Double Fourier Module

This module is the analytical module that performs the Double Fourier Modulation as the application of Fourier Transform Spectroscopy and Interferometry 

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Recent developments for a balloon based experiment, BETTII (Rinehart et al. 2009 Rinehart 2010a,b, 2011 Rinehart and BETTII Team 2010 Leisawitz 2008), and space based spectral-spatial interferometers such as SPIRIT (Leisawitz et al. 2007, 2008 Leisawitz 2008), SPECS, FIRI have identified fhaf some technology needs to be developed and demonstrated, for example high sensitivity detectors (NEPs 10 ° W/Hz ), cooled apertures, beam combination and data processing algorithms. In all these proposals, the common point is the technique employed to perform observations, the Double Fourier Modulation. 

The Sub-arcsecond Space-Based FIR Interferometer 1.3.2.1 Double Fourier Modulation... 

To achieve the angular resolution and sensitivity required for FIRI, one can use the so-called Spectral-Spatial Interferometry, Double Fourier Modulation, multi-Fourier Transform Spectroscopy or Double Interferometry (Mariotti and Ridgway 1988 Ohta et al. 2006, 2007), as a result of a combination of two well-known techniques Stellar Interferometry and Fourier Transform Spectroscopy. 

The fundamentals of Spectro-Spatial Interferometry (Mariotti and Ridgway 1988), also called Double Fourier Modulation (DFM) or Multi-Fourier Transform Spectroscopy (Ohta et al. 2007, 2006), are presented here and provide the background for the understanding of the following chapters. 

The goal of Double Fourier Modulation is to measure the spectral and spatial characteristics of an object simultaneously and it can be understood as the combination of two well known techniques Fourier transform spectroscopy (FTS) and Stellar Interferometry. The literature regarding both FTS and Stellar Interferometry is extensive, and the concepts presented here are the ones related to the work of this Thesis. 

In this thesis the CLEAN algorithm is used for the data synthesis of Double Fourier Modulation data and is described in detail in Chap. 5. In general terms, it is basically a numerical deconvolving process applied in the 0x, 0y) domain. It is an iterative process, which consist of breaking down the intensity distribution into point source responses, and then replacing each one with the corresponding response to a clean beam, this is, a beam free of side lobes. 

In this Chapter the theoretical background that led to the Double Fourier Modulation technique has been presented, this is Fourier Transform Spectroscopy and Stellar Interferometry. 

The Double Fourier Modulation technique is the combination of Fourier Transform Spectroscopy with Stellar Interferometry for a given interferometric baseline, one performs an FTS scan. With this technique measurements of the source brightness distribution and spectrum are performed simultaneously. 

The thermal system includes the Warm Optics Module and the Cold Optics Module, which given the optical set-up and the optical parameters of the different optical elements calculates the transmission of the sky map through the instmment. At this point the physical properties of the instrument are defined and the Double Fourier Modulation can be performed at the Double Fourier Module. Here is where the interferograms are computed analytically for different baseline positions. If pointing errors are selected, the Pointing Errors Module generates them and they are fed to the Double Fourier Moduie. 

PointingErrors allows pointing errors to be included in the Double Fourier Modulation. 

The Sky Simulator consists of two modules the Sky Generator Module and the Sky Photon Noise Module. The Sky Generator Module creates the input data cube to which a Double Fourier Modulation will be applied. Once the data cube is created, the Sky Photon Noise Module calculates the corresponding photon noise, that will be added to the interferograms at the Add Noise Module. 

In conclusion, these results suggest that the CLEAN algorithm is valid for Double Fourier Modulation data. Applying some FTS algorithms (i.e. phase correction algorithms) in localised areas where there is only one source or the sources are unresolved could be included to further improve the results in the spectral domain. 

Once the sky map has been defined both spatial and spectrally, the Double Fourier Modulation can be applied. For this simulation, the baselines are set from bmin = 142 mm to bmax = 392 mm, with a baseline separation of bstep = 5 mm, giving a total of 51 baselines. 

The current status of FllnS allows to perform simulations of what we call first order errors. For example, the simulation of the FTS drive response, non-linearities that occur in a real system (for example a vibrational frequency due to the mechanical motion involved) need to be modelled. By performing the Double Fourier Modulation via the cosine co-addition one can introduce these errors easily. 

Because of the nature of the work presented in this Thesis, the suggested future work is divided in the work to be performed with the FIRI testbed, the intended improvements of the instrument simulator FllnS and the possible solutions for the synthesis of Double Fourier Modulation data. 

The synthesis of Double Fourier Modulation data has been performed with a blind deconvolution algorithm and with the CLEAN algorithm via AIPS (Greisen et al. 2003). Only the second one has been proved robust enough for DFM data. 

This work presented here provides, for the first time, an end to end simulator of a Double Fourier Modulation Far Infrared Interferometer. It is intended to be a tool for the astronomical community to explore the limits of a space interferometer, as well as to test the performance and technical limits of such a system. 

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