Advanced Spectroscopy Technique for Biomedicine - Biomedical Optical Imaging Technologies: Design and Applications - page 12

Fig. 1.6 Diagram of a single
stage of an LCTF

Liquid
crystal

Fixed
waveplate

V

V Linear

polarizer

Linear
polarizer

polarized light is divided into two beams, ordinary and extraordinary. The optical
path difference between these two beams is given by [ 19 ]

./ D 2 nd ; (1.3)

where n is the birefringence of the material and d is the thickness of the liquid
crystal. The transmittance of the stage is given by
T./ D cos 2 ./
2

:

(1.4)

The total transmittance of a multiple-stage filter is the product of each filter in the
stack. For Lyot filters, the thickness and the subsequent optical path difference
increases in the powers of two for each successive stage. The spectral range of
a LCTF is determined by the thinnest element, and the band pass is determined
by the thickest element. The tunability of the LCTF is implemented by applying
an electrical field to the liquid crystal retarder, which changes the refractive index
under different electrical fields. For nematic liquid retarders, the refractive index is
n D 1:5, and the difference in refractive index can be 0.05-0.5. The response time is
approximately 50-75 ms. Liquid crystal tunable filters can cover the visible to NIR
range from 420 to 1,800 nm. The bandwidth of LCTF is wavelength dependent,
e.g., 10 nm at 550 nm to 16 nm at 700 nm. The main advantages of LCTFs are
that they are compact and have high acceptance angle, large optical aperture, fast
switching time, and relatively narrow bandwidth.

1.2.4.2 Acousto-Optical Tunable Filter

AOTF is based on the diffraction of a tunable grating which is generated by applying
an acoustic wave to an acoustic optical crystal, as shown in Fig. 1.7 a. The period of
the acoustic grating can be tuned by changing the frequency of the radio-frequency