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E.J. Schmahl (U Maryland/GSFC)
The High Energy Solar Spectroscopic Imager (HESSI) will acquire modulation collimator profiles of x-ray and gamma-ray flares, and these profiles can be directly converted into Fourier components, or visibilities. We discuss four basic ways these visibilities can be stored and processed for flare mapping, and identify figure of merits for each of those representations. These four methods are: (1) Rectangular FFT, (2) Direct Representation, (3) HXT-Style, and (4) Polar Coordinates.
Each of these has its own merits or disadvantages for storage, simplicity, ease of use, or processing speed. Until now, the HESSI team has focussed on the HXT style of imaging, but because of the far greater number of visibilities per flare that HESSI will acquire, the use of HXT-style modulation patterns appears to be very unwieldy, both for computer memory and speed of imaging.
Since the most commonly-used data unit for HESSI will be the 2-s half-rotation interval, we have studied the most efficient way to analyze that sort of data set. It turns out that if the visibilities are handled in cyclindrical/polar coordinates, there is more than an order-of-magnitude savings in storage requirements and image processing times over other representations. This is, perhaps, not particularly surprising, since the HESSI telescope is a rotating modulation collimator, and angular coordinates are its native playing field. The method is not without its difficulties, however, since arrays of Bessel functions are involved, but it turns out that these are faster to compute than even sines and cosines.
Examples of sectoral and annular maps of simulated flares will be shown, along with speed and memory comparisons using other methods.
If the author provided an email address or URL for general inquiries,
it is as follows:
http://hesperia.gsfc.nasa.gov/~schmahl/polar_uv/polar_uv.html