Suitability of Correlation Arrays and Superresolution for Minehunting ...

DSTO-TN-0443
3. Assumptions concerning time.
a. In RA, the image is two-dimensional, having no range component. In passive
sonar this situation again prevails, often or always. But in active sonar, there
is a range component; echo ranging is an essential part of the sonar imaging
process. 4 The theory applicable in RA needs to be extended to include a range
component in the image.
b. In RA, the time dimension can be used simply for averaging to eliminate
uncorrelated components in the signal and thus to improve the signal-tonoise
ratio; the time dimension is not already reserved for some other
purpose. By contrast, in any sonar system that employs echo ranging, a target
at range r is detected essentially by signals received at times very close to
2 r c . The question needs to be asked whether this use of the time dimension
can be combined with the use of time for the purpose of averaging.
c. In RA, a given correlation run can continue for essentially an indefinite
period, limited only by factors such as the rotation of the earth. By contrast,
in active sonar, in the case when a short pulse is used, it is suspected that only
a correspondingly short time is available for averaging. In sonar systems
using a continuous-wave (CW) transmission system instead of a short pulse,
this assumption of RA continues to hold. But there is little comfort in this
fact, since a CW system cannot measure range with good resolution.
4.2 Near Field
Regarding assumption 1, we consider whether the target’s being in the near field
precludes the working of a correlation telescope. Two reasons indicate that the near
field does not cause any such trouble. First, as shown in Blair [2002], the beam pattern
of an array in the near field is the same as in the far field, 5 provided that the image point
is within the main lobe or the first few sidelobes. This result applies whether the image
point is displaced in an angular direction or in the range direction (range sidelobes).
The second reason, not altogether distinct from the first, is that an argument given
in Section 4.3 below comes close to deriving Equation (3.5), the Fourier transform
relation for a correlation telescope, in the near field. The only problem in this argument
is that unwanted extra terms (cross terms) are obtained. However, these extra terms
have nothing to do with whether the target is in the near or the far field. The above
two reasons strongly suggest that the target’s being in the near field in no way precludes
the feasibility of the correlation telescope in the sonar context.
4 Obviously active probing is impossible in RA—with possible exceptions within the solar
system.
5 Some conditions apply to this result, but they are not very restrictive.
9