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Published in IET Radar, Sonar and Navigation

Received on 16th March 2006

Revised on 8th August 2007

doi:10.1049/iet-rsn:20060036

ISSN 1751-8784

Results from trials of a planar, incoherent,

synthetic aperture sonar for underwater

imaging

K.Y. Foo P.R. Atkins T. Collins

Department of Electronic, Electrical and Computer Engineering, University of Birmingham, Edgbaston, BirminghamB15 2TT,

UK

E-mail: andrewfoo@gmail.com

Abstract: Synthetic aperture sonar (SAS) techniques can yield high-resolution images with a small physical array.

Their application in the underwater environment is usually confined to the deployment and synthesis of linear

apertures. Incoherent SAS processing is a suboptimal approach compared with coherent SAS processing as the

absence of phase information results in an inferior along-track resolution and a higher sidelobe level. The

absence of phase information implies that incoherent processing is not constrained by phase-aliasing.

Incoherent SAS can accommodate non-uniform inter-ping spacing and is tolerant to trajectory estimation

errors of the order of the range-compressed pulse length. This presents new opportunities for a robust

surveying system. Apertures of nonlinear shapes can be synthesised depending on the nature and

requirement of the specific application and environment. Surveys can be conducted with minimal hardware

deployment, such as by a diver. On the basis of this concept, tank trial results of a 3-dimensional incoherent

SAS technique utilising the synthesis of 2D apertures are presented. Broadband pulses are employed to

achieve optimal survey resolution. The feasibility of this technique is demonstrated for both monostatic and

single-transmit, multiple-receive configurations. Practical results are shown for arbitrary-surface apertures

sampled at non-uniformly separated positions.

1Introduction

The need to map extended sea bottom targets with a

relatively small physical array calls for the application

of synthetic aperture sonar (SAS) techniques. The

concept of SAS is based upon synthesising the aperture

of a large array by making multiple transmissions on a

pre-determined path. The received echoes are spatially

integrated to form a beam with resolution comparable

to that of a large physical transducer. Coherently

synthesising the aperture, by utilising phase information

in the process of integration in the along-track

direction, yields a feature resolution patch size that is

proportional to the dimension of the transmit

transducer and independent of frequency and cross-

track range [1, 2]. For a narrowband system, this is

achieved provided that the trajectory of the towed

platform is accurately estimated to the order of a

fraction of the wavelength and that the inter-ping

distance is not larger than half the physical length of

the towed array [3]. In order to meet these

conditions, the mapping rate would be limited, or a

longer array needs to be deployed. The system would

also require expensive inertial navigation systems to

track and compensate for platform instability.

An alternative approach is to implement incoherent

SAS processing, a scheme that does not rely on phase

information in the along-track integration of echoes.

The absence of phase information produces images

that are inferior in along-track (or azimuth) resolution

and in image fidelity. However, this technique is not

restricted by the requirement to satisfy the classical

constraints designed to avoid phase-aliasing encountered

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in coherent SAS [4]. As a result, the inter-ping spacing

can be extended to achieve a higher mapping rate and

the transmissions need not be uniformly spaced [5].

For a narrowband system, the trajectory only needs to

be tracked to the accuracy of a fraction of the pulse-

compressed length, compared with a fraction of the

wavelengthwithcoherent

broadband system is employed, it is worth noting that

the requirements for the positional accuracy of both

coherent and incoherent approaches are similar.

However, it is likely that incoherent systems would be

deployed for bottom-mapping

alternative to multi-beam echo sounders. Thus, the

nominal operating frequency would be lower than that

of a conventional SAS imaging system, thus further

relaxing the positional tracking accuracy requirements.

The ability to process incoherently offers flexibility in

terms of the dimension of the array being synthesised.

Furthermore, an incoherent system is also capable of

operating in near-shore regions where there are rapid

changes of sound-velocity profile, forming non-

homogenous layers which introduce phase distortion.

Such phase distortion would degrade the performance

of a coherent SAS system when not adequately

compensated.

processing.Whena

operations asan

The desire to implement 3D beamforming or multi-

aspect imaging in the underwater environment [6]

necessitates the use of planar or arbitrary-surface

apertures, as opposed to simple linear apertures.

‘Linear’ here refers to the synthetic elements or spatial

samples lying on a line, as opposed to being distributed

on more than one line. The implementation of this

concept with phase-coherent systems is demonstrated

in the work on interferometric SAS [7] and multi-

aspect SAS [8]. With incoherent SAS processing, the

complexity of deployment is lower for synthesising

arbitrary-surface apertures. The synthesis of arbitrary-

surface apertures is attractive in situations where the

nature of deployment prohibits travel in a linear

manner and at constant velocity, such as surveys

conducted by a diver.

This work examines the alternative incoherent SAS

technique anddemonstrates

incoherent SAS in producing 2D synthetic apertures,

with the purpose of performing 3D surveys in an

underwater environment. Section 2 identifies the

fundamentals of incoherent SAS processing, introduces

the concept of a planar synthetic aperture and describes

the time-domain integration process required to

reconstruct an image representation. Details of a tank

experiment are reported in Section 3, where two

tungsten spheres are imaged with a 2D planar, mono-

static, synthetic aperture. Section 4 describes a second

experimentwherean arbitrary-surface

aperture is formed using a single-transmit, multiple-

receive configuration to produce the representation of a

theapplicationof

synthetic

metal rod in the water. A further trial was performed

and detailed in Section 5 to demonstrate the robustness

of an incoherent SAS processing strategy under a more

practical set of operating constraints. Section 6

concludes this paper.

2

2.1 Suboptimal approach

Incoherent SAS processing

In coherent synthetic aperture processing, phase

differences between consecutive echoes are exploited

to produce images with good along-track resolution.

The echoes are accurately time-aligned with respect to

a desired position within the image and then summed

coherently [2]. This process requires an accurate

knowledge of the position of the sonar platform as a

function of time. The coherent summation of echoes

with both magnitude and phase information leads to

an optimal processing strategy. However, in incoherent

processing, the phase information is removed before

the echoes are summed [4].

With coherent synthetic aperture processing, the

destructive interference actively reduces the along-

track sidelobes from the individual pings. This is not

the case for incoherent processing where phase

information is absent. Fig. 1 shows a comparison of

the integrated point-energy response for an adequately

sampledsyntheticaperture

without phase information under ideal conditions.

Both plots are normalised by the maximum value,

hence the pixels representing the point target have

values approaching 0 dB. The integrated sidelobe level

is ?9 dB greater for the incoherent processing strategy

when compared with the coherent processing strategy

for the illustrative example shown in Fig. 1. The peak

sidelobe level is 26 dB for the incoherent processing

case and 213 dB for the coherent processing case.

When surveying the seafloor, the average sidelobe

level affects the shadow contrast, whereas the peak

sidelobe level is related to the image contamination

that contributes toward false targets and degrades

image fidelity. It is therefore worth noting that with a

higher sidelobe level, incoherent synthetic aperture

processing is a suboptimal approach, especially for

data sets that can be successfully processed with

phase-coherent methods.

processedwith and

Incoherent synthetic aperture processing can also be

applied in tandem with coherent processing. An

example of such an application is where a towed array

is deployed. For each ping, the returns from the

elements of the array are coherently summed using

phased-array techniques. The output from the phased-

array can then be summed incoherently across multiple

pings, as demonstrated in [9].

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2.2 Along-track resolution of incoherent

SAS

The along-track resolution of an incoherent processing

scheme can be derived from the geometry as shown in

Fig. 2. Ra and Rb are two receiver positions with

23 dB half-beam angle ub. The dotted lines are iso-

range ambiguity loci with respect to the receiver

positions, and they correspond to the matched-filtered

responses from a point target marked ‘x’. The point

target matched-filtered responses range from 2Dr to

Dr, as a result of the limited system bandwidth

available. The azimuth resolution of the system is

defined in terms of the correlation of the overlapping

responses. This resolution is taken to be twice the

azimuth increment that causes the correlation to drop

to one-half of its peak value, considering only a slice

along the azimuth dimension of the azimuth-range

ambiguity function. Thus, the azimuth resolution, Px,

can be expressed as

Px¼ xb? xa

(1)

By trigonometric relationships and assuming ro? Dr,

one can derive that, at the 23 dB level [4]

Px¼4:5 Dr L

l

(2)

where L is the physical dimension of the receiver

transducer, l the wavelength of the signal and 2 Dr

the range resolution. Unlike the expression for the

azimuth resolution of a classical coherent SAS, the

incoherent azimuth resolution is also proportional to

the range resolution of the signal. The use of

broadband (i.e. linear frequency modulated or linear

period modulated) signals and pulse compression

therefore improves both the range and azimuth

resolution in incoherent processing.

2.3 Data collection

The main difference between incoherent and coherent

SAS signal processing functions is the removal of phase

information before SAS integration is performed on

the received ping returns. With an incoherent

strategy, the spacing between ping instances need not

be uniform and the tracking accuracies may be

reduced. Data collected with a phase coherent system

can be processed incoherently, but data collected with

an incoherent strategy will probably yield poor results

when processed coherently.

The trials presented in Sections 3 and 4 were

conducted with the aid of an X–Y positioning table

and therefore provided an idealised navigational setup.

This enabled the evaluation of the performance of an

incoherentSASimaging

conditions to verify that the performance matched the

theoretical predictions. Section 5 details a trial in

which a fully incoherent strategy was employed. The

robustnessof incoherent

demonstrated for the situation where the ping spacing

is non-uniform and wider than required in a coherent

system. No mechanical positioning system was used

and the localisation of the pings was based entirely

upon the time-of-flight ranging of pings sent out by

the transmit transducer.

systemunder optimal

SASprocessing is

Figure 2 Geometry of matched-filtered responses from

target ‘x’ resolved by two receiver positions, Raand Rb

Figure 1 Comparison of the integrated point-energy

response for an adequately sampled synthetic aperture

processed with and without phase information under

ideal conditions

a Point spread function obtained using phase-coherent

integration

b Using incoherent integration

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2.4 Image reconstruction

To perform image reconstruction, two separate

matrices, Idataand Iimage, are introduced to represent

thecollecteddataand

integration on the collected data, respectively. The

positionofeach of

corresponding to Idata is assumed to be known by

independent techniques.

the result ofazimuth

thetransmissionpings

Consider a broadband continuous-time signal, s(t),

being transmitted. Assuming a noise-free propagation

model with no Doppler scaling and no phase errors,

the received signal from a point target, r(t), will

be a delayed and attenuated version of the transmitted

pulse

r(r) ¼ Ams(t ? ta) (3)

where Amis the attenuation factor (which also accounts

for target reflectivity) and tathe two-way propagation

time delay of

s(t).

representations of the transmitted and received signals

are definedas

S( f )

The matched filter is performed by multiplication of

the received signal spectrum by the conjugate of the

replica signal spectrum. This is then converted into

the time domain (via the inverse Fourier transform)

to give

ð

The complex time-domain samples from the output of

the matched filter are then converted to a modulus-

squared form. This removes the phase information and

leaves an energy representation:

Thefrequency-domain

and

R( f ),respectively.

G(t) ¼R( f)S ? ( f)ej2pftdf

(4)

G2(t) ¼ G(t) G?(t)(5)

The discrete-time samples are then appended to the 2D

data matrix Idata, where the rows correspond to the ping

number and the columns correspond to the sample

number (range cells).

To reconstruct the SAS image, for each point on

Iimage, a sample will be chosen from each cross-track

slice of Idatabased on the back-projected ranges, and

then summed in the along-track direction, such that

Iimage[na, nr] ¼

X

N

n¼1

Idata[n, nd[n, na, nr]]w[n, na, nr]

(6)

where [na, nr] is the coordinate of the point of interest in

the along-track and cross-track direction, respectively

on Iimage, N the total number of pings in the

synthesised aperture, nd the sample delay that

determines which sample on the nth cross-track slice

is selected for summation and w[n] the weighting

matched to the angular response of the element with

respect to the point of interest.

Extending this to an arbitrary-surface synthetic

aperture, the coordinates in a 3D image environment

are represented by the x–y–z axes instead of the

along-track and cross-track axes. The z-axis represents

the depth from the surface, whereas the x- and y-axes

are perpendicular to the z-axis. Equation (6) now

becomes

Iimage[nx,ny,nz]¼

X

N

n¼1

Idata[n,nd[n,nx,ny,nz]]w[n,nx,ny,nz]

(7)

where [nx, ny, nz] is the current point in the 3D image

volume on which focusing is performed and nd

the sample delay from the current point of interest

to the corresponding arbitrary-surface synthetic array.

The sample delay ndis

nd[n,nx,ny,nz]¼2fsRn[nx,ny,nz]

c

(8)

where the range function Rnis a 3D vector dot product

between the location of the point of interest [nx, ny, nz]

and the location of the point P[a, b, x] on the arbitrary-

surface synthetic aperture, fsthe sampling frequency and

c the speed of sound. The arbitrary-surface synthetic

aperture may use a different coordinate system to that

of the image coordinate system.

In incoherent processing, obtaining a spatially

balanced energy distribution around a point target

improves the image representation and reduces the

occurrence of false targets. The energy distribution

can be observed from a range–loci plot (Fig. 3) and

is affected by the position of elements (linear

aperture) and the symmetry of the array (arbitrary-

surface aperture). This is taken into account by

the weighting function, w, which determines the level

of contribution from each element with respect to

a point of interest. Extending this to an arbitrary-

surface synthetic aperture, the weighting function is

expressed as

n

w[n,nx,ny,nz]¼wTsT[n],nx,ny,nz

o

wRsR[n],nx,ny,nz

no

(9)

wherewTandwRaretheweightingfunctionscorresponding

to the transmitting and receiving locations, respectively,

in order to take account of spatially separated

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transmit–receive configurations sT[n] and sR[n] are the

position vectors of the transmitting and receiving

elements, respectively, at ping n.

In the tank trials, a weighting function was used to

minimise the contribution from synthetic elements

that corresponds to angles close to, or exceeding, the

23 dB beamwidth with respect to a point of interest

while maximising the main-lobe contribution. This

effectively matched the spatial integration process

to the response of the transducer. In the second

trial with a spatially separated transmit–receive

configuration, a bi-lateral weighting was applied to

both the projector and the receiving elements. By

using only the effective, matched-weighted, synthetic

elements with respect to a point of interest, the point-

target energy response of the synthetic aperture is

improved. This is as a result of minimising the energy

spilling over from adjacent targets, which would

otherwise contribute to the noise floor of the current

point of interest.

3

aperture tank trial

Amonostaticconfigurationreferstotheco-locationofboth

thetransmittingandreceivingelements,wherethedistance

between them is either negligible or appropriately

compensated. Each transmitting synthesised element

location corresponds to a similar synthesised receiving

element location on the synthetic aperture. The trial was

conducted in a water tank with dimensions of width

1.5 m, length 1.5 m and depth 1.5 m. The bottom and

side walls of the tank were lined with acoustic absorbers.

A tungsten carbide sphere, 20 mm in diameter, was hung

by a thin string 0.2 m below the water surface, as

illustrated in Fig. 4. Two transducers with a resonant

frequency of 500 kHz were used, operating in transmit

and receive modes, respectively. The transducers were

guided by an X–Y positioning table.

Monostatic planar synthetic

A total of 75 measurements were taken in each

direction of the x–y plane, thus forming a 75 ? 75

element planar synthetic aperture with a uniform

separation between pings of 5 mm. The transducers

were maintained stationary during the transmit–

receive period. The transmitted signal was a linear

frequency modulated pulse with a bandwidth of

200 kHz, centred on 500 kHz and weighted by a Von

Hann window function. The pulse duration was 0.1 s.

The received signals were matched-filtered and

appended onto a data matrix Idata. Along-track

integration was then performed to obtain the total

energy return for each point of interest in order to

construct an image representation, Iimage, as defined

by (7). All elements were used in the integration to

Figure 4 Illustration of the water tank trial with a spherical

target suspended in water and the synthetic aperture

elements facing the bottom of the tank

Figure 3 Energy distribution

a Uniform range–loci spacing

b Point-energy response for non-uniform spacing

c Point-energy response for uniform range–loci spacing

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