Spatial heterodyne spectrometer: modeling and interferogram processing for calibrated spectral radiance measurements

Abstract

This work presents a radiometric model of a spatial heterodyne spectrometer (SHS) and a corresponding interferogram-processing algorithm for the calculation of calibrated spectral radiance measurements. The SHS relies on Fourier Transform Spectroscopy (FTS) principles, and shares design similarities with the Michelson Interferometer. The advantages of the SHS design, including the lack of moving parts, high throughput, and instantaneous spectral measurements, make it suitable as a field-deployable instrument. Operating in the long-wave infrared (LWIR), the imaging SHS design example included provides the capability of performing chemical detection based on reflectance and emissivity properties of surfaces of organic compounds. This LWIR SHS model outputs realistic, interferometric data and serves as a tool to find optimal SHS design parameters for desired performance requirements and system application. It also assists in the data analysis and system characterization. The interferogram-processing algorithm performs flat-fielding and phase corrections as well as apodization before recovering the measured spectral radiance from the recorded interferogram via the Inverse Fourier Transform (IFT). The model and processing algorithm demonstrate results comparable to those in the literature with a noise-equivalent change in temperature of 0.35K. Additional experiments show the algorithm's real-time processing capability, indicating the LWIR SHS system presented is feasible.

The phase uncertainty from the fringe contrast of interferogram in Doppler asymmetric spatial heterodyne spectroscopy

“…DASH is very similar to the Michelson Interferometer, using two diffraction gratings in place of the mirrors at the end of interferometer arms [35]. Moreover, to improve the wind measurement sensitivity, DASH adds an additional path difference in one arm, making the interferometer asymmetric as shown in figure 1.…”

Analysis and Classification of Liquid Samples Using Spatial Heterodyne Raman Spectroscopy

“…17,18 Methods for processing the SHS interferograms were discussed in a number of papers and included the flat-field correction, 19 phase error, 20 data reduction routines, 21 and interferogram distortion correction. 22 Spatial heterodyne spectroscopy figures of merit, namely the resolution, spectral range, and sensitivity have been discussed in Cooke et al 23 Lenzner and Diels, 24 and Perkins et al 25 Cooke et al 23 described the design of an infrared SHS with the resolving power of about 1000 and spectral coverage 8.5-9.5 µm. Lenzner and Diels 24 demonstrated the very high-resolving power of 22400 using the dense 1200 mm -1 gratings, however, at the expense of a spectral range that shrunk to about 1 nm.…”

“…They also assessed that the resolving power of SHS instruments is commonly overestimated as the tilt of the wave packet fronts and the low coherence of radiation are not taken into account. Perkins et al 25 presented an acute analysis of an overall performance of SHS based on modeling SHS systems. In general, SHS systems used for spectrochemical analyses, e.g., Raman and LIBS, exhibit resolving powers ~1000-6000 and spectral bandwidth between 150 nm and 50 nm depending on the grating density, typically 150 or 300 mm -1 as in [9][10][11][12]16,18,26 .…”

“…Spatial heterodyne spectroscopy figures of merit, namely, the resolution, spectral range, and sensitivity have been discussed in Cooke et al., 23 Lenzner and Diels, 24 and Perkins et al. 25 Cooke et al. 23 described the design of an infrared SHS with the resolving power of about 1000 and spectral coverage 8.5–9.5 µm.…”

“…Perkins et al. 25 presented an acute analysis of an overall performance of SHS based on modeling SHS systems. In general, SHS systems used for spectrochemical analyses, e.g., Raman and LIBS, exhibit resolving powers ∼1000–6000 and spectral bandwidth between 150 nm and 50 nm depending on the grating density, typically 150 or 300 mm −1 as in literature.…”