Abstract

The wavefront is an important characteristic for a dielectric mirror. Its measurement is usually performed with interferometers. We introduce a new method to evaluate only the coating wavefront distortion due to nonuniform thickness errors by using a reflectometer. This method uses some reflectance or transmittance maps at a wavenumber σm for which the reflectance or transmittance factor variation is high. These variations are translated into some central wavenumber σc variations, which enables the determination of a phase map from experimental treatment.

© 2011 Optical Society of America

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  1. Ph. Belleville, C. Bonnin, and J. J. Priotton, “Room-temperature mirror preparation using sol-gel chemistry and laminar-flow coating technique,” J. Sol-Gel Sci. Technol. 19, 223–226 (2000).
    [CrossRef]
  2. Ph. Belleville, Ph. Prené, C. Bonnin, and Y. Montouillout, “Use of sol-gel hybrids for laser optical thin films,” in Materials Research Society Symposium Proceeding, Vol. 726 (Materials Research Society, 2002), pp. 369–380.
  3. F. Sabary, D. Marteau, P. Hamel, and H. Piombini, “High reflectivity protected silver coatings on stainless steel and aluminium substrates,” in Proceedings of the Society of Vacuum Coaters, 47th Annual Technical Conference (Society of Vacuum Coaters, 2004), pp. 358–361.
  4. B. Bertussi, H. Piombini, D. Damiani, M. Pommiès, X. Le Borgne, and D. Plessis, “SOCRATE: an optical bench dedicated to the understanding and improvement of a laser conditioning process,” Appl. Opt. 45, 8506–8516(2006).
    [CrossRef] [PubMed]
  5. H. Piombini and Ph. Voarino, “Dispositif et procédé de mesure de caractérisation par réflectométrie,” PCT WO2007/138032A1 (6 December 2007).
  6. H. Piombini and Ph. Voarino, “Apparatus designed for very accurate measurement of the optical reflection,” Appl. Opt. 46, 8609–8618 (2007).
    [CrossRef] [PubMed]
  7. Ph. Voarino, H. Piombini, F. Sabary, D. Marteau, J. Dubard, J. Hameury, and J. R. Filtz, “High-accuracy measurements of the normal specular reflectance,” Appl. Opt. 47, C303–C309(2008).
    [CrossRef] [PubMed]
  8. H. Piombini, D. Soler, and Ph. Voarino, “New device to measure the reflectivity on steeply curved surface,” Proc. SPIE 7018, 70181B (2008).
    [CrossRef]
  9. H. Piombini, S. Bruynooghe, and Ph. Voarino, “Spectral measurement in reflection on steeply aspheric surfaces,” Proc. SPIE 7102, 71021C (2008).
    [CrossRef]
  10. J. Dubard, J. Hameury, J.-R. Filtz, D. Soler, Ph. Voarino, and H. Piombini, Normal Reflectance Measurement Based on High Reflectivity Dielectric Mirrors Reference Standard (Newrad, 2008), pp. 13–15.
  11. H. Piombini and L. Caillon, “Reflectance measurement of spherical samples,” Opt. Rev. 16, 571–574 (2009).
    [CrossRef]
  12. H. Piombini, Ph. Voarino, and F. Lemarchand, “Is it possible to check micro-component coatings?” Appl. Opt. 50, C424–C432(2011).
    [CrossRef] [PubMed]
  13. H. Piombini, “Procédé de mesure et procédé de visualisation d’une surface d’onde par spectrophotométrie,” French patent FR0950613 (30 January 2009).
  14. F. Abeles, “Recherches sur la propagation des ondes électromagnétiques sinusoidales dans les milieux stratifiés,” Ann. Phys. 5, 596–706 (1950).
  15. H. A. MacLeod, Thin-Film Optical Filters, 2nd ed. (Hilger, 1986).
    [CrossRef]
  16. T. Csendes, “Nonlinear parameter estimation by global optimization—efficiency and reliability,” Acta Cybern. 8, 361–370 (1988).

2011 (1)

2009 (1)

H. Piombini and L. Caillon, “Reflectance measurement of spherical samples,” Opt. Rev. 16, 571–574 (2009).
[CrossRef]

2008 (3)

H. Piombini, D. Soler, and Ph. Voarino, “New device to measure the reflectivity on steeply curved surface,” Proc. SPIE 7018, 70181B (2008).
[CrossRef]

H. Piombini, S. Bruynooghe, and Ph. Voarino, “Spectral measurement in reflection on steeply aspheric surfaces,” Proc. SPIE 7102, 71021C (2008).
[CrossRef]

Ph. Voarino, H. Piombini, F. Sabary, D. Marteau, J. Dubard, J. Hameury, and J. R. Filtz, “High-accuracy measurements of the normal specular reflectance,” Appl. Opt. 47, C303–C309(2008).
[CrossRef] [PubMed]

2007 (1)

2006 (1)

2000 (1)

Ph. Belleville, C. Bonnin, and J. J. Priotton, “Room-temperature mirror preparation using sol-gel chemistry and laminar-flow coating technique,” J. Sol-Gel Sci. Technol. 19, 223–226 (2000).
[CrossRef]

1988 (1)

T. Csendes, “Nonlinear parameter estimation by global optimization—efficiency and reliability,” Acta Cybern. 8, 361–370 (1988).

1950 (1)

F. Abeles, “Recherches sur la propagation des ondes électromagnétiques sinusoidales dans les milieux stratifiés,” Ann. Phys. 5, 596–706 (1950).

Abeles, F.

F. Abeles, “Recherches sur la propagation des ondes électromagnétiques sinusoidales dans les milieux stratifiés,” Ann. Phys. 5, 596–706 (1950).

Belleville, Ph.

Ph. Belleville, C. Bonnin, and J. J. Priotton, “Room-temperature mirror preparation using sol-gel chemistry and laminar-flow coating technique,” J. Sol-Gel Sci. Technol. 19, 223–226 (2000).
[CrossRef]

Ph. Belleville, Ph. Prené, C. Bonnin, and Y. Montouillout, “Use of sol-gel hybrids for laser optical thin films,” in Materials Research Society Symposium Proceeding, Vol. 726 (Materials Research Society, 2002), pp. 369–380.

Bertussi, B.

Bonnin, C.

Ph. Belleville, C. Bonnin, and J. J. Priotton, “Room-temperature mirror preparation using sol-gel chemistry and laminar-flow coating technique,” J. Sol-Gel Sci. Technol. 19, 223–226 (2000).
[CrossRef]

Ph. Belleville, Ph. Prené, C. Bonnin, and Y. Montouillout, “Use of sol-gel hybrids for laser optical thin films,” in Materials Research Society Symposium Proceeding, Vol. 726 (Materials Research Society, 2002), pp. 369–380.

Bruynooghe, S.

H. Piombini, S. Bruynooghe, and Ph. Voarino, “Spectral measurement in reflection on steeply aspheric surfaces,” Proc. SPIE 7102, 71021C (2008).
[CrossRef]

Caillon, L.

H. Piombini and L. Caillon, “Reflectance measurement of spherical samples,” Opt. Rev. 16, 571–574 (2009).
[CrossRef]

Csendes, T.

T. Csendes, “Nonlinear parameter estimation by global optimization—efficiency and reliability,” Acta Cybern. 8, 361–370 (1988).

Damiani, D.

Dubard, J.

Ph. Voarino, H. Piombini, F. Sabary, D. Marteau, J. Dubard, J. Hameury, and J. R. Filtz, “High-accuracy measurements of the normal specular reflectance,” Appl. Opt. 47, C303–C309(2008).
[CrossRef] [PubMed]

J. Dubard, J. Hameury, J.-R. Filtz, D. Soler, Ph. Voarino, and H. Piombini, Normal Reflectance Measurement Based on High Reflectivity Dielectric Mirrors Reference Standard (Newrad, 2008), pp. 13–15.

Filtz, J. R.

Filtz, J.-R.

J. Dubard, J. Hameury, J.-R. Filtz, D. Soler, Ph. Voarino, and H. Piombini, Normal Reflectance Measurement Based on High Reflectivity Dielectric Mirrors Reference Standard (Newrad, 2008), pp. 13–15.

Hamel, P.

F. Sabary, D. Marteau, P. Hamel, and H. Piombini, “High reflectivity protected silver coatings on stainless steel and aluminium substrates,” in Proceedings of the Society of Vacuum Coaters, 47th Annual Technical Conference (Society of Vacuum Coaters, 2004), pp. 358–361.

Hameury, J.

Ph. Voarino, H. Piombini, F. Sabary, D. Marteau, J. Dubard, J. Hameury, and J. R. Filtz, “High-accuracy measurements of the normal specular reflectance,” Appl. Opt. 47, C303–C309(2008).
[CrossRef] [PubMed]

J. Dubard, J. Hameury, J.-R. Filtz, D. Soler, Ph. Voarino, and H. Piombini, Normal Reflectance Measurement Based on High Reflectivity Dielectric Mirrors Reference Standard (Newrad, 2008), pp. 13–15.

Le Borgne, X.

Lemarchand, F.

MacLeod, H. A.

H. A. MacLeod, Thin-Film Optical Filters, 2nd ed. (Hilger, 1986).
[CrossRef]

Marteau, D.

Ph. Voarino, H. Piombini, F. Sabary, D. Marteau, J. Dubard, J. Hameury, and J. R. Filtz, “High-accuracy measurements of the normal specular reflectance,” Appl. Opt. 47, C303–C309(2008).
[CrossRef] [PubMed]

F. Sabary, D. Marteau, P. Hamel, and H. Piombini, “High reflectivity protected silver coatings on stainless steel and aluminium substrates,” in Proceedings of the Society of Vacuum Coaters, 47th Annual Technical Conference (Society of Vacuum Coaters, 2004), pp. 358–361.

Montouillout, Y.

Ph. Belleville, Ph. Prené, C. Bonnin, and Y. Montouillout, “Use of sol-gel hybrids for laser optical thin films,” in Materials Research Society Symposium Proceeding, Vol. 726 (Materials Research Society, 2002), pp. 369–380.

Piombini, H.

H. Piombini, Ph. Voarino, and F. Lemarchand, “Is it possible to check micro-component coatings?” Appl. Opt. 50, C424–C432(2011).
[CrossRef] [PubMed]

H. Piombini and L. Caillon, “Reflectance measurement of spherical samples,” Opt. Rev. 16, 571–574 (2009).
[CrossRef]

Ph. Voarino, H. Piombini, F. Sabary, D. Marteau, J. Dubard, J. Hameury, and J. R. Filtz, “High-accuracy measurements of the normal specular reflectance,” Appl. Opt. 47, C303–C309(2008).
[CrossRef] [PubMed]

H. Piombini, D. Soler, and Ph. Voarino, “New device to measure the reflectivity on steeply curved surface,” Proc. SPIE 7018, 70181B (2008).
[CrossRef]

H. Piombini, S. Bruynooghe, and Ph. Voarino, “Spectral measurement in reflection on steeply aspheric surfaces,” Proc. SPIE 7102, 71021C (2008).
[CrossRef]

H. Piombini and Ph. Voarino, “Apparatus designed for very accurate measurement of the optical reflection,” Appl. Opt. 46, 8609–8618 (2007).
[CrossRef] [PubMed]

B. Bertussi, H. Piombini, D. Damiani, M. Pommiès, X. Le Borgne, and D. Plessis, “SOCRATE: an optical bench dedicated to the understanding and improvement of a laser conditioning process,” Appl. Opt. 45, 8506–8516(2006).
[CrossRef] [PubMed]

H. Piombini, “Procédé de mesure et procédé de visualisation d’une surface d’onde par spectrophotométrie,” French patent FR0950613 (30 January 2009).

J. Dubard, J. Hameury, J.-R. Filtz, D. Soler, Ph. Voarino, and H. Piombini, Normal Reflectance Measurement Based on High Reflectivity Dielectric Mirrors Reference Standard (Newrad, 2008), pp. 13–15.

H. Piombini and Ph. Voarino, “Dispositif et procédé de mesure de caractérisation par réflectométrie,” PCT WO2007/138032A1 (6 December 2007).

F. Sabary, D. Marteau, P. Hamel, and H. Piombini, “High reflectivity protected silver coatings on stainless steel and aluminium substrates,” in Proceedings of the Society of Vacuum Coaters, 47th Annual Technical Conference (Society of Vacuum Coaters, 2004), pp. 358–361.

Plessis, D.

Pommiès, M.

Prené, Ph.

Ph. Belleville, Ph. Prené, C. Bonnin, and Y. Montouillout, “Use of sol-gel hybrids for laser optical thin films,” in Materials Research Society Symposium Proceeding, Vol. 726 (Materials Research Society, 2002), pp. 369–380.

Priotton, J. J.

Ph. Belleville, C. Bonnin, and J. J. Priotton, “Room-temperature mirror preparation using sol-gel chemistry and laminar-flow coating technique,” J. Sol-Gel Sci. Technol. 19, 223–226 (2000).
[CrossRef]

Sabary, F.

Ph. Voarino, H. Piombini, F. Sabary, D. Marteau, J. Dubard, J. Hameury, and J. R. Filtz, “High-accuracy measurements of the normal specular reflectance,” Appl. Opt. 47, C303–C309(2008).
[CrossRef] [PubMed]

F. Sabary, D. Marteau, P. Hamel, and H. Piombini, “High reflectivity protected silver coatings on stainless steel and aluminium substrates,” in Proceedings of the Society of Vacuum Coaters, 47th Annual Technical Conference (Society of Vacuum Coaters, 2004), pp. 358–361.

Soler, D.

H. Piombini, D. Soler, and Ph. Voarino, “New device to measure the reflectivity on steeply curved surface,” Proc. SPIE 7018, 70181B (2008).
[CrossRef]

J. Dubard, J. Hameury, J.-R. Filtz, D. Soler, Ph. Voarino, and H. Piombini, Normal Reflectance Measurement Based on High Reflectivity Dielectric Mirrors Reference Standard (Newrad, 2008), pp. 13–15.

Voarino, Ph.

H. Piombini, Ph. Voarino, and F. Lemarchand, “Is it possible to check micro-component coatings?” Appl. Opt. 50, C424–C432(2011).
[CrossRef] [PubMed]

H. Piombini, S. Bruynooghe, and Ph. Voarino, “Spectral measurement in reflection on steeply aspheric surfaces,” Proc. SPIE 7102, 71021C (2008).
[CrossRef]

Ph. Voarino, H. Piombini, F. Sabary, D. Marteau, J. Dubard, J. Hameury, and J. R. Filtz, “High-accuracy measurements of the normal specular reflectance,” Appl. Opt. 47, C303–C309(2008).
[CrossRef] [PubMed]

H. Piombini, D. Soler, and Ph. Voarino, “New device to measure the reflectivity on steeply curved surface,” Proc. SPIE 7018, 70181B (2008).
[CrossRef]

H. Piombini and Ph. Voarino, “Apparatus designed for very accurate measurement of the optical reflection,” Appl. Opt. 46, 8609–8618 (2007).
[CrossRef] [PubMed]

J. Dubard, J. Hameury, J.-R. Filtz, D. Soler, Ph. Voarino, and H. Piombini, Normal Reflectance Measurement Based on High Reflectivity Dielectric Mirrors Reference Standard (Newrad, 2008), pp. 13–15.

H. Piombini and Ph. Voarino, “Dispositif et procédé de mesure de caractérisation par réflectométrie,” PCT WO2007/138032A1 (6 December 2007).

Acta Cybern. (1)

T. Csendes, “Nonlinear parameter estimation by global optimization—efficiency and reliability,” Acta Cybern. 8, 361–370 (1988).

Ann. Phys. (1)

F. Abeles, “Recherches sur la propagation des ondes électromagnétiques sinusoidales dans les milieux stratifiés,” Ann. Phys. 5, 596–706 (1950).

Appl. Opt. (4)

J. Sol-Gel Sci. Technol. (1)

Ph. Belleville, C. Bonnin, and J. J. Priotton, “Room-temperature mirror preparation using sol-gel chemistry and laminar-flow coating technique,” J. Sol-Gel Sci. Technol. 19, 223–226 (2000).
[CrossRef]

Opt. Rev. (1)

H. Piombini and L. Caillon, “Reflectance measurement of spherical samples,” Opt. Rev. 16, 571–574 (2009).
[CrossRef]

Proc. SPIE (2)

H. Piombini, D. Soler, and Ph. Voarino, “New device to measure the reflectivity on steeply curved surface,” Proc. SPIE 7018, 70181B (2008).
[CrossRef]

H. Piombini, S. Bruynooghe, and Ph. Voarino, “Spectral measurement in reflection on steeply aspheric surfaces,” Proc. SPIE 7102, 71021C (2008).
[CrossRef]

Other (6)

J. Dubard, J. Hameury, J.-R. Filtz, D. Soler, Ph. Voarino, and H. Piombini, Normal Reflectance Measurement Based on High Reflectivity Dielectric Mirrors Reference Standard (Newrad, 2008), pp. 13–15.

Ph. Belleville, Ph. Prené, C. Bonnin, and Y. Montouillout, “Use of sol-gel hybrids for laser optical thin films,” in Materials Research Society Symposium Proceeding, Vol. 726 (Materials Research Society, 2002), pp. 369–380.

F. Sabary, D. Marteau, P. Hamel, and H. Piombini, “High reflectivity protected silver coatings on stainless steel and aluminium substrates,” in Proceedings of the Society of Vacuum Coaters, 47th Annual Technical Conference (Society of Vacuum Coaters, 2004), pp. 358–361.

H. Piombini, “Procédé de mesure et procédé de visualisation d’une surface d’onde par spectrophotométrie,” French patent FR0950613 (30 January 2009).

H. A. MacLeod, Thin-Film Optical Filters, 2nd ed. (Hilger, 1986).
[CrossRef]

H. Piombini and Ph. Voarino, “Dispositif et procédé de mesure de caractérisation par réflectométrie,” PCT WO2007/138032A1 (6 December 2007).

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Figures (24)

Fig. 1
Fig. 1

Reflectance factor and phase versus σ / σ c for three mirrors centered at 900, 990, and 1000 nm, respectively.

Fig. 2
Fig. 2

Determination of the local center wave number σ c 990 and its shift Δ σ c from a measurement giving a level R σ c 990 at σ m and the theoretical spectral curve (green curve with circles, initially centered at σ c 1000 = 10 , 000 cm 1 ).

Fig. 3
Fig. 3

Determination of a wavenumber σ f permitting the phase shift computation Φ ( σ u ) at σ u from the theoretical spectral curve (green curve with circles) for a mirror initially centered at 10 , 000 cm 1 , having a heterogeneity that induces a shift at 11 , 111 cm 1 (blue solid curve).

Fig. 4
Fig. 4

Spectral reflectance for both mirror formulas.

Fig. 5
Fig. 5

Phase reflection at 1060 nm for both mirror formulas.

Fig. 6
Fig. 6

Reflectance factor at 946 nm versus λ c .

Fig. 7
Fig. 7

Phase at 633 nm versus λ c .

Fig. 8
Fig. 8

Phase at 1060 nm versus λ c .

Fig. 9
Fig. 9

Thickness variation map of a simulated mirror.

Fig. 10
Fig. 10

Reflectance mapping at 946 nm of a simulated mirror.

Fig. 11
Fig. 11

Phase mapping at 1060 nm of a simulated mirror given in mechanical thickness.

Fig. 12
Fig. 12

Phase mapping at 633 nm of a simulated mirror given in mechanical thickness.

Fig. 13
Fig. 13

Difference between a phase mapping at 1060 nm and 633 nm of a simulated mirror.

Fig. 14
Fig. 14

Measurement wavenumber shift extracted from reflectance mapping in Fig. 6 and spectral curve in Fig. 4.

Fig. 15
Fig. 15

λ c variation extracted from a measurement wavenumber shift map in Fig. 14 and Eq. (2).

Fig. 16
Fig. 16

Phase shift map extracted from a λ c mapping in Fig. 15, Eq. (3), and the spectral curve in Fig. 5 and expressed as mechanical thickness thanks to Eq. (4).

Fig. 17
Fig. 17

Difference between Figs. 16, 11.

Fig. 18
Fig. 18

Transmittance curves of solgel mirror on two different sites.

Fig. 19
Fig. 19

Experimental setup of the CEA device.

Fig. 20
Fig. 20

Three measurements of solgel mirror spectral reflectance over a range from 400 to 950 nm on the same site.

Fig. 21
Fig. 21

Reflectance mapping at 930 nm over an area of 80 mm × 30 mm .

Fig. 22
Fig. 22

Reflectance mapping at 920 nm over an area of 80 mm × 30 mm .

Fig. 23
Fig. 23

Reflectance mapping at 910 nm over an area of 80 mm × 30 mm .

Fig. 24
Fig. 24

Phase shift mapping at 1060 nm over an area of 80 mm × 30 mm .

Tables (2)

Tables Icon

Table 1 Quarter-Wave and Computed Formulas of S ( H L ) 11 H Mirror Centered at 1060 nm

Tables Icon

Table 2 Measurement Spectral Range Limits

Equations (7)

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R ( λ ) T ( λ ) Φ ( λ ) ,
δ i = λ i . Δ Φ i / 2 π .
W σ m / σ c 1000 2 + Δ σ m = W σ m / σ c 990 2 + Δ σ c i Δ σ m = Δ σ c i + W σ m / σ c 1000 2 ( W σ m / σ c 990 W σ m / σ c 1000 1 ) , Δ σ m = Δ σ c i + W σ m / σ c 1000 2 ( σ c 990 σ c 1000 1 ) Δ σ m = Δ σ c i ( 1 + W σ m / σ c 1000 2 σ c 1000 ) , Δ σ c i = Δ σ m 1 + W σ m / σ c i 2 . σ c i ,
Φ ( σ u σ C 900 ) = Φ ( σ u σ C 1000 × σ C 1000 σ C 900 ) = Φ ( σ C 1000 σ C 900 × σ u σ C 1000 ) = Φ ( σ f σ C 1000 ) σ f = σ C 1000 σ C 900 σ u = σ u σ C 1000 + Δ σ C i .
σ f = σ u 1 + Δ σ c i σ c i ,
Δ t = ( Φ Φ 0 ) * λ / 4 Π .
R ( λ ) = K ( λ ) V Measurement ( λ ) V Measurement background ( λ ) V Reference ( λ ) V Reference background ( λ ) ,

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