Abstract

It is difficult to search for interference fringes in Linnik white light interferometry with an extremely short coherence length because of the optical path mismatch of two interference arms and the defocus of the reference mirror and the test surface. We present an automated method to tackle this problem in this paper. The determination of best foci of the reference mirror and the test surface is implemented by the astigmatic method based on a modified commercial DVD pickup head embedded in the interference system. The astigmatic method is improved by setting a threshold value in the sum signal to truncate the normalized focus error signal (NFES). The truncated NFES has a monotonic relationship with the displacement of the test surface, which removes the position ambiguity of the test surface during the autofocus process. The developed autofocus system is confirmed experimentally with a dynamic range of 190μm, average sensitivity of 70mV/μm, average standard deviation of 0.041μm, displayed resolution of 4.4nm, and accuracy of 55nm. The minimization of the optical path difference of two interference arms is carried out by finding the maximum fringe contrast of the image captured by a CCD camera with the root mean square fringe contrast (RMSFC) function. The RMSFC function, combined with a 4×4 pixel binning of the CCD camera, is recommended to improve the computational efficiency. Experimental tests show that the automated method can be effectively utilized to search for interference fringes in Linnik white light interferometry.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Pförtner and J. Schwider, “Dispersion error in white-light Linnik interferometers and its implications for evaluation procedures,” Appl. Opt. 40, 6223–6228 (2001).
    [CrossRef]
  2. J. Schmit, K. Creath, and J. C. Wyant, “Surface profilers, multiple wavelength, and white light interferometry,” in Optical Shop Testing, D.Malacara, ed. (Wiley & Sons, 2007), Chap. 15, pp. 696–697.
  3. D. K. Cohen, J. D. Ayres, and E. R. Cochran, “Apparatus and method for automatically focusing an interference microscope,” U.S. patent 5,122,648 (16 June 1992).
  4. R. W. Swinford, D. J. Aziz, B. W. Guenther, and P. R. Unruh, “Automated minimization of optical path difference and reference mirror focus in white-light interference microscope objective,” U.S. patent 6,552,806 (22 April 2003).
  5. L. L. Deck, “Method and apparatus for automated focusing of an interferometric optical system,” U.S. patent 5,208,451 (4 May 1993).
  6. L. L. Deck and H. Chakmakjian, “Method and apparatus for automatically and simultaneously determining best focus and orientation of objects to be measured by broad-band interferometric means,” U.S. patent 5,784,164 (21 July 1998).
  7. J. C. Wyant, “White light interferometry,” Proc. SPIE 4737, 98–107 (2002).
    [CrossRef]
  8. D. K. Cohen, W. H. Gee, M. Ludeke, and J. Lewkowicz, “Automatic focus control: the astigmatic lens approach,” Appl. Opt. 23, 565–570 (1984).
    [CrossRef] [PubMed]
  9. M. Mansuripur, “Analysis of astigmatic focusing and push-pull tracking error signals in magnetooptical disk systems,” Appl. Opt. 26, 3981–3986 (1987).
    [CrossRef] [PubMed]
  10. F. Quercioli, A. Mannoni, and B. Tiribilli, “Correlation optical velocimetry with a compact disk pickup,” Appl. Opt. 36, 6372–6375 (1997).
    [CrossRef]
  11. J. H. Zhang and L. L. Cai, “An autofocusing measurement system with the piezoelectric translator,” IEEE Trans. Mechatron. 2, 213–216 (1997).
    [CrossRef]
  12. A. Bartoli, P. Poggi, F. Quercioli, and B. Tiribilli, “Fast one-dimensional profilometer with a compact disc pickup,” Appl. Opt. 40, 1044–1048 (2001).
    [CrossRef]
  13. K. C. Fan, C. Y. Lin, and L. H. Shyu, “The development of a low-cost focusing probe for profile measurement,” Meas. Sci. Technol. 11, N1–N7 (2000).
    [CrossRef]
  14. K. C. Fan, C. L. Chu, and J. I. Mou, “Development of a low-cost autofocusing probe for profile measurement,” Meas. Sci. Technol. 12, 2137–2146 (2001).
    [CrossRef]
  15. C. H. Liu, and Z. H. Li, “Application of the astigmatic method to the thickness measurement of glass substrates,” Appl. Opt. 47, 3968–3972 (2008).
    [CrossRef] [PubMed]
  16. W. Y. Hsu, C. S. Lee, P. J. Chen, N.-T. Chen, F.-Z. Chen, Z.-R. Yu, C.-H. Kuo, and C.-H. Hwang, “Development of the fast astigmatic auto-focus microscope system,” Meas. Sci. Technol. 20, 045902 (2009).
    [CrossRef]
  17. C. H. Liu, S. C. Yeh, and H. L. Huang, “Thickness measurement system for transparent plates using dual digital versatile disc (DVD) pickups,” Appl. Opt. 49, 637–643(2010).
    [CrossRef] [PubMed]
  18. N. Islam, R. M. Parkin, M. R. Jackson, and Z. Kesy, “Development of a novel profile measurement system for actively planed surfaces,” Measurement 44, 466–477 (2011).
    [CrossRef]
  19. B. Hnilicka, A. Voda, and H.-J. Schroder, “Modeling the characteristics of a photodetector in a DVD player,” Sens. Actuators A 120, 494–506 (2005).
    [CrossRef]
  20. E. F. Erickson, and R. M. Brown, “Calculation of fringe visibility in a laser-illuminated interferometer,” J. Opt. Soc. Am. 57, 367–368 (1967).
    [CrossRef]

2011

N. Islam, R. M. Parkin, M. R. Jackson, and Z. Kesy, “Development of a novel profile measurement system for actively planed surfaces,” Measurement 44, 466–477 (2011).
[CrossRef]

2010

2009

W. Y. Hsu, C. S. Lee, P. J. Chen, N.-T. Chen, F.-Z. Chen, Z.-R. Yu, C.-H. Kuo, and C.-H. Hwang, “Development of the fast astigmatic auto-focus microscope system,” Meas. Sci. Technol. 20, 045902 (2009).
[CrossRef]

2008

2005

B. Hnilicka, A. Voda, and H.-J. Schroder, “Modeling the characteristics of a photodetector in a DVD player,” Sens. Actuators A 120, 494–506 (2005).
[CrossRef]

2002

J. C. Wyant, “White light interferometry,” Proc. SPIE 4737, 98–107 (2002).
[CrossRef]

2001

2000

K. C. Fan, C. Y. Lin, and L. H. Shyu, “The development of a low-cost focusing probe for profile measurement,” Meas. Sci. Technol. 11, N1–N7 (2000).
[CrossRef]

1997

J. H. Zhang and L. L. Cai, “An autofocusing measurement system with the piezoelectric translator,” IEEE Trans. Mechatron. 2, 213–216 (1997).
[CrossRef]

F. Quercioli, A. Mannoni, and B. Tiribilli, “Correlation optical velocimetry with a compact disk pickup,” Appl. Opt. 36, 6372–6375 (1997).
[CrossRef]

1987

1984

1967

Ayres, J. D.

D. K. Cohen, J. D. Ayres, and E. R. Cochran, “Apparatus and method for automatically focusing an interference microscope,” U.S. patent 5,122,648 (16 June 1992).

Aziz, D. J.

R. W. Swinford, D. J. Aziz, B. W. Guenther, and P. R. Unruh, “Automated minimization of optical path difference and reference mirror focus in white-light interference microscope objective,” U.S. patent 6,552,806 (22 April 2003).

Bartoli, A.

Brown, R. M.

Cai, L. L.

J. H. Zhang and L. L. Cai, “An autofocusing measurement system with the piezoelectric translator,” IEEE Trans. Mechatron. 2, 213–216 (1997).
[CrossRef]

Chakmakjian, H.

L. L. Deck and H. Chakmakjian, “Method and apparatus for automatically and simultaneously determining best focus and orientation of objects to be measured by broad-band interferometric means,” U.S. patent 5,784,164 (21 July 1998).

Chen, F.-Z.

W. Y. Hsu, C. S. Lee, P. J. Chen, N.-T. Chen, F.-Z. Chen, Z.-R. Yu, C.-H. Kuo, and C.-H. Hwang, “Development of the fast astigmatic auto-focus microscope system,” Meas. Sci. Technol. 20, 045902 (2009).
[CrossRef]

Chen, N.-T.

W. Y. Hsu, C. S. Lee, P. J. Chen, N.-T. Chen, F.-Z. Chen, Z.-R. Yu, C.-H. Kuo, and C.-H. Hwang, “Development of the fast astigmatic auto-focus microscope system,” Meas. Sci. Technol. 20, 045902 (2009).
[CrossRef]

Chen, P. J.

W. Y. Hsu, C. S. Lee, P. J. Chen, N.-T. Chen, F.-Z. Chen, Z.-R. Yu, C.-H. Kuo, and C.-H. Hwang, “Development of the fast astigmatic auto-focus microscope system,” Meas. Sci. Technol. 20, 045902 (2009).
[CrossRef]

Chu, C. L.

K. C. Fan, C. L. Chu, and J. I. Mou, “Development of a low-cost autofocusing probe for profile measurement,” Meas. Sci. Technol. 12, 2137–2146 (2001).
[CrossRef]

Cochran, E. R.

D. K. Cohen, J. D. Ayres, and E. R. Cochran, “Apparatus and method for automatically focusing an interference microscope,” U.S. patent 5,122,648 (16 June 1992).

Cohen, D. K.

D. K. Cohen, W. H. Gee, M. Ludeke, and J. Lewkowicz, “Automatic focus control: the astigmatic lens approach,” Appl. Opt. 23, 565–570 (1984).
[CrossRef] [PubMed]

D. K. Cohen, J. D. Ayres, and E. R. Cochran, “Apparatus and method for automatically focusing an interference microscope,” U.S. patent 5,122,648 (16 June 1992).

Creath, K.

J. Schmit, K. Creath, and J. C. Wyant, “Surface profilers, multiple wavelength, and white light interferometry,” in Optical Shop Testing, D.Malacara, ed. (Wiley & Sons, 2007), Chap. 15, pp. 696–697.

Deck, L. L.

L. L. Deck and H. Chakmakjian, “Method and apparatus for automatically and simultaneously determining best focus and orientation of objects to be measured by broad-band interferometric means,” U.S. patent 5,784,164 (21 July 1998).

L. L. Deck, “Method and apparatus for automated focusing of an interferometric optical system,” U.S. patent 5,208,451 (4 May 1993).

Erickson, E. F.

Fan, K. C.

K. C. Fan, C. L. Chu, and J. I. Mou, “Development of a low-cost autofocusing probe for profile measurement,” Meas. Sci. Technol. 12, 2137–2146 (2001).
[CrossRef]

K. C. Fan, C. Y. Lin, and L. H. Shyu, “The development of a low-cost focusing probe for profile measurement,” Meas. Sci. Technol. 11, N1–N7 (2000).
[CrossRef]

Gee, W. H.

Guenther, B. W.

R. W. Swinford, D. J. Aziz, B. W. Guenther, and P. R. Unruh, “Automated minimization of optical path difference and reference mirror focus in white-light interference microscope objective,” U.S. patent 6,552,806 (22 April 2003).

Hnilicka, B.

B. Hnilicka, A. Voda, and H.-J. Schroder, “Modeling the characteristics of a photodetector in a DVD player,” Sens. Actuators A 120, 494–506 (2005).
[CrossRef]

Hsu, W. Y.

W. Y. Hsu, C. S. Lee, P. J. Chen, N.-T. Chen, F.-Z. Chen, Z.-R. Yu, C.-H. Kuo, and C.-H. Hwang, “Development of the fast astigmatic auto-focus microscope system,” Meas. Sci. Technol. 20, 045902 (2009).
[CrossRef]

Huang, H. L.

Hwang, C.-H.

W. Y. Hsu, C. S. Lee, P. J. Chen, N.-T. Chen, F.-Z. Chen, Z.-R. Yu, C.-H. Kuo, and C.-H. Hwang, “Development of the fast astigmatic auto-focus microscope system,” Meas. Sci. Technol. 20, 045902 (2009).
[CrossRef]

Islam, N.

N. Islam, R. M. Parkin, M. R. Jackson, and Z. Kesy, “Development of a novel profile measurement system for actively planed surfaces,” Measurement 44, 466–477 (2011).
[CrossRef]

Jackson, M. R.

N. Islam, R. M. Parkin, M. R. Jackson, and Z. Kesy, “Development of a novel profile measurement system for actively planed surfaces,” Measurement 44, 466–477 (2011).
[CrossRef]

Kesy, Z.

N. Islam, R. M. Parkin, M. R. Jackson, and Z. Kesy, “Development of a novel profile measurement system for actively planed surfaces,” Measurement 44, 466–477 (2011).
[CrossRef]

Kuo, C.-H.

W. Y. Hsu, C. S. Lee, P. J. Chen, N.-T. Chen, F.-Z. Chen, Z.-R. Yu, C.-H. Kuo, and C.-H. Hwang, “Development of the fast astigmatic auto-focus microscope system,” Meas. Sci. Technol. 20, 045902 (2009).
[CrossRef]

Lee, C. S.

W. Y. Hsu, C. S. Lee, P. J. Chen, N.-T. Chen, F.-Z. Chen, Z.-R. Yu, C.-H. Kuo, and C.-H. Hwang, “Development of the fast astigmatic auto-focus microscope system,” Meas. Sci. Technol. 20, 045902 (2009).
[CrossRef]

Lewkowicz, J.

Li, Z. H.

Lin, C. Y.

K. C. Fan, C. Y. Lin, and L. H. Shyu, “The development of a low-cost focusing probe for profile measurement,” Meas. Sci. Technol. 11, N1–N7 (2000).
[CrossRef]

Liu, C. H.

Ludeke, M.

Mannoni, A.

Mansuripur, M.

Mou, J. I.

K. C. Fan, C. L. Chu, and J. I. Mou, “Development of a low-cost autofocusing probe for profile measurement,” Meas. Sci. Technol. 12, 2137–2146 (2001).
[CrossRef]

Parkin, R. M.

N. Islam, R. M. Parkin, M. R. Jackson, and Z. Kesy, “Development of a novel profile measurement system for actively planed surfaces,” Measurement 44, 466–477 (2011).
[CrossRef]

Pförtner, A.

Poggi, P.

Quercioli, F.

Schmit, J.

J. Schmit, K. Creath, and J. C. Wyant, “Surface profilers, multiple wavelength, and white light interferometry,” in Optical Shop Testing, D.Malacara, ed. (Wiley & Sons, 2007), Chap. 15, pp. 696–697.

Schroder, H.-J.

B. Hnilicka, A. Voda, and H.-J. Schroder, “Modeling the characteristics of a photodetector in a DVD player,” Sens. Actuators A 120, 494–506 (2005).
[CrossRef]

Schwider, J.

Shyu, L. H.

K. C. Fan, C. Y. Lin, and L. H. Shyu, “The development of a low-cost focusing probe for profile measurement,” Meas. Sci. Technol. 11, N1–N7 (2000).
[CrossRef]

Swinford, R. W.

R. W. Swinford, D. J. Aziz, B. W. Guenther, and P. R. Unruh, “Automated minimization of optical path difference and reference mirror focus in white-light interference microscope objective,” U.S. patent 6,552,806 (22 April 2003).

Tiribilli, B.

Unruh, P. R.

R. W. Swinford, D. J. Aziz, B. W. Guenther, and P. R. Unruh, “Automated minimization of optical path difference and reference mirror focus in white-light interference microscope objective,” U.S. patent 6,552,806 (22 April 2003).

Voda, A.

B. Hnilicka, A. Voda, and H.-J. Schroder, “Modeling the characteristics of a photodetector in a DVD player,” Sens. Actuators A 120, 494–506 (2005).
[CrossRef]

Wyant, J. C.

J. C. Wyant, “White light interferometry,” Proc. SPIE 4737, 98–107 (2002).
[CrossRef]

J. Schmit, K. Creath, and J. C. Wyant, “Surface profilers, multiple wavelength, and white light interferometry,” in Optical Shop Testing, D.Malacara, ed. (Wiley & Sons, 2007), Chap. 15, pp. 696–697.

Yeh, S. C.

Yu, Z.-R.

W. Y. Hsu, C. S. Lee, P. J. Chen, N.-T. Chen, F.-Z. Chen, Z.-R. Yu, C.-H. Kuo, and C.-H. Hwang, “Development of the fast astigmatic auto-focus microscope system,” Meas. Sci. Technol. 20, 045902 (2009).
[CrossRef]

Zhang, J. H.

J. H. Zhang and L. L. Cai, “An autofocusing measurement system with the piezoelectric translator,” IEEE Trans. Mechatron. 2, 213–216 (1997).
[CrossRef]

Appl. Opt.

IEEE Trans. Mechatron.

J. H. Zhang and L. L. Cai, “An autofocusing measurement system with the piezoelectric translator,” IEEE Trans. Mechatron. 2, 213–216 (1997).
[CrossRef]

J. Opt. Soc. Am.

Meas. Sci. Technol.

K. C. Fan, C. Y. Lin, and L. H. Shyu, “The development of a low-cost focusing probe for profile measurement,” Meas. Sci. Technol. 11, N1–N7 (2000).
[CrossRef]

K. C. Fan, C. L. Chu, and J. I. Mou, “Development of a low-cost autofocusing probe for profile measurement,” Meas. Sci. Technol. 12, 2137–2146 (2001).
[CrossRef]

W. Y. Hsu, C. S. Lee, P. J. Chen, N.-T. Chen, F.-Z. Chen, Z.-R. Yu, C.-H. Kuo, and C.-H. Hwang, “Development of the fast astigmatic auto-focus microscope system,” Meas. Sci. Technol. 20, 045902 (2009).
[CrossRef]

Measurement

N. Islam, R. M. Parkin, M. R. Jackson, and Z. Kesy, “Development of a novel profile measurement system for actively planed surfaces,” Measurement 44, 466–477 (2011).
[CrossRef]

Proc. SPIE

J. C. Wyant, “White light interferometry,” Proc. SPIE 4737, 98–107 (2002).
[CrossRef]

Sens. Actuators A

B. Hnilicka, A. Voda, and H.-J. Schroder, “Modeling the characteristics of a photodetector in a DVD player,” Sens. Actuators A 120, 494–506 (2005).
[CrossRef]

Other

J. Schmit, K. Creath, and J. C. Wyant, “Surface profilers, multiple wavelength, and white light interferometry,” in Optical Shop Testing, D.Malacara, ed. (Wiley & Sons, 2007), Chap. 15, pp. 696–697.

D. K. Cohen, J. D. Ayres, and E. R. Cochran, “Apparatus and method for automatically focusing an interference microscope,” U.S. patent 5,122,648 (16 June 1992).

R. W. Swinford, D. J. Aziz, B. W. Guenther, and P. R. Unruh, “Automated minimization of optical path difference and reference mirror focus in white-light interference microscope objective,” U.S. patent 6,552,806 (22 April 2003).

L. L. Deck, “Method and apparatus for automated focusing of an interferometric optical system,” U.S. patent 5,208,451 (4 May 1993).

L. L. Deck and H. Chakmakjian, “Method and apparatus for automatically and simultaneously determining best focus and orientation of objects to be measured by broad-band interferometric means,” U.S. patent 5,784,164 (21 July 1998).

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 (15)

Fig. 1
Fig. 1

Overall system layout of the Linnik white light interference system based on a modified commercial DVD pickup head: LD, laser diode; G, grating; BSP1, BSP2, beam splitter plate; AL, astigmatic lens; QD, quadrant detector; ABCD, four signal outputs of the QD; M1, M2, mirrors; C, collimator; HLS, halogen light source; LG, light guide; CL, condenser lens; BSC, beam splitter cube; S1, S2, stops; MO1, MO2: microscope objectives; PZT, piezoelectric transducer; BSF, bandstop filter; TL, tube lens; CCD, charge-coupled device. The red (inner) lines indicate the light beam emitted from the DVD pickup head, and the blue (outer) lines indicate the light beam emitted from the HLS.

Fig. 2
Fig. 2

Simultaneously measured FES and the SS using the modified DVD pickup head (Hitachi HOP-1000) assembled with the microscope objective in the time domain. Inset, laser spot patterns of the FES on the QD.

Fig. 3
Fig. 3

NFES and the synchronized FES tested using (a) the flat mirror surface and (b) the glass surface. Note that the FES voltage values represented by a grid for (a) and (b) are different.

Fig. 4
Fig. 4

(a) The TFES or (b) TNFES is obtained if the GS is true (i.e., at a high voltage value) when the SS is larger than the threshold value: FES, focus error signal; SS, sum signal; GS, gate signal; TFES, truncated focus error signal; TNFES, truncated normalized focus error signal. Note that the different channels for (a) and (b) have different voltage values represented by a grid.

Fig. 5
Fig. 5

The NFES creates more than one zero crossing points indicated by the white dots because of the misalignment of the system, while the TNFES has only one zero crossing point that identifies true focus within the lock-on range.

Fig. 6
Fig. 6

Normalized LD output voltages against operating time with APC and without APC.

Fig. 7
Fig. 7

(a) Flow chart to clarify the method of automated setting the threshold value. (b) Autofocus closed-loop control.

Fig. 8
Fig. 8

NFES versus the displacement of the test surface. Note that the TNFES and the NFES have the same sensitivity and dynamic range. The focal lengths f and the corresponding nu merical apertures (N.A.) are taken from the specification of the Mitutoyo microscope objectives.

Fig. 9
Fig. 9

(a) TNFES versus displacement of the test surface. (b) The sensitivity plot of the TNFES.

Fig. 10
Fig. 10

Repeatability test results of the TNFES for nine times.

Fig. 11
Fig. 11

FCs calculated by three algorithms for (a) no binning, (b)  2 × 2 binning, (c)  4 × 4 binning, and (d)  8 × 8 binning. FC, fringe contrast γ; ALV, average lateral variation V avg ; RMSFC, root mean square fringe contrast γ RMS . Note that the three types of curves indicate the discrete values, although the curves themselves are continuous.

Fig. 12
Fig. 12

Measured interference fringe with our system. The coherence length (FWHM) is estimated to be 2.6 μm .

Fig. 13
Fig. 13

Flow chart to clarify the working principle of minimizing the OPD.

Fig. 14
Fig. 14

Autofocus procedures of (a) the reference mirror and (b) the sample.

Fig. 15
Fig. 15

(a) RMSFC values for a 2 mm long scan range during the minimization of OPD. The black dot labeled P2 corresponds to the maximum FC position. (b) Three images labeled P1, P2, and P3 are the interferograms corresponding to the positions marked by the black dots labeled P1, P2, and P3, respectively.

Tables (2)

Tables Icon

Table 1 Repeatability Test Results

Tables Icon

Table 2 Computational Efficiencies of Three Algorithms for Four Types of Pixel Binning (Unit: s)

Equations (8)

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

FES = ( V A + V C ) ( V B + V D ) ,
SS = ( V A + V B + V C + V D ) ,
NFES = FES SS = ( V A + V C ) ( V B + V D ) ( V A + V C + V B + V D ) .
γ = I max I min I max + I min .
V ( x , y ) = abs ( M ( x , y ) [ M ( x + G x , y ) + M ( x G x , y ) + M ( x , y + G y ) + M ( x , y G y ) ] / 4 ) ,
V avg = 1 M N y = 1 N x = 1 M V ( x , y ) .
γ RMS = 1 M N y = 1 N x = 1 M ( M ( x , y ) M ¯ ) 2 ,
θ = 4 π · Δ h / λ ¯ ,

Metrics