Abstract

A method for fabricating an achromatic, athermalized quarter-wave retarder is presented that involves monitoring retardance during polishing. A design specified by thicknesses alone is unlikely to meet specification due to uncertainties in birefringence. This method facilitates successful fabrication to a retardance specification despite these uncertainties. A retarder made from sapphire, MgF2, and quartz was designed, fabricated, and its performance validated for the 0.470 to 0.865μm wavelength region. Its specifications are as follows: at wavebands centered at 0.470, 0.660, and 0.865μm, the band-averaged retardance should be 90°±10° for all fields and retardance should change less than 0.1° for a 1° change in temperature. Retarder fabrication accommodated birefringence and thickness uncertainties via the following steps. The first plate was polished to a target thickness. The retardance spectrum of the first plate was then measured and used to determine a retardance target for the second plate. The retardance spectrum of the combined first and second plates was then used to specify a retardance target for the third plate. The retardance spectrum of the three plates in combination was then used to determine when the final thickness of the third plate was reached.

© 2011 Optical Society of America

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References

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  1. D. Diner, R. Chipman, N. Beaudry, B. Cairns, L. D. Foo, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
    [CrossRef]
  2. D. J. Diner, A. Davis, B. Hancock, G. Gutt, R. A. Chipman, and B. Cairns, “Dual-photoelastic-modulator-based polarimetric imaging concept for aerosol remote sensing,” Appl. Opt. 46, 8428–8445 (2007).
    [CrossRef] [PubMed]
  3. D. J. Diner, A. Davis, B. Hancock, S. Geier, B. Rheingans, V. Jovanovic, M. Bull, D. M. Rider, R. A. Chipman, A. Mahler, and S. C. McClain, “First results from a dual photoelastic-modulator-based polarimetric camera,” Appl. Opt. 49, 2929–2946 (2010).
    [CrossRef] [PubMed]
  4. A. Mahler and R. Chipman, “Tolerancing and alignment of a three-mirror off-axis telesope,” Proc. SPIE 6676, 66760I(2007).
    [CrossRef]
  5. A. Mahler, P. K. Smith, and R. A. Chipman, “Low polarization optical system design,” Proc. SPIE 6682, 66820V (2007).
    [CrossRef]
  6. A. Mahler, N. A. Raouf, P. K. Smith, S. C. McClain, and R. A. Chipman, “Minimizing instrumental polarization in the Multiangle SpectroPolarimetric Imager (MSPI) using diattenuation balancing between the three mirror coatings,” Proc. SPIE 7013, 701355 (2008).
    [CrossRef]
  7. A. Mahler, D. J. Diner, and R. A. Chipman are preparing a manuscript to be called “Analysis of static and time-varying polarization errors in the Multiangle SpectroPolarimetric Imager.”
  8. D. Clark, “Achromatic halfwave plates and linear polarization rotators,” J. Mod. Opt. 14, 343–350 (1967).
    [CrossRef]
  9. J. M. Beckers, “Achromatic linear retarders,” Appl. Opt. 10, 973–975 (1971).
    [CrossRef] [PubMed]
  10. P. Hariharan, “Broad-band apochromatic retarder: choice of materials,” Opt. Laser Technol. 34, 509–511 (2002).
    [CrossRef]
  11. S. Pancharatnam, “Achromatic combinations of birefringent plates,” Proc. Indian Acad. Sci. A , 41, 130–136 (1955).
  12. K. Serkowsky, “Retarders,” Proc. Indian Acad. Sci. A 41, 137–144 (1955).
  13. R. W. Goodrich, “High efficiency ‘superachromatic’ polarimetry optics for use in optical astronomical spectrographs,” Publ. Astron. Soc. Pac. 103, 1314–1322, (1991).
    [CrossRef]
  14. P. Hariharan and P. Ciddor, “Broad-band superachromatic retarders and circular polarizers for the UV, visible and near infrared,” J. Mod. Opt. 15, 2315–2322 (2004).
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    [CrossRef] [PubMed]
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    [CrossRef]
  17. G. Ghosh, Handbook of Thermo-Optic Coefficients of Optical Materials with Applications (Academic, 1998).
  18. E. Palik, Handbook of Optical Constants of Solids (Academic, 1991).
  19. CVI Melles Griot, “Dispersion equations,” http://www.cvimellesgriot.com/products/Documents/Catalog/Dispersion_Equations.pdf.
  20. T. Baur, Meadowlark Optics, Inc., 5964 Iris Parkway, Frederick, Colo. 80530 (personal communication, 2008).
  21. R. Kapler, Meller Optics, Inc., 120 Corliss Street, Providence, R.I. 02904 (personal communication 2008).
  22. V. Vats, Karl Lambrecht Corporation, 4204 N. Lincoln Ave., Chicago, Ill. 60618 (personal communication 2008)
  23. P. Hariharan, “Achromatic and apochromatic halfwave and quarterwave retarders,” Opt. Eng. 35, 3335–3337(1996).
    [CrossRef]

2010 (1)

2008 (4)

A. Mahler, N. A. Raouf, P. K. Smith, S. C. McClain, and R. A. Chipman, “Minimizing instrumental polarization in the Multiangle SpectroPolarimetric Imager (MSPI) using diattenuation balancing between the three mirror coatings,” Proc. SPIE 7013, 701355 (2008).
[CrossRef]

T. Baur, Meadowlark Optics, Inc., 5964 Iris Parkway, Frederick, Colo. 80530 (personal communication, 2008).

R. Kapler, Meller Optics, Inc., 120 Corliss Street, Providence, R.I. 02904 (personal communication 2008).

V. Vats, Karl Lambrecht Corporation, 4204 N. Lincoln Ave., Chicago, Ill. 60618 (personal communication 2008)

2007 (4)

2005 (1)

D. Diner, R. Chipman, N. Beaudry, B. Cairns, L. D. Foo, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

2004 (1)

P. Hariharan and P. Ciddor, “Broad-band superachromatic retarders and circular polarizers for the UV, visible and near infrared,” J. Mod. Opt. 15, 2315–2322 (2004).

2002 (1)

P. Hariharan, “Broad-band apochromatic retarder: choice of materials,” Opt. Laser Technol. 34, 509–511 (2002).
[CrossRef]

1998 (1)

G. Ghosh, Handbook of Thermo-Optic Coefficients of Optical Materials with Applications (Academic, 1998).

1996 (1)

P. Hariharan, “Achromatic and apochromatic halfwave and quarterwave retarders,” Opt. Eng. 35, 3335–3337(1996).
[CrossRef]

1991 (2)

E. Palik, Handbook of Optical Constants of Solids (Academic, 1991).

R. W. Goodrich, “High efficiency ‘superachromatic’ polarimetry optics for use in optical astronomical spectrographs,” Publ. Astron. Soc. Pac. 103, 1314–1322, (1991).
[CrossRef]

1988 (1)

1971 (1)

1967 (1)

D. Clark, “Achromatic halfwave plates and linear polarization rotators,” J. Mod. Opt. 14, 343–350 (1967).
[CrossRef]

1955 (2)

S. Pancharatnam, “Achromatic combinations of birefringent plates,” Proc. Indian Acad. Sci. A , 41, 130–136 (1955).

K. Serkowsky, “Retarders,” Proc. Indian Acad. Sci. A 41, 137–144 (1955).

Baur, T.

T. Baur, Meadowlark Optics, Inc., 5964 Iris Parkway, Frederick, Colo. 80530 (personal communication, 2008).

Beaudry, N.

D. Diner, R. Chipman, N. Beaudry, B. Cairns, L. D. Foo, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

Beckers, J. M.

Bull, M.

Cairns, B.

D. J. Diner, A. Davis, B. Hancock, G. Gutt, R. A. Chipman, and B. Cairns, “Dual-photoelastic-modulator-based polarimetric imaging concept for aerosol remote sensing,” Appl. Opt. 46, 8428–8445 (2007).
[CrossRef] [PubMed]

D. Diner, R. Chipman, N. Beaudry, B. Cairns, L. D. Foo, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

Chipman, R.

A. Mahler and R. Chipman, “Tolerancing and alignment of a three-mirror off-axis telesope,” Proc. SPIE 6676, 66760I(2007).
[CrossRef]

D. Diner, R. Chipman, N. Beaudry, B. Cairns, L. D. Foo, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

Chipman, R. A.

D. J. Diner, A. Davis, B. Hancock, S. Geier, B. Rheingans, V. Jovanovic, M. Bull, D. M. Rider, R. A. Chipman, A. Mahler, and S. C. McClain, “First results from a dual photoelastic-modulator-based polarimetric camera,” Appl. Opt. 49, 2929–2946 (2010).
[CrossRef] [PubMed]

A. Mahler, N. A. Raouf, P. K. Smith, S. C. McClain, and R. A. Chipman, “Minimizing instrumental polarization in the Multiangle SpectroPolarimetric Imager (MSPI) using diattenuation balancing between the three mirror coatings,” Proc. SPIE 7013, 701355 (2008).
[CrossRef]

D. J. Diner, A. Davis, B. Hancock, G. Gutt, R. A. Chipman, and B. Cairns, “Dual-photoelastic-modulator-based polarimetric imaging concept for aerosol remote sensing,” Appl. Opt. 46, 8428–8445 (2007).
[CrossRef] [PubMed]

A. Mahler, P. K. Smith, and R. A. Chipman, “Low polarization optical system design,” Proc. SPIE 6682, 66820V (2007).
[CrossRef]

A. Mahler, D. J. Diner, and R. A. Chipman are preparing a manuscript to be called “Analysis of static and time-varying polarization errors in the Multiangle SpectroPolarimetric Imager.”

Ciddor, P.

P. Hariharan and P. Ciddor, “Broad-band superachromatic retarders and circular polarizers for the UV, visible and near infrared,” J. Mod. Opt. 15, 2315–2322 (2004).

Clark, D.

D. Clark, “Achromatic halfwave plates and linear polarization rotators,” J. Mod. Opt. 14, 343–350 (1967).
[CrossRef]

Cunningham, T. J.

D. Diner, R. Chipman, N. Beaudry, B. Cairns, L. D. Foo, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

Davis, A.

Day, G. W.

Diner, D.

D. Diner, R. Chipman, N. Beaudry, B. Cairns, L. D. Foo, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

Diner, D. J.

Foo, L. D.

D. Diner, R. Chipman, N. Beaudry, B. Cairns, L. D. Foo, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

Geier, S.

Ghosh, G.

G. Ghosh, Handbook of Thermo-Optic Coefficients of Optical Materials with Applications (Academic, 1998).

Goodrich, R. W.

R. W. Goodrich, “High efficiency ‘superachromatic’ polarimetry optics for use in optical astronomical spectrographs,” Publ. Astron. Soc. Pac. 103, 1314–1322, (1991).
[CrossRef]

Gutt, G.

Hale, P. D.

Hancock, B.

Hariharan, P.

P. Hariharan and P. Ciddor, “Broad-band superachromatic retarders and circular polarizers for the UV, visible and near infrared,” J. Mod. Opt. 15, 2315–2322 (2004).

P. Hariharan, “Broad-band apochromatic retarder: choice of materials,” Opt. Laser Technol. 34, 509–511 (2002).
[CrossRef]

P. Hariharan, “Achromatic and apochromatic halfwave and quarterwave retarders,” Opt. Eng. 35, 3335–3337(1996).
[CrossRef]

Jovanovic, V.

Kapler, R.

R. Kapler, Meller Optics, Inc., 120 Corliss Street, Providence, R.I. 02904 (personal communication 2008).

Keller, C.

D. Diner, R. Chipman, N. Beaudry, B. Cairns, L. D. Foo, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

Macenka, S. A.

D. Diner, R. Chipman, N. Beaudry, B. Cairns, L. D. Foo, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

Mahler, A.

D. J. Diner, A. Davis, B. Hancock, S. Geier, B. Rheingans, V. Jovanovic, M. Bull, D. M. Rider, R. A. Chipman, A. Mahler, and S. C. McClain, “First results from a dual photoelastic-modulator-based polarimetric camera,” Appl. Opt. 49, 2929–2946 (2010).
[CrossRef] [PubMed]

A. Mahler, N. A. Raouf, P. K. Smith, S. C. McClain, and R. A. Chipman, “Minimizing instrumental polarization in the Multiangle SpectroPolarimetric Imager (MSPI) using diattenuation balancing between the three mirror coatings,” Proc. SPIE 7013, 701355 (2008).
[CrossRef]

A. Mahler and R. Chipman, “Tolerancing and alignment of a three-mirror off-axis telesope,” Proc. SPIE 6676, 66760I(2007).
[CrossRef]

A. Mahler, P. K. Smith, and R. A. Chipman, “Low polarization optical system design,” Proc. SPIE 6682, 66820V (2007).
[CrossRef]

A. Mahler, D. J. Diner, and R. A. Chipman are preparing a manuscript to be called “Analysis of static and time-varying polarization errors in the Multiangle SpectroPolarimetric Imager.”

McClain, S. C.

D. J. Diner, A. Davis, B. Hancock, S. Geier, B. Rheingans, V. Jovanovic, M. Bull, D. M. Rider, R. A. Chipman, A. Mahler, and S. C. McClain, “First results from a dual photoelastic-modulator-based polarimetric camera,” Appl. Opt. 49, 2929–2946 (2010).
[CrossRef] [PubMed]

A. Mahler, N. A. Raouf, P. K. Smith, S. C. McClain, and R. A. Chipman, “Minimizing instrumental polarization in the Multiangle SpectroPolarimetric Imager (MSPI) using diattenuation balancing between the three mirror coatings,” Proc. SPIE 7013, 701355 (2008).
[CrossRef]

Palik, E.

E. Palik, Handbook of Optical Constants of Solids (Academic, 1991).

Pancharatnam, S.

S. Pancharatnam, “Achromatic combinations of birefringent plates,” Proc. Indian Acad. Sci. A , 41, 130–136 (1955).

Raouf, N. A.

A. Mahler, N. A. Raouf, P. K. Smith, S. C. McClain, and R. A. Chipman, “Minimizing instrumental polarization in the Multiangle SpectroPolarimetric Imager (MSPI) using diattenuation balancing between the three mirror coatings,” Proc. SPIE 7013, 701355 (2008).
[CrossRef]

Rheingans, B.

Rider, D. M.

Serkowsky, K.

K. Serkowsky, “Retarders,” Proc. Indian Acad. Sci. A 41, 137–144 (1955).

Seshadri, S.

D. Diner, R. Chipman, N. Beaudry, B. Cairns, L. D. Foo, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

Smith, P. K.

A. Mahler, N. A. Raouf, P. K. Smith, S. C. McClain, and R. A. Chipman, “Minimizing instrumental polarization in the Multiangle SpectroPolarimetric Imager (MSPI) using diattenuation balancing between the three mirror coatings,” Proc. SPIE 7013, 701355 (2008).
[CrossRef]

A. Mahler, P. K. Smith, and R. A. Chipman, “Low polarization optical system design,” Proc. SPIE 6682, 66820V (2007).
[CrossRef]

Vaccaro, P.

Vats, V.

Wilson, S. M.

Appl. Opt. (4)

J. Mod. Opt. (2)

P. Hariharan and P. Ciddor, “Broad-band superachromatic retarders and circular polarizers for the UV, visible and near infrared,” J. Mod. Opt. 15, 2315–2322 (2004).

D. Clark, “Achromatic halfwave plates and linear polarization rotators,” J. Mod. Opt. 14, 343–350 (1967).
[CrossRef]

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

Opt. Eng. (1)

P. Hariharan, “Achromatic and apochromatic halfwave and quarterwave retarders,” Opt. Eng. 35, 3335–3337(1996).
[CrossRef]

Opt. Laser Technol. (1)

P. Hariharan, “Broad-band apochromatic retarder: choice of materials,” Opt. Laser Technol. 34, 509–511 (2002).
[CrossRef]

Proc. Indian Acad. Sci. A (2)

S. Pancharatnam, “Achromatic combinations of birefringent plates,” Proc. Indian Acad. Sci. A , 41, 130–136 (1955).

K. Serkowsky, “Retarders,” Proc. Indian Acad. Sci. A 41, 137–144 (1955).

Proc. SPIE (4)

A. Mahler and R. Chipman, “Tolerancing and alignment of a three-mirror off-axis telesope,” Proc. SPIE 6676, 66760I(2007).
[CrossRef]

A. Mahler, P. K. Smith, and R. A. Chipman, “Low polarization optical system design,” Proc. SPIE 6682, 66820V (2007).
[CrossRef]

A. Mahler, N. A. Raouf, P. K. Smith, S. C. McClain, and R. A. Chipman, “Minimizing instrumental polarization in the Multiangle SpectroPolarimetric Imager (MSPI) using diattenuation balancing between the three mirror coatings,” Proc. SPIE 7013, 701355 (2008).
[CrossRef]

D. Diner, R. Chipman, N. Beaudry, B. Cairns, L. D. Foo, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

Publ. Astron. Soc. Pac. (1)

R. W. Goodrich, “High efficiency ‘superachromatic’ polarimetry optics for use in optical astronomical spectrographs,” Publ. Astron. Soc. Pac. 103, 1314–1322, (1991).
[CrossRef]

Other (7)

A. Mahler, D. J. Diner, and R. A. Chipman are preparing a manuscript to be called “Analysis of static and time-varying polarization errors in the Multiangle SpectroPolarimetric Imager.”

G. Ghosh, Handbook of Thermo-Optic Coefficients of Optical Materials with Applications (Academic, 1998).

E. Palik, Handbook of Optical Constants of Solids (Academic, 1991).

CVI Melles Griot, “Dispersion equations,” http://www.cvimellesgriot.com/products/Documents/Catalog/Dispersion_Equations.pdf.

T. Baur, Meadowlark Optics, Inc., 5964 Iris Parkway, Frederick, Colo. 80530 (personal communication, 2008).

R. Kapler, Meller Optics, Inc., 120 Corliss Street, Providence, R.I. 02904 (personal communication 2008).

V. Vats, Karl Lambrecht Corporation, 4204 N. Lincoln Ave., Chicago, Ill. 60618 (personal communication 2008)

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Figures (15)

Fig. 1
Fig. 1

Compilation of sapphire, MgF 2 , and quartz birefringence models from published sources [17, 18, 19] and vendors [20, 21, 22] (left) and their differences from one of the birefringence spectra (right).

Fig. 2
Fig. 2

Retardance of Design B, a three-material compound retarder made of sapphire, MgF 2 , and quartz is shown. Exactly 90 ° of retardance is achieved at the three center wavelengths, and band-averaged retardance meets the 90 ° ± 5 ° requirement, shown by the dotted lines.

Fig. 3
Fig. 3

Retardance of Design C meets the specifications for band-averaged retardance and athermalization. The solid, dashed, and dotted–dashed curves indicate the nominal temperature, the nominal + 50 ° C , and the nominal 50 ° C performance, respectively. Design C is an athermalized sapphire, MgF 2 , and quartz design with thicknesses 406.9, 204.6, and 610.7 μm , respectively, and was chosen as the baseline design for fabrication.

Fig. 4
Fig. 4

Modeled AirMSPI compound retarder retardance is shown for 0.660 μm as a function of incident x and y angles in air for both the first (left) and second (right) retarders. Points show the range of angles of incidence for AirMSPI fields. Arrow indicates fast axis orientation.

Fig. 5
Fig. 5

Monte Carlo fabrication simulation results of retardance difference ( ° ) from 90 ° are shown for 1000 trials. Variables took random values governed by their tolerances. The vertical dotted line indicates the 90 ° ± 10 ° retardance specification, which has a probability of success of nearly 1 for the on-axis field.

Fig. 6
Fig. 6

Monte Carlo fabrication simulation results of change in retardance ( ° ) per 1 ° C are shown for 1000 trials. Variables took random values governed by their tolerances. The vertical dotted line indicates the 0.1 ° retardance change for 1 ° C specification, which has a probability of success of 0.6.

Fig. 7
Fig. 7

(a) Retardance error due to a birefringence offset of 2.9 × 10 5 (dashed curve), and following a 1.9 μm thickness compensation (solid curve). (b) Retardance error due to birefringence slope and offset error (dashed curve), and following a 1.9 μm thickness compensation (solid curve).

Fig. 8
Fig. 8

Simulated transmission of a 407 μm thick sapphire plate at 45 ° between crossed polarizers. Half- and full-wave wavelengths occur at transmission minima and maxima, respectively.

Fig. 9
Fig. 9

Sapphire thickness estimates based on the half-wave measurements of sapphire. Black points were calculated using the less-precise spectrometer measurements, the gray point was calculated from the more-precise spectrometer, and the dotted line indicates the target sapphire thickness.

Fig. 10
Fig. 10

Simulated transmission curves between parallel linear polarizers are shown for sapphire and MgF 2 in combination using Design C thicknesses. Half-wave wavelengths occur at transmission minima.

Fig. 11
Fig. 11

MgF 2 thickness estimates based on the half-wave measurements of sapphire and MgF 2 . Black points were calculated from measurements when the two retarder fast axes were aligned, gray points from when the two retarder fast axes were crossed, and the dotted line indicates the target MgF 2 thickness. Thickness estimates calculated from crossed and aligned fast axis measurements agree.

Fig. 12
Fig. 12

Two estimates of compound retardance are shown based on different methods of determining the new quartz thickness target. The smooth curve was calculated using birefringence models, estimates of MgF 2 , and sapphire thicknesses from the half-wave point measurements, and the quartz thickness that resulted in the best retardance spectrum ( 610.7 μm ). The jagged curve was calculated using MgF 2 and sapphire combined retardance measurements, and the quartz birefringence model and thickness that resulted in the best retardance spectrum ( 611.0 μm ).

Fig. 13
Fig. 13

Transmission measurement of the compound retarder between parallel polarizers shows transmission close to 0.5 across the wavelength region, which is what is expected of a quarter-wave retarder in this test. These calibrated transmission measurements were then used to calculate retardance.

Fig. 14
Fig. 14

The thin curve shows retardance of the compound retarder design. The thick curve shows a calculation of actual retardance based on the irradiance measurements from the half-wave wavelength test before cementing. The points show UofA MMIP retardance measurements following cementing.

Fig. 15
Fig. 15

Compound retarder retardance ( ° ) measurements are shown as a function of temperature ( ° C ) at three wavelengths. Slopes for the 0.470, 0.660, and 0.865 μm wavelength data are 0.03 ° , 0.04 ° , and 0.05 ° retardance per ° C . The compound retarder meets the thermal specification at all three wavelengths.

Tables (3)

Tables Icon

Table 1 Design A Element Thickness, Retardance, Birefringence, and Birefringence Tolerance at 0.470 μm

Tables Icon

Table 2 Thickness and Retardance of Each Individual Retarder and of the Combination is Shown for Design B at the Three Design Wavelengths

Tables Icon

Table 3 Thickness and Retardance of Each Individual Retarder and of the Combination is Shown for Design C at the Three Design Wavelengths

Equations (11)

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

δ e ( λ ) = 2 π λ t b ( λ ) ,
δ ( λ ) = π 2 = 2 π λ ( Δ n 1 ( λ ) t 1 + Δ n 2 ( λ ) t 2 + Δ n 3 ( λ ) t 3 ) , δ ( λ ) = π 2 = 2 π λ ( Δ n 1 ( λ ) t 1 + Δ n 2 ( λ ) t 2 + Δ n 3 ( λ ) t 3 ) , δ ( λ ) = π 2 = 2 π λ ( Δ n 1 ( λ ) t 1 + Δ n 2 ( λ ) t 2 + Δ n 3 ( λ ) t 3 ) .
γ = 1 δ δ T = 1 t t T + 1 Δ n Δ n T ,
0 = δ 1 ( λ a ) γ 1 ( λ a ) + δ 2 ( λ a ) γ 2 ( λ a ) + δ 3 ( λ a ) γ 3 ( λ a ) .
δ ( λ ) = π 2 = 2 π λ ( Δ n 1 ( λ ) t 1 + Δ n 2 ( λ ) t 2 + Δ n 3 ( λ ) t 3 ) , δ ( λ ) = π 2 = 2 π λ ( Δ n 1 ( λ ) t 1 + Δ n 2 ( λ ) t 2 + Δ n 3 ( λ ) t 3 ) , 0 = δ 1 ( λ a ) γ 1 ( λ a ) + δ 2 ( λ a ) γ 2 ( λ a ) + δ 3 ( λ a ) γ 3 ( λ a ) .
δ nominal ( λ ) = 2 π λ Δ n ( λ ) t ,
Δ δ ϵ t ( λ ) = δ nominal ( λ ) 2 π λ Δ n ( λ ) ( t + ϵ t ) = 2 π λ Δ n ( λ ) ϵ t ,
Δ δ b o ( λ ) = δ nominal ( λ ) 2 π λ ( Δ n ( λ ) + b o ) t = 2 π λ t b o ,
Δ δ b s ( λ ) ( λ ) = δ nominal ( λ ) 2 π λ ( Δ n ( λ ) + b s ( λ ) ) t = 2 π λ t b s ( λ ) .
Δ δ e 1 ( λ ) = Δ δ ϵ t ( λ ) + Δ δ b o ( λ ) = 2 π λ ( Δ n ( λ ) ϵ t + t b o ) ,
Δ δ e 2 ( λ ) = Δ δ ϵ t ( λ ) + Δ δ b s ( λ ) ( λ ) = 2 π λ ( Δ n ( λ ) ϵ t + t b s ( λ ) ) .

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