Abstract

In previous research [C. C. Asmail et al.Appl. Opt. 33, 6084–6091 (1994)] an estimate was given of the low-level bidirectional reflectance distribution function (BRDF) limit due to Rayleigh scattering from the air molecules within the detector field of view. Although the underlying model was correct, a fault in the derivation led to a conclusion that contains an erroneous angular factor. A cosine factor in the equivalent BRDF derived by Asmail et al. [Appl. Opt. 33, 6084–6091 (1994)], which was considered unphysical in that treatment, is incorrect and can obscure the correction in certain circumstances. The treatment below calculates the scattered flux from the gas molecules in the field of view and compares it with the flux scattered from a sample in the same incident beam.

© 1999 Optical Society of America

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References

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  1. C. C. Asmail, J. J. Hsia, A. C. Parr, J. Hoeft, “Rayleigh scattering limits for low-level bidirectional reference distribution function measurements,” Appl. Opt. 33, 6084–6091 (1994).
    [CrossRef] [PubMed]
  2. The BRDF caused by instrument limitations when there is no sample scatter present is called the equivalent BRDF or the instrument signature.
  3. C. C. Asmail, C. L. Cromer, J. E. Proctor, J. J. Hsia, “Instrumentation at the National Institute of Standards and Technology for bidirectional reflectance distribution function (BRDF) measurements,” in Stray Radiation in Optical Systems III, R. P. Bereault, ed., Proc. SPIE2260, 52–61 (1994).
    [CrossRef]
  4. J. C. Stover, V. I. Ivakhnenko, C. A. Scheer, “Comparison of surface PSD’s calculated from both AFM profiles and scatter data,” in Flatness, Roughness, and Discrete Defects Characterization for Computer Disks, Wafers, and Flat Panel Displays II, J. C. Stover, ed., Proc. SPIE3275, 37–46 (1998).
    [CrossRef]
  5. T. A. Germer, C. C. Asmail, “A goniometric optical scatter instrument for bidirectional reflectance distribution function measurements with out-of-plane and polarimetry capabilities,” in Scattering and Surface Roughness, Z.-H. Gu, A. A. Maradudin, eds., Proc. SPIE3141, 220–231 (1997).
    [CrossRef]

1994 (1)

Asmail, C. C.

C. C. Asmail, J. J. Hsia, A. C. Parr, J. Hoeft, “Rayleigh scattering limits for low-level bidirectional reference distribution function measurements,” Appl. Opt. 33, 6084–6091 (1994).
[CrossRef] [PubMed]

T. A. Germer, C. C. Asmail, “A goniometric optical scatter instrument for bidirectional reflectance distribution function measurements with out-of-plane and polarimetry capabilities,” in Scattering and Surface Roughness, Z.-H. Gu, A. A. Maradudin, eds., Proc. SPIE3141, 220–231 (1997).
[CrossRef]

C. C. Asmail, C. L. Cromer, J. E. Proctor, J. J. Hsia, “Instrumentation at the National Institute of Standards and Technology for bidirectional reflectance distribution function (BRDF) measurements,” in Stray Radiation in Optical Systems III, R. P. Bereault, ed., Proc. SPIE2260, 52–61 (1994).
[CrossRef]

Cromer, C. L.

C. C. Asmail, C. L. Cromer, J. E. Proctor, J. J. Hsia, “Instrumentation at the National Institute of Standards and Technology for bidirectional reflectance distribution function (BRDF) measurements,” in Stray Radiation in Optical Systems III, R. P. Bereault, ed., Proc. SPIE2260, 52–61 (1994).
[CrossRef]

Germer, T. A.

T. A. Germer, C. C. Asmail, “A goniometric optical scatter instrument for bidirectional reflectance distribution function measurements with out-of-plane and polarimetry capabilities,” in Scattering and Surface Roughness, Z.-H. Gu, A. A. Maradudin, eds., Proc. SPIE3141, 220–231 (1997).
[CrossRef]

Hoeft, J.

Hsia, J. J.

C. C. Asmail, J. J. Hsia, A. C. Parr, J. Hoeft, “Rayleigh scattering limits for low-level bidirectional reference distribution function measurements,” Appl. Opt. 33, 6084–6091 (1994).
[CrossRef] [PubMed]

C. C. Asmail, C. L. Cromer, J. E. Proctor, J. J. Hsia, “Instrumentation at the National Institute of Standards and Technology for bidirectional reflectance distribution function (BRDF) measurements,” in Stray Radiation in Optical Systems III, R. P. Bereault, ed., Proc. SPIE2260, 52–61 (1994).
[CrossRef]

Ivakhnenko, V. I.

J. C. Stover, V. I. Ivakhnenko, C. A. Scheer, “Comparison of surface PSD’s calculated from both AFM profiles and scatter data,” in Flatness, Roughness, and Discrete Defects Characterization for Computer Disks, Wafers, and Flat Panel Displays II, J. C. Stover, ed., Proc. SPIE3275, 37–46 (1998).
[CrossRef]

Parr, A. C.

Proctor, J. E.

C. C. Asmail, C. L. Cromer, J. E. Proctor, J. J. Hsia, “Instrumentation at the National Institute of Standards and Technology for bidirectional reflectance distribution function (BRDF) measurements,” in Stray Radiation in Optical Systems III, R. P. Bereault, ed., Proc. SPIE2260, 52–61 (1994).
[CrossRef]

Scheer, C. A.

J. C. Stover, V. I. Ivakhnenko, C. A. Scheer, “Comparison of surface PSD’s calculated from both AFM profiles and scatter data,” in Flatness, Roughness, and Discrete Defects Characterization for Computer Disks, Wafers, and Flat Panel Displays II, J. C. Stover, ed., Proc. SPIE3275, 37–46 (1998).
[CrossRef]

Stover, J. C.

J. C. Stover, V. I. Ivakhnenko, C. A. Scheer, “Comparison of surface PSD’s calculated from both AFM profiles and scatter data,” in Flatness, Roughness, and Discrete Defects Characterization for Computer Disks, Wafers, and Flat Panel Displays II, J. C. Stover, ed., Proc. SPIE3275, 37–46 (1998).
[CrossRef]

Appl. Opt. (1)

Other (4)

The BRDF caused by instrument limitations when there is no sample scatter present is called the equivalent BRDF or the instrument signature.

C. C. Asmail, C. L. Cromer, J. E. Proctor, J. J. Hsia, “Instrumentation at the National Institute of Standards and Technology for bidirectional reflectance distribution function (BRDF) measurements,” in Stray Radiation in Optical Systems III, R. P. Bereault, ed., Proc. SPIE2260, 52–61 (1994).
[CrossRef]

J. C. Stover, V. I. Ivakhnenko, C. A. Scheer, “Comparison of surface PSD’s calculated from both AFM profiles and scatter data,” in Flatness, Roughness, and Discrete Defects Characterization for Computer Disks, Wafers, and Flat Panel Displays II, J. C. Stover, ed., Proc. SPIE3275, 37–46 (1998).
[CrossRef]

T. A. Germer, C. C. Asmail, “A goniometric optical scatter instrument for bidirectional reflectance distribution function measurements with out-of-plane and polarimetry capabilities,” in Scattering and Surface Roughness, Z.-H. Gu, A. A. Maradudin, eds., Proc. SPIE3141, 220–231 (1997).
[CrossRef]

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Equations (5)

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f = L s / E I ,
Φ R = f R Φ I Ω   cos   θ R ,
Φ Gas = A p lN   k 4 | α | 2   Φ I r 2 ,
Φ R Φ Gas = f R   cos   θ R lNk 4 | α | 2 .
f = lNk 4 | α | 2 .

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