OPTICAL MATERIAL SCIENCE AND TECHNOLOGY

How the color temperature of the light source affects the color parameters ofinterference filters

M. Kh. Azamatov, I. S. Ga nutdinov, R. S. Sabirov, and R. G. Safin

NPO State Institute of Applied Optics, Kazan

A. V. Mikha lov

NPK S. I. Vavilov State Optical Institute, St. Petersburg�Submitted October 4, 2006�Opticheski� Zhurnal 74, 76–78 �May 2007�

This paper discusses the dependence of the color parameters of interference filters on the colortemperature of the light source. The values of the color difference of narrow-band and band-passinterference filters for various regions of the spectrum are discussed. © 2007 Optical Society ofAmerica.

The color parameters of optical coatings, in particularinterference filters, depend on their spectral characteristicsand the illumination conditions, i.e., the light source beingused. The dependence of the color of an interference filter onthe light source follows from the expressions that determinethe values of the color parameters—the chromaticitycoordinates1,2

x =X

X + Y + Z,

y =Y

X + Y + Z,

where

X = k�380

780

����x�������d� , �1�

Y = k�380

780

����y�������d� , �2�

Z = k�380

780

����z�������d� . �3�

In Eqs. �1�–�3�, X, Y, and Z are the tristimulus values,���� is the relative spectral distribution of the energy of thelight source, x���, y���, and z��� are the relative amounts ofthe primary colors of the CIE color system 1931 �the match-ing curves�, ���� is the spectral transmittance of the interfer-ence filter under investigation, and k is a normalizing factor.

The spectral distribution of the radiation of a light source���� is connected with its temperature and can be calculatedfrom Planck’s formula for an absolute blackbody �ABB�:

���T� = C1�−5�exp�C2/�T� − 1�−1,

where ���T� is the spectral density of the radiant flux, � isthe wavelength, T is the ABB temperature, and C1 and C2 areconstants.

362 J. Opt. Technol. 74 �5�, May 2007 1070-9762/2007/050

The energy distribution of the radiation of many actuallight sources corresponds to ABB radiation at a definite tem-perature called the color temperature. The color points of anABB on the CIE 1931 color diagram at various values of thecolor temperature form the color-temperature curve. Thus,source A �corresponding to a 100-W incandescent tungstenlamp�, adopted by the Commission Internationale del’Éclairage as a standard, has a color temperature of2855.6 K; i.e., its spectral radiation distribution correspondsto the radiation distribution of an ABB at that temperature.

The correlated color temperature is used to describethose light sources whose spectral radiation does not corre-spond to ABB radiation �contains transmission or absorptionpeaks on certain sections of the visible region�. The corre-lated color temperature corresponds to a chromaticity pointlying outside the color temperature curve. The standard CIEsource D65 can serve as an example of a radiation source thatthe correlated color temperature is used to describe. Its cor-related color temperature is 6504 K.

The position of the color-temperature curve on the CIE1931 chromaticity diagram, as well as the position of thechromaticity point of the color temperature of standard ra-diation source A and the correlated color temperature of stan-dard radiation source D65, are shown in Fig. 1.

In a study that the authors carried out, the difference ofthe color parameters of interference filters under conditionsof illumination by sources A and D65 was considered. Toquantitatively determine the difference of the color param-eters, we used the CIE-recommended L*a*b* color space�1976�, whose coordinates are

L* = 116�Y/Y0�1/3 − 16 when Y/Y0 � 0.008856,

L* = 903.3�Y/Y0� when Y/Y0 � 0.008856,

a* = 500��X/X0�1/3 − �Y/Y0�1/3� ,

b* = 200��Y/Y �1/3 − �Z/Z �1/3� .

0 0

362362-03$15.00 © 2007 Optical Society of America

¯

Tristimulus values X0, Y0, and Z0 relate to the lightsource, and tristimulus values X, Y, and Z relate to the testobject �in our case, the interference filter�.

The L* scale of L*a*b* space characterizes the luminos-ity, a* the red/green components of the color, and b* theblue/yellow components of the color.

The color difference of filters illuminated by sources Aand D65 in L*a*b* space �1976� is determined by

�Eab* = ���L*�2 + ��a*�2 + ��b*�2�1/2,

where �L*=LA* −LD

* , �a*=aA* −aD

* , and �b*=bA* −bD

* .A value of �Eab

* equal to unity is called the color-difference threshold. It is assumed that the average observerwill not discern a difference in the color of objects having avalue of �Eab

* �2.In the course of the study, two groups of interference

filters were considered: narrow-band, with a relative half-width of 1.0%, and band-pass, with a relative half-width of10%. There were fifteen filters in each group, differing fromeach other by the position of the central wavelength �0. Thecentral wavelength of the filters of each group constituted a

FIG. 1. CIE 1931 color diagram.

FIG. 2. Spectral transmission characteristics of the filters under investiga-tion. 1—narrow-band filter, 2—band-pass filter, �0 is the centralwavelength.

363 J. Opt. Technol. 74 �5�, May 2007

uniform series from 400 to 750 nm, with a step of 25 nm.The samples of spectral characteristics of the filters of eachgroup are shown in Fig. 2 �1—narrow-band filter, 2—band-pass filter, and �0 is the central wavelength�.

The results of a comparison of the color difference of thefilters under investigation are shown in Fig. 3 �1—color dif-ference of the narrow-band filters, and 2—color difference ofthe band-pass filters�.

It can be seen that the color difference of the filters underconditions of illumination by standard sources A and D65 isnonuniformly distributed over the spectrum and is moststrongly expressed in the short-wavelength region�400–500 nm�. The color difference on all the sections ofthe spectrum is greater in the band-pass filters. The correla-tion of the color difference of the filters is tracked with agraph of the relative quantities of the primary colors x���,y���, z��� of the CIE 1931 color system.

The possibility of achieving the smallest color differenceof the filters by the spectral shift of the central wavelengthwas also investigated. The results of such an investigationare shown in Fig. 4. It became clear that it is impossible tocompletely eliminate the color difference of the filters illu-minated by sources A and D65 in this way. The shift of thecentral wavelength of a filter operating with a type-A sourceby 5–15 nm toward longer wavelengths makes it possible toreduce the color difference of the filters on almost all thesections of the spectrum. An exception is the 450–475-nmregion, in which the central wavelength of a filter operatingwith source A needs to be shifted toward shorter wavelengths

FIG. 3. Color difference of the narrow-band �1� and band-pass �2� filtersunder investigation when standard radiation sources A and D65 are used.

FIG. 4. How the spectral shift of the central wavelength �0 of the narrow-band �1� and band-pass �2� filters under investigation affects their colordifference.

363Azamatov et al.

to achieve the smallest color differences of the band-passfilters. In narrow-band filters in the indicated region of thespectrum, the smallest color difference is achieved when thecentral wavelength of the filter using a type-A source shiftstoward longer wavelengths by 2 nm.

An analysis of the studies that have been carried outshows that the color parameters of interference coatings, in

364 J. Opt. Technol. 74 �5�, May 2007

particular narrow-band and band-pass filters, substantiallydepend on the color temperature of the radiation sources thatare used.

1D. B. Judd and G. Wyszecki, Color in Business, Science, and Industry�Wiley, New York, 1975; Mir, Moscow, 1978�.

2G. A. Agoston, Color Theory and Its Application in Art and Design�Springer-Verlag, Berlin, 1987; Mir, Moscow, 1982�.

364Azamatov et al.