Biomedical Engineering Reference
In-Depth Information
2π
n
k
d
k
i
=
k
d
=
λ
0
2π
V
k
a
=
f
β
λ
0
f
sin β =
2
nV
k
a
k
i
FIGURE 3.2
Wave vector diagram for AO diffraction.
and development of compact RF spectrum analyzers as well as Bragg cell
correlators and convolvers for radar signal processing that are smaller and
lighter than their digital VLSE and RF electronic counterparts.
3.2 BasicBraggCellSpectrumAnalyzer
The components of a Bragg cell receiver are shown in Figure 3.3 [5]. The light
source is a laser for optimum performance. The beam expander, or collima-
tor, evenly distributes the light along the acoustic wavefront (top to bottom
in Figure 3.3) to match the interaction aperture of the Bragg cell. After light is
diffracted into the RF signal components a lens, called the Fourier Transform
lens, focuses the light beams into a photodetector (PD) array that is mounted
at the lens focal point. Each pixel of the PD array corresponds to a small fre-
quency band, the sum of which makes up the entire bandwidth of the Bragg
cell. The minimum frequency difference of two RF signals that are resolv-
able is approximately equal to 1/τ, where τ is the acoustic transit time across
the interaction aperture.
The time bandwidth of the Bragg cell,
N
= τΔ
f
, where Δ
f
is the bandwidth of
the Bragg cell, theoretically provides the total number of signals that can be
simultaneously resolved by the Bragg cell receiver [6]. One virtue of an AO
material is the high time bandwidth product. Figure 3.4a shows bandwidth-
resolution contours for some materials [7]. The frequency bandwidth is the ver-
tical axis, and the time delay is the horizontal axis. The time delay relates to the
frequency resolution by Δ
f = k/T
, where
T
is in μs,
f
in KHz, and
k
is a constant of
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