The concept of the Fabry-Perot interferometer is
illustrated in Figure 1. Two highly reflective surfaces on planar
optical plates are separated by a gap of distance, d. Collimated light
enters the Fabry-Perot and reflects multiple times within the
interferometer cavity. For the on-axis case, light of wavelength equal
to d/2 constructively interferes and, therefore, transmits the
Fabry-Perot; all other light destructively interferes. The Fabry-Perot
can be used in concert with a focal plane array as a hyperspectral
imager.
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| Figure 1 - Tunable Filter (Fabry-Perot) Spectroscopy |
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The transmitted intensity signal is given by:
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where R is the reflection coefficient and the phase term, δ, is given by:
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n is the refractive index of the medium between the plates, d is the
plate separation, θ is the angle of incidence of the incoming light, λ
is the wavelength of the light, and Φ(λ) is the combined wavelength
dependent phase shift upon reflection off the dielectric coatings for
both mirrors. By noting that maximum transmission occurs when d =
2m*pi, where m is the order number, equation 2 can be solved to obtain
the maximum transmission wavelength for a given plate separation and
order number.
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| System performance parameters Free Spectral Range, Spectral
Resolution, and Finesse can be derived from the following
equations:
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| Equations 4 and 5 show the dependence of the Free Spectral Range and
spectral resolution on the phase dispersion, dΦ(λ)/dλ which is
controlled through the careful design of the dielectric reflective
coating on the etalons.
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