Abstract

A new type of two-stage reflectometer is proposed for the measurement of directional hemispherical reflectance. The proposed reflectometer consists of a primary collecting mirror coupled to a secondary mirror chosen to eliminate the Fresnel variation of the detector (or source) response. The secondary mirror shape needed is an inverted nonimaging compound parabolic concentrator (CPC). For direct mode operation, the detector is placed at the larger CPC aperture. Ray tracing of a CPC/ellipsoid reflectometer indicates that the throughput is high and isotropic. Design trade-offs and two-stage reflectometers employing a hemisphere and dual paraboloid primary are also discussed.

© 1987 Optical Society of America

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References

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  1. U. S. Touloukian et al., Eds., Thermophysical Properties of Matter, Vol. 9, Thermal Radiative properties: Coatings (IFI/Plenum, New York, 1972).
  2. W. W. Coblentz, “The Diffuse Reflecting Power of Various Substances,” Bull. Natl. Bur. Stand. 9, 283 (1913).
    [CrossRef]
  3. R. V. Dunkle, “Spectral Reflectance Measurements,” in Surface Effects on Spacecraft Materials, F. J. Clauss, Ed. (Wiley, New York, 1960), pp. 117–37.
  4. S. T. Dunn et al., “Ellipsoidal Mirror Reflectometer, J. Res. Natl. Bur. Stand. Sect. C 70, No. 2, 75 (1966).
  5. W. M. Brandenburg, “Focusing Properties of Hemispherical and Ellipsoidal Mirror Reflectometers,” J. Opt. Soc. Am. 54, 1235 (1964).
    [CrossRef]
  6. J. A. Jacquez et al., “An Integrating Sphere for Measuring Diffuse Reflectance in the Near Infrared,” J. Opt. Soc. Am. 45, 781 (1955).
    [CrossRef]
  7. S. T. Dunn, “Flux Averaging Device for the Infrared,” NBS-TN-279 (1965).
  8. K. A. Snail, L. M. Hanssen, “Integrating Sphere Designs with Isotropic Throughput,” to be submitted to Appl. Opt.
  9. W. W. Welford, R. Winston, The Optics of Nonimaging Concentrators: Light and Solar Energy (Academic, New York, 1978).
  10. K. A. Snail, “Multiple Reflection Effects in Hemi-Ellipsoid Reflectometers,” presented at the Optical Society of America Annual Meeting, Rochester, NY (1987).
  11. K. A. Snail, “New Optical Systems for the Measurement of Diffuse Reflectance,” Proc. Soc. Photo-Opt. Instrum. Eng. 643, 84 (1986).
  12. H. Hinterberger, R. Winston, “Efficient Light Coupler for Threshold Cerenkov Counters,” Rev. Sci. Instrum. 37, 1094 (1966).
    [CrossRef]
  13. R. Winston, “Light Collection Within the Framework of Geometrical Optics,” J. Opt. Soc. Am. 60, 245 (1970).
    [CrossRef]
  14. D. B. Leviton, J. W. Leitch, “Experimental and Raytrace Results for Throat-to-Throat Compound Parabolic Concentrators,” Appl. Opt. 25, 2821 (1986).
    [CrossRef] [PubMed]
  15. Rays undergoing multiple reflections on the sample and ellipsoid were not considered in this analysis. Future work will consider this effect (see Ref. 10).
  16. J. Baars, F. Sorger, “Reststrahlen Spectra of HgTe and CdxHg1−xTe,” Solid State Commun. 10, 875 (1972).
    [CrossRef]
  17. M. A. Ordal, R. J. Bell, R. W. Alexander, L. L. Long, M. R. Querry, “Optical Properties of Au, Ni, and Pb at Submillimeter Wavelengths,” Appl. Opt. 26, 744 (1987).
    [CrossRef] [PubMed]
  18. A. Rabl, “Optical and Thermal Properties of Compound Parabolic Concentrators,” Sol. Energy 18, 497 (1976).
    [CrossRef]
  19. D. G. Goebel, “Generalized Integrating Sphere Theory,” Appl. Opt. 6, 125 (1967).
    [CrossRef] [PubMed]
  20. M. G. Lang, K. D. Masterson, “Compound Ellipsoid Concentrator Baffled Integrating Sphere,” J. Opt. Soc. Am. 70, 1564 (1980).
  21. H. L. Tardy, “Flux Concentrators in Integrating Sphere Experiments: Potential for Increased Detector Signal,” Appl. Opt. 24, 3914 (1985).
    [CrossRef] [PubMed]
  22. K. A. Snail, K. F. Carr, “Optical Design of an Integrating Sphere—Fourier Transform Spectrophotometer (FTS) Emissometer,” Proc. Soc. Photo-Opt. Instrum. Eng. 643, 75 (May1986).

1987 (1)

1986 (3)

K. A. Snail, K. F. Carr, “Optical Design of an Integrating Sphere—Fourier Transform Spectrophotometer (FTS) Emissometer,” Proc. Soc. Photo-Opt. Instrum. Eng. 643, 75 (May1986).

K. A. Snail, “New Optical Systems for the Measurement of Diffuse Reflectance,” Proc. Soc. Photo-Opt. Instrum. Eng. 643, 84 (1986).

D. B. Leviton, J. W. Leitch, “Experimental and Raytrace Results for Throat-to-Throat Compound Parabolic Concentrators,” Appl. Opt. 25, 2821 (1986).
[CrossRef] [PubMed]

1985 (1)

1980 (1)

M. G. Lang, K. D. Masterson, “Compound Ellipsoid Concentrator Baffled Integrating Sphere,” J. Opt. Soc. Am. 70, 1564 (1980).

1976 (1)

A. Rabl, “Optical and Thermal Properties of Compound Parabolic Concentrators,” Sol. Energy 18, 497 (1976).
[CrossRef]

1972 (1)

J. Baars, F. Sorger, “Reststrahlen Spectra of HgTe and CdxHg1−xTe,” Solid State Commun. 10, 875 (1972).
[CrossRef]

1970 (1)

1967 (1)

1966 (2)

H. Hinterberger, R. Winston, “Efficient Light Coupler for Threshold Cerenkov Counters,” Rev. Sci. Instrum. 37, 1094 (1966).
[CrossRef]

S. T. Dunn et al., “Ellipsoidal Mirror Reflectometer, J. Res. Natl. Bur. Stand. Sect. C 70, No. 2, 75 (1966).

1965 (1)

S. T. Dunn, “Flux Averaging Device for the Infrared,” NBS-TN-279 (1965).

1964 (1)

1955 (1)

1913 (1)

W. W. Coblentz, “The Diffuse Reflecting Power of Various Substances,” Bull. Natl. Bur. Stand. 9, 283 (1913).
[CrossRef]

Alexander, R. W.

Baars, J.

J. Baars, F. Sorger, “Reststrahlen Spectra of HgTe and CdxHg1−xTe,” Solid State Commun. 10, 875 (1972).
[CrossRef]

Bell, R. J.

Brandenburg, W. M.

Carr, K. F.

K. A. Snail, K. F. Carr, “Optical Design of an Integrating Sphere—Fourier Transform Spectrophotometer (FTS) Emissometer,” Proc. Soc. Photo-Opt. Instrum. Eng. 643, 75 (May1986).

Coblentz, W. W.

W. W. Coblentz, “The Diffuse Reflecting Power of Various Substances,” Bull. Natl. Bur. Stand. 9, 283 (1913).
[CrossRef]

Dunkle, R. V.

R. V. Dunkle, “Spectral Reflectance Measurements,” in Surface Effects on Spacecraft Materials, F. J. Clauss, Ed. (Wiley, New York, 1960), pp. 117–37.

Dunn, S. T.

S. T. Dunn et al., “Ellipsoidal Mirror Reflectometer, J. Res. Natl. Bur. Stand. Sect. C 70, No. 2, 75 (1966).

S. T. Dunn, “Flux Averaging Device for the Infrared,” NBS-TN-279 (1965).

Goebel, D. G.

Hanssen, L. M.

K. A. Snail, L. M. Hanssen, “Integrating Sphere Designs with Isotropic Throughput,” to be submitted to Appl. Opt.

Hinterberger, H.

H. Hinterberger, R. Winston, “Efficient Light Coupler for Threshold Cerenkov Counters,” Rev. Sci. Instrum. 37, 1094 (1966).
[CrossRef]

Jacquez, J. A.

Lang, M. G.

M. G. Lang, K. D. Masterson, “Compound Ellipsoid Concentrator Baffled Integrating Sphere,” J. Opt. Soc. Am. 70, 1564 (1980).

Leitch, J. W.

Leviton, D. B.

Long, L. L.

Masterson, K. D.

M. G. Lang, K. D. Masterson, “Compound Ellipsoid Concentrator Baffled Integrating Sphere,” J. Opt. Soc. Am. 70, 1564 (1980).

Ordal, M. A.

Querry, M. R.

Rabl, A.

A. Rabl, “Optical and Thermal Properties of Compound Parabolic Concentrators,” Sol. Energy 18, 497 (1976).
[CrossRef]

Snail, K. A.

K. A. Snail, K. F. Carr, “Optical Design of an Integrating Sphere—Fourier Transform Spectrophotometer (FTS) Emissometer,” Proc. Soc. Photo-Opt. Instrum. Eng. 643, 75 (May1986).

K. A. Snail, “New Optical Systems for the Measurement of Diffuse Reflectance,” Proc. Soc. Photo-Opt. Instrum. Eng. 643, 84 (1986).

K. A. Snail, “Multiple Reflection Effects in Hemi-Ellipsoid Reflectometers,” presented at the Optical Society of America Annual Meeting, Rochester, NY (1987).

K. A. Snail, L. M. Hanssen, “Integrating Sphere Designs with Isotropic Throughput,” to be submitted to Appl. Opt.

Sorger, F.

J. Baars, F. Sorger, “Reststrahlen Spectra of HgTe and CdxHg1−xTe,” Solid State Commun. 10, 875 (1972).
[CrossRef]

Tardy, H. L.

Welford, W. W.

W. W. Welford, R. Winston, The Optics of Nonimaging Concentrators: Light and Solar Energy (Academic, New York, 1978).

Winston, R.

R. Winston, “Light Collection Within the Framework of Geometrical Optics,” J. Opt. Soc. Am. 60, 245 (1970).
[CrossRef]

H. Hinterberger, R. Winston, “Efficient Light Coupler for Threshold Cerenkov Counters,” Rev. Sci. Instrum. 37, 1094 (1966).
[CrossRef]

W. W. Welford, R. Winston, The Optics of Nonimaging Concentrators: Light and Solar Energy (Academic, New York, 1978).

Appl. Opt. (4)

Bull. Natl. Bur. Stand. (1)

W. W. Coblentz, “The Diffuse Reflecting Power of Various Substances,” Bull. Natl. Bur. Stand. 9, 283 (1913).
[CrossRef]

J. Opt. Soc. Am. (4)

J. Res. Natl. Bur. Stand. Sect. C (1)

S. T. Dunn et al., “Ellipsoidal Mirror Reflectometer, J. Res. Natl. Bur. Stand. Sect. C 70, No. 2, 75 (1966).

NBS-TN-279 (1)

S. T. Dunn, “Flux Averaging Device for the Infrared,” NBS-TN-279 (1965).

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

K. A. Snail, “New Optical Systems for the Measurement of Diffuse Reflectance,” Proc. Soc. Photo-Opt. Instrum. Eng. 643, 84 (1986).

K. A. Snail, K. F. Carr, “Optical Design of an Integrating Sphere—Fourier Transform Spectrophotometer (FTS) Emissometer,” Proc. Soc. Photo-Opt. Instrum. Eng. 643, 75 (May1986).

Rev. Sci. Instrum. (1)

H. Hinterberger, R. Winston, “Efficient Light Coupler for Threshold Cerenkov Counters,” Rev. Sci. Instrum. 37, 1094 (1966).
[CrossRef]

Sol. Energy (1)

A. Rabl, “Optical and Thermal Properties of Compound Parabolic Concentrators,” Sol. Energy 18, 497 (1976).
[CrossRef]

Solid State Commun. (1)

J. Baars, F. Sorger, “Reststrahlen Spectra of HgTe and CdxHg1−xTe,” Solid State Commun. 10, 875 (1972).
[CrossRef]

Other (6)

Rays undergoing multiple reflections on the sample and ellipsoid were not considered in this analysis. Future work will consider this effect (see Ref. 10).

K. A. Snail, L. M. Hanssen, “Integrating Sphere Designs with Isotropic Throughput,” to be submitted to Appl. Opt.

W. W. Welford, R. Winston, The Optics of Nonimaging Concentrators: Light and Solar Energy (Academic, New York, 1978).

K. A. Snail, “Multiple Reflection Effects in Hemi-Ellipsoid Reflectometers,” presented at the Optical Society of America Annual Meeting, Rochester, NY (1987).

U. S. Touloukian et al., Eds., Thermophysical Properties of Matter, Vol. 9, Thermal Radiative properties: Coatings (IFI/Plenum, New York, 1972).

R. V. Dunkle, “Spectral Reflectance Measurements,” in Surface Effects on Spacecraft Materials, F. J. Clauss, Ed. (Wiley, New York, 1960), pp. 117–37.

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Figures (10)

Fig. 1
Fig. 1

Origin of detector overfilling in ellipsoidal mirror reflectometers. Rays striking the ellipse in the same quadrant as the sample are magnified whereas those striking the detector quadrant are concentrated.

Fig. 2
Fig. 2

Ellipse variables for longitudinal magnification calculation.

Fig. 3
Fig. 3

Ray trace results on ellipsoid magnification for a circular parallel source (D0/a = 0.1) at five angles (−89, −44.5, 0, 44.5, 89°) as measured in the x-z plane. For (b) the source beam is inclined at an angle of 80° to the x-z plane. Note the dramatic decrease in magnification as the eccentricity decreases from 0.312 to 0.100.

Fig. 4
Fig. 4

Ray trace results for incidence angles of (a) 20, (b) 40, (c) 60, and (d) 80° in meridional plane of CPC. Notice the limited range (≤30°) of incidence angles on the detector surface for 80° incidence on the CPC.

Fig. 5
Fig. 5

CPC/ellipsoid reflectometer concept. The beam is directed to sample with mirrors M1 and M2; CPC eliminates the Fresnel response of the detector. Ellipsoid eccentricity is chosen so as to underfill CPC. For absolute measurement, remove sample and rotate mirror M1 by 90°. The second mirror M2 is repositioned below the ellipsoid as shown.

Fig. 6
Fig. 6

CPC Lambertian radiation source. The acceptance angle of CPC is chosen so as to minimize the emissivity variation of the high-temperature surface. Water cooling of CPC may be required.

Fig. 7
Fig. 7

Ray trace results for ellipsoid reflectometer throughput vs angle of reflected radiation, as measured in three planes which contain the x axis and make angles of 2, 30, and 90° with respect to the x-y plane. Note the poor performance at large angles.

Fig. 8
Fig. 8

Throughput of CPC/ellipsoid reflectometer vs angle in the same three planes as Fig. 7. The increase in throughput at small angles in the 90° plane is caused by rays which undergo zero reflections in passing through the CPC.

Fig. 9
Fig. 9

Average number of reflections 〈n〉 for CPC/ellipsoid reflectometer (CPC half-angle θ = 30°) vs reflected angle, as measured in the same three planes of Fig. 7. Note the dip in the 90° plane caused by rays traversing the CPC without reflections and the increase at large angles in all planes caused by skew rays.

Fig. 10
Fig. 10

Paraboloid/CPC reflectometer concept. The CPC and sample are placed at foci of matched paraboloids. The movable mirror M1 permits sample illumination at various angles. Absolute measurements can be made by removing the sample and tilting M1 so that the beam passes through the focus of the upper paraboloid.

Equations (6)

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D 0 cos θ / d = D I cos θ / ( 2 a d ) ,
M L = [ 2 ( a / d ) 1 ] 2 .
M L = | 1 + x 1 x | 2 | 1 + 1 | 2 ,
C = A 1 / A 2 1 / sin 2 θ c ,
τ = ρ e ρ n ,
τ sph = F i ρ w / [ 1 ( 1 F j ) ρ w ] ,

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