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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 31, Iss. 5 — May. 1, 2014
  • pp: 1040–1048

Origin and nature of measurement bias in catadioptric parallel goniophotometers

Boris Karamata and Marilyne Andersen  »View Author Affiliations


JOSA A, Vol. 31, Issue 5, pp. 1040-1048 (2014)
http://dx.doi.org/10.1364/JOSAA.31.001040


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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

OCIS Codes
(120.3930) Instrumentation, measurement, and metrology : Metrological instrumentation
(120.4570) Instrumentation, measurement, and metrology : Optical design of instruments
(120.5820) Instrumentation, measurement, and metrology : Scattering measurements
(290.1483) Scattering : BSDF, BRDF, and BTDF

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: December 20, 2013
Revised Manuscript: March 5, 2014
Manuscript Accepted: March 7, 2014
Published: April 11, 2014

Citation
Boris Karamata and Marilyne Andersen, "Origin and nature of measurement bias in catadioptric parallel goniophotometers," J. Opt. Soc. Am. A 31, 1040-1048 (2014)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-31-5-1040


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References

  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]

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