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2. DEVELOPMENT OF THE FABRY-PEROT DOPPLER IMAGING SYSTEM 19
Now the transmittance of light Tr is given by
where
Tr, = TT*(1R)2 (2.7)
1 — 2R cos 6 -I- R2
R r2 12 (2.8)
627r— 2x =—A 2nd cos 0---2x. (2.9)
In the above equations, R is the reflectance at the reflective surfaces on the etalon plates, and
6 denotes the total phase difference which includes both the phase difference cD corresponding
to the optical path difference and the phase change x due to reflection on each surface.
Equation 2.7 is called Airy function' . Equation 2.7 shows that the transmittance TF has
a maximum at 6 = 27-n7r (in = 0, 1,2, • - -), i.e.,
7ri-1- —X) = 2nd cos 0 (m = 0, 1, 2, • -). (2.10)
7r
Figure 2.2 shows transmittance curves of the etalon as a function of the phase 6 for various
values of the reflectance R as parameters. When the value of R is greater than 0.9, the
transmittance of the etalon has a very sharp peak around 6 = 2m7r, and is nearly zero for
other values of 6.
2.2 Principle of the Fabry-Perot Doppler imaging
The Fabry-Perot Doppler Imaging System (FPDIS) was first developed by our optical
group of Tohoku University in 1989. The FPDIS is a two-dimensional Fabry-Perot inter-
ferometer system with an extremely high spectroscopic resolution and a high temporal and
spatial resolution. Compared with conventional Fabry-Perot interferometers, the FPDIS
developed in 1989 has the following characteristics;
1) The FPDIS employs an all-sky fish-eye objective lens to match a field of view of the
interference fringes on the focal plane to a wide field of view (FOV = 165°) in the sky.
2) The FPDIS employs a very sensitive two-dimensional photon detector which consists of
a photon counting imager and a charge coupled device (CCD) camera.