Abstract

The spectral response matching of photodetectors under diffused illumination is required in almost all applications, especially in vision research. Compared with the others, the full-filter method has been used widely due to its precision and simplicity. Traditionally, the design is made by an iterative method. With the specular transmittance and reflectance, which are functions of thickness, of the filter under collimated illumination as the input, one can obtain an optimal value of filter thickness so that the experimental data can be matched. This procedure may not converge because of the diffused illumination condition. We propose a more efficient method by introducing the equivalent distance to substitute for the random distance that light traveled in the filters. From this assumption, the equivalent coefficient, which is the ratio of the equivalent and actual distance, is found to be where n is the index of refraction of the filter. The equivalent incident angle of a collimating light beam can also be expressed by c: Therefore, the transmittance and reflectance under diffused illumination can easily be calculated. We measured these parameters for various optical glass. The data conform to the theory very well. The spectral matching algorithm of the detector takes two steps. First, we calculate the initial thickness of the filters according to the transmittance and reflectance, neglecting the multiple reflection between the surfaces of the filters. The theoretical results are then compared with measured data to obtain the coefficient of multiple reflection. The final parameters are to be calculated when this coefficient is taken into consideration.

© 1988 Optical Society of America