki, “Generalized zonal wavefront reconstruction for high spatial resolution in lateral shearing interferometry,” J. Opt. Soc. Am. A 29(9), 2038–2047 (2012).
    [CrossRef] [PubMed]
  14. H.-G. Rhee, Y.-S. Ghim, J. Lee, H.-S. Yang, Y.-W. Lee, “Correction of rotational inaccuracy in lateral shearing interferometry for freeform measurement,” Opt. Express 21(21), 24799–24808 (2013).
    [CrossRef] [PubMed]
  15. M. Takeda, H. Yamamoto, “Fourier-transform speckle profilometry: three-dimensional shape measurements of diffuse objects with large height steps and/or spatially isolated surfaces,” Appl. Opt. 33(34), 7829–7837 (1994).
    [CrossRef] [PubMed]
  16. M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72(1), 156–160 (1982).
    [CrossRef]
  17. Y.-S. Ghim, S.-W. Kim, “Thin-film thickness profile and its refractive index measurements by dispersive white-light interferometry,” Opt. Express 14(24), 11885–11891 (2006).
    [CrossRef] [PubMed]
  18. L. L. Deck, “Fourier-transform phase-shifting interferometry,” Appl. Opt. 42(13), 2354–2365 (2003).
    [CrossRef] [PubMed]
  19. W. H. Southwell, “Wave-front estimation from wave-front slope measurements,” J. Opt. Soc. Am. 70(8), 998–1006 (1980).
    [CrossRef]
  20. D. Malacara-Doblado, I. Ghozeil, “Hartmann, Hartmann-Shack, and Other Screen Tests,” in optical shop testing 3rd ed., Wiley Series in Pure and Applied Optics (Wiley, 2007), 361–397.
  21. ASME B46.1–2002, “Terminology and measurement procedures for profiling, contact, skidless instruments,”in Surface texture (Surface roughness, waviness, and lay). (Amer. Soc. of Mech. Engrs., 2003), Section 3.

2013

2012

2011

R. Henselmans, L. A. Cacace, G. F. Y. Kramer, P. C. J. N. Rosielle, M. Steinbuch, “The NANOMEFOS non-contact measurement machine for freeform optics,” Precis. Eng. 35(4), 607–624 (2011).
[CrossRef]

2008

2007

E. Savio, L. D. Chiffre, R. Schmitt, “Metrology of freeform shaped parts,” Annals of the CIRP 56(2), 810–835 (2007).
[CrossRef]

2006

2003

2000

1994

1982

1980

1975

1974

1973

1964

Cacace, L. A.

R. Henselmans, L. A. Cacace, G. F. Y. Kramer, P. C. J. N. Rosielle, M. Steinbuch, “The NANOMEFOS non-contact measurement machine for freeform optics,” Precis. Eng. 35(4), 607–624 (2011).
[CrossRef]

Chiffre, L. D.

E. Savio, L. D. Chiffre, R. Schmitt, “Metrology of freeform shaped parts,” Annals of the CIRP 56(2), 810–835 (2007).
[CrossRef]

Dai, F.

Deck, L. L.

Ding, J.

Ettl, S.

Ghim, Y.-S.

Guo, C.-S.

Häusler, G.

Henselmans, R.

R. Henselmans, L. A. Cacace, G. F. Y. Kramer, P. C. J. N. Rosielle, M. Steinbuch, “The NANOMEFOS non-contact measurement machine for freeform optics,” Precis. Eng. 35(4), 607–624 (2011).
[CrossRef]

Ina, H.

Jin, Z.

Kaminski, J.

Kamiya, K.

Kim, S.-W.

Knauer, M. C.

Kobayashi, S.

Kramer, G. F. Y.

R. Henselmans, L. A. Cacace, G. F. Y. Kramer, P. C. J. N. Rosielle, M. Steinbuch, “The NANOMEFOS non-contact measurement machine for freeform optics,” Precis. Eng. 35(4), 607–624 (2011).
[CrossRef]

Lee, H.-H.

Lee, J.

Lee, Y.-W.

Liang, P.

Miyashiro, H.

Murty, M. V. R. K.

Nomura, T.

Okuda, S.

Park, S.-H.

Rhee, H.-G.

Rimmer, M. P.

Rosielle, P. C. J. N.

R. Henselmans, L. A. Cacace, G. F. Y. Kramer, P. C. J. N. Rosielle, M. Steinbuch, “The NANOMEFOS non-contact measurement machine for freeform optics,” Precis. Eng. 35(4), 607–624 (2011).
[CrossRef]

Sasaki, O.

Savio, E.

E. Savio, L. D. Chiffre, R. Schmitt, “Metrology of freeform shaped parts,” Annals of the CIRP 56(2), 810–835 (2007).
[CrossRef]

Schmitt, R.

E. Savio, L. D. Chiffre, R. Schmitt, “Metrology of freeform shaped parts,” Annals of the CIRP 56(2), 810–835 (2007).
[CrossRef]

Southwell, W. H.

Steinbuch, M.

R. Henselmans, L. A. Cacace, G. F. Y. Kramer, P. C. J. N. Rosielle, M. Steinbuch, “The NANOMEFOS non-contact measurement machine for freeform optics,” Precis. Eng. 35(4), 607–624 (2011).
[CrossRef]

Takeda, M.

Tang, F.

Tashiro, H.

Wang, H.-T.

Wang, X.

Wyant, J. C.

Yamamoto, H.

Yang, H.-S.

Yoshikawa, K.

You, J.-H.

Annals of the CIRP

E. Savio, L. D. Chiffre, R. Schmitt, “Metrology of freeform shaped parts,” Annals of the CIRP 56(2), 810–835 (2007).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Express

Opt. Lett.

Precis. Eng.

R. Henselmans, L. A. Cacace, G. F. Y. Kramer, P. C. J. N. Rosielle, M. Steinbuch, “The NANOMEFOS non-contact measurement machine for freeform optics,” Precis. Eng. 35(4), 607–624 (2011).
[CrossRef]

Other

C. Faber, E. Olesch, R. Krobot, and G. Häusler, “Deflectometry challenges interferometry – the competition gets tougher!,” Proc. SPIE 8493, 0R-1-0R-15(2013).

G. Häusler, C. Faber, E. Olesch, and S. Ettl, “Deflectometry vs. Interferometry,” Proc. SPIE 8788, 1C–1-1C–11(2013).

D. Malacara-Doblado, I. Ghozeil, “Hartmann, Hartmann-Shack, and Other Screen Tests,” in optical shop testing 3rd ed., Wiley Series in Pure and Applied Optics (Wiley, 2007), 361–397.

ASME B46.1–2002, “Terminology and measurement procedures for profiling, contact, skidless instruments,”in Surface texture (Surface roughness, waviness, and lay). (Amer. Soc. of Mech. Engrs., 2003), Section 3.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

A schematic diagram of lateral shearing interferometer for measurement of freeform optics; s-pol: s-polarized light, p-pol: p-polarized light, CL: collimating lens, HWP: half wave plate, PBS: polarizing beam splitter, QWP: quarter wave plate, BS: beam splitter, RP: right-angle prism, IL: imaging lens; (a) optical layout and beam path for measurement mode and (b) optical layout and beam path for calibration mode.

Fig. 2
Fig. 2

The details of lateral shearing part illustrating how to obtain the lateral sheared interferograms in two orthogonal directions; (a) the x-sheared interferogram and its corresponding grid shifted images from measurement and calibration modes when translating the right-angle prism I along the z-axis (b) the y-sheared interferogram and its corresponding grid shifted images from measurement and calibration modes when rotating the right-angle prism I about the z-axis. The y-sheared wave front exiting the beam splitter is tilted at an angle along the y-axis (out of the plane of the page).

Fig. 3
Fig. 3

Comparisons of measurement results: (a) the x-sheared interferogram viewed in monochromatic light and its corresponding 3D surface slope map, (b) the y-sheared interferogram viewed in monochromatic light and its corresponding 3D surface slope map, (c) the reconstructed 3D surface map with x-and y-slope integrations after the piston and tilt being subtracted, and (d) 3D surface map measured with the Zygo Fizeau interferometer.

Fig. 4
Fig. 4

A freeform optical surface measurement result: (a) the x-sheared interferogram viewed in monochromatic light and its corresponding 3D surface slope map, (b) the y-sheared interferogram viewed in monochromatic light and its corresponding 3D surface slope map, (c) the reconstructed 3D surface map with x-and y-slope integrations with piston and tilt removed, and (d) comparison to a stylus measurement of the line profile A-A′ of (c)

Tables (1)

Tables Icon

Table 1 Details of the apparatus used for experiments.

Equations (5)

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

I ( x , y ; k ) = I 0 ( x , y ; k ) { 1 + cos [ 2 ( k k 0 ) Δ W ( x , y ) + 2 k Λ ] } = I 0 ( x , y ; k ) [ 1 + cos ( Φ ( x , y ; k ) + 2 k Λ ) ] = I 0 ( x , y ; k ) + I 1 ( x , y ; k ) e j 2 k Λ + I 1 ( x , y ; k ) * e j 2 k Λ .
FT [ I ( x , y ; k ) ] = Γ 0 ( x , y ; f k ) + Γ 1 ( x , y ; f k Λ ) + Γ 1 ( x , y ; f k + Λ ) * .
FT 1 [ Γ 1 ( x , y ; f k ) ] = FT -1 FT [ 1 2 I 0 ( x , y ; k ) e j Φ ( x , y ; k ) ] = 1 2 I 0 ( x , y ; k ) e j Φ ( x , y ; k ) .
Δ W = 1 2 Φ ( x , y ; k ) k .
Δ W = 1 2 k 0 arg [ Γ 1 ( x , y ; f k ) ] .

Metrics