Abstract

We briefly categorize and compare parallel goniophotometers, which are instruments capable of simultaneously measuring the far-field distribution of light scattered by a surface or emitted by a source over a large solid angle. Little is known about the accuracy and reliability of an appealing category, the catadioptric parallel goniophotometers (CPGs), which exploit a curved reflector and a lens system. We analyzed the working principle common to all the different design configurations of a CPG and established the specifications implicitly imposed on the lens system. Based on heuristic considerations, we show that the properties of a real (thick) lens system are not fully compatible with these specifications. This causes a bias to the measurements that increases with the acceptance angle of the lens system. Depending on the angular field, the measured sample area can be drastically reduced and shifted relative to the center of the sample. To gain insights into the nature and importance of the measurement bias, it was calculated with our model implemented in MATLAB for the CPG configuration incorporating a lens system with a very large acceptance angle (fisheye lens). Our results demonstrate that, due to the spatio-angular-filtering properties of the fisheye lens, this category of CPGs is so severely biased as to give unusable measurements. In addition, our findings raise the question of the importance of the bias in the other types of CPGs that rely on a lens system with a lower acceptance angle.

© 2014 Optical Society of America

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  1. J. C. Stover, Optical Scattering: Measurement and Analysis, R. E. Fisher and W. J. Smith, eds., Optical and Electro-optical Engineering Series (McGraw-Hill, 1990).
  2. W. Sipke and S. Baumer, “Appearance characterization by a scatterometer employing a hemispherical screen,” Proc. SPIE 5189, 163–173 (2003).
    [CrossRef]
  3. K. J. Dana, B. van Ginneken, S. K. Nayar, and J. J. Koendrik, “Reflectance and texture of the real world surface,” ACM Trans. Graph. 18, 1–34 (1999).
    [CrossRef]
  4. G. J. Ward, “Measuring and modeling anisotropic reflection,” in 19th Annual Conference of the Association for Computing Machinery: Computer Graphics and Interactive Techniques (SIGGRAPH), Vol. 26 of Computer Graphics (1992), pp. 265–272.
  5. G. J. Ward and R. Shakespeare, Rendering with Radiance: The Art and Science of Lighting Visualization (Morgan Kaufmann, 1997).
  6. C. F. Reinhart and S. Herkel, “The simulation of annual daylight illuminance distributions—A state-of-the-art comparison of six RADIANCE-based methods,” Energy Build. 32, 167–187 (2000).
    [CrossRef]
  7. G. L. Petersen, “Stray light calculation methods with optical ray trace software,” Proc. SPIE 3780, 132–137 (1999).
    [CrossRef]
  8. R. Yeo, R. Rykowski, D. Kreysar, and K. Chittim, “The imaging sphere—the first appearance meter?” in The 5th Oxford Conference on Spectroscopy (National Physics Laboratory, 2006), pp. 87–103.
  9. Commission Internationale de l’Eclairage, “Radiometric and photometric characteristics of materials and their measurement,” Standard (CIE, 1977).
  10. The term scatterometer can be confusing since it encompasses indiscriminately a wide scope of instruments for scattering measurements such as goniophotometer, polarimeter, ellipsometer, or TIS devices. The term reflectometer is sometimes also used for instruments measuring the BRDF.
  11. D. R. White, P. Saunders, S. J. Bonsey, J. van de Ven, and H. Edgar, “Reflectometer for measuring the bidirectional reflectance of rough surfaces,” Appl. Opt. 37, 3450–3454 (1998).
    [CrossRef]
  12. M. Andersen and J. de Boer, “Goniophotometry and assessment of bidirectional photometric properties of complex fenestration systems,” Energy Build. 38, 836–848 (2006).
    [CrossRef]
  13. A. W. Bailey, E. A. Early, K. S. Keppler, V. I. Villavicencio, P. Kennedy, R. J. Thomas, J. J. Zohner, and G. Megaloudis, “Dynamic bidirectional reflectance functions: Measurement and representation,” J. Laser Appl. 20, 22–36 (2008).
    [CrossRef]
  14. So far, no common terminology has been adopted to designate these types of instruments. For instance, they have been designated by an imaging scatterometer, an angular imaging device, or a viewing angle instrument.
  15. Following the terminology of E. Hecht [30] below (see pp. 156 and 197), dioptrics denotes the optics of refracting elements (such as lenses), whereas catoptrics denotes the optics of reflecting surfaces. A combination of reflecting (catopric) and refracting (dioptric) elements is called a catadioptric system.
  16. J. R. McNeil and S. R. Wilson, “Two-dimensional optical scatterometer apparatus and process,” U.S. patent5,241,369 (August31, 1993).
  17. P. Yeh and C. Gu, “Conoscopy,” in Optics of Liquid Crystal Displays (John Wiley & Sons, 1999), Chap. 4.4., pp 139.
  18. P. Boher, M. Luet, and T. Leroux, “Light scattered measurements using Fourier optics: A new tool for surface characterization,” Proc. SPIE 5457, 344–354 (2004).
    [CrossRef]
  19. K. J. Dana Ren and J. Wang, “Device for convenient measurement of spatially varying bidirectional reflectance,” J. Opt. Soc. Am. A 21, 1–12 (2004).
    [CrossRef]
  20. C. Hahlweg and H. Rothe, “Design of a full-hemispherical spectro-radiometer with high dynamic range for characterization of surface properties using multi-spectral BRDF data from VIS to NIR,” Proc. SPIE 5965, 596519 (2005).
    [CrossRef]
  21. J. Ren and J. Zhao, “Measurement of a bidirectional reflectance distribution and system achievement based on a hemi-parabolic mirror,” Opt. Lett. 35, 1458–1460 (2010).
    [CrossRef]
  22. P. R. Mattison, M. S. Dombrowski, J. Lorenz, K. Davis, H. Mann, P. Johnson, and B. Foos, “Hand-held directional reflectometer: an angular imaging device to measure BRDF and HDR in real-time,” Proc. SPIE 3426, 240–251 (1998).
    [CrossRef]
  23. D. G. Stavenga, H. L. Leertouwer, P. Pirih, and M. F. Wehling, “Imaging scatterometry of butterfly wing scales,” Opt. Express 17, 193–202 (2009).
    [CrossRef]
  24. M. Andersen, E. Stokes, N. Gayeski, and C. Browne, “Using digital imaging to assess spectral solar-optical properties of complex fenestration materials: A new approach in video–goniophotometry,” Sol. Energy 84, 549–562 (2010).
    [CrossRef]
  25. M. Rosete-Aguilar, O. G. Rodriguez-Herrera, and N. C. Bruce, “Optical design of a scatterometer with an ellipsoidal mirror,” Opt. Eng. 42, 1772–1777 (2003).
    [CrossRef]
  26. Y. Mugaigawa, K. Sumino, and Y. Yagi, “Multiplexed illumination for measuring BRDF using an ellipsoidal mirror and projector,” in Computer Vision—ACCV 2007, 8th Asian Conference on Computer Vision, Proceedings, Part II, Vol. 4844 of Lecture Notes in Computer Science (Springer, 2007), pp. 246–257.
  27. The fabrication of a large reflector, required for the measurement of large samples and/or high angular resolution, is very challenging and can have a strong impact on cost.
  28. S. Kuthirummal and S. K. Nayar, “Multiview radial catadioptric imaging for scene capture,” ACM Trans. Graph. 25, 916–923 (2006).
    [CrossRef]
  29. The exact name of the shape is a spheroid, which is a specific case of an ellipsoid in which two of the three axes are equal. A spheroid is generated by rotating an ellipse around one of its axes.
  30. E. Hecht, “Geometrical optics—paraxial theory,” in Optics, 2nd ed. (Addison-Wesley, 1987), pp. 128–152.
  31. C. Hahlweg and H. Rothe, “Utilization of the Scheimpflug-principle in scatterometer design,” Proc. SPIE 7065, 706507 (2008).
    [CrossRef]
  32. C. Hughes, P. Denny, E. Jones, and M. Galvin, “Accuracy of fish-eye lens models,” Appl. Opt. 49, 3338–3347 (2010).
    [CrossRef]
  33. D. B. Gennery, “Generalized camera calibration including fish-eye lenses,” Int. J. Comput. Vis. 68, 239–266 (2006).
    [CrossRef]
  34. W. J. Smith, “Stops and apertures,” in Modern Optical Engineering, 3rd ed. (McGraw-Hill, 2000), pp. 153–154.
  35. M. Laikin, Lens Design, 4th ed. (CRC Press, 2007).
  36. J. Kumler and M. Bauer, “Fisheye lens designs and their relative performance,” Proc. SPIE 4093, 360–369 (2000).
  37. R. R. Carter and L. K. Pleskot, “Imaging scatterometer,” U.S. patent5,912,741 (June15, 1999).
  38. S. Baker and S. K. Nayar, “A theory of single-viewpoint catadioptric image formation,” Int. J. Comput. Vis. 35, 175–196 (1999).
    [CrossRef]

2010

M. Andersen, E. Stokes, N. Gayeski, and C. Browne, “Using digital imaging to assess spectral solar-optical properties of complex fenestration materials: A new approach in video–goniophotometry,” Sol. Energy 84, 549–562 (2010).
[CrossRef]

J. Ren and J. Zhao, “Measurement of a bidirectional reflectance distribution and system achievement based on a hemi-parabolic mirror,” Opt. Lett. 35, 1458–1460 (2010).
[CrossRef]

C. Hughes, P. Denny, E. Jones, and M. Galvin, “Accuracy of fish-eye lens models,” Appl. Opt. 49, 3338–3347 (2010).
[CrossRef]

2009

2008

C. Hahlweg and H. Rothe, “Utilization of the Scheimpflug-principle in scatterometer design,” Proc. SPIE 7065, 706507 (2008).
[CrossRef]

A. W. Bailey, E. A. Early, K. S. Keppler, V. I. Villavicencio, P. Kennedy, R. J. Thomas, J. J. Zohner, and G. Megaloudis, “Dynamic bidirectional reflectance functions: Measurement and representation,” J. Laser Appl. 20, 22–36 (2008).
[CrossRef]

2006

D. B. Gennery, “Generalized camera calibration including fish-eye lenses,” Int. J. Comput. Vis. 68, 239–266 (2006).
[CrossRef]

M. Andersen and J. de Boer, “Goniophotometry and assessment of bidirectional photometric properties of complex fenestration systems,” Energy Build. 38, 836–848 (2006).
[CrossRef]

S. Kuthirummal and S. K. Nayar, “Multiview radial catadioptric imaging for scene capture,” ACM Trans. Graph. 25, 916–923 (2006).
[CrossRef]

2005

C. Hahlweg and H. Rothe, “Design of a full-hemispherical spectro-radiometer with high dynamic range for characterization of surface properties using multi-spectral BRDF data from VIS to NIR,” Proc. SPIE 5965, 596519 (2005).
[CrossRef]

2004

P. Boher, M. Luet, and T. Leroux, “Light scattered measurements using Fourier optics: A new tool for surface characterization,” Proc. SPIE 5457, 344–354 (2004).
[CrossRef]

K. J. Dana Ren and J. Wang, “Device for convenient measurement of spatially varying bidirectional reflectance,” J. Opt. Soc. Am. A 21, 1–12 (2004).
[CrossRef]

2003

W. Sipke and S. Baumer, “Appearance characterization by a scatterometer employing a hemispherical screen,” Proc. SPIE 5189, 163–173 (2003).
[CrossRef]

M. Rosete-Aguilar, O. G. Rodriguez-Herrera, and N. C. Bruce, “Optical design of a scatterometer with an ellipsoidal mirror,” Opt. Eng. 42, 1772–1777 (2003).
[CrossRef]

2000

J. Kumler and M. Bauer, “Fisheye lens designs and their relative performance,” Proc. SPIE 4093, 360–369 (2000).

C. F. Reinhart and S. Herkel, “The simulation of annual daylight illuminance distributions—A state-of-the-art comparison of six RADIANCE-based methods,” Energy Build. 32, 167–187 (2000).
[CrossRef]

1999

G. L. Petersen, “Stray light calculation methods with optical ray trace software,” Proc. SPIE 3780, 132–137 (1999).
[CrossRef]

K. J. Dana, B. van Ginneken, S. K. Nayar, and J. J. Koendrik, “Reflectance and texture of the real world surface,” ACM Trans. Graph. 18, 1–34 (1999).
[CrossRef]

S. Baker and S. K. Nayar, “A theory of single-viewpoint catadioptric image formation,” Int. J. Comput. Vis. 35, 175–196 (1999).
[CrossRef]

1998

D. R. White, P. Saunders, S. J. Bonsey, J. van de Ven, and H. Edgar, “Reflectometer for measuring the bidirectional reflectance of rough surfaces,” Appl. Opt. 37, 3450–3454 (1998).
[CrossRef]

P. R. Mattison, M. S. Dombrowski, J. Lorenz, K. Davis, H. Mann, P. Johnson, and B. Foos, “Hand-held directional reflectometer: an angular imaging device to measure BRDF and HDR in real-time,” Proc. SPIE 3426, 240–251 (1998).
[CrossRef]

Andersen, M.

M. Andersen, E. Stokes, N. Gayeski, and C. Browne, “Using digital imaging to assess spectral solar-optical properties of complex fenestration materials: A new approach in video–goniophotometry,” Sol. Energy 84, 549–562 (2010).
[CrossRef]

M. Andersen and J. de Boer, “Goniophotometry and assessment of bidirectional photometric properties of complex fenestration systems,” Energy Build. 38, 836–848 (2006).
[CrossRef]

Bailey, A. W.

A. W. Bailey, E. A. Early, K. S. Keppler, V. I. Villavicencio, P. Kennedy, R. J. Thomas, J. J. Zohner, and G. Megaloudis, “Dynamic bidirectional reflectance functions: Measurement and representation,” J. Laser Appl. 20, 22–36 (2008).
[CrossRef]

Baker, S.

S. Baker and S. K. Nayar, “A theory of single-viewpoint catadioptric image formation,” Int. J. Comput. Vis. 35, 175–196 (1999).
[CrossRef]

Bauer, M.

J. Kumler and M. Bauer, “Fisheye lens designs and their relative performance,” Proc. SPIE 4093, 360–369 (2000).

Baumer, S.

W. Sipke and S. Baumer, “Appearance characterization by a scatterometer employing a hemispherical screen,” Proc. SPIE 5189, 163–173 (2003).
[CrossRef]

Boher, P.

P. Boher, M. Luet, and T. Leroux, “Light scattered measurements using Fourier optics: A new tool for surface characterization,” Proc. SPIE 5457, 344–354 (2004).
[CrossRef]

Bonsey, S. J.

Browne, C.

M. Andersen, E. Stokes, N. Gayeski, and C. Browne, “Using digital imaging to assess spectral solar-optical properties of complex fenestration materials: A new approach in video–goniophotometry,” Sol. Energy 84, 549–562 (2010).
[CrossRef]

Bruce, N. C.

M. Rosete-Aguilar, O. G. Rodriguez-Herrera, and N. C. Bruce, “Optical design of a scatterometer with an ellipsoidal mirror,” Opt. Eng. 42, 1772–1777 (2003).
[CrossRef]

Carter, R. R.

R. R. Carter and L. K. Pleskot, “Imaging scatterometer,” U.S. patent5,912,741 (June15, 1999).

Chittim, K.

R. Yeo, R. Rykowski, D. Kreysar, and K. Chittim, “The imaging sphere—the first appearance meter?” in The 5th Oxford Conference on Spectroscopy (National Physics Laboratory, 2006), pp. 87–103.

Dana, K. J.

K. J. Dana, B. van Ginneken, S. K. Nayar, and J. J. Koendrik, “Reflectance and texture of the real world surface,” ACM Trans. Graph. 18, 1–34 (1999).
[CrossRef]

Dana Ren, K. J.

Davis, K.

P. R. Mattison, M. S. Dombrowski, J. Lorenz, K. Davis, H. Mann, P. Johnson, and B. Foos, “Hand-held directional reflectometer: an angular imaging device to measure BRDF and HDR in real-time,” Proc. SPIE 3426, 240–251 (1998).
[CrossRef]

de Boer, J.

M. Andersen and J. de Boer, “Goniophotometry and assessment of bidirectional photometric properties of complex fenestration systems,” Energy Build. 38, 836–848 (2006).
[CrossRef]

Denny, P.

Dombrowski, M. S.

P. R. Mattison, M. S. Dombrowski, J. Lorenz, K. Davis, H. Mann, P. Johnson, and B. Foos, “Hand-held directional reflectometer: an angular imaging device to measure BRDF and HDR in real-time,” Proc. SPIE 3426, 240–251 (1998).
[CrossRef]

Early, E. A.

A. W. Bailey, E. A. Early, K. S. Keppler, V. I. Villavicencio, P. Kennedy, R. J. Thomas, J. J. Zohner, and G. Megaloudis, “Dynamic bidirectional reflectance functions: Measurement and representation,” J. Laser Appl. 20, 22–36 (2008).
[CrossRef]

Edgar, H.

Foos, B.

P. R. Mattison, M. S. Dombrowski, J. Lorenz, K. Davis, H. Mann, P. Johnson, and B. Foos, “Hand-held directional reflectometer: an angular imaging device to measure BRDF and HDR in real-time,” Proc. SPIE 3426, 240–251 (1998).
[CrossRef]

Galvin, M.

Gayeski, N.

M. Andersen, E. Stokes, N. Gayeski, and C. Browne, “Using digital imaging to assess spectral solar-optical properties of complex fenestration materials: A new approach in video–goniophotometry,” Sol. Energy 84, 549–562 (2010).
[CrossRef]

Gennery, D. B.

D. B. Gennery, “Generalized camera calibration including fish-eye lenses,” Int. J. Comput. Vis. 68, 239–266 (2006).
[CrossRef]

Gu, C.

P. Yeh and C. Gu, “Conoscopy,” in Optics of Liquid Crystal Displays (John Wiley & Sons, 1999), Chap. 4.4., pp 139.

Hahlweg, C.

C. Hahlweg and H. Rothe, “Utilization of the Scheimpflug-principle in scatterometer design,” Proc. SPIE 7065, 706507 (2008).
[CrossRef]

C. Hahlweg and H. Rothe, “Design of a full-hemispherical spectro-radiometer with high dynamic range for characterization of surface properties using multi-spectral BRDF data from VIS to NIR,” Proc. SPIE 5965, 596519 (2005).
[CrossRef]

Hecht, E.

E. Hecht, “Geometrical optics—paraxial theory,” in Optics, 2nd ed. (Addison-Wesley, 1987), pp. 128–152.

Herkel, S.

C. F. Reinhart and S. Herkel, “The simulation of annual daylight illuminance distributions—A state-of-the-art comparison of six RADIANCE-based methods,” Energy Build. 32, 167–187 (2000).
[CrossRef]

Hughes, C.

Johnson, P.

P. R. Mattison, M. S. Dombrowski, J. Lorenz, K. Davis, H. Mann, P. Johnson, and B. Foos, “Hand-held directional reflectometer: an angular imaging device to measure BRDF and HDR in real-time,” Proc. SPIE 3426, 240–251 (1998).
[CrossRef]

Jones, E.

Kennedy, P.

A. W. Bailey, E. A. Early, K. S. Keppler, V. I. Villavicencio, P. Kennedy, R. J. Thomas, J. J. Zohner, and G. Megaloudis, “Dynamic bidirectional reflectance functions: Measurement and representation,” J. Laser Appl. 20, 22–36 (2008).
[CrossRef]

Keppler, K. S.

A. W. Bailey, E. A. Early, K. S. Keppler, V. I. Villavicencio, P. Kennedy, R. J. Thomas, J. J. Zohner, and G. Megaloudis, “Dynamic bidirectional reflectance functions: Measurement and representation,” J. Laser Appl. 20, 22–36 (2008).
[CrossRef]

Koendrik, J. J.

K. J. Dana, B. van Ginneken, S. K. Nayar, and J. J. Koendrik, “Reflectance and texture of the real world surface,” ACM Trans. Graph. 18, 1–34 (1999).
[CrossRef]

Kreysar, D.

R. Yeo, R. Rykowski, D. Kreysar, and K. Chittim, “The imaging sphere—the first appearance meter?” in The 5th Oxford Conference on Spectroscopy (National Physics Laboratory, 2006), pp. 87–103.

Kumler, J.

J. Kumler and M. Bauer, “Fisheye lens designs and their relative performance,” Proc. SPIE 4093, 360–369 (2000).

Kuthirummal, S.

S. Kuthirummal and S. K. Nayar, “Multiview radial catadioptric imaging for scene capture,” ACM Trans. Graph. 25, 916–923 (2006).
[CrossRef]

Laikin, M.

M. Laikin, Lens Design, 4th ed. (CRC Press, 2007).

Leertouwer, H. L.

Leroux, T.

P. Boher, M. Luet, and T. Leroux, “Light scattered measurements using Fourier optics: A new tool for surface characterization,” Proc. SPIE 5457, 344–354 (2004).
[CrossRef]

Lorenz, J.

P. R. Mattison, M. S. Dombrowski, J. Lorenz, K. Davis, H. Mann, P. Johnson, and B. Foos, “Hand-held directional reflectometer: an angular imaging device to measure BRDF and HDR in real-time,” Proc. SPIE 3426, 240–251 (1998).
[CrossRef]

Luet, M.

P. Boher, M. Luet, and T. Leroux, “Light scattered measurements using Fourier optics: A new tool for surface characterization,” Proc. SPIE 5457, 344–354 (2004).
[CrossRef]

Mann, H.

P. R. Mattison, M. S. Dombrowski, J. Lorenz, K. Davis, H. Mann, P. Johnson, and B. Foos, “Hand-held directional reflectometer: an angular imaging device to measure BRDF and HDR in real-time,” Proc. SPIE 3426, 240–251 (1998).
[CrossRef]

Mattison, P. R.

P. R. Mattison, M. S. Dombrowski, J. Lorenz, K. Davis, H. Mann, P. Johnson, and B. Foos, “Hand-held directional reflectometer: an angular imaging device to measure BRDF and HDR in real-time,” Proc. SPIE 3426, 240–251 (1998).
[CrossRef]

McNeil, J. R.

J. R. McNeil and S. R. Wilson, “Two-dimensional optical scatterometer apparatus and process,” U.S. patent5,241,369 (August31, 1993).

Megaloudis, G.

A. W. Bailey, E. A. Early, K. S. Keppler, V. I. Villavicencio, P. Kennedy, R. J. Thomas, J. J. Zohner, and G. Megaloudis, “Dynamic bidirectional reflectance functions: Measurement and representation,” J. Laser Appl. 20, 22–36 (2008).
[CrossRef]

Mugaigawa, Y.

Y. Mugaigawa, K. Sumino, and Y. Yagi, “Multiplexed illumination for measuring BRDF using an ellipsoidal mirror and projector,” in Computer Vision—ACCV 2007, 8th Asian Conference on Computer Vision, Proceedings, Part II, Vol. 4844 of Lecture Notes in Computer Science (Springer, 2007), pp. 246–257.

Nayar, S. K.

S. Kuthirummal and S. K. Nayar, “Multiview radial catadioptric imaging for scene capture,” ACM Trans. Graph. 25, 916–923 (2006).
[CrossRef]

K. J. Dana, B. van Ginneken, S. K. Nayar, and J. J. Koendrik, “Reflectance and texture of the real world surface,” ACM Trans. Graph. 18, 1–34 (1999).
[CrossRef]

S. Baker and S. K. Nayar, “A theory of single-viewpoint catadioptric image formation,” Int. J. Comput. Vis. 35, 175–196 (1999).
[CrossRef]

Petersen, G. L.

G. L. Petersen, “Stray light calculation methods with optical ray trace software,” Proc. SPIE 3780, 132–137 (1999).
[CrossRef]

Pirih, P.

Pleskot, L. K.

R. R. Carter and L. K. Pleskot, “Imaging scatterometer,” U.S. patent5,912,741 (June15, 1999).

Reinhart, C. F.

C. F. Reinhart and S. Herkel, “The simulation of annual daylight illuminance distributions—A state-of-the-art comparison of six RADIANCE-based methods,” Energy Build. 32, 167–187 (2000).
[CrossRef]

Ren, J.

Rodriguez-Herrera, O. G.

M. Rosete-Aguilar, O. G. Rodriguez-Herrera, and N. C. Bruce, “Optical design of a scatterometer with an ellipsoidal mirror,” Opt. Eng. 42, 1772–1777 (2003).
[CrossRef]

Rosete-Aguilar, M.

M. Rosete-Aguilar, O. G. Rodriguez-Herrera, and N. C. Bruce, “Optical design of a scatterometer with an ellipsoidal mirror,” Opt. Eng. 42, 1772–1777 (2003).
[CrossRef]

Rothe, H.

C. Hahlweg and H. Rothe, “Utilization of the Scheimpflug-principle in scatterometer design,” Proc. SPIE 7065, 706507 (2008).
[CrossRef]

C. Hahlweg and H. Rothe, “Design of a full-hemispherical spectro-radiometer with high dynamic range for characterization of surface properties using multi-spectral BRDF data from VIS to NIR,” Proc. SPIE 5965, 596519 (2005).
[CrossRef]

Rykowski, R.

R. Yeo, R. Rykowski, D. Kreysar, and K. Chittim, “The imaging sphere—the first appearance meter?” in The 5th Oxford Conference on Spectroscopy (National Physics Laboratory, 2006), pp. 87–103.

Saunders, P.

Shakespeare, R.

G. J. Ward and R. Shakespeare, Rendering with Radiance: The Art and Science of Lighting Visualization (Morgan Kaufmann, 1997).

Sipke, W.

W. Sipke and S. Baumer, “Appearance characterization by a scatterometer employing a hemispherical screen,” Proc. SPIE 5189, 163–173 (2003).
[CrossRef]

Smith, W. J.

W. J. Smith, “Stops and apertures,” in Modern Optical Engineering, 3rd ed. (McGraw-Hill, 2000), pp. 153–154.

Stavenga, D. G.

Stokes, E.

M. Andersen, E. Stokes, N. Gayeski, and C. Browne, “Using digital imaging to assess spectral solar-optical properties of complex fenestration materials: A new approach in video–goniophotometry,” Sol. Energy 84, 549–562 (2010).
[CrossRef]

Stover, J. C.

J. C. Stover, Optical Scattering: Measurement and Analysis, R. E. Fisher and W. J. Smith, eds., Optical and Electro-optical Engineering Series (McGraw-Hill, 1990).

Sumino, K.

Y. Mugaigawa, K. Sumino, and Y. Yagi, “Multiplexed illumination for measuring BRDF using an ellipsoidal mirror and projector,” in Computer Vision—ACCV 2007, 8th Asian Conference on Computer Vision, Proceedings, Part II, Vol. 4844 of Lecture Notes in Computer Science (Springer, 2007), pp. 246–257.

Thomas, R. J.

A. W. Bailey, E. A. Early, K. S. Keppler, V. I. Villavicencio, P. Kennedy, R. J. Thomas, J. J. Zohner, and G. Megaloudis, “Dynamic bidirectional reflectance functions: Measurement and representation,” J. Laser Appl. 20, 22–36 (2008).
[CrossRef]

van de Ven, J.

van Ginneken, B.

K. J. Dana, B. van Ginneken, S. K. Nayar, and J. J. Koendrik, “Reflectance and texture of the real world surface,” ACM Trans. Graph. 18, 1–34 (1999).
[CrossRef]

Villavicencio, V. I.

A. W. Bailey, E. A. Early, K. S. Keppler, V. I. Villavicencio, P. Kennedy, R. J. Thomas, J. J. Zohner, and G. Megaloudis, “Dynamic bidirectional reflectance functions: Measurement and representation,” J. Laser Appl. 20, 22–36 (2008).
[CrossRef]

Wang, J.

Ward, G. J.

G. J. Ward and R. Shakespeare, Rendering with Radiance: The Art and Science of Lighting Visualization (Morgan Kaufmann, 1997).

G. J. Ward, “Measuring and modeling anisotropic reflection,” in 19th Annual Conference of the Association for Computing Machinery: Computer Graphics and Interactive Techniques (SIGGRAPH), Vol. 26 of Computer Graphics (1992), pp. 265–272.

Wehling, M. F.

White, D. R.

Wilson, S. R.

J. R. McNeil and S. R. Wilson, “Two-dimensional optical scatterometer apparatus and process,” U.S. patent5,241,369 (August31, 1993).

Yagi, Y.

Y. Mugaigawa, K. Sumino, and Y. Yagi, “Multiplexed illumination for measuring BRDF using an ellipsoidal mirror and projector,” in Computer Vision—ACCV 2007, 8th Asian Conference on Computer Vision, Proceedings, Part II, Vol. 4844 of Lecture Notes in Computer Science (Springer, 2007), pp. 246–257.

Yeh, P.

P. Yeh and C. Gu, “Conoscopy,” in Optics of Liquid Crystal Displays (John Wiley & Sons, 1999), Chap. 4.4., pp 139.

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R. Yeo, R. Rykowski, D. Kreysar, and K. Chittim, “The imaging sphere—the first appearance meter?” in The 5th Oxford Conference on Spectroscopy (National Physics Laboratory, 2006), pp. 87–103.

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A. W. Bailey, E. A. Early, K. S. Keppler, V. I. Villavicencio, P. Kennedy, R. J. Thomas, J. J. Zohner, and G. Megaloudis, “Dynamic bidirectional reflectance functions: Measurement and representation,” J. Laser Appl. 20, 22–36 (2008).
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M. Rosete-Aguilar, O. G. Rodriguez-Herrera, and N. C. Bruce, “Optical design of a scatterometer with an ellipsoidal mirror,” Opt. Eng. 42, 1772–1777 (2003).
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Other

Y. Mugaigawa, K. Sumino, and Y. Yagi, “Multiplexed illumination for measuring BRDF using an ellipsoidal mirror and projector,” in Computer Vision—ACCV 2007, 8th Asian Conference on Computer Vision, Proceedings, Part II, Vol. 4844 of Lecture Notes in Computer Science (Springer, 2007), pp. 246–257.

The fabrication of a large reflector, required for the measurement of large samples and/or high angular resolution, is very challenging and can have a strong impact on cost.

So far, no common terminology has been adopted to designate these types of instruments. For instance, they have been designated by an imaging scatterometer, an angular imaging device, or a viewing angle instrument.

Following the terminology of E. Hecht [30] below (see pp. 156 and 197), dioptrics denotes the optics of refracting elements (such as lenses), whereas catoptrics denotes the optics of reflecting surfaces. A combination of reflecting (catopric) and refracting (dioptric) elements is called a catadioptric system.

J. R. McNeil and S. R. Wilson, “Two-dimensional optical scatterometer apparatus and process,” U.S. patent5,241,369 (August31, 1993).

P. Yeh and C. Gu, “Conoscopy,” in Optics of Liquid Crystal Displays (John Wiley & Sons, 1999), Chap. 4.4., pp 139.

J. C. Stover, Optical Scattering: Measurement and Analysis, R. E. Fisher and W. J. Smith, eds., Optical and Electro-optical Engineering Series (McGraw-Hill, 1990).

G. J. Ward, “Measuring and modeling anisotropic reflection,” in 19th Annual Conference of the Association for Computing Machinery: Computer Graphics and Interactive Techniques (SIGGRAPH), Vol. 26 of Computer Graphics (1992), pp. 265–272.

G. J. Ward and R. Shakespeare, Rendering with Radiance: The Art and Science of Lighting Visualization (Morgan Kaufmann, 1997).

R. Yeo, R. Rykowski, D. Kreysar, and K. Chittim, “The imaging sphere—the first appearance meter?” in The 5th Oxford Conference on Spectroscopy (National Physics Laboratory, 2006), pp. 87–103.

Commission Internationale de l’Eclairage, “Radiometric and photometric characteristics of materials and their measurement,” Standard (CIE, 1977).

The term scatterometer can be confusing since it encompasses indiscriminately a wide scope of instruments for scattering measurements such as goniophotometer, polarimeter, ellipsometer, or TIS devices. The term reflectometer is sometimes also used for instruments measuring the BRDF.

The exact name of the shape is a spheroid, which is a specific case of an ellipsoid in which two of the three axes are equal. A spheroid is generated by rotating an ellipse around one of its axes.

E. Hecht, “Geometrical optics—paraxial theory,” in Optics, 2nd ed. (Addison-Wesley, 1987), pp. 128–152.

R. R. Carter and L. K. Pleskot, “Imaging scatterometer,” U.S. patent5,912,741 (June15, 1999).

W. J. Smith, “Stops and apertures,” in Modern Optical Engineering, 3rd ed. (McGraw-Hill, 2000), pp. 153–154.

M. Laikin, Lens Design, 4th ed. (CRC Press, 2007).

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Figures (6)

Fig. 1.
Fig. 1.

Working principle of a catadioptric parallel goniophotometer (CPG) with key components and parameters. The red lines represent a parallel ray bundle scattered by the sample of finite size diameter (s) in a direction SDi(θ,φ) and reflected by the ellipsoidal mirror in a direction RDi(α,β). A thin lens (TL), with an entrance pupil diameter p, focuses the ray bundle of largest radial size ρi on a two-dimensional array of detectors (D). The red dotted lines represent the chief ray of the ray bundle that passes by the two focal points F1 and F2 of the ellipsoid. The angle Ω is the largest focusing angle of the beam composed of all light scattered within π sr after reflection on the ellipsoidal mirror.

Fig. 2.
Fig. 2.

Origin and nature of the measurement bias in a CPG caused by the spatio-angular-filtering properties of its lens system (LS). The angular-field-dependent entrance pupil (AP(α)), which is different than the paraxial entrance pupil (EP), determines the size (d) and the trajectory of the chief ray (CR) of the ray bundles entering LS at an angular field (α). The ray trajectories imposed by the truncated ray bundles determine the measured sample dimension (s), as well as the angular resolution ω.

Fig. 3.
Fig. 3.

Catadioptric parallel goniophotometer (CPG) configurations relying either on a parabolic reflector (P) or on an ellipsoidal reflector (E1, E2, E3). Key components and parameters: sample (S), lens system (LS), detector array (D), collection angle of scattered light (Ψ), and minimal acceptance angle required for LS (Φ). The angles quoted Φ/2 have an extent of Φ in the xz dimension.

Fig. 4.
Fig. 4.

Fisheye lens modeled in ZEMAX with ray-tracing at the angular field (α) for each 15° between 0° and 90°. Parameters include: entrance pupil (EP), vector of direction of a chief ray (VCR), and radial offset (ρ0) relative to F2. Inset: cross section Σ of the prolongation of an entering ray bundle in the horizontal plane containing F2, which is approximated by an ellipse with semi-axes aΣ and bΣ.

Fig. 5.
Fig. 5.

Key parameters for a CPG of design configuration E3 incorporating a fisheye lens centered on focal point F2: semi-axes of the ellipsoid (a,b), diameter of sample centered on focal point F1 (s). The ray-trace shows the measured area Γ(α,β) as a function of the ray bundle cross section in the sample plane [Σ(α,β)] determined by the spatio-angular-filtering properties of the fisheye lens.

Fig. 6.
Fig. 6.

Typical measurement bias in a CPG obtained for the “Heliodome” design incorporating a typical fisheye lens. Calculation results for the size and position of the sample areas Γ(α,β) measured by the CPG in the sample plane as a function of the areas Σ(α,β) determined by the spatio-angular-properties of the fisheye lens at F2 in the CPG for the direction of detection defined by the pair of polar angles α and β, which are varied in steps of 15° and 30°, respectively. The footprint of a circular sample centered on F1 with a diameter of s=10mm is shown for visual reference.

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