Liquid Crystal Tunable Filters
Liquid crystal tunable filters (LCTFs) use electrically controlled liquid crystal elements to select a specific visible wavelength of light for transmission through the filter at the exclusion of all others. This type of filter is ideal for use with electronic imaging devices, such as charge-coupled devices (CCDs), because it offers excellent imaging quality with a simple linear optical pathway.
A typical wavelength-selective liquid crystal tunable filter is constructed from a stacked of fixed filters consisting of interwoven birefringent crystal/liquid-crystal combinations and linear polarizers. The spectral region passed by LCTFs is dependent upon the choice of polarizers, optical coatings, and the liquid crystal characteristics (nematic, cholesteric, smectic, etc.). In general, visible-wavelength devices of this type usually perform quite well in the 400 to 700 nanometer region.
The LCTF utilized in this interactive tutorial is a simplified example of a Lyot filter, in which four polarizers are separated by three layers of liquid crystals sandwiched between birefringent crystals. Retardation in birefringent crystals is dependent upon crystal thickness (d) and the refractive index difference between the ordinary (n(o)) and extraordinary (n(e)) light rays produced at the wavelength of incident illumination:
where R is the retardation expressed in nanometers. The propagation speed of the extraordinary and ordinary ray differ, and they emerge from the anisotropic stack with a phase delay that is dependent upon the wavelength of light (λ) entering the stack:
Transmission of light through the crystal (T) is dependent upon the value of Γ, and is given by the following equation:
Crystals in a typical Lyot filter are often selected for a binary sequence of retardation so that transmission is maximum at the wavelength determined by the thickest crystal retarder. Other stages in the filter serve to block the transmission of unwanted wavelengths. In the tutorial, retardation values were chosen in binary steps of R, 2R, and 4R, with each stage producing a series of transmission bands that can be observed by toggling through the Stage radio buttons. The absolute retardation value and wavelength(s) passed through the LCTF can be adjusted with the Retardation slider.
Individual transmission bands from each stage in the filter are illustrated in the upper graph on the left-hand side of the tutorial window. As the Stages are toggled into action utilizing the radio buttons, the additional wavelengths are presented in this graph. The combined transmission spectrum from all stages is presented in the lower graph where normalized transmission through the filter is plotted as a function of wavelength. In practice, a Lyot LCTF may have as many as 11 polarizers and 10 liquid crystalline layers and can even be equipped with an internal microprocessor to tune all of the stages.