We derive a simple equation to predict the center-wavelength shift of a Fabry-Perot type narrow-bandpass filter by using the conventional characteristic matrix method and the elastic strain model as the temperature varies. We determine the thermal expansion coefficient of substrate from the zero-shift condition of the center wavelength of the filter. The calculated shifts are in a good agreement with the experimental ones, in which the narrow-bandpass filters are prepared by plasma ion-assisted deposition on four substrates with different thermal expansion coefficients.
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