Astronomical spectroscopy using an aliased step-and-integrate Fourier transform spectrometer

Abstract

Fourier Transform Spectrometers (FTS) are commonly operated in a rapid-scan (RS) mode, in which an interferogram of an astronomical source is obtained as quickly as possible, followed by one of a nearby background position. In an alternate operating mode, known as step-and-integrate (SI), the optical path difference in the interferometer is incremented in discrete steps, and the signal is integrated only when the interferometer mirrors are stationary. This mode requires some other means of modulating the signal, such as chopping the secondary mirror so that the detector alternately views source and background. The noise bandwidth in the SI mode (typically ~1 Hz) is much smaller than in the RS mode (~1 KHz), which in principle can lead to an increase in overall sensitivity. The main problem with the SI mode is that it takes much longer (~30x) to acquire an interferogram. At submillimetre wavelengths, through the use of narrowband optical filters, which are matched to regions of low atmospheric opacity, it is possible to sample the interferogram at less than the interval determined from the DC band limited Nyquist frequency (a condition known as aliasing) and still unambiguously recover the spectral information. We describe in detail the aliased, SI mode of operation of an FTS at the JCMT and present first results of astronomical spectra obtained using this mode. The resulting spectra are compared and contrasted to data obtained in the RS mode.

Signal-to-noise ratio trade-offs associated with coarsely sampled Fourier transform spectroscopy

“…We consider the signal-to-noise (SNR) trade-offs associated with coarse sampling [4][5][6][7][8] for Fourier transform spectroscopy (FTS) using the step-and-integrate method of data collection [7,8]. For the case of an ideal Michelsoninterferometer-based instrument, the response, h͑͒, of a detector at the output plane of the interferometer varies with the time delay, , between the arms of the interferometer as [9]…”

“…Coarse sampling is a well-known technique [4][5][6][7][8] and has several advantages over Nyquist sampling related to the fact that coarse sampling can obtain the same spectral resolution as Nyquist sampling, but with fewer measurements. In imaging FTS, where raw data sets can be very large and even problematic, coarse sampling by a factor of 2-4 can provide some data reduction.…”

“…Coarse sampling requires fewer mechanical stepping motions during data collection, which can be easier on hardware. If SNR is not an issue, coarse sampling can be used to reduce the total data collection time [7,8]. However, SNR is often one of the most important issues.…”

Increased Efficiency through Undersampling in Fourier Transform Spectroscopy

“…The main problem with the SI mode is that it takes much longer to acquire an interferogram. At submillimetre wavelengths, through the use of narrowband optical filters which are matched to regions of low atmospheric opacity, we have shown that it is possible to sample the interferogram at less than the interval determined from the DC band limited Nyquist frequency (a condition known as undersampling) and still unambiguously recover the spectral information [1].…”

An update on the imaging Fourier transform spectrometer for SCUBA-2

“…We are also investigating the potential use of a step-and-integrate operating mode 8 . In this mode, the optical path difference in the interferometer is incremented in discrete steps and data is read out only when the mirrors are stationary, thereby ensuring that the interferogram is sampled on a uniform position grid.…”