Abstract

We present a novel microscope interferometric technique based on the heterodinization of two Gaussian beams for measuring roughness of optical surfaces in microscopic areas. One of the beams is used as a probe beam, focussed and reflected by the surface under test. The second beam interferes with the first beam and introduces a time varying modulating signal. The modulating light beam is obtained from the first diffraction order of a Bragg cell. The two beams are superimposed and added coherently at the sensitive plane of a photodetector that integrates the overall intensity of the beams. We show analytically that it is possible to find appropriate working conditions in which the system has a linear response. Under these conditions, the size of the probe beam at the plane of detection as well as the amplitude of the time varying signal at the output of the photodetector, are both proportional to the local vertical height of the surface under test. As a narrow bandwidth amplifier is used to detect the time varying signal the system exhibits a high signal to noise ratio. We also include experimental results of the measurement of the topography of a sample consisting in a blazed-reflecting grating.

© 2007 Optical Society of America

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References

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  1. J. M. Bennett, "Comparison of techniques for measuring the roughness of optical surfaces," Opt. Eng. 24, 380-387 (1985).
  2. J. M. Bennett and J. H. Dancy, "Stylus profiling instrument for measuring statistical properties of smooth optical surfaces," Appl. Opt. 20, 1785 (1981).
    [CrossRef] [PubMed]
  3. D. Walker, H. Yang and S. Kim, "Novel hybrid stylus for nanometric profilometry for large optical surfaces," Opt. Express 11, 1793-1798 (2003).
    [CrossRef] [PubMed]
  4. H. J. Tiziani, "Optical methods for precision measurements," Opt. Quantum Electron. 21, 253-282 (1989).
    [CrossRef]
  5. S. R. Clark, and J. E. Greivenkap, "Optical reference profilometry," Opt. Eng. 40, 2845 (2001).
    [CrossRef]
  6. G. S. Kino and S. S. C. Chim, "Mirau correlation microscope," Appl. Opt. 29, 3775-3783 (1990).
    [CrossRef] [PubMed]
  7. W. Zhou, Z. Zhou and G. Chi, "Investigation of common-path interference profilometry," Opt. Eng. 36, 3172-3175 (1997).
    [CrossRef]
  8. M. B. Suddendorf, C. W. See, M. G. Somekh, "Combined differential amplitude and phase interferometer with a single probe beam," Appl. Phys. Lett,  67, 28-30 (1995).
    [CrossRef]
  9. Z. F. Zhou, T. Zhang, W. Zhou and W. Li "Profilometer for measuring superfine surfaces," Opt. Eng. 40, 1646-1652 (2001).
    [CrossRef]
  10. G. E. Sommargren, "Optical heterodyne profilometry," Appl. Opt. 20, 335-343 (1981).
    [CrossRef]
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  12. J. C. Wyant, "Optical profilers for surface roughness," Proc. SPIE 525, 174-180 (1985).
  13. M. Davidson, K. Kaufman, I. Mazor, and F. Cohen, "An application of interference microscopy to integrated circuit inspection and metrology," Proc. SPIE 775, 233-247 (1987).
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    [CrossRef] [PubMed]
  15. G. W. Johnson, D. C. Leiner and D. T. Moore, "Phase-locked Interferometry," Proc. SPIE 126, 152-160 (1977).
  16. K. Creath and J. C. Wyant, "Absolute measurement of surface roughness," Appl. Opt. 29, 3823-3827 (1990).
    [CrossRef] [PubMed]
  17. B. S. Lee and T. C. Strand, "Profilometry with a coherence scanning microscope," Appl. Opt. 29, 3784-3788 (1990).
    [CrossRef] [PubMed]
  18. B. Barrientos, M. Cywiak and M. Servín, "Profilometry of optically smooth surfaces by a Gaussian probe beam," Opt. Eng. 42, 3004-3012 (2003).
    [CrossRef]
  19. M. Cywiak, J. F. Aguilar and B. Barrientos, "Low-numerical-aperture Gaussian beam confocal system for profiling optically smooth," Opt. Eng. 44, 1-7 (2005).
    [CrossRef]
  20. J. Murakowski, M. Cywiak, B. Rosner, and D. van der Weide, "Far field optical imaging with subwavelength resolution," Opt. Commun. 185, 295-303 (2000).
    [CrossRef]
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    [CrossRef]

2005 (1)

M. Cywiak, J. F. Aguilar and B. Barrientos, "Low-numerical-aperture Gaussian beam confocal system for profiling optically smooth," Opt. Eng. 44, 1-7 (2005).
[CrossRef]

2003 (3)

A. Kühle, B. Rosén and J. Garnaes, "Comparison of roughness measurement with atomic force microscopy and interference microscopy," Proc. SPIE 5188, 154-161 (2003).
[CrossRef]

B. Barrientos, M. Cywiak and M. Servín, "Profilometry of optically smooth surfaces by a Gaussian probe beam," Opt. Eng. 42, 3004-3012 (2003).
[CrossRef]

D. Walker, H. Yang and S. Kim, "Novel hybrid stylus for nanometric profilometry for large optical surfaces," Opt. Express 11, 1793-1798 (2003).
[CrossRef] [PubMed]

2001 (2)

S. R. Clark, and J. E. Greivenkap, "Optical reference profilometry," Opt. Eng. 40, 2845 (2001).
[CrossRef]

Z. F. Zhou, T. Zhang, W. Zhou and W. Li "Profilometer for measuring superfine surfaces," Opt. Eng. 40, 1646-1652 (2001).
[CrossRef]

2000 (2)

J. Murakowski, M. Cywiak, B. Rosner, and D. van der Weide, "Far field optical imaging with subwavelength resolution," Opt. Commun. 185, 295-303 (2000).
[CrossRef]

M. Cywiak, J. Murakowski, and G. Wade., "Beam blocking method for optical characterization of surfaces," Int. J. Imaging Syst. Technol. 11, 164-169 (2000).

1997 (1)

W. Zhou, Z. Zhou and G. Chi, "Investigation of common-path interference profilometry," Opt. Eng. 36, 3172-3175 (1997).
[CrossRef]

1995 (1)

M. B. Suddendorf, C. W. See, M. G. Somekh, "Combined differential amplitude and phase interferometer with a single probe beam," Appl. Phys. Lett,  67, 28-30 (1995).
[CrossRef]

1993 (1)

1990 (3)

1989 (1)

H. J. Tiziani, "Optical methods for precision measurements," Opt. Quantum Electron. 21, 253-282 (1989).
[CrossRef]

1987 (1)

M. Davidson, K. Kaufman, I. Mazor, and F. Cohen, "An application of interference microscopy to integrated circuit inspection and metrology," Proc. SPIE 775, 233-247 (1987).

1985 (2)

J. C. Wyant, "Optical profilers for surface roughness," Proc. SPIE 525, 174-180 (1985).

J. M. Bennett, "Comparison of techniques for measuring the roughness of optical surfaces," Opt. Eng. 24, 380-387 (1985).

1984 (1)

C-C. Huang, "Optical heterodyne profilometer," Opt. Eng. 23, 365-370 (1984).

1981 (2)

1977 (1)

G. W. Johnson, D. C. Leiner and D. T. Moore, "Phase-locked Interferometry," Proc. SPIE 126, 152-160 (1977).

Appl. Opt. (6)

Appl. Phys. Lett (1)

M. B. Suddendorf, C. W. See, M. G. Somekh, "Combined differential amplitude and phase interferometer with a single probe beam," Appl. Phys. Lett,  67, 28-30 (1995).
[CrossRef]

Int. J. Imaging Syst. Technol. (1)

M. Cywiak, J. Murakowski, and G. Wade., "Beam blocking method for optical characterization of surfaces," Int. J. Imaging Syst. Technol. 11, 164-169 (2000).

Opt. Commun. (1)

J. Murakowski, M. Cywiak, B. Rosner, and D. van der Weide, "Far field optical imaging with subwavelength resolution," Opt. Commun. 185, 295-303 (2000).
[CrossRef]

Opt. Eng. (7)

B. Barrientos, M. Cywiak and M. Servín, "Profilometry of optically smooth surfaces by a Gaussian probe beam," Opt. Eng. 42, 3004-3012 (2003).
[CrossRef]

M. Cywiak, J. F. Aguilar and B. Barrientos, "Low-numerical-aperture Gaussian beam confocal system for profiling optically smooth," Opt. Eng. 44, 1-7 (2005).
[CrossRef]

Z. F. Zhou, T. Zhang, W. Zhou and W. Li "Profilometer for measuring superfine surfaces," Opt. Eng. 40, 1646-1652 (2001).
[CrossRef]

C-C. Huang, "Optical heterodyne profilometer," Opt. Eng. 23, 365-370 (1984).

J. M. Bennett, "Comparison of techniques for measuring the roughness of optical surfaces," Opt. Eng. 24, 380-387 (1985).

S. R. Clark, and J. E. Greivenkap, "Optical reference profilometry," Opt. Eng. 40, 2845 (2001).
[CrossRef]

W. Zhou, Z. Zhou and G. Chi, "Investigation of common-path interference profilometry," Opt. Eng. 36, 3172-3175 (1997).
[CrossRef]

Opt. Express (1)

Opt. Quantum Electron. (1)

H. J. Tiziani, "Optical methods for precision measurements," Opt. Quantum Electron. 21, 253-282 (1989).
[CrossRef]

Proc. SPIE (4)

J. C. Wyant, "Optical profilers for surface roughness," Proc. SPIE 525, 174-180 (1985).

M. Davidson, K. Kaufman, I. Mazor, and F. Cohen, "An application of interference microscopy to integrated circuit inspection and metrology," Proc. SPIE 775, 233-247 (1987).

A. Kühle, B. Rosén and J. Garnaes, "Comparison of roughness measurement with atomic force microscopy and interference microscopy," Proc. SPIE 5188, 154-161 (2003).
[CrossRef]

G. W. Johnson, D. C. Leiner and D. T. Moore, "Phase-locked Interferometry," Proc. SPIE 126, 152-160 (1977).

Other (1)

W. J. Goodman, Introduction to Fourier Optics, Second ed., (Mc Graw-Hill, New York, 2000). Chaps. 4, 5.

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Figures (6)

Fig. 1.
Fig. 1.

Experimental setup. (x 0, y 0) are the coordinates of a plane at the output of the Bragg-cell. (x, y) are the coordinates of the focal plane I of lens L1. (x 1, y 1) are the coordinates of the focal plane II. (x 2, y 2) are the coordinates of the focal plane II when the beam reaches again this plane after being reflected from the object under test. (x F, y F) are the coordinates of the focal plane I when the beam reaches this plane again in its way towards the photodedector. Finally, (ξ, η) are the coordinates at the plane of detection. M1 and M2 are mirrors, BS1 and BS2 are 50-50 beam splitters, and L1 is the focusing lens. For the description, the distance between the focal plane II and the object plane has been exaggerated.

Fig. 2.
Fig. 2.

Absolute amplitude distribution of the Gaussian beams at the plane of detection.

Fig. 3.
Fig. 3.

Semi-widths of the probe (continuos trace) and modulating (dotted line) beams at the detection plane, (ξ, η), as functions of the defocusing distance zp .

Fig. 4.
Fig. 4.

Total collected power as a function of the defocusing distance zp . The operating point is selected around the value zp = 3μm, within the range marked by the little segments on the graph.

Fig. 5.
Fig. 5.

Profile obtained with the proposed technique for the sampled grating. The pitch is 300 lines/mm.

Fig. 6.
Fig. 6.

Profile obtained with the atomic force microscope in a near vicinity of the measure shown in Fig. 5 when scanning a similar distance.

Equations (31)

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Ψ ( x 0 , y 0 ) = ( 2 P 0 π r 0 2 ) 1 2 exp [ x 0 2 + y 0 2 r 0 2 ] ,
Ψ ( x , y ) = exp ( i ω l t ) 1 iλz Ψ ( x 0 , y 0 ) exp { i π λz [ ( x x 0 ) 2 + ( y y 0 ) 2 ] } dx 0 dy 0 ,
Ψ ( x , y ) = r 0 2 λz r 0 2 2 P 0 π r 0 2 exp ( i ω l t ) exp [ ( π 2 r 0 2 iπλz λ 2 z 2 + π 2 r 0 4 ) ( x 2 + y 2 ) ] ,
Ψ ( x 1 , y 1 ) = 1 λf Ψ ( x , y ) exp [ - i 2 π λf ( x x 1 yy 1 ) ] dx dy .
Ψ ( x 1 , y 1 ) = r 0 2 λf 2 P 0 π r 0 2 exp ( i ω l t ) exp [ ( π π r 0 2 + iλz λ 2 f 2 ) ( x 1 2 + y 1 2 ) ] .
Ψ ( x 2 , y 2 ) = 1 z p Ψ ( x 1 , y 1 ) exp { i π λ z p [ ( x 2 x 1 ) 2 + ( y 2 y 1 ) 2 ] } dx 1 dy 1 .
Ψ ( x 2 , y 2 ) = π r 0 2 f π r 0 2 z p + ( z z p f 2 ) 2 P 0 π r 0 2 exp ( i ω l t ) ×
exp { π πλ f 2 r 0 2 i [ π 2 r 0 4 z p + λ 2 z ( z z p f 2 ) ] λ [ π 2 r 0 4 z p 2 + λ 2 ( z z p f 2 ) 2 ] ( x 2 2 + y 2 2 ) }
Ψ ( x F , y F ) = A 2 P 0 π r 0 2 exp ( i ω l t ) exp [ ( 1 r 2 + i π λR ) ( x F 2 + y F 2 ) ] ,
A = r 0 2 π r 0 2 z p + ( z z p f 2 ) × π 2 r 0 4 z p 2 + λ 2 ( z z p f 2 ) 2 π λ f 2 r 0 2 i [ π 2 r 0 4 z p + λ 2 z ( z z p f 2 ) ] ,
r = π 2 λ 2 f 4 r 0 4 + [ π 2 r 0 4 z p + λ 2 z ( z z p f 2 ) ] 2 [ π 2 r 0 4 z p 2 + λ 2 ( z z p f 2 ) 2 ] π 2 r 0 2 ,
R = f 2 × π 2 λ 2 f 4 r 0 4 + [ π 2 r 0 4 z p + λ 2 z ( z z p f 2 ) ] 2 [ π 2 r 0 4 z p 2 + λ 2 ( z z p f 2 ) 2 ] [ π 2 r 0 4 z p + λ 2 z ( z z p f 2 ) ]
Ψ p ( ξ , η ) = B 2 P 0 π r 0 2 exp ( i ω l t ) exp [ ( 1 r p 2 i π λ R p ) ( ξ 2 + η 2 ) ] ,
B = A × r 2 R z 2 + r 2 ( z 2 R )
r p = ( R λz 2 ) 2 + π 2 r 4 ( z 2 R ) 2 π 2 r 2 R 2
R p = ( R λz 2 ) 2 + π 2 r 4 ( z 2 R ) 2 ( ) 2 z 2 + π 2 r 4 ( z 2 R ) 2 .
Ψ m ( ξ , η ) = C 2 P 0 π r 0 2 exp [ i ( ω l + ω s ) t ] exp [ ( 1 r m 2 i π λ R m ) ( ξ 2 + η 2 ) ] .
C = r 0 2 λ z 3 r 0 2
r m = λ 2 z 3 2 + π 2 r 0 4 π 2 r 0 2
R m = ( λ 2 z 3 2 + π 2 r 0 4 ) λ 2 z 3 .
Ψ T ( ξ , η ) = Ψ p ( ξ , η ) + Ψ m ( ξ , η ) ,
I ( ξ , η ) = Ψ T ( ξ , η ) Ψ T * ( ξ , η ) ,
I ξ η = D B 2 exp [ 2 r p 2 ( ξ 2 + η 2 ) ] + D C 2 exp [ 2 r m 2 ( ξ 2 + η 2 ) ] +
BC * D exp [ i ( ω s t ) ] exp [ ( α + ) ] [ ξ 2 + η 2 ] +
B * CD exp [ i ( ω s t ) ] exp [ ( α ) ] [ ξ 2 + η 2 ]
D = 2 P 0 π r 0 2 ,
α = r m 2 + r p 2 r m 2 r p 2 ,
β = π λ R m R p ( R p R m ) ,
P ( z p ) = I ξ η dξdη .
P = D B 2 π r p 2 2 + D C 2 π r m 2 2 + B C * D π ( α ) α 2 + β 2 exp ( i ω s t ) + B * CD π ( α + ) α 2 + β 2 exp ( i ω s t ) .
P = P DC + P AC cos ( ω s t + φ ) .

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