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We develop a simple, one-dimensional model for super-resolution in absolute optical instruments that is able to describe the interplay between sources and detectors. Our model explains the subwavelength sensitivity of a point detector to a point source reported in previous computer simulations and experiments (Miñano 2011 New J. Phys.13 125009; Miñano 2014 New J. Phys.16 033015).Perfect imaging with positive refraction [1] has been subject to considerable controversy [2-17] that has given important insight into the matter. Much of the controversy has centred on the role of detection in perfect imaging-the perfect transfer of the electromagnetic field from object to image is only possible if the image is detected. Another important point was noticed in a computer simulation [18] and a subsequent experiment [19] by Miñano et al: at specific resonance frequencies of the instrument a point detector is sensitive to displacements of a point source with an accuracy that is significantly better than the diffraction limit. No physical explanation for this feature has been found yet. Here we develop a simple model that captures both issues, the role of the detection and the role of the resonance, which allows us to deduce both physical explanations and analytic expressions for the sensitivity.Perfect-imaging devices with positive refraction are absolute optical instruments [20] with closed loops of rays [21,22]. The archetype of such instruments is Maxwell's fish eye [23] where light goes in circles and where all light circles originating from any given point intersect at a corresponding image point. Luneburg [24] discovered a geometrical picture that explains the properties of Maxwell's fish eye: the refractive-index profile of Maxwell's device appears to light as the surface of a sphere in two-dimensional (2D) and hypersphere in threedimensional (3D) space; light propagates in the medium of the fish eye as if it were confined to spherical surfaces. The geodesics on the sphere appear as the circles of light (by stereographic projection), object and image correspond to antipodal points on the sphere where geodesics intersect. Let us consider the simplest case of perfect imaging, the one-dimensional (1D) sphere: the circle (figure 1). Imagine that light is confined to a circle, say a fibre loop or ring resonator. Here light can go in only two directions, to the right or to the left. An 'image' is formed when the two rays meeting have the same phase, which happens when both are antipodal. Light is coupled in and out of the circle by two 1D channels that represent the source and the detector. These 1D channels are idealizations of the cables used for injecting and extracting radiation in the simulation [18] and experiment [19]. Clearly, this 1D system represents a rather primitive model, but it is going to reproduce the findings of the experiment [19], the model is simple, but not too simple.We are going to show how a point detecter is able to sense minute displacements of a point source. Note that this is not imaging in the ...

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The development of monolithic arrays of multiplexed, high-gain avalanche photodiodes suitable for use in a spectroscopic radiation-imaging device is underway at RMD. We have developed a relatively simple readout scheme using row-column addressing to dramatically reduce the electronics required to support a large array of discrete pixels. By adding a step to the avalanche photodiode creation, it was possible to place two separate diode contacts onto the back of each photodiode in the array. These isolation diodes allow the readout of an entire row or column of photodiodes through a common readout line. A data-decoding matrix uniquely determines the position in the array while simultaneously supporting the goal of reducing the number of signal readout lines and support electronics. This approach reduces the number of pre-amplifiers, pulse-shaping circuits, and sample-and-hold stages from n 2 to 2n (n pixels on a side) per array. Recent research has been carried out with 14 x 14 pixel, planar-processed avalanche photodiode array having pixels 2.00 mm on a side with 2.25-mm pitch. These arrays will be paneled to form the photodetector of a radiation imager of approximately 100-cm 2 sensitive area. To reduce the contribution of noise from each pixel to the common readout lines, research is being carried out to develop a discriminator with an adjustable threshold for each avalanche photodiode readout connection. Initial performance results from multiplexed arrays, a discussion of the active discrimination contacts, and the current status of the imager research project are given.

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