High-Energy Physics - Signal Processing Systems - page 161

than x % of the total color saturation, where x is a programmable threshold value. In
the CMS system, a new image is delivered from the sensors every 25 ns; the particle
identification circuitry must therefore be fast enough to process up to 40 million of
these images each second.

ECAL
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T hreshold (1)

+

Whereas Eq. ( 1 ) is a seemingly simple equation, it is only an approximation; the real
system requires complex special-case handling to deal with non-linear effects in the
sensors at high energy. For this reason, in previous accelerators this identification
algorithm has been implemented using large and expensive RAM-based look-up
tables. As discussed in Sect. 4.2 , table-based algorithm implementation provides
a great deal of flexibility to change an algorithm (by loading a new set of values
into the table) without needing to change the underlying hardware. It also provides
an effective way to implement Eq. ( 1 ) with the additional special-case handling.
Research from the SLHC upgrade project has investigated a set of alternative FPGA
implementation methods for this algorithm, including hardware reprogramming and
the use of multi-level hashing to fit the look-up tables on-chip [ 33 ] . By using a
parallel implementation across many FPGAs and a pipelined architecture, these
designs are capable of performing the electron/photon identification across the entire
sensor image in approximately 30 ns.

5.2 Jet Reconstruction

In some cases, physicists are interested in large groups of particles rather than indi-
vidual ones. Certain physical phenomena may generate highly-energetic bunches
of particles known as “jets”. Unlike individual particles, whose data is isolated
to a few adjacent sensors—or a few pixels in the image processing analogy—the
data from jets may be spread across tens or hundreds of sensors. From a physics
standpoint, in CMS it is ideal to consider a region of at least 8 8 sensors (pixels)

when identifying a jet [ 11 ] . In the process of jet detection, any group of pixels
representing a sufficiently high total energy may be considered a jet, provided that
there is a bright spot (energy deposit) at the center of the region. Several stages of
processing must be applied to each jet. First, the energy from every pixel in the jet
must be summed to calculate the total jet energy. Next, a weighted energy position
must be calculated within the jet. For example, if there are more bright pixels to the
right of the jet's center than to the left, the jet's center of energy is somewhere right-
of-center in the region. Finally, all of the jets must be sorted based on descending
total energy. However, this process is more difficult than simply sorting integers,
because multiple jets may occur at overlapping locations.

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