Theoretical aspects of Fourier Transform Spectrometry and common path triangular interferometers

Abstract

Recent investigations have induced relevant advancements of imaging interferometry, which is becoming a viable option for Earth remote sensing. Various research programs have chosen the Sagnac configuration for new imaging interferometers. Due to the growing diffusion of this technique, we have developed a self-contained theory for describing the signal produced by triangular FTSs and its optimal processing. We investigate the relevant disadvantages of multiplexing, and compare dispersive with FTS instruments. The paper addresses some methods for correcting the phase error, and the non-unitary transformation performed by a Sagnac interferometer. The effect of noise on spectral estimations is discussed.

Wide spectral range imaging interferometer

“…Regarding to Felgett's advantage for imaging interferometer, an analytical comparison of system performance (estimation of amplitude of the effective signal and Signal-to-Noise ratio) between the interferometric technique and the traditional dispersive spectrometers performed in a previous paper [5], brought to a new interpretation of it., showing that the informative tail of the acquired interferogram to be resolved requires a radiometric resolution much finer (depending on the illumination source's bandwidth) than that is needed for a dispersive spectrometer operating at the same high spectral resolution [5].…”

“…The Optical Path Difference (OPD) between the recombining beams linearly changes with the angle (slope) of the entering ray onto the instrument optical axis. It can be shown that the BS provides part of the phase-delay between the two interfering rays, the remaining part being originated outside the BS, and that the overall OPD linearly changes with varying the angle of the entering ray with respect to the instrumental optical axis [3][4][5]. Due to the absence of entrance slit the device acquires the image of the target superimposed to a fixed pattern of interference fringes.…”

“…The airborne prototype operating in the visible -near infrared range and developed in the framework of the MIOSAT, has been calibrated and tested during several laboratory measurements [5]. Fig.…”

Optical design constrains in triangular Sagnac imaging interferometers for earth observation

“…Regarding to Felgett's advantage for imaging interferometer, an analytical comparison of system performance (estimation of amplitude of the effective signal and Signal-to-Noise ratio) between the interferometric technique and the traditional dispersive spectrometers performed in a previous paper [4], brought to a new interpretation of it, concluding that in the past Fellgett's advantage has been not well understood. In fact the informative tail of the acquired interferogram to be resolved requires a radiometric resolution much finer (depending on the illumination source's bandwidth) than that is needed for a dispersive spectrometer operating at the same high spectral resolution [4].…”

Compressive sensing for hyperspectral earth observation from space

“…Fourier Transform Spectroscopy (FTS), experimenters attempted to gain corresponding SNR benefits in the domain of panchromatic or multiband imaging, just applying a multiplex configuration to traditional instruments [10]. However, recent investigations [11][12][13] have shown that any multiplex techniques give rise to poorer radiometric performance with respect to the direct signal measurement operated by longestablished optical configurations.…”