Proceedings with Extended Abstracts (single PDF file) - Radio ...

98IN BEAM RADAR IMAGING OFIONOSPHERIC IRREGULARITIESD. L. Hysell , M. F. Larsen ¡ , and J. L. Chau ¢(1) Earth and Atmospheric Sciences, CornellUniversity, Ithaca, New York USA(2) Department of Physics, ClemsonUniversity, Clemson, South Carolina USA(3) Jicamarca Radio Observatory, Lima, PeruSynthetic aperture imaging was introducedto the radar community at Jicamarca byKudeki and Sürücü (1991) who used it to observeprimary plasma waves in the equatorialelectrojet for the first time. In the years since,high-resolution observations of E and F regionplasma irregularities at Jicamarca havebeen made with a growing number of interferometrybaselines (Hysell, 2000; Hysell andChau, 2002). Radar imaging has also beenimplemented at the Piura MST radar and theMU radar in Japan for studies of midlatitudesporadic E layers and neutral atmosphericturbulence (Chau et al., 2003; Hysell et al.,2002). Presently, it is being utilized at theHigh Latitude Monitoring Station (HLMS)in Anchorage to monitor 30 MHz backscatterfrom the auroral electrojet on a campaignbasis. Wherever radar systems with multiplereceivers are available, aperture synthesisimaging can be used to produce unambiguous,high-resolution images of the radarbackscatter from the illuminated volume withminimal reliance on assumptions about thescatterers present and the data quality.It is well known that interferometry usinga single antenna baseline yields two momentsof the radio brightness distribution, the distributionof received power versus bearing (Farleyet al., 1981). Interferometry with multiplebaselines yields multiple moments, andthe totality of these moments can be invertedto reconstruct the brightness distribution versusazimuth and zenith angle. The inversionessentially amounts to performing a Fouriertransform of the interferometry cross-spectraor visibility (Thompson, 1986). However,since the cross-spectra are inevitably sampledincompletely due to the limited number of interferometrybaselines available, and in viewof the presence of statistical fluctuations inthe data, the inversion is underdetermined andill-conditioned must be performed using statisticalinverse methods to achieve satisfactoryresults (Jaynes, 1982).For imaging work at Jicamarca, we employedthe MAXent algorithm pioneered forapplications in radio astronomy and motivatedby the “first principle of data reduction”[Ables, 1974, p. 383]: “The result of anytransformation imposed on the experimentaldata shall incorporate and be consistentwith all relevant data and be maximally noncommittalwith regard to unavailable data.”The transformation from the visibility to thebrightness spectrum that adheres to this philosophyis the one which maximizes the “entropy”of the map in the information theorysense. Shannon and Weaver (1949) definedentropy as a measure of the uncertainty associatedwith a probability distribution function;the greater the entropy of a proposition,the greater the number of questions thatmust be asked to ascertain if the propositionis true. Choosing a proposition (or an image)with less than the maximum entropy impliesthat the analyst knows the answers andis therefore only warranted if existing datasupport the departure. Jaynes’ principle thensays that maximizing the entropy of an imagewhile maintaining consistency with the measurementsin a chi-squared sense is the wayto obey Ables’ principle.In the case of aperture synthesis imaging,the image with the highest entropy isthe one least committal to unmeasured data.Not only is it the most likely brightness spectrum,it is the one near which most otherpossible spectra are concentrated in solutionspace. To choose a spectrum with lower entropywould be to ignore the majority of possibleoutcomes of the inversion problem andfocus on a less likely subclass of solutions,an unwarranted step unless the data supportit. By merely formulating the problem interms of entropy, we exclude from the solutionspace images with negative componentswhich are obviously unsuitable. The