Time-resolved and energy-resolved coded aperture images with URA tagging

Coded aperture imaging with uniformly redundant arrays (URAs) is the standard technique for imaging above the limit of grazing incident x-ray telescopes. It is an ideal technique for high energy astrophysics because it has high throughput, excellent performance on point sources, and the ability to measure simultaneously signal and background. However, many sources of interest in high energy astrophysics are time variable or require detailed energy spectra. Until now, to obtain a single time (or energy) sample, the photons from the particular time (or energy) interval must be formed into an encoded pattern, then processed to obtain an image for that sample. Therefore, massive computations are required to cover the entire time and energy parameter space. We present a new method of coded aperture analysis called URA tagging, which provides time and/or energy resolved histories of sources with known positions without using a correlation operation. It can easily reduce the computation time by orders of magnitude compared to the next fastest method, the fast delta Hadamard transform. URA tagging can also correct for improperly encoded images or motion blurred images. Whereas previous methods for quantifying performance have not taken into account the finite resolution or the quantized sampling, URA tagging provides a SNR equation that includes all such effects. URA tagging analysis explains why delta decoding has a somewhat poorer SNR than balanced correlation; naively, one expects the better angular resolution to yield a better SNR. In addition, we show that complementary URAs (exchange opaque and transparent elements) have different properties, and those with an even number of transparent elements should be preferred