## Effective emissivities of isothermal blackbody cavities calculated by the Monte Carlo method using the three-component bidirectional reflectance distribution function model |

Applied Optics, Vol. 51, Issue 13, pp. 2322-2332 (2012)

http://dx.doi.org/10.1364/AO.51.002322

Enhanced HTML Acrobat PDF (853 KB)

### Abstract

This paper proposes a three-component bidirectional reflectance distribution function (3C BRDF) model consisting of diffuse, quasi-specular, and glossy components for calculation of effective emissivities of blackbody cavities and then investigates the properties of the new reflection model. The particle swarm optimization method is applied for fitting a 3C BRDF model to measured BRDFs. The model is incorporated into the Monte Carlo ray-tracing algorithm for isothermal cavities. Finally, the paper compares the results obtained using the 3C model and the conventional specular-diffuse model of reflection.

© 2012 Optical Society of America

**OCIS Codes**

(120.5630) Instrumentation, measurement, and metrology : Radiometry

(230.6080) Optical devices : Sources

(290.1483) Scattering : BSDF, BRDF, and BTDF

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: October 11, 2011

Revised Manuscript: December 23, 2011

Manuscript Accepted: December 23, 2011

Published: May 1, 2012

**Citation**

Alexander Prokhorov, "Effective emissivities of isothermal blackbody cavities calculated by the Monte Carlo method using the three-component bidirectional reflectance distribution function model," Appl. Opt. **51**, 2322-2332 (2012)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-51-13-2322

Sort: Year | Journal | Reset

### References

- J. Hollandt, J. Seidel, R. Klein, G. Ulm, A. Migdall, and M. Ware, “Primary sources for use in radiometry,” Optical Radiometry, A. C. Parr, R. U. Datla, and J. L. Gardner, eds. (Academic, 2005), pp. 213–290.
- J. Hartmann, J. Hollandt, B. Khlevnoy, S. Morozova, S. Ogarev, and F. Sakuma, “Blackbody and other calibration sources,” Radiometric Temperature Measurements. I. Fundamentals, Z. M. Zhang, B. K. Tsai, and G. Machin, eds. (Academic, 2010), pp. 241–295.
- F. J. Kelly, “On Kirchhoff’s law and its generalized application to absorption and emission by cavities,” J. Res. Natl. Bur. Stand. B 69, 165–171 (1965).
- R. E. Bedford, “Calculation of effective emissivities of cavity sources of thermal radiation,” Theory and Practice if Radiation Thermometry, D. P. DeWitt and G. D. Nutter, eds. (Wiley, 1988), pp. 653–772.
- A. V. Prokhorov, L. M. Hanssen, and S. N. Mekhontsev, “Calculation of the radiation characteristics of blackbody radiation sources,” in Radiometric Temperature Measurements: I. Fundamentals, Z. M. Zhang, B. K. Tsai, and G. Machin, eds. (Academic, 2010), Vol. 42, pp. 181–240.
- A. Ono, “Calculation of the directional emissivities of the cavities by the Monte Carlo method,” J. Opt. Soc. Am. 70, 547–554 (1980). [CrossRef]
- M. J. Ballico, “Modeling of the effective emissivity of a graphite tube black body,” Metrologia 32, 259–265 (1995). [CrossRef]
- K. A. Snail, D. P. Brown, J. P. Costantino, W. C. Shemano, C. W. Schmidt, W. F. Lynn, C. L. Seaman, and T. R. Knowles, “Optical characterization of black appliqués,” Proc. SPIE 2864, 465–474 (1996). [CrossRef]
- M. J. Persky, “Review of black surfaces for space-borne infrared systems,” Rev. Sci. Instrum. 70, 2193–2217 (1999). [CrossRef]
- S. R. Meier, “Characterization of highly absorbing black appliqués in the infrared,” Appl. Opt. 40, 2788–2795 (2001). [CrossRef]
- S. R. Meier, “Reflectance and scattering properties of highly absorbing black appliqués over a broadband spectral region,” Appl. Opt. 40, 6260–6264 (2001). [CrossRef]
- J. Hartmann, “High-temperature measurement techniques for the application in photometry, radiometry and thermometry,” Phys. Rep. 469, 205–269 (2009). [CrossRef]
- F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” NBS Monograph 160 (U.S. Department of Commerce, National Bureau of Standards, 1977).
- A. S. Glassner, Principles of Digital Image Synthesis (Morgan Kaufmann, 1995), Vol. II.
- P. Shirley, Fundamentals of Computer Graphics (A K Peters, 2002).
- P. Dutré, P. Bekaert, and K. Bala, Advanced Global Illumination (A K Peters, 2003).
- M. Pharr and C. Humphreys, Physically Based Rendering: from Theory to Implementation (Morgan Kaufmann, 2010).
- M. Kurt and D. Edwards, “A survey of BRDF models for computer graphics,” Comput. Graphics43, 4 (2009).
- K. Schwenk, “A survey of shading models for real-time rendering,” http://www.karsten-schwenk.de/downloads/a_survey_of_shading_models.pdf (2011).
- O. Engelsen, B. Pinty, M. M. Verstraete, and J. V. Martonchik, “Parametric bidirectional reflectance factor models: evaluation, improvements and applications” (Space Applications Institute, Joint Research Centre, European Commission, ECSC-EC-EAEC, 1996).
- S. Liang, Quantitative Remote Sensing of Land Surfaces(Wiley, 2004).
- D. L. B. Jupp, “A compendium of kernel and other (semi-)empirical BRDF models” (CSIRO Office of Space Science Applications—Earth Observation Centre, 2000), http://www.eoc.csiro.au/tasks/brdf/k_summ.pdf .
- A. F. Sarofim and H. C. Hottel, “Radiation exchange among non-Lambert surfaces,” J. Heat Transfer 88C, 37–44 (1964).
- J. Zeng and L. Hanssen, “Development of an infrared optical scattering instrument from 1 μm to 5 μm,” Proc. SPIE 7453, 7453Q1 (2009). [CrossRef]
- L. M. Hanssen and A. V. Prokhorov, “Stochastic modeling of non-Lambertian surfaces for Monte Carlo computations in optical radiometry,” Proc. SPIE 7427, 742707 (2009). [CrossRef]
- L. M. Hanssen, S. N. Mekhontsev, J. Zeng, and A. V. Prokhorov, “Evaluation of blackbody cavity emissivity in the infrared using total integrated scatter measurements,” Int. J. Thermophys. 29, 352–369 (2008). [CrossRef]
- J. S. Liu, Monte Carlo Strategies in Scientific Computing (Springer, 2001).
- D. Geisler-Moroder and A. Dür, “A new ward BRDF model with bounded albedo,” Comput. Graph. Forum 29, 1391–1398 (2010). [CrossRef]
- K. E. Torrance and E. M. Sparrow, “Theory for off-specular reflection from roughened surfaces,” J. Opt. Soc. Am. 57, 1105–1114 (1967). [CrossRef]
- C. Schlick, “An inexpensive BRDF model for physically based rendering,” Comput. Graph. Forum 13, 233–246(1994). [CrossRef]
- P. van Dooren and L. de Ridder, “An adaptive algorithm for numerical integration over an n-dimensional cube,” J. Comp. Appl. Math. 2, 207–217 (1976). [CrossRef]
- M. Clerc, Particle Swarm Optimization (ISTE, 2006).
- M. Clerc and J. Kennedy, “The particle swarm—explosion, stability, and convergence in a multidimensional complex space,” IEEE Trans. Evol. Comput. 6, 58–73 (2002). [CrossRef]
- A. S. Glassner, “An overview of ray tracing,” in An Introduction to Ray TracingA. S. Glassner, ed. (Academic, 1993), pp. 1–32.
- E. M. Sparrow and R. D. Cess, Radiation Heat Transfer(Hemisphere, 1978).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

### Figures

Fig. 1. |
Fig. 2. |
Fig. 3. |

Fig. 4. |
Fig. 5. |
Fig. 6. |

Fig. 7. |
Fig. 8. |
Fig. 9. |

Fig. 10. |
Fig. 11. |
Fig. 12. |

« Previous Article | Next Article »

OSA is a member of CrossRef.