This chapter will address the optical principles that underpin any imaging spectrometer and then delve into the details of the dominant optical designs. The complete imaging spectrometer typically includes a scan mechanism, such as a rotating mirror, a telescope fore optic to image the scene at the input of a spectrometer, the spectrometer, which can accomplish the separation of the radiance into the different wavelength bins either through dispersive or interferometric means, and the focal plane array where the signal is converted to digital numbers. The optical flow from the scene to the resulting digital signals is depicted in Figure 4.1. The details of the optical system are presented and the description focuses on the concepts required to enable the reader to understand, at an introductory level, how these complex systems work.

This chapter will also introduce the unifying concept of the measurement equation. All imaging spectrometers share spatial, spectral, and radiometric properties, which can be mathematically described in a general way. Important concepts that are common to all of the optical forms presented are captured succinctly in a simple and elegant way. It is the measurement equation that provides the explanatory framework upon which the optical details will be built. An understanding of Gaussian or geometrical optics is required, and an overview that includes the basics of image formation and the concepts of pupils and stops is presented as an appendix. The appendix also includes an introduction to optical aberrations. Some of the equations that are developed in the appendix are referenced in this chapter.

Optically, imaging spectrometers are properly thought of as integrated systems rather than being comprised of the individual subsystems of the fore optics, the spectrometer, and the detector or detector array. The optical design engineer considers the system in its entirety during the design phase to ensure that the spatial, spectral, radiometric, and signal-to-noise ratio goals are accomplished and that the imaging spectrometer is manufacturable. This is a rather obvious observation, but merits emphasis. An imaging spectrometer is a system and not the sum of its parts, even though they will be addressed here through a subsystem analysis.