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Applied Optics

Applied Optics


  • Vol. 40, Iss. 3 — Jan. 20, 2001
  • pp: 413–416

Fractional bandwidth normalization for optical spectra with application to the solar blackbody spectrum

Garret Moddel  »View Author Affiliations

Applied Optics, Vol. 40, Issue 3, pp. 413-416 (2001)

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Optical spectra are typically normalized per unit wavelength or per unit photon energy, yielding two different expressions or curves. It is advantageous instead to normalize a spectrum to a constant fractional bandwidth, providing a unique expression independent of whether the bandwidth is in dimensions of wavelength or of photon energy. For the Sun, whereas a per-unit-wavelength spectrum peaks in the green and a per-unit-photon-energy spectrum peaks in the IR, when the proposed normalization is used, the output peaks in the red. This approach applies to any spectral source and provides curves of constant spectral resolving power, as produced by many spectrometers.

© 2001 Optical Society of America

OCIS Codes
(000.6850) General : Thermodynamics
(120.5240) Instrumentation, measurement, and metrology : Photometry
(120.6200) Instrumentation, measurement, and metrology : Spectrometers and spectroscopic instrumentation
(300.2140) Spectroscopy : Emission
(300.6170) Spectroscopy : Spectra
(330.6180) Vision, color, and visual optics : Spectral discrimination
(350.5610) Other areas of optics : Radiation

Original Manuscript: March 20, 2000
Revised Manuscript: October 4, 2000
Published: January 20, 2001

Garret Moddel, "Fractional bandwidth normalization for optical spectra with application to the solar blackbody spectrum," Appl. Opt. 40, 413-416 (2001)

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  1. L. D. Landau, E. M. Lifshitz, Statistical Physics, 3rd ed. (Butterworth-Heinemann, Oxford, 1980), pp. 184–187.
  2. This is the irradiance at the surface of the Sun. To obtain the irradiance intercepting the Earth, this expression must be divided by the square of the ratio of the Earth–Sun distance to the radius of the Sun.
  3. B. H. Soffer, D. K. Lynch, “Some paradoxes, errors, and resolutions concerning the spectral optimization of human vision,” Am. J. Phys. 67, 946–953 (1999). [CrossRef]
  4. Although the spectrum is centered in the red, we do not perceive the Sun as being red. This can be explained by the fact that the spectrum covers our visible range and as a result of our physiological ability to redefine perceived colors with reference to the illumination source. See R. Mausfeld, “Color perception: from Grassmann codes to a dual code for object and illumination colors,” in Color Vision Perspectives from Different DisciplinesW. G. K. Backhaus, R. Kliegl, J. S. Werner, eds. (de Gruyter, Berlin, 1998), Chap. 12.
  5. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), p. 333.
  6. Ref. 5, pp. 406–407.

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