OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 50, Iss. 32 — Nov. 10, 2011
  • pp: 6073–6083

Dirac bra-ket in radiometry of quasi-homogeneous sources

Andrey V. Gitin  »View Author Affiliations


Applied Optics, Vol. 50, Issue 32, pp. 6073-6083 (2011)
http://dx.doi.org/10.1364/AO.50.006073


View Full Text Article

Enhanced HTML    Acrobat PDF (945 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The concept of “throughput” is used in traditional radiometry of Lambertian sources for computing and estimating the radiant flux passed through a pair of stops, in particular through the window and the pupil of an optical system. It is shown that in a more general case of quasi-homogeneous sources for energetic calculations of the perfect optical system, one must use instead of the throughput a functional that is similar to the famous “Dirac bra-ket.” This functional takes into account the radiation pattern of the source. As the Dirac bra-ket satisfies the axioms of the inner product, powerful mathematical tools of functional analysis for the energy calculation of the optical systems are used. The main equations and principles of radiometry (the principle of reversibility and Maxwell’s principle) are reformulated from the concept “throughput” into the concept “Dirac bra-ket.” For generalization of Maxwell’s principle to the class of quasi-homogeneous sources the concept of “effective stops” is introduced.

© 2011 Optical Society of America

OCIS Codes
(030.5620) Coherence and statistical optics : Radiative transfer
(030.5630) Coherence and statistical optics : Radiometry
(080.2740) Geometric optics : Geometric optical design
(260.2160) Physical optics : Energy transfer
(080.2175) Geometric optics : Etendue
(110.2945) Imaging systems : Illumination design

ToC Category:
Coherence and Statistical Optics

History
Original Manuscript: April 18, 2011
Revised Manuscript: June 14, 2011
Manuscript Accepted: June 17, 2011
Published: November 3, 2011

Citation
Andrey V. Gitin, "Dirac bra-ket in radiometry of quasi-homogeneous sources," Appl. Opt. 50, 6073-6083 (2011)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-50-32-6073


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. M. Planck, The Theory of Heat Radiation (Dover, 1959).
  2. E. W. Marchand and E. Wolf, “Radiometry with sources of any state of coherence,” J. Opt. Soc. Am. 64, 1219–1226 (1974). [CrossRef]
  3. G. Kirchhoff, “On the relation between the radiating and the absorbing powers of different bodies for light and heat,” Philos. Mag. Series 4 20, 1–21 (1860).
  4. J. H. Lambert, Photometria, Sive de Mensura et Gradibus Luminis, Colorum et Umbrae (Augsburg, 1760).
  5. Y. A. Cengel and A. J. Ghajar, Heat and Mass Transfer: Fundamentals and Applications (McGraw-Hill, 2011).
  6. D. S. Goodman, “General principles of geometrical optics,” in Handbook of Optics, Vol.  1, 2nd ed., M.Bass, ed. (McGraw-Hill, 1995).
  7. W. H. Steele, “Luminosity, throughput or etendue?” Appl. Opt. 14, 252 (1975). [CrossRef]
  8. A. C. Parr, R. U. Datla, and J. Gardner, Optical Radiometry (Elsevier, 2005).
  9. F. Grum and R. J. Becherer, “Radiometry,” in Optical Radiation Measurement (Academic, 1979), Vol.  1.
  10. W. L. Wolfe, Introduction to Radiometry (SPIE Optical Press, 1998). [CrossRef]
  11. W. L. Wolfe, “Radiometry,” in Applied Optics and Optical Engineering, vol.  8, R.R.Shannon, and J.C.Wyant, ed. (Academic, 1980).
  12. R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67, 717–754 (2004). [CrossRef]
  13. D. S. Volosov and M. V. Tsivkin, Theory and Design of Photo-Optical Systems (Moskow, 1960), in Russian.
  14. W. H. A. Fincham, and M. H. Freeman, Optics(Butterworths, 1980).
  15. A. Walther, “Radiometry and coherence,” J. Opt. Soc. Am. 58, 1256–1259 (1968). [CrossRef]
  16. A. V. Gitin, “Optical systems for measuring the Wigner function of a laser beam by the method of phase-spatial tomography,” Quantum Electron. 37, 85–91 (2007). [CrossRef]
  17. T. Jannson, S. Kupiec, A. Kostrzewski, K. Spariosu, D. Minyzer, M. Rud, I. Tengara, and A. Vasiliev, “Phase-space formalism and ray-tracing modeling of photometric quantities in photometric engineering,” Proc. SPIE 3140, 36–47 (1997). [CrossRef]
  18. I. N. Tarnakin, “Determination of illumination and light flux by an optical-system eikonal,” Opt. Spectrosc. 44, 463–465(1978).
  19. D. Marcuse and H. M. Presby, “Index profile measurements of fibers and their evaluation,” Proc. IEEE 68, 1198–1203(1980). [CrossRef]
  20. G. K. Grau, “Comments on index profile measurement of fibers and their evaluation,” Proc. IEEE 69, 753–754 (1981). [CrossRef]
  21. A. Arkangy, “Liouville’s theorem and the intensity of beam,” Am. J. Phys. 25, 519–525 (1957). [CrossRef]
  22. A. V. Gitin, “Effect of the radiation pattern of a quasihomogeneous source on the point-spread function of an isoplanar optical system,” J. Opt. Technol. 60, 372–374 (1993).
  23. A. V. Gitin and Ur. A. Fligontov, “Equation of radiation transfer through optical media in the Hamiltonian approximation,” Opt. Spectrosc. 66, 371–374 (1989).
  24. A. V. Gitin, “Radiometry. A complex approach,” J. Opt. Technol. 65, 132–140 (1998).
  25. A. V. Gitin, “Radiometry of optical systems with quasihomogeneous sources: a linear systems approach,” Optik 122, 1713–1718 (2011). [CrossRef]
  26. A. V. Gitin, “Energy calculation of optical systems by a methods of the harmonious analysis,” in Pulse Photometry: Collection of Papers (Mashinostroenie, 1986) (in Russian).
  27. A. V. Gitin, “Radiometry as a section of optical system theory,” Opt. Spectrosc. 63, 106–109 (1987).
  28. A. V. Gitin, “Method of an energy calculation of the viewfinder of a reflex camera having a focusing screen,” J. Opt. Technol. 56, 440–442 (1989).
  29. A. V. Gitin, “Laser beam pumping homogenizator calculation,” Photonics No. 2, 26–29 (2009) (in Russian), http://www.photonics.su/issue/2009/2/6.
  30. A. V. Gitin, “Laser pulses compressor,” Photonics No. 5, 8–13 (2009) (in Russian), http://www.photonics.su/issue/2009/5/2.
  31. P. Dirac, Principles of Quantum Mechanics (Clarendon, 1930).
  32. M. M. Gurevich, Photometry (Theory of the Methods and Apparatus) (Energoatomizdat, Leningrad).
  33. R. Kingslake, “Illumination in Optical Images,” in Applied Optics and Optical Engineering, Vol.  2, R.Kingslake, ed. (Academic, 1965).
  34. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
  35. W. J. Smith, Modern Optical Engineering (McGraw-Hill, 2000).
  36. W. Brouwer and A. Walther, “Geometrical optics,” in Advanced Optical Techniques (North-Holland, 1967).
  37. H. Gross, “Radiometry,” in Handbook of Optical Systems, Vol.  1, Fundamentals of Technical Optics (Wiley-VCH, 2005). [CrossRef]
  38. M. Reiss, “The Cos4 law of illumination,” J. Opt. Soc. Am. 35, 283–288 (1945). [CrossRef]
  39. M. Reiss, “Notes on the Cos4 law of illumination,” J. Opt. Soc. Am. 38, 980–986 (1948). [CrossRef] [PubMed]
  40. W. B. Wetherell, “The calculation of image quality,” in Applied Optics and Optical Engineering, vol.  8, R.R.Shannon and J.C.Wyant, ed. (Academic, 1980).
  41. J. C. Maxwell, “On the general laws of optical instruments,” in The Scientific Papers of James Clerk Maxwell, Vol.  1, W.D.Niven, ed. (The University Press, 1890).
  42. V. Guillemin and S. Sternberg, Geometric Asymptotics(American Mathematical Society, 1977).
  43. R. H. Akin and J. M. Hood, “Photometry,” in Display System Engineering, H.R.Luxenberg and R.L.Kuehn, ed. (McGraw-Hill, 1968).
  44. S. Liebes, Jr., “On the ray invariance of B/n2,” Am. J. Phys. 37, 932–934 (1969). [CrossRef]
  45. R. Clausius, “Ueber die Concentration vom Wa¨rme und Lichtstrahlen und die Grenzen ihrer Wirkung,” Annalen der Physik und Chemie 197, 1–44 (1864). [CrossRef]
  46. J. C. Maxwell, “On the theory of compound colours and the relation of the colours of the spectrum,” in The Scientific Papers of James Clerk Maxwell, Vol.  1, W.D.Niven, ed. (University Press, 1890).
  47. P. M. Tikhodeev, Light Measurements in Illumination Engineering (Gos. Energo. Izd., 1962) (in Russian).
  48. J. M. Lloyd, Thermal Imaging Systems (Plenum, 1975).
  49. A. V. Gitin, “The effective point source,” Opt. Spectrosc. 76 (1), 157–158 (1994).
  50. A. V. Gitin, “Technique for checking the correctness of computer programs intended for calculating the energy of optical systems,” J. Opt. Technol. 67, 844–845 (2000). [CrossRef]
  51. A. V. Gitin, “Radiometry of the light-scattering characteristics of liquid crystal elements,” J. Opt. Technol. 61, 131–135(1994).
  52. A. A. Gershun, “Telecentric method of measuring the intensity of light,” in Selected Works on Photometry and Illumination Engineering (Phys. Math. Gos. Izd., 1958) (in Russian).
  53. F. E. Nicodemua, “Radiance,” Am. J. Phys. 31, 368–377(1963). [CrossRef]

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.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited