Abstract

Numerical calculation is performed to validate the principles of a single optical technique devoted to real time probing or imaging of submultilayers within interferential coatings.

© 2008 Optical Society of America

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  1. F. J. Van Milligen, B. Bovard, M. R. Jacobson, J. Mueller, R. Potoff, R. L. Shoemaker, and H. A. Macleod, “Development of an automated scanning monochromator for monitoring thin films,” Appl. Opt. 24, 1799-1802 (1985).
    [CrossRef] [PubMed]
  2. B. Bovard, F. J. Van Milligen, M. J. Messerly, S. G. Saxe, and H. A. Macleod, “Optical constants derivation for an inhomogeneous thin film from in situ transmission measurements,” Appl. Opt. 24, 1803-1807 (1985).
    [CrossRef] [PubMed]
  3. A. V. Tikhonravov, M. K. Trubetskov, M. A. Kokarev, T. V. Amotchkina, A. Duparré, E. Quesnel, D. Ristau, and S. Günster, “Effect of systematic errors in spectral photometric data on the accuracy of determination of optical parameters of dielectric thin films,” Appl. Opt. 41, 2555-2560 (2002).
    [CrossRef] [PubMed]
  4. S. Bosch and F. Monzonis, “General inversion method for single-wavelength ellipsometry of samples with an arbitrary number of layers,” J. Opt. Soc. Am. A 12, 1375-1379 (1995).
    [CrossRef]
  5. A. Dubois, K. Grieve, G. Moneron, R. Lecaque, L. Vabre, and C. Boccara, “Ultrahigh resolution full-field optical coherence tomography,” Appl. Opt. 43, 2874-2883 (2004).
    [CrossRef] [PubMed]
  6. C. Amra and C. Deumié, “Z-probing of optical multilayers: theory,” Opt. Lett. 31, 2704-2706 (2006).
    [CrossRef] [PubMed]
  7. D. Ausserré and M. P. Valignat, “Wide-field optical imaging of surface nanostructures,” Nano. Lett. 6, 1384-1388 (2006).
    [CrossRef] [PubMed]
  8. C. Amra, C. Deumié, and O. Gilbert, “Elimination of polarized light scattered by surface roughness or bulk heterogeneity,”Opt. Exp. 13, 10854-10864 (2005).
    [CrossRef]
  9. G. Georges, C. Deumié, and C. Amra, “Selective probing and imaging in random media based on the elimination of polarized scattering,” Opt. Exp. 15, 9804-9816 (2007).
    [CrossRef]

2007 (1)

G. Georges, C. Deumié, and C. Amra, “Selective probing and imaging in random media based on the elimination of polarized scattering,” Opt. Exp. 15, 9804-9816 (2007).
[CrossRef]

2006 (2)

D. Ausserré and M. P. Valignat, “Wide-field optical imaging of surface nanostructures,” Nano. Lett. 6, 1384-1388 (2006).
[CrossRef] [PubMed]

C. Amra and C. Deumié, “Z-probing of optical multilayers: theory,” Opt. Lett. 31, 2704-2706 (2006).
[CrossRef] [PubMed]

2005 (1)

C. Amra, C. Deumié, and O. Gilbert, “Elimination of polarized light scattered by surface roughness or bulk heterogeneity,”Opt. Exp. 13, 10854-10864 (2005).
[CrossRef]

2004 (1)

A. Dubois, K. Grieve, G. Moneron, R. Lecaque, L. Vabre, and C. Boccara, “Ultrahigh resolution full-field optical coherence tomography,” Appl. Opt. 43, 2874-2883 (2004).
[CrossRef] [PubMed]

2002 (1)

A. V. Tikhonravov, M. K. Trubetskov, M. A. Kokarev, T. V. Amotchkina, A. Duparré, E. Quesnel, D. Ristau, and S. Günster, “Effect of systematic errors in spectral photometric data on the accuracy of determination of optical parameters of dielectric thin films,” Appl. Opt. 41, 2555-2560 (2002).
[CrossRef] [PubMed]

1995 (1)

S. Bosch and F. Monzonis, “General inversion method for single-wavelength ellipsometry of samples with an arbitrary number of layers,” J. Opt. Soc. Am. A 12, 1375-1379 (1995).
[CrossRef]

1985 (2)

B. Bovard, F. J. Van Milligen, M. J. Messerly, S. G. Saxe, and H. A. Macleod, “Optical constants derivation for an inhomogeneous thin film from in situ transmission measurements,” Appl. Opt. 24, 1803-1807 (1985).
[CrossRef] [PubMed]

F. J. Van Milligen, B. Bovard, M. R. Jacobson, J. Mueller, R. Potoff, R. L. Shoemaker, and H. A. Macleod, “Development of an automated scanning monochromator for monitoring thin films,” Appl. Opt. 24, 1799-1802 (1985).
[CrossRef] [PubMed]

Amotchkina, T. V.

A. V. Tikhonravov, M. K. Trubetskov, M. A. Kokarev, T. V. Amotchkina, A. Duparré, E. Quesnel, D. Ristau, and S. Günster, “Effect of systematic errors in spectral photometric data on the accuracy of determination of optical parameters of dielectric thin films,” Appl. Opt. 41, 2555-2560 (2002).
[CrossRef] [PubMed]

Amra, C.

G. Georges, C. Deumié, and C. Amra, “Selective probing and imaging in random media based on the elimination of polarized scattering,” Opt. Exp. 15, 9804-9816 (2007).
[CrossRef]

C. Amra and C. Deumié, “Z-probing of optical multilayers: theory,” Opt. Lett. 31, 2704-2706 (2006).
[CrossRef] [PubMed]

C. Amra, C. Deumié, and O. Gilbert, “Elimination of polarized light scattered by surface roughness or bulk heterogeneity,”Opt. Exp. 13, 10854-10864 (2005).
[CrossRef]

Ausserré, D.

D. Ausserré and M. P. Valignat, “Wide-field optical imaging of surface nanostructures,” Nano. Lett. 6, 1384-1388 (2006).
[CrossRef] [PubMed]

Boccara, C.

A. Dubois, K. Grieve, G. Moneron, R. Lecaque, L. Vabre, and C. Boccara, “Ultrahigh resolution full-field optical coherence tomography,” Appl. Opt. 43, 2874-2883 (2004).
[CrossRef] [PubMed]

Bosch, S.

S. Bosch and F. Monzonis, “General inversion method for single-wavelength ellipsometry of samples with an arbitrary number of layers,” J. Opt. Soc. Am. A 12, 1375-1379 (1995).
[CrossRef]

Bovard, B.

F. J. Van Milligen, B. Bovard, M. R. Jacobson, J. Mueller, R. Potoff, R. L. Shoemaker, and H. A. Macleod, “Development of an automated scanning monochromator for monitoring thin films,” Appl. Opt. 24, 1799-1802 (1985).
[CrossRef] [PubMed]

B. Bovard, F. J. Van Milligen, M. J. Messerly, S. G. Saxe, and H. A. Macleod, “Optical constants derivation for an inhomogeneous thin film from in situ transmission measurements,” Appl. Opt. 24, 1803-1807 (1985).
[CrossRef] [PubMed]

Deumié, C.

G. Georges, C. Deumié, and C. Amra, “Selective probing and imaging in random media based on the elimination of polarized scattering,” Opt. Exp. 15, 9804-9816 (2007).
[CrossRef]

C. Amra and C. Deumié, “Z-probing of optical multilayers: theory,” Opt. Lett. 31, 2704-2706 (2006).
[CrossRef] [PubMed]

C. Amra, C. Deumié, and O. Gilbert, “Elimination of polarized light scattered by surface roughness or bulk heterogeneity,”Opt. Exp. 13, 10854-10864 (2005).
[CrossRef]

Dubois, A.

A. Dubois, K. Grieve, G. Moneron, R. Lecaque, L. Vabre, and C. Boccara, “Ultrahigh resolution full-field optical coherence tomography,” Appl. Opt. 43, 2874-2883 (2004).
[CrossRef] [PubMed]

Duparré, A.

A. V. Tikhonravov, M. K. Trubetskov, M. A. Kokarev, T. V. Amotchkina, A. Duparré, E. Quesnel, D. Ristau, and S. Günster, “Effect of systematic errors in spectral photometric data on the accuracy of determination of optical parameters of dielectric thin films,” Appl. Opt. 41, 2555-2560 (2002).
[CrossRef] [PubMed]

Georges, G.

G. Georges, C. Deumié, and C. Amra, “Selective probing and imaging in random media based on the elimination of polarized scattering,” Opt. Exp. 15, 9804-9816 (2007).
[CrossRef]

Gilbert, O.

C. Amra, C. Deumié, and O. Gilbert, “Elimination of polarized light scattered by surface roughness or bulk heterogeneity,”Opt. Exp. 13, 10854-10864 (2005).
[CrossRef]

Grieve, K.

A. Dubois, K. Grieve, G. Moneron, R. Lecaque, L. Vabre, and C. Boccara, “Ultrahigh resolution full-field optical coherence tomography,” Appl. Opt. 43, 2874-2883 (2004).
[CrossRef] [PubMed]

Günster, S.

A. V. Tikhonravov, M. K. Trubetskov, M. A. Kokarev, T. V. Amotchkina, A. Duparré, E. Quesnel, D. Ristau, and S. Günster, “Effect of systematic errors in spectral photometric data on the accuracy of determination of optical parameters of dielectric thin films,” Appl. Opt. 41, 2555-2560 (2002).
[CrossRef] [PubMed]

Jacobson, M. R.

Kokarev, M. A.

A. V. Tikhonravov, M. K. Trubetskov, M. A. Kokarev, T. V. Amotchkina, A. Duparré, E. Quesnel, D. Ristau, and S. Günster, “Effect of systematic errors in spectral photometric data on the accuracy of determination of optical parameters of dielectric thin films,” Appl. Opt. 41, 2555-2560 (2002).
[CrossRef] [PubMed]

Lecaque, R.

A. Dubois, K. Grieve, G. Moneron, R. Lecaque, L. Vabre, and C. Boccara, “Ultrahigh resolution full-field optical coherence tomography,” Appl. Opt. 43, 2874-2883 (2004).
[CrossRef] [PubMed]

Macleod, H. A.

F. J. Van Milligen, B. Bovard, M. R. Jacobson, J. Mueller, R. Potoff, R. L. Shoemaker, and H. A. Macleod, “Development of an automated scanning monochromator for monitoring thin films,” Appl. Opt. 24, 1799-1802 (1985).
[CrossRef] [PubMed]

B. Bovard, F. J. Van Milligen, M. J. Messerly, S. G. Saxe, and H. A. Macleod, “Optical constants derivation for an inhomogeneous thin film from in situ transmission measurements,” Appl. Opt. 24, 1803-1807 (1985).
[CrossRef] [PubMed]

Messerly, M. J.

B. Bovard, F. J. Van Milligen, M. J. Messerly, S. G. Saxe, and H. A. Macleod, “Optical constants derivation for an inhomogeneous thin film from in situ transmission measurements,” Appl. Opt. 24, 1803-1807 (1985).
[CrossRef] [PubMed]

Moneron, G.

A. Dubois, K. Grieve, G. Moneron, R. Lecaque, L. Vabre, and C. Boccara, “Ultrahigh resolution full-field optical coherence tomography,” Appl. Opt. 43, 2874-2883 (2004).
[CrossRef] [PubMed]

Monzonis, F.

S. Bosch and F. Monzonis, “General inversion method for single-wavelength ellipsometry of samples with an arbitrary number of layers,” J. Opt. Soc. Am. A 12, 1375-1379 (1995).
[CrossRef]

Mueller, J.

Potoff, R.

Quesnel, E.

A. V. Tikhonravov, M. K. Trubetskov, M. A. Kokarev, T. V. Amotchkina, A. Duparré, E. Quesnel, D. Ristau, and S. Günster, “Effect of systematic errors in spectral photometric data on the accuracy of determination of optical parameters of dielectric thin films,” Appl. Opt. 41, 2555-2560 (2002).
[CrossRef] [PubMed]

Ristau, D.

A. V. Tikhonravov, M. K. Trubetskov, M. A. Kokarev, T. V. Amotchkina, A. Duparré, E. Quesnel, D. Ristau, and S. Günster, “Effect of systematic errors in spectral photometric data on the accuracy of determination of optical parameters of dielectric thin films,” Appl. Opt. 41, 2555-2560 (2002).
[CrossRef] [PubMed]

Saxe, S. G.

B. Bovard, F. J. Van Milligen, M. J. Messerly, S. G. Saxe, and H. A. Macleod, “Optical constants derivation for an inhomogeneous thin film from in situ transmission measurements,” Appl. Opt. 24, 1803-1807 (1985).
[CrossRef] [PubMed]

Shoemaker, R. L.

Tikhonravov, A. V.

A. V. Tikhonravov, M. K. Trubetskov, M. A. Kokarev, T. V. Amotchkina, A. Duparré, E. Quesnel, D. Ristau, and S. Günster, “Effect of systematic errors in spectral photometric data on the accuracy of determination of optical parameters of dielectric thin films,” Appl. Opt. 41, 2555-2560 (2002).
[CrossRef] [PubMed]

Trubetskov, M. K.

A. V. Tikhonravov, M. K. Trubetskov, M. A. Kokarev, T. V. Amotchkina, A. Duparré, E. Quesnel, D. Ristau, and S. Günster, “Effect of systematic errors in spectral photometric data on the accuracy of determination of optical parameters of dielectric thin films,” Appl. Opt. 41, 2555-2560 (2002).
[CrossRef] [PubMed]

Vabre, L.

A. Dubois, K. Grieve, G. Moneron, R. Lecaque, L. Vabre, and C. Boccara, “Ultrahigh resolution full-field optical coherence tomography,” Appl. Opt. 43, 2874-2883 (2004).
[CrossRef] [PubMed]

Valignat, M. P.

D. Ausserré and M. P. Valignat, “Wide-field optical imaging of surface nanostructures,” Nano. Lett. 6, 1384-1388 (2006).
[CrossRef] [PubMed]

Van Milligen, F. J.

F. J. Van Milligen, B. Bovard, M. R. Jacobson, J. Mueller, R. Potoff, R. L. Shoemaker, and H. A. Macleod, “Development of an automated scanning monochromator for monitoring thin films,” Appl. Opt. 24, 1799-1802 (1985).
[CrossRef] [PubMed]

B. Bovard, F. J. Van Milligen, M. J. Messerly, S. G. Saxe, and H. A. Macleod, “Optical constants derivation for an inhomogeneous thin film from in situ transmission measurements,” Appl. Opt. 24, 1803-1807 (1985).
[CrossRef] [PubMed]

Appl. Opt. (3)

A. Dubois, K. Grieve, G. Moneron, R. Lecaque, L. Vabre, and C. Boccara, “Ultrahigh resolution full-field optical coherence tomography,” Appl. Opt. 43, 2874-2883 (2004).
[CrossRef] [PubMed]

B. Bovard, F. J. Van Milligen, M. J. Messerly, S. G. Saxe, and H. A. Macleod, “Optical constants derivation for an inhomogeneous thin film from in situ transmission measurements,” Appl. Opt. 24, 1803-1807 (1985).
[CrossRef] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, M. A. Kokarev, T. V. Amotchkina, A. Duparré, E. Quesnel, D. Ristau, and S. Günster, “Effect of systematic errors in spectral photometric data on the accuracy of determination of optical parameters of dielectric thin films,” Appl. Opt. 41, 2555-2560 (2002).
[CrossRef] [PubMed]

Appl. Opt. (1)

J. Opt. Soc. Am. A (1)

S. Bosch and F. Monzonis, “General inversion method for single-wavelength ellipsometry of samples with an arbitrary number of layers,” J. Opt. Soc. Am. A 12, 1375-1379 (1995).
[CrossRef]

Nano. Lett. (1)

D. Ausserré and M. P. Valignat, “Wide-field optical imaging of surface nanostructures,” Nano. Lett. 6, 1384-1388 (2006).
[CrossRef] [PubMed]

Opt. Exp. (2)

C. Amra, C. Deumié, and O. Gilbert, “Elimination of polarized light scattered by surface roughness or bulk heterogeneity,”Opt. Exp. 13, 10854-10864 (2005).
[CrossRef]

G. Georges, C. Deumié, and C. Amra, “Selective probing and imaging in random media based on the elimination of polarized scattering,” Opt. Exp. 15, 9804-9816 (2007).
[CrossRef]

Opt. Lett. (1)

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Figures (9)

Fig. 1
Fig. 1

Basic principles for the cancellation of polarized reflection from a multilayer.

Fig. 2
Fig. 2

Choice of two arbitrary submultilayers (0) and (1) within a stack.

Fig. 3
Fig. 3

Definition of reflection and transmission factors from submultilayers (0) and (1).

Fig. 4
Fig. 4

Elimination of back submultilayer (1).

Fig. 5
Fig. 5

S-reflection factor (bold curve, left-hand side vertical units) of a Fabry–Perot filter probed at 50° incident angle and the remaining signal (dashed curve, right-hand side vertical units) after elimination of the back mirror.

Fig. 6
Fig. 6

Position of analyzer (dashed curve) and retardation (bold curve) plates versus wavelength for cancellation of the back mirror of the Fabry–Perot filter in Fig. 5.

Fig. 7
Fig. 7

Situation in which the top stack should be eliminated or minimized.

Fig. 8
Fig. 8

Same as Fig. 5, but the influence of the top mirror is minimized.

Fig. 9
Fig. 9

Same as Fig. 5, but the design is an 11-layer quarterwave mirror probed at 50° incidence. The top stack is defined by the first five thin-film layers of the mirror.

Equations (18)

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

E = E S + E P = ( A S + A P ) exp ( j k ρ ) ,
k = k 0 ( sin i , 0 , cos i ) ,
A S = A S ,     A P = A P exp ( j η ) .
A * = r S cos ψ A S + r P sin ψ exp ( j η * ) A P ,
A S = A P A * / A S = r S cos ψ + r P sin ψ exp [ j ( η + η * ) ] .
f ( r ) = f ( r S , r P ) = cos ψ [ r S + z r P exp ( j η ) ] ,
z ( ψ , η * ) = tan ψ exp ( j η * ) .
z = z 0 = ( r S / r P ) exp ( j η ) f ( z 0 , r ) = 0 ,
tan ψ = r S / r P ,     η * = π ( δ + η ) ,
r S = R S 0.5 exp ( j δ S ) ,     r P = R P 0.5 exp ( j δ P ) .
f e x t 2 = [ R S 0.5 cos ψ ± R P 0.5 sin ψ ] 2 .
r = r 0 + t 0 t 0 r 1 exp ( j 2 κ ) + t 0 t 0 r 0 r 1 2 exp ( j 4 κ ) + = n r n ,
r = ( n ˜ 0 Y 0 ) / ( n ˜ 0 + Y 0 )
f ( n r n ) = n f ( r n )
z = z i = ( r i , S / r i , P ) exp ( j η ) f ( z i , r i ) = 0 .
r = n r n = r 0 + t 0 t 0 r 1 exp ( j 2 κ ) [ 1 / ( 1 r 0 r 1 exp ( j 2 κ ) ) ] = r 0 + E .
f ( z b a c k , E ) = 0 f ( z b a c k , r ) = f ( z b a c k , r 0 ) .
f ( z t o p , r G ) = 0 f ( z t o p , r ) = f ( z t o p , G ) .

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