Millimetre-Wave Spatial Interferometry of
Extended Thermal Sources.
J. C. G. Lesurf & M. R. Robertson
May 1993
Abstract.
This paper considers the application of mm-wave spatial interferometry to thermal sources. It concentrates on the example of a simple three-port interferometer system which is designed to simultaneously recover spatial and spectral information. We examine how the detected signals depend upon the source extent and indicate how the technique might be used to determine the range of thermal sources or absorbers in a translucent medium such as the atmosphere.
1. Introduction.
The use of a three-port interferometer system to locate coherent, point-like sources has already been considered elsewhere[1]. Quasi-Optical circuit techniques are now being applied to an increasing diversity of signal processing tasks[2] [3] [4]. Here we concentrate upon the use of a quasi-optical arrangement to identify and locate spatial distributions of extended thermal (i.e. broadband) sources or layers of absorbing matter placed between the instrument and a more distant source. Although we will confine our attention to using a mm-wave system as a phase interferometer it should be noted that intensity fluctuation interferometry methods similar to those considered by Hanbury-Brown[5] may also be employed where appropriate.
For the sake of clarity we will confine our analysis to sources and absorbers which have no distinct spectral features. Although this simplifies the following arguments it should be noted that the spatial interferometer system we are considering is quite suitable for tasks where the atmosphere (and any other sources/absorbers in the field of view) possess obvious spectral signatures. The main purpose of this paper is to outline the basic properties of a technique which may well prove useful for a variety of applications which include mapping atmospheric and pollutant species, and locating objects such as aircraft without the need for coherent emissions.
The quasi-optical circuit under consideration is illustrated in figure 1. This is nominally identical to the system considered in reference 1, but its physical details (aperture diameters, etc) may differ as required for a specific application. The circuit symbols used in this diagram are as defined in that analysis[6]. The properties of this instrument when used to observe extended distributed thermal sources can be outlined by generalising the resulting obtained in reference 1 in four steps.
Firstly, we consider the effect of a narrow-band source which has a finite size, but is confined to a plane at a specific distance from the instrument. Secondly, we combine the effects of incoherent radiation from such a source over a wide range of wavelengths. Thirdly, we consider the effect of a series of translucent layers placed in the instrument's field of view at various ranges. Finally, we consider the effect of a specific object or inhomogeneity located some distance from the instrument in a translucent distribution.
2. Observations of an Extended Planar Source.
Consider the situation illustrated in figure 2. Here the interferometer observes a source located with its centre on the boresight axis of the instrument (i.e. the optical axis of the beam of the centre-port) which extends completely across the instrument's field of view in the y-direction. The source is assumed to have a uniform surface brightness and radiates a spatially incoherent field distribution.
The extended source may be modelled as an array of linear incremental sources, each of width, dx, located at a nominal offset, x, from the boresight axis and extending far enough along the y-direction for its ends to be outside the field of view. From reference 1 we can say that, the imbalances in the output levels from the detector pairs, 
, produced by signal power from a each linear incremetntal source in the frequency interval, df, centered upon the frequency, f, may be represented by 
where
where 
is the source power spectral density and 
. 
represets the instrument's antenna pattern and 
represents the system gain/responsivity. Since the radiation emitted by each line source is assumed to be uncorrelated with that from its companions we can say that interferogram contributions from the extended source corresponding to a frequency centred on f will be
[1] Lesurf, J. C. G, & Robertson, M. R, MM-Wave Spatial Interferometry as an Alternative to Radar for Coherent Point Sources. (Submitted to IR&MMWaves)
[2] Harvey, A., & Lesurf, J. C. G. Lesurf, A Millimetre-Wave, Single-Mode, Quasi-Optical Complex Reflectometer Operating as a Nulling Bridge. Conf. Digest T2.8 198-200, 15th Int. Conf. on I.R. & MM Waves, Orlando, 10-14th Dec. 1990 SPIE Vol. 1514
[3] Smith, G. M., & Lesurf, J. C. G., A Highly Sensitive Millimetre-Wave Quasi-Optical FM Noise Measurement System. IEEE MTT-39(12) 2229-36 (1991)
[4] Brune, J., A Flexible Quasi-Optical System for Polarimetric Submillimetre-Wave Reflectometry. IEEE MTT-40(12) 2321-4 (1992)
[5] Hanbury-Brown, The Intensity Interferometer. Taylor & Francis, London 1974
[6] Lesurf, J. C. G., Millimetre-Wave Optics, Devices, & Systems. IOP Press, Bristol & New York, 1990
