User:Mike foster IS instruments/sandbox

Static Fourier Transform spectrometers
The term static Fourier Transform spectrometer (SFTS) refers to a class of spectrometers that combines the properties of a dispersive spectrometer, such as a Czerny Turner instrument, and a Fourier Transform Spectrometer. There are a number of designs of these types of systems, but typically they are arranged in an interferometer setup with dispersive elements replacing the mirrors in a Michelson or Sagnac Interferometer. The dispersive elements are arranged to form a interference fringe pattern in space which is then imaged. The fringe pattern is then Fourier transformed to extract the spectral information. This configuration results in the etendue of the SFTS matching that of a Michelson Interferometer, increasing the light gathering capacity 200 fold over a conventional dispersive system such as a Czerny Turner spectrometer. Unlike a Michelson instrument there are no moving parts as the fringe pattern is formed in space and not time. This makes these systems ideal for monitoring diffuse targets such as galaxies or bulk measurement of samples as required in quality control measurements. It should be noted that this throughput advantage does not provide any increase in the instruments internal transmission. The resolution and spectral range is typically determined by the number of lines used in the system to produce the fringe pattern. This makes the design of the system flexible and thus can be targeted either at high or low resolution applications. The use of the devices has become prominent in recent years due the increased availability of high quality imaging detectors, such as CCD and CMOS systems.

The Spatial Heterodyne spectrometer
An established example of these devices is the spatial heterodyne spectrometer (SHS) originally developed by Harlander 1989. The design of this system is presented in Fig 1. The figure shows the classic Michelson configuration but the mirrors are replaced by reflective diffraction gratings. In this configuration the system forms fizeau fringes, the spatial frequency of which are derived from the diffraction grating properties

k [ sin (Ө) + sin (Ө – Φ)] = m/d

Where k is the wavenumber of light, m is the order of diffraction, d is the spacing between the lines on the diffraction grating, Ө is the littrow angle and Φ is the diffraction angle. The intensity of the fringe pattern is given by

I(x)=∫B(k)1+cos(2π[4(k-k0 )x tanθ]) dk

Where k0 is the littrow wavenumber, x is the detector element. Fig 2 shows both a monochromatic source and a broad band spectral source. For the broad band case the spectral pattern forms a centre burst pattern. The instruments resolving power is given by                    Rp=2NL Gw

Where NL is the number of lines per mm on the gratings and Gw is the width of the grating imaged. It follow that the Field of view of the instrument is Ω = 2π/Rp

Initially these systems were developed for high resolution UV applications particularly in astronomy and similar fields. In recent times these systems have been used in Raman spectrometers where the large throughput is of particular interest when the bulk measurement of a sample is required.

Strengths and Weaknesses
The primary advantage of this class of spectrometer over traditional dispersive system is the etendue (A Ω product) or throughput of the system that can be achieved for a given resolution. This allows the system to collect a greater amount of light from a given target (assuming the target itself has an etendue equal of greater than that of the spectrometer) by a factor of 100 - 200. Therefore unlike a Czerny Turner system the devices do not require a slit and can be directly coupled to a multimode fibre. In these cases the system can achieve a significant improvement in the signal to noise that can be achieved. Unlike a FT spectrometer these instrument have no moving parts making them robust and relatively simple to align. This has led to the system being adopted for applications in Earth observations (SHIMMER), and investigated for applications on Mars. Operating in Fourier space the performance of these device can be improved by data processing techniques. This includes factors such as zero filling and phase correction. One factor when determining the expected performance of this class of instruments is the multiplex disadvantage. As the spectrum is extracted from an interference fringe pattern the total noise is observed at all the wavelengths observed. This is also true for the detector dark noise and any readout noise. The signal to noise for a given wavelength is therefore

SNR = Sλ/(sqrt( S + N D + Nr2)

Where sλ is the number of signal photons from the wavelength of interest, S is the the total photons from all the light entering the spectrometer ND is the total detector dark noise and Nr is the total detector read noise. Therefore when studying broad band (relative to the instruments resolution) spectral signatures, the improvement in the SNR achieved by the greater throughput can be eliminated by the total multiplex noise.