Crossed Interferometric Dispersive Spectroscopy

Abstract

A novel design is described which combines dispersive and interferometric spectrometric instrumentation for ultraviolet visible spectroscopy, offering significant advantages in comparison to conventional spectroscopic configurations. The optical system incorporates the triangular common-path interferometer with an additional cross-dispersive element, allowing spectra to be obtained in a format compatible with rectangular CTD array detectors. The use of a cross-dispersive optical element reduces the distributive multiplex effects of interferometry in a rugged, compact, optically simple system.

Suppressing the Multiplex Disadvantage in Photon-Noise Limited Interferometry Using Cross-Dispersed Spatial Heterodyne Spectrometry

“…Typically, this is achieved by utilizing bandpass filters that reject spectral light beyond the Nyquist wavelength or that select for desired spectral features. 9,10 This design choice, although effective in limiting multiplicative photon noise, undermines the throughput advantage and wavelength coverage of SHS. Other attempts have been made to limit the spectral density within an SHS interferogram, notably the echelle grating SHS variant that utilizes various high diffraction grating orders to spatially offset narrow bandpasses onto an CCD.…”

Retrieval of Spectra from Interferograms with a Small Optical Path Difference Using a Genetic Algorithm

“…Parallel recording of sections of the interferogram on a two-dimensional photodetector and "splicing" them into one interferogram with a large effective length requires, in addition to complicated post-processing, an increase in the dimensions of the optical part of the instrument while maintaining light beam homogeneity [8]. Recording the interferograms from different spectral intervals on different regions of the same two-dimensional array decreases the infl uence of noise at individual frequencies on the rest of the spectrum, but the spectral resolution for each of the intervals remains poor since the interferogram is short [9].Alternatives to the Fourier transform method for spectral estimation in some cases (more often for quasi-line spectra) let us improve the spectral resolution without increasing the maximum path difference. For example, knowing the mathematical model for the signal a priori in autoregression methods [10,11] and eigenvector methods [12] lets us estimate the characteristics of the interferogram beyond the recorded segment.…”

“…Parallel recording of sections of the interferogram on a two-dimensional photodetector and "splicing" them into one interferogram with a large effective length requires, in addition to complicated post-processing, an increase in the dimensions of the optical part of the instrument while maintaining light beam homogeneity [8]. Recording the interferograms from different spectral intervals on different regions of the same two-dimensional array decreases the infl uence of noise at individual frequencies on the rest of the spectrum, but the spectral resolution for each of the intervals remains poor since the interferogram is short [9].…”

“…First of all, according to the generalized Kotelnikov theorem, the number of readings required for the retrieval decreases, which is important when using pixel photodetectors. Secondly, the infl uence of noise on the individual spectral segments is reduced over the entire interferogram [9]. Due to the smaller size of the instrumental function matrix, the error in spectral estimation by solution of an integral equation, reduced to an ill-posed system of equations [16], decreases and consequently the spectral resolution increases [14].…”

“…A narrow range can be identifi ed, for example, by using a dispersive element crossed with a static interferometer and detection on a two-dimensional array detector as in [9].…”