While dispersive and Fourier transform spectrometers are the predominate instruments used for hyperspectral remote sensing applications, there are a variety of other instruments that have also been developed for this purpose, and novel imaging spectrometer concepts continue to be explored. Some of these devices are developed for niche applications where specific characteristics of interest are not supported by more-conventional instrument designs. One such characteristic is the ability to perform hyperspectral imaging in a staring format in a stationary observation scenario without resorting to interferometric concepts or mechanical scanning components. The variety of innovative spectrometer approaches reported in the literature is quite extensive and diverse. This chapter merely outlines the principles of operation underlying a few of these hyperspectral imaging approaches.
9.1 Fabry-Pérot Imaging Spectrometer
A Fabry-Pérot interferometer, also known as an etalon, consists of two optically flat, parallel mirrors that are precisely spaced to support constructive interference for a specified optical wavelength (Pedrotti and Pedrotti, 1987). Consider the example shown in Fig. 9.1, where the mirrors are characterized by an amplitude transmissivity t, amplitude reflectivity r, and phase shift upon reflection of φ. The mirrors are assumed to be spaced by a distance d, and the material in the optical cavity between the mirrors is assumed to exhibit a dielectric index n that can be wavelength dependent but ideally is not. According to the coherent dielectric thin film analysis described in Chapter 3, a steady-state condition of the form
can be written for an incident plane wave with an incident angle θ from the optical axis, where ε is the incident electric field amplitude on the second mirror, ε0 is the incident electric field amplitude on the interferometer, and σ is the wavenumber of the incident plane wave. Solving Eq. (9.1) for ε leads to