Abstract

A general method is presented for accurately finding the spectral tuning formula for a Lyot birefringent filter based on a limited number of measured tune solutions, that is, tuning element angles in the filter that provide maximum monochromatic transmission at wavelengths spanning the useful operating range of the filter. The ambiguous determination of retardation from the tuning element angle in a measured tune solution is resolved for each tuning element by extrapolation in the retardation of the next spectrally coarser tuning element assuming that the effective ratio of tuning element thicknesses is slowly varying in wavelength. Applying this to the Sacramento Peak Observatory Universal Birefringent Filter we find: (1) The retardations for adjacent tuning elements made of the same birefringent material are fit by a linear function to within a fraction of the measurement accuracy of the tune solutions over the entire 4000–7000-Å spectral range, a precision of ~2 parts in 10⁶. (2) The retardations for a tuning element with quartz compared with a tuning element with calcite birefringent material show excursion from a straight line of ~1 part in 75 and are fit by a quadratic to a fraction of the measurement accuracy of the coarser tuning elements, ~1 part in 5000. (3) The retardation of calcite as a function of inverse wavelength shows excursion from a straight line of ~1 part in 40 and is fit without systematic error by a restricted quintic. Using this parametrization to tune to a selected wavelength gives a tuning element angular positioning accuracy of better than 1° over the entire visible spectrum and an absolute spectral positioning of better than 0.010 Å. A spectral stability much better than this is reproduced consistently during a day’s run and from day to day after correction for a uniform temperature variation within the filter determined by monitoring the wavelength of a spectral reference feature, most often the He–Ne laser line.

© 1984 Optical Society of America

A Tunable Birefringent Filter

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