Biomedical Engineering Reference
In-Depth Information
correlation of the time series with many different templates, each a resampled
version of a master template with a different sample rate. The software declares a
detection if any dot product exceeds a settable threshold. There is one subtlety: faster
particles give smaller dot products, so for accurate measurement of fluorescence
intensity, templates must be scaled to correct for this (not-quite-linear) effect.
With coded masks, and hence aperiodic signals, there may also be an issue with
computational speed. Simultaneous correlation with a great many templates may
be slow, even with FFTs, so we generally use templates at fairly coarse steps, for
example, 1 m per second, 1.02, 1:02
2
, 1:02
3
, and so forth. Dependent upon the
channel geometry and particle sizes, speed can vary by 3
from slowest to fastest,
so that up to
60 templates may be necessary.
With a regularly striped mask and periodic signals, there is no need to compute
the correlation with many different templates. In this case, the signal is sufficiently
concentrated in the frequency domain that a simple algorithm suffices (Fig.
3.2
),
one that declares a detection if any single power spectrum value within the expected
frequency range exceeds background values by a preset threshold. We have found,
however, that this simple algorithm is best used only to detect the presence and
approximate speed of a particle, with accurate intensity computed using time-
domain correlation as before.
3.2.2.3
Overlapping Signals
With a large-area sensor, there is a significant chance of sensing two or more
particles at once. Overlapping signals (Fig.
3.2
) can be hard to detect and separate,
especially in the case of periodic signals and unequal intensities. The data analysis
software takes a two-pass approach: it detects isolated particles first, removes
them, and then detects what is left of overlapping particles. This approach appears
successful for particles that overlap by less than
80 %, at which point even the
human eye cannot reliably separate the signals. Except in the case of particles that
physically stick to each other, we have found that overlapping signals occur at the
rate one would predict by a Poisson process, that is, if there is at least one particle
in the detector 20 % of the time, then there are two particles about 0:2
4 %
of the time. Aperiodic masks are more reliable than periodic masks for the detection
of overlapping particles because two particles of the same speed but opposite phase
can sum to a long blur rather than a periodic signal as they pass behind a periodic
mask. Not all aperiodic masks are equally good at separating overlapping particles,
and mask designs that give low autocorrelation side lobes (e.g., masks based on
Barker codes) outperform other masks.
0:2
D
3.2.2.4
Multiply Tagged Particles
As described below, we have run particles tagged with two dyes, an identifier and
a reporter, through a detector equipped with a periodic mask and two read-out
