Spectral Imaging: Methods, Design, and Applications - Biomedical Optical Imaging Technologies: Design and Applications - page 126

Fig. 4.7 Liquid crystal tunable filter (LCTF) that can be used for spectral imaging. a The light is
transmitted through a linear polarizer and a fixed phase retarder. By rotating the polarization with
the liquid crystal in a wavelength-dependent manner, only a single band is transmitted through
the second linear polarizer. By using few elements in a series, the transmitted bandwidth can be
narrowed as desired. b A 35-mm aperture LCTF with the enclosure open. Note the multiple stages
of the optics “stack” and the wiring harness for the LC cells. The control circuitry normally also
present in the enclosure is not shown here for reasons of clarity (Image courtesy of Cambridge
Research & Instrumentation, Inc. (CRi), now part of Caliper)

that, together with the two linear polarizers around it, transmits a polarized light
with a wavelength-dependent intensity that is equal to
I./ D I 0 cos 2 2 (4.2)

where I 0 is the amplitude that is transmitted through the device, is the phase
retardation of the ordinary and extraordinary beams caused by the change in index
of refraction of each of these waves, and is the wavelength of light [ 22 , 26 ]. Such
a transmission is shown in Fig. 4.8 (first stage). When few stages are used, so that
each stage increases the retardation by a factor of 2, each stage transmits the
spectrum that entered to it multiplied by a similar cosine function with a doubled
frequency (Fig. 4.8 ). Therefore, after few stages, the output spectrum is a narrow
band given by FWHM D =2 N ,whereN is the number of stages in the system.
The FWHM can be in the range of 5-20 nm and even less. By applying a different
voltage on the liquid crystals, the value of changes (linearly to the first order) and
the transmitted wavelength is shifted. It therefore acts as a tunable filter. The out-
of-band transmission can be very low, practically less than 0.01 %. The system also
has a relatively large angle of acceptance that does not affect the spectral properties
of the transmitted light.
The damage threshold for reasonably long-term exposure of the filters to visible
(VIS) and near-infrared (NIR) energy is 500 mW=cm 2 . LCTF filters absorb light that
is out of the required spectral range by using hot-mirror elements to reflect unwanted