Abstract

The resolution of an angle-scanning technique for measuring transparent optical wafers is analyzed, and it is shown both theoretically and experimentally that subnanometer resolution can be readily achieved. Data are acquired simultaneously over the whole area of the wafer, producing two-dimensional thickness variation maps in as little as 10 s. Repeatabilities of 0.07nm have been demonstrated, and wafers of up to 100mm diameter have been measured, with 1mm or better spatial resolution. A technique for compensating wafer and system aberrations is incorporated and analyzed.

© 2007 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  11. G. Hernandez, Fabry-Perot Interferometers (Cambridge U.P., Cambridge; Melbourne, 1986).
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    [CrossRef] [PubMed]
  13. P. A. Wilksch, "Instrument function of the Fabry-Perot spectrometer," Appl. Opt. 24, 1502-1511 (1985).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  15. G. J. Edwards and M. Lawrence, "A temperature-dependent dispersion-equation for congruently grown lithium-niobate," Opt. Quantum Electron. 16, 373-375 (1984).
    [CrossRef]
  16. B. F. Alexander and K. C. Ng, "Elimination of systematic-error in subpixel accuracy centroid estimation," Opt. Eng. 30, 1320-1331 (1991).
    [CrossRef]
  17. M. Berman, L. M. Bischof, S. J. Davies, A. A. Green, and M. Craig, "Estimating band-to-band misregistrations in aliased imagery," CVGIP: Graph. Models Image Process. 56, 479-493 (1994).
    [CrossRef]

2006 (3)

2005 (3)

2004 (2)

V. M. Pillet, J. A. Bonet, M. Collados, and L. Jochum, "The Imaging Magnetograph Experiment for the Sunrise Balloon Antarctica Project," Proc. SPIE 5487, 1152-1164 (2004).
[CrossRef]

J. M. Barr, J. C. Baker, M. N. Bremer, R. W. Hunstead, and J. Bland-Hawthorn, "Tunable-filter imaging of quasar fields at Z similar to 1. II. The star-forming galaxy environments of radio-loud quasars," Astron. J. 128, 2660-2676 (2004).
[CrossRef]

2003 (1)

1995 (1)

J. C. Brasunas and G. M. Cushman, "Interferometric but nonspectroscopic technique for measuring the thickness of a transparent plate," Opt. Eng. 34, 2126-2130 (1995).
[CrossRef]

1994 (1)

M. Berman, L. M. Bischof, S. J. Davies, A. A. Green, and M. Craig, "Estimating band-to-band misregistrations in aliased imagery," CVGIP: Graph. Models Image Process. 56, 479-493 (1994).
[CrossRef]

1991 (1)

B. F. Alexander and K. C. Ng, "Elimination of systematic-error in subpixel accuracy centroid estimation," Opt. Eng. 30, 1320-1331 (1991).
[CrossRef]

1985 (1)

1984 (2)

G. J. Edwards and M. Lawrence, "A temperature-dependent dispersion-equation for congruently grown lithium-niobate," Opt. Quantum Electron. 16, 373-375 (1984).
[CrossRef]

G. J. Sloggett, "Fringe broadening in Fabry-Perot interferometers," Appl. Opt. 23, 2427-2432 (1984).
[CrossRef] [PubMed]

Abel-Tiberini, L.

J. Floriot, F. Lemarchand, L. Abel-Tiberini, and M. Lequime, "High accuracy measurement of the residual air gap thickness of thin-film and solid-spaced filters assembled by optical contacting," Opt. Commun. 260, 324-328 (2006).
[CrossRef]

Alexander, B. F.

B. F. Alexander and K. C. Ng, "Elimination of systematic-error in subpixel accuracy centroid estimation," Opt. Eng. 30, 1320-1331 (1991).
[CrossRef]

Arkwright, J.

Arkwright, J. W.

Baker, J. C.

J. M. Barr, J. C. Baker, M. N. Bremer, R. W. Hunstead, and J. Bland-Hawthorn, "Tunable-filter imaging of quasar fields at Z similar to 1. II. The star-forming galaxy environments of radio-loud quasars," Astron. J. 128, 2660-2676 (2004).
[CrossRef]

Barr, J. M.

J. M. Barr, J. C. Baker, M. N. Bremer, R. W. Hunstead, and J. Bland-Hawthorn, "Tunable-filter imaging of quasar fields at Z similar to 1. II. The star-forming galaxy environments of radio-loud quasars," Astron. J. 128, 2660-2676 (2004).
[CrossRef]

Berman, M.

M. Berman, L. M. Bischof, S. J. Davies, A. A. Green, and M. Craig, "Estimating band-to-band misregistrations in aliased imagery," CVGIP: Graph. Models Image Process. 56, 479-493 (1994).
[CrossRef]

Bischof, L. M.

M. Berman, L. M. Bischof, S. J. Davies, A. A. Green, and M. Craig, "Estimating band-to-band misregistrations in aliased imagery," CVGIP: Graph. Models Image Process. 56, 479-493 (1994).
[CrossRef]

Bland-Hawthorn, J.

J. M. Barr, J. C. Baker, M. N. Bremer, R. W. Hunstead, and J. Bland-Hawthorn, "Tunable-filter imaging of quasar fields at Z similar to 1. II. The star-forming galaxy environments of radio-loud quasars," Astron. J. 128, 2660-2676 (2004).
[CrossRef]

Bonet, J. A.

V. M. Pillet, J. A. Bonet, M. Collados, and L. Jochum, "The Imaging Magnetograph Experiment for the Sunrise Balloon Antarctica Project," Proc. SPIE 5487, 1152-1164 (2004).
[CrossRef]

Brasunas, J. C.

J. C. Brasunas and G. M. Cushman, "Interferometric but nonspectroscopic technique for measuring the thickness of a transparent plate," Opt. Eng. 34, 2126-2130 (1995).
[CrossRef]

Bremer, M. N.

J. M. Barr, J. C. Baker, M. N. Bremer, R. W. Hunstead, and J. Bland-Hawthorn, "Tunable-filter imaging of quasar fields at Z similar to 1. II. The star-forming galaxy environments of radio-loud quasars," Astron. J. 128, 2660-2676 (2004).
[CrossRef]

Burke, J.

J. Burke, B. F. Oreb, R. P. Netterfield, and K. Hibino, "Metrology challenges of thin optical wafers for high finesse etalons," OptiFab 2003, SPIE Technical Digest TD-02 (SPIE, 2003), pp. 116-118.

Collados, M.

V. M. Pillet, J. A. Bonet, M. Collados, and L. Jochum, "The Imaging Magnetograph Experiment for the Sunrise Balloon Antarctica Project," Proc. SPIE 5487, 1152-1164 (2004).
[CrossRef]

Coppola, G.

Craig, M.

M. Berman, L. M. Bischof, S. J. Davies, A. A. Green, and M. Craig, "Estimating band-to-band misregistrations in aliased imagery," CVGIP: Graph. Models Image Process. 56, 479-493 (1994).
[CrossRef]

Cushman, G. M.

J. C. Brasunas and G. M. Cushman, "Interferometric but nonspectroscopic technique for measuring the thickness of a transparent plate," Opt. Eng. 34, 2126-2130 (1995).
[CrossRef]

Davies, S. J.

M. Berman, L. M. Bischof, S. J. Davies, A. A. Green, and M. Craig, "Estimating band-to-band misregistrations in aliased imagery," CVGIP: Graph. Models Image Process. 56, 479-493 (1994).
[CrossRef]

De Nicola, S.

Edwards, G. J.

G. J. Edwards and M. Lawrence, "A temperature-dependent dispersion-equation for congruently grown lithium-niobate," Opt. Quantum Electron. 16, 373-375 (1984).
[CrossRef]

Farrant, D.

Farrant, D. I.

Ferraro, P.

Floriot, J.

J. Floriot, F. Lemarchand, L. Abel-Tiberini, and M. Lequime, "High accuracy measurement of the residual air gap thickness of thin-film and solid-spaced filters assembled by optical contacting," Opt. Commun. 260, 324-328 (2006).
[CrossRef]

Gillen, G. D.

Green, A. A.

M. Berman, L. M. Bischof, S. J. Davies, A. A. Green, and M. Craig, "Estimating band-to-band misregistrations in aliased imagery," CVGIP: Graph. Models Image Process. 56, 479-493 (1994).
[CrossRef]

Gross, M.

Guha, S.

Hernandez, G.

G. Hernandez, Fabry-Perot Interferometers (Cambridge U.P., Cambridge; Melbourne, 1986).

Hibino, K.

J. Burke, B. F. Oreb, R. P. Netterfield, and K. Hibino, "Metrology challenges of thin optical wafers for high finesse etalons," OptiFab 2003, SPIE Technical Digest TD-02 (SPIE, 2003), pp. 116-118.

Hunstead, R. W.

J. M. Barr, J. C. Baker, M. N. Bremer, R. W. Hunstead, and J. Bland-Hawthorn, "Tunable-filter imaging of quasar fields at Z similar to 1. II. The star-forming galaxy environments of radio-loud quasars," Astron. J. 128, 2660-2676 (2004).
[CrossRef]

Iodice, M.

Jang, M. J.

M. J. Jang and C. F. Lu, "A measurement system for determining the thickness of an optical wave plate," Opt. Commun. 253, 2-9 (2005).
[CrossRef]

Jochum, L.

V. M. Pillet, J. A. Bonet, M. Collados, and L. Jochum, "The Imaging Magnetograph Experiment for the Sunrise Balloon Antarctica Project," Proc. SPIE 5487, 1152-1164 (2004).
[CrossRef]

Lawrence, M.

G. J. Edwards and M. Lawrence, "A temperature-dependent dispersion-equation for congruently grown lithium-niobate," Opt. Quantum Electron. 16, 373-375 (1984).
[CrossRef]

Lemarchand, F.

J. Floriot, F. Lemarchand, L. Abel-Tiberini, and M. Lequime, "High accuracy measurement of the residual air gap thickness of thin-film and solid-spaced filters assembled by optical contacting," Opt. Commun. 260, 324-328 (2006).
[CrossRef]

Lequime, M.

J. Floriot, F. Lemarchand, L. Abel-Tiberini, and M. Lequime, "High accuracy measurement of the residual air gap thickness of thin-film and solid-spaced filters assembled by optical contacting," Opt. Commun. 260, 324-328 (2006).
[CrossRef]

Lu, C. F.

M. J. Jang and C. F. Lu, "A measurement system for determining the thickness of an optical wave plate," Opt. Commun. 253, 2-9 (2005).
[CrossRef]

Netterfield, R. P.

J. Burke, B. F. Oreb, R. P. Netterfield, and K. Hibino, "Metrology challenges of thin optical wafers for high finesse etalons," OptiFab 2003, SPIE Technical Digest TD-02 (SPIE, 2003), pp. 116-118.

Ng, K. C.

B. F. Alexander and K. C. Ng, "Elimination of systematic-error in subpixel accuracy centroid estimation," Opt. Eng. 30, 1320-1331 (1991).
[CrossRef]

Oreb, B. F.

J. Burke, B. F. Oreb, R. P. Netterfield, and K. Hibino, "Metrology challenges of thin optical wafers for high finesse etalons," OptiFab 2003, SPIE Technical Digest TD-02 (SPIE, 2003), pp. 116-118.

Pereira, N.

Pillet, V. M.

V. M. Pillet, J. A. Bonet, M. Collados, and L. Jochum, "The Imaging Magnetograph Experiment for the Sunrise Balloon Antarctica Project," Proc. SPIE 5487, 1152-1164 (2004).
[CrossRef]

Sloggett, G. J.

Underhill, I.

Wilksch, P. A.

Zhang, J.

Appl. Opt. (4)

Astron. J. (1)

J. M. Barr, J. C. Baker, M. N. Bremer, R. W. Hunstead, and J. Bland-Hawthorn, "Tunable-filter imaging of quasar fields at Z similar to 1. II. The star-forming galaxy environments of radio-loud quasars," Astron. J. 128, 2660-2676 (2004).
[CrossRef]

CVGIP: Graph. Models Image Process. (1)

M. Berman, L. M. Bischof, S. J. Davies, A. A. Green, and M. Craig, "Estimating band-to-band misregistrations in aliased imagery," CVGIP: Graph. Models Image Process. 56, 479-493 (1994).
[CrossRef]

Opt. Commun. (2)

J. Floriot, F. Lemarchand, L. Abel-Tiberini, and M. Lequime, "High accuracy measurement of the residual air gap thickness of thin-film and solid-spaced filters assembled by optical contacting," Opt. Commun. 260, 324-328 (2006).
[CrossRef]

M. J. Jang and C. F. Lu, "A measurement system for determining the thickness of an optical wave plate," Opt. Commun. 253, 2-9 (2005).
[CrossRef]

Opt. Eng. (2)

B. F. Alexander and K. C. Ng, "Elimination of systematic-error in subpixel accuracy centroid estimation," Opt. Eng. 30, 1320-1331 (1991).
[CrossRef]

J. C. Brasunas and G. M. Cushman, "Interferometric but nonspectroscopic technique for measuring the thickness of a transparent plate," Opt. Eng. 34, 2126-2130 (1995).
[CrossRef]

Opt. Express (3)

Opt. Quantum Electron. (1)

G. J. Edwards and M. Lawrence, "A temperature-dependent dispersion-equation for congruently grown lithium-niobate," Opt. Quantum Electron. 16, 373-375 (1984).
[CrossRef]

Proc. SPIE (1)

V. M. Pillet, J. A. Bonet, M. Collados, and L. Jochum, "The Imaging Magnetograph Experiment for the Sunrise Balloon Antarctica Project," Proc. SPIE 5487, 1152-1164 (2004).
[CrossRef]

Other (2)

J. Burke, B. F. Oreb, R. P. Netterfield, and K. Hibino, "Metrology challenges of thin optical wafers for high finesse etalons," OptiFab 2003, SPIE Technical Digest TD-02 (SPIE, 2003), pp. 116-118.

G. Hernandez, Fabry-Perot Interferometers (Cambridge U.P., Cambridge; Melbourne, 1986).

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Figures (8)

Fig. 1
Fig. 1

Intensity transmittance contours of a 280 μm thick wafer as a function of both angle of incidence and physical thickness (white is high transmittance).

Fig. 2
Fig. 2

Wafer angle-scanning system, plan view.

Fig. 3
Fig. 3

(Color online) Physical thickness variation map of a 0.28 mm thick lithium niobate wafer.

Fig. 4
Fig. 4

(Color online) Physical thickness variation map of a 9 mm thick lithium niobate wafer.

Fig. 5
Fig. 5

Physical thickness resolution as a function of nominal physical thickness for a lithium niobate wafer and an angular step size of 0.001°.

Fig. 6
Fig. 6

Thickness error contour plot for a 0.3 mm thick, circular (upper half) lithium niobate wafer at 3° angle of incidence in a 0.1° FOV beam (contours are in nanometers; 0 and ± 1 on the position axes represent wafer center and edges, respectively).

Fig. 7
Fig. 7

Thickness error contour plot for a 9 mm thick, circular (upper half) lithium niobate wafer at 0.6° angle of incidence in a 0.1° FOV beam (contours are in nanometers; 0 and ± 1 on the position axes represent wafer center and edges, respectively). Note the curvature in the contours.

Fig. 8
Fig. 8

Geometry of wafer and illumination beam.

Equations (19)

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T = 1 1 + [ 4 R / ( 1 R ) 2 ] sin 2 δ ,
δ = 2 π λ n d cos θ ,
θ = sin 1 ( sin θ i n ) .
m λ = 2 n d ( x , y ) cos θ ( x , y ) ,
d ( x , y ) = d 0 / cos θ ( x , y ) .
F R = π R / ( 1 R ) .
T e ( λ ) = 1 M N x = 1 M y = 1 N T [ d ( x , y ) ,   θ ( x , y ) ,   λ ] .
λ = 2 n d ( 1 cos Δ θ ) ,
Δ θ i n λ / d ,
θ a ( x , y ) = [ θ 2 ( x , y ) + θ + 2 ( x , y ) ] / 2 .
θ ( x , y ) = θ 1 ( x , y ) θ a ( x , y ) .
Δ d = d m = λ / 2 n ,
δ d = δ θ d ( x , y ) θ ( x , y ) d 0 θ i δ θ i n 2 ,
δ d δ θ i λ d / n 3 ,
ε ( x , y ) = n d 0 [ 1 cos θ ( x , y ) 1 cos θ i ( x , y ) ] ,
N = sin θ N i + cos θ N k .
U = sin θ U cos ϕ U i + sin θ U sin ϕ U j + cos θ U k .
cos θ = U N / | U | | N |
= sin θ N sin θ U cos ϕ U + cos θ N cos θ U .

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