Recent advances in superconducting-mixer simulations

Over the last few years, considerable progress have been made in the development of techniques for fabricating high-quality superconducting circuits, and this success, together with major advances in the theoretical understanding of quantum detection and mixing at millimeter and submillimeter wavelengths, has made the development of CAD techniques for superconducting nonlinear circuits an important new enterprise. For example, arrays of quasioptical mixers are now being manufactured, where the antennas, matching networks, filters and superconducting tunnel junctions are all fabricated by depositing niobium and a variety of oxides on a single quartz substrate. There are no adjustable tuning elements on these integrated circuits, and therefore, one must be able to predict their electrical behavior precisely. This requirement, together with a general interest in the generic behavior of devices such as direct detectors and harmonic mixers, has lead us to develop a range of CAD tools for simulating the large-signal, small-signal, and noise behavior of superconducting tunnel junction circuits

Simulations of astronomical imaging phased arrays

We describe a theoretical procedure for analyzing astronomical phased arrays with overlapping beams, and apply the procedure to simulate a simple example. We demonstrate the effect of overlapping beams on the number of degrees of freedom of the array, and on the ability of the array to recover a source. We show that the best images are obtained using overlapping beams, contrary to common practise, and show how the dynamic range of a phased array directly affects the image quality.Comment: 16 pages, 26 figures, submitted to Journal of the Optical Society of America

Optical Physics of Imaging and Interferometric Phased Arrays

Microwave, submillimetre-wave, and far-infrared phased arrays are of considerable importance for astronomy. We consider the behaviour imaging phased arrays and interferometric phased arrays from a functional perspective. It is shown that the average powers, field correlations, power fluctuations, and correlations between power fluctuations at the output ports of an imaging or interferometric phased array can be found once the synthesised reception patterns are known. The reception patterns do not have to be orthogonal or even linearly independent. It is shown that the operation of phased arrays is intimately related to the mathematical theory of frames, and that the theory of frames can be used to determine the degree to which any class of intensity or field distribution can be reconstructed unambiguously from the complex amplitudes of the travelling waves at the output ports. The theory can be used to set up a likelihood function that can, through Fisher information, be used to determine the degree to which a phased array can be used to recover the parameters of a parameterised source. For example, it would be possible to explore the way in which a system, perhaps interferometric, might observe two widely separated regions of the sky simultaneously

Simulations of partially coherent focal plane imaging arrays: Fisher matrix approach to performance evaluation

Focal plane arrays of bolometers are increasingly employed in astronomy at far--infrared to millimetre wavelengths. The focal plane fields and the detectors are both partially coherent in these systems, but no account has previously been taken of the effect of partial coherence on array performance. In this paper, we use our recently developed coupled--mode theory of detection together with Fisher information matrix techniques from signal processing to characterize the behaviour of partially coherent imaging arrays. We investigate the effects of the size and coherence length of both the source and the detectors, and the packing density of the array, on the amount of information that can be extracted from observations with such arrays.Comment: 14 pages, 7 figures, submitted to MNRAS 7th March 200

Modal decomposition of astronomical images with application to shapelets

The decomposition of an image into a linear combination of digitised basis functions is an everyday task in astronomy. A general method is presented for performing such a decomposition optimally into an arbitrary set of digitised basis functions, which may be linearly dependent, non-orthogonal and incomplete. It is shown that such circumstances may result even from the digitisation of continuous basis functions that are orthogonal and complete. In particular, digitised shapelet basis functions are investigated and are shown to suffer from such difficulties. As a result the standard method of performing shapelet analysis produces unnecessarily inaccurate decompositions. The optimal method presented here is shown to yield more accurate decompositions in all cases.Comment: 12 pages, 17 figures, submitted to MNRA