3.4. Birefringent Filters
The underlying principle of the birefringent filter is that light originating in a single polarization state can be made to interfere with itself. An optically anisotropic, birefringent medium can be used to produce a relative delay between ordinary and extraordinary rays aligned along the fast and slow axes of the crystal. (A birefringent medium has two different refractive indices, depending on the plane of light propagation through the medium.) Title and collaborators have discussed at length the relative merits of different types of birefringent filters. The filters are characterised by a series of perfect polarizers (Lyot filter), partial polarizers, or only an entrance and an exit polarizer (Solc filter). The highly anisotropic off-axis behaviour of uniaxial crystals give birefringent filters a major advantage. Their solid acceptance angle is one to two orders of magnitude larger than is possible with interference filters although this is partly offset by half the light being lost at the entrance polarizer.
Lyot filter: This is conceptually the easiest to understand and forms the basis for many variants. The entrance polarizer is oriented 45° to the fast and slow axes so that the linearly polarized, ordinary and extraordinary rays have equal intensity. The time delay through a crystal of thickness d of one ray with respect to the other is simply d µ / c where µ is the difference in refractive index between the fast and slow axes. The combined beam emerging from the exit polarizer shows intensity variations described by I2 cos(2 d µ / ) where I is the wave amplitude. As originally illustrated by Lyot (see Fig. 3), we can isolate an arbitrarily narrow spectral band-pass by placing a number of birefringent crystals in sequence where each element is half the thickness of the preceding crystal. This also requires the use of a polarizer between each crystal so that the exit polarizer for any element serves as the entrance polarizer for the next. The resolution of the instrument is dictated by the thickness of the thinnest element. With quarter-wave plates placed between each of the retarder elements, can be tuned over a wide spectral range by rotating the crystal elements. But to retain the transmissions in phase requires that each crystal element be rotated about the optical axis by half the angle of the preceding thicker crystal.
Figure 3. The transmission profile of a simple Lyot cascade with (top to bottom) 1, 2, 3, 4 and 5 stages. The thinnest element has retardance R and the following elements have thicknesses which are multiples of this element. The polaroids P are aligned with each other and oriented at 45° to the retarders.
Woodgate (NASA Goddard Space Flight Center) has made a Lyot filter utilising eight quartz retarders with a 10 cm entrance window. The retarders, each of which are sandwiched with half-wave and quarter-wave plates in addition to the polarizers, are rotated independently with stepping motors under computer control. They achieve a bandpass of 0.4-0.8 nm tuneable over half the optical wavelength range (350-700 nm).
Solc (1) filter: These highly non-intuitive filters use only two polarizers and a chain of identical retarders with varying position angles (Evans 1958). There are folded (zigzag) and fanned designs with the former having the better performance. Title has made a tunable Solc filter with 7 cm clear aperture. It has the extraordinary capability of tuning the spectral profile: an n-element Solc filter can have a profile that is determined by n Fourier coefficients. The same can be achieved with polarizing filters by proper choice of crystal lengths.
Liquid crystal filter (LCTF): These are rapid switching, electronically tuned devices which employ either ferroelectric or nematic liquid crystals (LC). The more commonly used nematic LCTF (Morris, Hoyt & Treado 1994) comprises a series of liquid crystal elements whose thicknesses are cascaded in the same way as the Lyot filter. However, the tuning is achieved by electronically rotating the crystal axes of the LC waveplate. When no voltage is applied, the retardance is at a maximum; at large applied voltages, the retardance reaches a minimum. The retardance can be tuned continuously to allow the wavelength to be tuned.
Liquid crystal filters are now commercially available from Cambridge Research & Instrumentation, Inc. The biggest device we have seen has a clear aperture of 4 cm, requires about 5 V to scan a single order of interference, and appears to have good image quality. The tunable band for a single stage device is about ~ 5 but can be tuned over the optical window. The peak transmissions are 30% or less.
1 The proper Czech pronunciation is
1 The proper Czech pronunciation is `Sholtz' Back.