WO2008062199A2

WO2008062199A2 - Imaging method and apparatus

Info

Publication number: WO2008062199A2
Application number: PCT/GB2007/004470
Authority: WO
Inventors: Ben Cox; Paul Beard
Original assignee: Ucl Business Plc
Priority date: 2006-11-24
Filing date: 2007-11-22
Publication date: 2008-05-29
Also published as: GB2444078A; WO2008062199A3; GB0623475D0

Abstract

An imaging system comprises a sensor arrangement for detecting an acoustic signal which emanates from a sample; and means for analysing the sensor arrangement output signals to derive a property for different portions of the sample. A reflector arrangement reflects a portion of the signal generated within the sample which is not directed to the sensor arrangement, such that it is reflected to the sensor arrangement. The sensor arrangement output signals are processed over a time period which covers the direct receipt of the signal generated within the sample by the sensor arrangement as well as the reflected portion of the signal generated within the sample.

Description

IMAGING METHOD AND APPARATUS

Field of the invention

This invention relates to an imaging method and apparatus, in particular to an imaging method based on acoustic signals emanating from a sample.

Background of the invention

There are various imaging techniques which use the generation of an acoustic signal within a sample to enable signal analysis to provide an imaging function. The generation of the acoustic signal can be stimulated by an excitation source (optical, electric, thermal or magnetic) or samples may emit acoustic signals without such excitation.

One well known type of imaging technology is photoacoustic tomography. Biomedical photoacoustic tomography (PAT) is a soft-tissue imaging modality which combines the high spatial resolution of ultrasound (US) with the contrast and spectroscopic opportunities afforded by imaging optical absorption.

In biomedical photoacoustic tomography (PAT), soft tissue is illuminated with a short pulse of monochromatic light, and the acoustic (ultrasonic) pressure pulses that are emitted from the regions in which the light is absorbed are detected at the tissue surface. By recording these acoustic waves over an array of receivers (or with a single, scanned detector) the distribution of the absorbed optical energy density can be estimated.

An image of the absorbed energy density obtained in this way is called a photoacoustic, or optoacoustic, image. When the excitation light is replaced by microwave or RF radiation the technique is called thermoacoustic tomography.

PAT has been used successfully in a variety of applications, including imaging of vasculature, visualisation of breast tumours and functional brain imaging in small animals. Image reconstruction in PAT may be considered an inverse source problem in the sense that the absorbed energy distribution that is to be recovered acts as a source term in the associated forward or direct problem. The acoustic pressure:

obeys the wave equation:

in which the sound speed c and the Gruneisen parameter f are both constant in the volume V. The Gruneisen parameter is :

r = &/c_r

where β is the volume thermal expansivity and Cp the constant pressure specific heat capacity. The parameter is dimensionless and quantifies the efficiency of conversion from heat to pressure.

H(x, t) is the energy per unit volume and per unit time deposited in the fluid at position:

x € Ω c V

and it is the rate of change of this quantity with time that drives the emission of acoustic waves.

Time histories are measured on all or part of the surface S which surrounds the volume V containing the source region Ω.

In the analysis used below to explain the invention, the 2D case is considered where: although the concepts are equally applicable to, and may be straightforwardly extended to 3D space. Equation (1) holds in the linear (acoustic) approximation in the absence of viscosity and absorption, and assumes that the fluid is stationary, the sound is generated by a purely thermoelastic mechanism, and the thermal conductivity may be neglected. This last requirement is satisfied for sufficiently short light pulse durations, a regime known as thermal confinement.

The aim in PAT is to recover the absorbed energy distribution from measured acoustic pressure time histories, p(x_s, t), where x_s are points on, or on parts of, the surface S, which surrounds V . In other words, the acoustic measurements are made over a surface lying outside the source region. For light pulse durations much shorter than the transit time across the heated region ('stress confinement') the propagation and absorption of the light can be approximated as instantaneous and the source term written as a delta-function:

H(x_>t) = h(κ)δ(t) with the time t = 0 defined as the instant of the pulse.

In this case, the forward problem becomes an initial value problem with the initial pressure distribution: p(x_< 0) = Tft(x) and dp/dt = 0

equivalent to zero initial particle velocity. The inverse problem reduces to one of recovering the function p(x,0), or h(x), from a set of integrals over spheres centred at the measurement positions. Closed form reconstruction algorithms have been devised for measurement surfaces with spherical, cylindrical and planar measurement surfaces.

Image reconstruction based on a numerical model, which can thus accommodate a measurement surface with arbitrary geometry, has also been proposed.

A planar geometry is considered below. As weir as the practical experimental advantages that a flat measurement surface offers, planar ultrasound arrays composed of piezoelectric or optical elements with small element sizes and high temporal resolution are readily available, and, most importantly, an exact and efficient reconstruction algorithm based on Fourier transforms in Cartesian coordinates is known for this case. For example reference is made to the paper "Temporal backward projection of photoacoustic pressure transients using Fourier Transform methods", Koestli, K., Frenz, M., Bebie, H., and Weber H., Physics in Medicine and Biology, 46, 1863-1872 (2001).

Perhaps the main limitation of using a planar sensor is its finite size, and the resulting limitation on the measurement aperture. While a spherical surface can measure over a solid angle of 4π steradians, and the infinite planar sensor over 2π steradians (still sufficient to reconstruct an exact image), any planar sensor with a finite aperture is limited to solid angles somewhat smaller than this, often 1 steradian or less.

An image reconstructed from limited aperture data may contain artefacts, and sharp boundaries may be blurred. More specifically, only boundaries where the normal to the boundary crosses the measurement surface can be reconstructed accurately which means that, for a small aperture, many of the boundaries in the image, especially those perpendicular to the measurement surface, become indistinct.

The invention therefore aims to provide an imaging technique and apparatus which enables a small sensor to be used to obtain imaging data which has reduced image artefacts.

Summary of the invention

According to the invention, there is provided an imaging system comprising: a sensor arrangement for detecting an acoustic signal which emanates from a sample; and means for analysing the sensor arrangement output signals to derive a property for different portions of the sample; and a reflector arrangement for reflecting a portion of the signal generated within the sample which is not directed to the sensor arrangement, such that it is reflected to the sensor arrangement, wherein the analysing means is adapted to process sensor arrangement output signals over a time period which covers the direct receipt of the signal generated within the sample by the sensor arrangement as well as the reflected portion of the signal generated within the sample.

This apparatus has a reflector arrangement associated with the measurement aperture so that the sample emissions that would not have been recorded with just a finite aperture that would have missed the sensor, are recorded as reverberation. Thus, the invention uses measurement of reflected or multiply reflected fields (reverberant fields) to reduce image artefacts and improve image resolution.

The image reconstructed from this reverberant field contains fewer artefacts because more of the acoustic data has been used in the reconstruction. The reflector arrangement acts to extend the aperture width beyond the size of the sensor to an 'effective' aperture which depends on the duration of the measurement. Boundaries within the image whose normals cross this 'effective measurement aperture' can be reconstructed well. The reflector arrangement preferably enables multiple reflections to reach the sensor arrangement.

This enables a low complexity sensor, for example a planar sensor device, to be used to generate high quality images, even perpendicular to the detection plane. The reflector arrangement then comprises at least one planar reflector perpendicular to the plane of the sensor device.

The invention is of particular interest for a photoacoustic tomography imaging system. In this case, the excitation source comprises a light source, for example a pulsed light source. The wavelength may be in the range 600 to 900nm, although other wavelengths may be used, such as RF or microwave signals. However, a continuous light source modulated at an acoustic frequency may instead be used, and this enables narrowband detection electronics such as a lock-in amplifier to be used to improve the signal to noise ratio.

The sensor arrangement may for example comprise a piezoelectric detector array or an interferometer device or other optical ultrasound sensing device.

In one preferred example, a processor implements an algorithm based on the Fast Fourier Transform. The periodicity provided by the reflector arrangement enables particularly good signal analysis using a Fourier Transform (FFT or DFT). The invention also provides an imaging method comprising: detecting an acoustic signal which emanates from a sample using a sensor arrangement; and analysing the acoustic signal to derive a property for different portions of the sample, wherein the signal analysis comprises processing monitored signal data over a time period which covers the direct receipt of the signal emanating from the sample by a sensor arrangement as well as receipt of reverberant reflected fields by the sensor arrangement.

The method may further comprise exposing a sample to be imaged with an excitation signal, thereby to stimulate the emanation of the acoustic signal.

Brief description of the drawings

An example of the invention will now be described in detail with reference to the accompanying drawings, in which: Fig. 1 shows some of the entities necessary for a mathematical description of a photoacoustic imaging system;

Fig. 2 is a schematic diagram of the arrangement of a planar sensor array and acoustic reflectors in accordance with the invention;

Fig. 3A shows an absorbed energy distribution, used for simulation; Fig. 3B shows the simulated pressure time histories (C);

Fig. 3C shows the reconstructed energy distribution based on modelling of a known sensor arrangement, which does not incorporate reverberant field data;

Fig. 4 shows how vertical reflectors should be arranged, and how they are positioned relative to the individual elements in the sensor array; Fig. 5A shows time series from the absorbed energy distribution in Figure

3A when reflecting walls are present, and thus includes the reverberant field;

Fig 5B to 5D show simulations of the reconstructed absorbed energy distribution from the pressure time series shown in Fig. 5A for time histories from 0 to 14μs (Fig. 5B), extended to 20 μs (Fig. 5C)₁ and extended to 40 μs (Fig. 5D);

Fig. 6 shows a ³A width aperture which can be used in the system of the invention;

Fig. 7 shows a simulation of the reconstructed absorbed energy distribution using the aperture of Fig. 6, without reflectors (Fig. 7A) and with reflectors (Fig. 7B);

Fig. 8 shows how the effective aperture width is governed by the time over which the reverberation is recorded t and the height of the source z above the detector plane; Fig. 9 shows the magnitude of the gradient of the image shown in Fig. 5B, reconstructed from short duration time histories and including the reverberation due to the reflectors; and

Fig. 10 shows the magnitude of the gradient of the image shown in Fig. 3(C).

Detailed description

The invention relates to an imaging system in which a reflector arrangement is used to reflect a portion of the signal emanating from a sample to be imaged which is not directed to a sensor arrangement, such that it is reflected to the sensor arrangement. This means that reverberant fields can be processed.

The invention will be explained in detail with reference to the preferred use of the system within a photoacoustic tomography system, but it will be understood by those skilled in the art that the invention has applications based on other imaging technologies.

To visualise the effect of a reflector arrangement on the acoustic field, it is appropriate to consider the acoustic image sources they introduce, as shown in Figure 2.

Figure 2 shows a planar sensor detector (between positions x=0 and x=X), and a pair of lateral reflectors, perpendicular to the plane of the detector. The reflectors create virtual image sources, as shown, with a repeating pattern of dimension 2X where X is the sensor dimension in the lateral direction.

As there are two parallel reflectors, the number of image sources is infinite and the acoustic field may be considered as infinitely periodic with a period of twice the distance between the reflectors. The periodically repeating sound field of the virtual sources can be reconstructed substantially exactly from measurements of reverberation made over the finite aperture of the sensor array.

A very efficient PAT reconstruction algorithm, which is in common use, constructs an image from the Fast Fourier Transform (FFT) of the acoustic measurements made over a plane. As the FFT algorithm assumes that the data to be transformed is periodic, which is not normally the case, the image can be blurred and contain artefacts.

By introducing additional virtual image sources, and thereby making the acoustic field effectively periodic, this algorithm can be used to reconstruct the initial pressure distribution exactly.

Planar ultrasound arrays composed of piezoelectric or optical detector elements with small element sizes and fast acquisition times are readily available, making them an attractive option for imaging applications. To capture sufficient data for an exact PAT reconstruction with a planar geometry requires an infinitely wide array. In practice, of course, it will be finite, resulting in a loss of resolution and introducing artefacts into the image.

When the light pulse can be approximated as instantaneous (under conditions of stress confinement), the reconstruction problem becomes one of recovering a function from its mean values over spheres centred on a planar measurement surface. In the case of PAT the function to be recovered is

P(X, 0) = ΓA(X)

The measurements p(x_s,t) are related to the values of p(x, 0) integrated over spheres of radius ct centred on x_s by:

The spherical surfaces A are given by |x_s - x| = ct with area:

In other words, the mean value of the time-integrated pressure time history recorded up to time t at x_s is equal to the mean value of the initial pressure distribution on the sphere with radius ct centred at x_s.

Many reconstruction algorithms for PAT, with various measurement surface geometries, have been described.

The text below is based on an algorithm designed for reconstructing an image from acoustic data measured over a plane.

There is a fundamental difference between measurements made over spherical and planar surfaces. When the measurement surface surrounds the source region, all the emitted acoustic waves are recorded, and the absorbed energy distribution, h(x), can be recovered exactly. However, for a single planar measurement surface - even if infinite in extent - at most half of the acoustic emissions can be measured. Nevertheless it is still possible, in principle, to recover h(x) fully, as there is a two-fold data redundancy in photoacoustic imaging, as the sources generate two sets of waves travelling in opposite directions.

The reconstruction algorithm which can be used, and similar frequency- wavenumber schemes for measurements made on a plane, appear in the literature on inverse scattering problems, such as seismic migration, ultrasound imaging, and synthetic aperture radar, as well as in the mathematical literature on reconstructing a function from spherical averages. It was first described explicitly for PAT by K. P. Kostli, M. Frenz, H. Bebie, and H. P. Weber, in "Temporal backward projection of optoacoustic pressure transients using Fourier transform methods," Phys. Med. Biol., vol. 46, no. 7, pp. 1863-1872, 2001. Reference is made to this paper for an example of the mathematical analysis of pressure distributions.

A reconstruction routine can be obtained by considering an infinite and continuous planar measurement surface, then discretising the continuous solution to obtain a practical reconstruction routine.

Figure 3 shows a mathematical simulation of the conventional results of using a finite planar sensor with no processing of reverberant fields.

Figure 3(A) shows an example of simulated absorbed energy distribution, and pressure time histories are simulated as shown in Figure 3(B)₁ for an array of detectors positioned along the line z = 0. Forward calculations were performed using a time-stepping k-space model, on a 512*512 pixel, square grid corresponding to 10mm^χ10mm, or spatial steps of 39 μm, in 5000 time steps of 7.8 ns, corresponding to a Nyquist frequency of about 64 MHz.

An absorbed energy distribution consisting of a grid of circular sources as shown in Figure 3(A) is chosen to demonstrate how the quality of the recovered image varies with position. This source distribution is smoothed to ensure no frequencies greater than the Nyquist frequency are included in the simulated data.

Gaussian noise is added to the simulated pressure data at a signal-to-noise ratio of 30 dB. To solve the inverse problem, a discrete reconstruction algorithm is used. This involves use of a Fourier transform, a conversion from units of pressure to energy density, and an inverse Fourier transform. The resulting estimate of the absorbed energy density is shown Figure 3(C).

The features closest to the centre of the detection surface are recovered accurately. However, the distortion and blurring of the image increases quickly further from the centre of the detector plane, particularly in the direction of increasing z. The circles in the top line (about 17 mm from the detector plane), are almost blurred together in the reconstructed image, despite there being 1 mm gaps between them. The image resolution is strongly dependent on the distance from the detector and also, but to a lesser extent, on the distance from x = O₁ in this finite aperture case.

The blurring and distortion problems arise because, in moving from a continuous model to a practical, discrete one, it is necessary to approximate the infinite aperture by one of finite width. In addition, the fact that it is necessary to discretise the continuous functions both in the spatial and wavenumber domains, means that the data mapping can only be done approximately.

Of the errors introduced by moving from a conceptual to a practical algorithm, it is those due to the finite aperture that will be by far the most significant. The errors and artefacts arise, then, due to the fact that the measurement surface does not extend to infinity in both directions, and therefore only part of the acoustic data has been recorded: the angle subtended by the measurement aperture at any given point is limited by its finite width.

By increasing the width of the aperture, and thus capturing more data, the image can be improved. However, measuring over large planar apertures soon becomes impracticable due to the increasing technical complexity and prohibitive cost of very large arrays. For measurement surfaces that, to a greater or lesser extent, surround the source, such as a spherical measurement surface, the effect of this finite aperture problem can be reduced. However, the efficiency and accuracy of the FFT reconstruction algorithm is then lost, because, for equivalent^ fast reconstructions from any other measurement geometry, only approximate algorithms are available.

The effect of introducing acoustic reflectors perpendicular to each end of a planar sensor array is now considered, so that the acoustic data from a larger solid angle can be captured as reverberation, while the measurements are still made on a planar measurement surface. This effectively results in an increase in the measurement aperture, as described further below.

Because the measurements have been made on a planar surface, the same reconstruction algorithm is applicable. This can be implemented using FFTs, resulting in a fast reconstruction. However, it is well known that the DFT assumes that the data to be transformed is part of a periodic function. Or, to put it the other way, transforming a function given at only discrete wavenumbers implicitly assumes that the resulting function, in this case h(x), is ever-repeating.

As the true absorbed energy distr ibution is not, in fact, periodic, and so the measured acoustic time histories do not originate from a periodic source distribution, the estimate of that source distribution is distorted. The origin of the distortion can be traced back to the measured data, which includes the sound that has travelled from the region of absorbed energy h(x, z), but does not include the sound from the infinite number of repeating replicas which would appear in h(x) if it were periodic, but actually do not exist.

A more commonly-encountered consequence of the fact that the DFT implicitly assumes periodic data is that if one end of the data does not match with the other, then the output of the FFT contains spurious high frequency components. Windowing functions are often used to force the ends of the data to agree to some degree of smoothness and thereby limit this effect. Windowing, though, will not overcome the underlying problem here, which is that the measured data is not part of a periodic function, and does not originate from a periodic distribution h(x).

The invention enables the image quality to be improved not by increasing the aperture size, but, as mentioned above, by recording the reverberation between acoustic reflectors placed perpendicular to each end of the measurement aperture, at x = 0 and X. If the reflectors are perpendicular to a planar measurement surface, an infinite number of acoustic image sources results, making the absorbed energy h(x, z) into an infinitely-repeating pattern with period 2X, and thereby fulfilling the DFT requirement for a periodic function, as shown in Figure 2. The data measured from X < x < 2X is mirrored to give a repeating function

/ p(x) 0 < x < X

{ p(2X - x) X < z < 2X

which repeats every 2X.

The same DFT reconstruction algorithm used in the conventional example can be used to reconstruct an image from this reverberant data, giving this method the twin advantages of greater capture angle ('effective' aperture width) and efficient reconstruction. In essence, more information about the source distribution has been captured by recording over a longer time rather than a larger aperture.

Most of the image artefacts in Fig. 3 do not occur when the finite measurement array forms the base of an open-topped box with acoustically-reflecting side walls as shown further below.

It is also necessary to consider the requirements on the sampling of the discrete data. Sampling theorem states that the discrete function h_nm represents its continuous counterpart h(x, z) uniquely if h(x, z) contains no spatial frequency components higher than half the spatial sampling frequency (the spatial Nyquist wavenumber). In the time domain, an analogue anti-aliasing filter is used to attenuate components at frequencies greater than half the sampling frequency. In an analagous way, components at high spatial wavenumbers can be attenuated by using a sensor that is insensitive to wavenumbers above the spatial Nyquist wavenumber. For a circular pressure sensor of radius a, this criterion can be written as:

For most types of sensor array, the radius of the sensitive element, a, is fixed. However, for optically addressed arrays it can sometimes be chosen arbitrarily, thereby allowing control of the spatial anti-aliasing. If, instead of 30 dB, 15 dB attenuation at the Nyquist spatial frequency is considered sufficient to remove spatial aliasing, then the requirement above, which is equivalent to eight measurement points per sensing element diameter, can be reduced to two measurements points per diameter, or Δx < a.

As well as being sampled in space, the measured signals are also sampled in time.

Because p is not periodic in time it may be necessary to window the signal. Often, though, it is close to zero at both ends and windowing is unnecessary.

When measurements are made with the perpendicular (vertical) reflectors in place, the positions of the spatial sampling points with respect to these reflectors is important, to ensure that the samples represent a repeating pattern. The reflectors must be placed a distance Δx/2 from the first and last measurements. In other words, p(x) must be sampled at positions (2n+1)Δx/2, n = 0, . . . ,N -1 , giving the measured data

{po, pi, . . . , PN-_I}, SO that this can be made into a repeating sequence by mirroring about x = X. The data vector for the reconstruction is then Pn = {Po, . . . , P2N-i}, where p_2N-n-i = Pn, n = 0, . . . ,N -1.

This is illustrated in Figure 4. The sampled pressure is mirrored about the reflector at X to obtain the repeating sequence of length 2N with period 2X.

Because of the reverberation caused by the vertical reflectors, the pressure time- histories will, in theory, continue forever. In practice, however, due to geometric spreading and absorption, the signal will decay to below the noise in a finite length of time.

Figure 5(A) shows a time history corresponding to Figure 3(A) but including the reverberation due to the acoustic reflectors, and Figures 5(B) to (D) show images reconstructed from those time histories. Figure 5 again is for an array of detectors along the line z = O₁ for a 20 mm aperture, -10mm<= x <10mm, bounded by vertical reflectors. The data is simulated using the same k-space model as for Fig. 3(B) and the same level of noise added. Fig. 5(B), (C) and (D) used time histories with durations of 14, 20 and 40 μs respectively. The improvement in the reconstruction from Fig. 3(C) - the reduction in the artefacts and the considerably reduced blurring - is striking even for short duration data (14 μs in Fig. 5(B) compared to 20 μs in Fig. 3(C)).

The quality of the reconstruction in Fig. 3(C) depends on the position in the image (close to the centre of the sensor the image is accurately reconstructed and as one moves further from this point the image quality deteriorates), whereas a different pattern emerges in Figs. 5(B) to (D). The quality of the reconstruction does not depend on the distance from the centre of the sensor - the circles at each depth are equally well recovered - but only on the distance from the measurement plane, the depth z.

This depth dependence is reduced as more reverberation is used in the reconstruction. These improvements can be considered to be the result of an increased 'effective measurement aperture'.

Artefacts, taking the form of vertical strips aligned with each column of circles, are however more clearly visible in Figs. 5(B)-(D) than in Fig. 3(C) because of the decreased blurring in the former. These are believed to be due to the fact that the evanescent, non-radiating, part of the acoustic spectrum is neglected in the image reconstruction.

When it is not possible for the measurement aperture to extend over the full width of the base of the box, perhaps due to the way the reflectors are fixed to the plane, or because only a sensor array smaller than the box is available, it is still advantageous to include the reflectors. Figure 6 shows an aperture which covers only three-quarters of the distance between the reflectors. Figure 7(A) shows the reconstruction of Figure 3(C) and Figure 7(B) shows the image measured for the arrangement of Figure 6. Whilst there are artefacts in Fig. 7(B), the edges of many of the circles are recovered much more satisfactorily. The reason that this is so can again be understood using a concept of an 'effective measurement aperture'.

Many imaging targets of interest will contain sharp boundaries delimiting regions of different contrast, such as is the case with the circles in Fig. 3(A) or, for instance, blood vessels in tissue. In order to reconstruct the shapes of these regions accurately, the imaging scheme must be able to reconstruct the boundaries - i.e. where the contrast changes rapidly over a short distance. A result from a microlocal analysis of reconstruction algorithms states that "a boundary located at position x can be reconstructed stably if and only if one of the two normal directions to the boundary at x intersects the measurement surface" ("Image Reconstruction in photoacoustic tomography with truncated cylindrical measurement apertures", Proc. SPIE, vol. 6086, p. 608610, 2006).

A boundary that can, in principle, be reconstructed stably i.e. accurately without blurring, is called 'visible'. The accuracy with which a visible boundary is actually reconstructed depends on the particular reconstruction algorithm used. Boundaries that cannot be reconstructed stably even in principle are called 'invisible', and usually appear smoothed. This result highlights a problem with finite width planar apertures. For an infinitely-wide planar aperture, where a normal to every conceivable boundary must cross the measurement surface somewhere, all the boundaries in the image can be stably reconstructed, but using data from an array with a finite-aperture means that some of the boundaries cannot be reconstructed. However, it is clear, by comparing Figs. 3(C) and 5(D) that by including the reflectors, the boundaries, i.e. the edges of the circles, have been reconstructed more accurately. This is so even though the side walls are not per se part of the measurement array, which consists of just the planar surface perpendicular to, and between, the reflectors. Adding the reflectors is effectively increasing the width of the measurement aperture, which then allows more of the boundaries to be reconstructed.

An intuitive definition of this 'effective measurement aperture' is presented below. The 'effective measurement aperture', for a point at (x, z), is defined as the region in the plane z = 0 for which the distance from (x, z) to the plane is less than or equal to ct, as shown in Fig. 8, where t is the duration of the measurements. Some simple trigonometry shows that the 'effective' aperture width is given by:

X& = 2^)2 - ₂2

This expression for the effective aperture shows that for z«ct, doubling the length of time over which the reverberation is recorded doubles the effective aperture. It can also be seen that the angle θ subtended by an actual aperture of width X at a height z is given by tan(θ/2) = X/(2z), whereas the angle θ_eff subtended by the effective aperture is given by:

The issue is then whether or not this effective measurement aperture acts like a measurement surface. In other words, if the normal to a boundary at a point X₀ crosses the effective measurement aperture - even if not the actual sensor - is the boundary at X₀ stably reconstructed?

Figure 9 shows a plot of the magnitude of the gradient of Figure 5(B), which was reconstructed from measurements made over 14 μs. Superimposed on the plot are lines showing the angle subtended by the effective measurement apertures, as given in Fig. 8, for three of the circles in the image.

The superimposed radial lines mark out the effective aperture. The boundaries of the circles in the image can be visibly reconstructed within the angle subtended by the effective aperture. A normal to one of the reconstructed boundaries is shown with an arrow. While there are no clear cut-off points between where a boundary is well recovered and where it is poorly recovered, nevertheless, there is clearly a correspondence between those parts of the boundary that have been recovered with a large gradient - and therefore sharply - and those parts of the boundary whose normals lie in between the two lines bounding the angle subtended by the effective measurement aperture, one of which is shown.

This short-time-history example is chosen so that the effective aperture is narrow enough to be displayed easily. In addition, the boundaries in images Fig. 5(C) and (D) were so well recovered that the plot of the gradient varies little from circle to circle.

For comparison, Fig. 10 shows a plot of the magnitude of the gradient of Fig. 3(C). Again, superimposed on this image are lines showing the angles subtended by the actual measurement aperture. The boundaries of the circles in the image can again be visibly reconstructed within the angle subtended by the aperture.

As expected, the boundaries are recovered better within these angles than outside. It is also clear why the image quality in Figs. 5(B) to (D) does not depend on position in the same way as Fig. 3(C). Every point in Figure 9 is in the centre of its effective measurement aperture, whereas only the points on the line x = 0 are in the centre of the actual measurement aperture in Fig. 10. The other points lie either one side or the other of this line, leading to an asymmetry in the measurements and thus asymmetry in the distortion of the image.

The main advantage of introducing image sources by using acoustic reflectors as outlined above, perpendicular to the planar sensor, is the improvement in the image quality due to the reduction of blurring and artefacts. There are other advantages and practicalities, and other applications of the system.

Small arrays with a small number of elements are often preferable to large arrays, due to reasons of technical complexity and cost. Furthermore, they are more efficient in terms of data storage. Considering a 2D detector array consisting of N xN equally spaced elements, doubling the aperture of this array in both directions will require a 2N*2N array, a four-fold increase in the number of individual elements. By using reflectors with the smaller array, however, it is possible to achieve an effective aperture size similar to the larger array simply by recording the reverberant data for twice as long. The increased technical complexity of making measurements over a larger array, and the much greater cost, can therefore be avoided. It is simpler to increase measurement duration than array size.

For measurements over a 2D surface, the amount of data recorded is N²*M, where M is the number of samples in time. It was outlined above that doubling the duration of the measurement, doubling M, is equivalent to doubling N when z«ct. Doubling the measurement aperture in both dimensions leads to four times as much data, (2N)² *M, but doubling the duration of the measurement gives only twice as much N² *(2M). For high resolution images, which require a large number of sampling points, this saving of a factor of two in the storage requirement may be beneficial. The reverberant-field data carries the information of the source distribution more efficiently than the free-field data.

One way to improve an image such as Fig. 3(C) is to deconvolve the point spread function (PSF) of the imaging system from the image. The point spread function will consist of two parts, one due to the nature of the detector and the other due to the finite measurement aperture. The first part is often spatially invariant, but the effect of the finite aperture on the PSF is to introduce considerable spatial variation. It is this variation that causes the spatial-dependent blurring in Fig. 3(C).

Imaging with image sources over a sufficiently long time duration removes this spatially-dependent part of the PSF, as shown in Fig. 5(D). This is significant, for it is considerably easier to deconvolve a spatially-independent PSF from an image than a spatially-dependent one. Indeed, a spatially-independent PSF can be deconvolved very efficiently using FFTs, whereas there is no straightforward way to deconvolve a spatially-dependent PSF. The examples above are based on simulated data and so do not suffer from the distorting effects of a real sensor. However, for real measurements made with a real sensor, the PSF, either calculated from a model or obtained by imaging a point source near the centre of the sensor where the finite aperture effects are insignificant, can be deconvolved from the image, improving image quality and resolution still further.

It has been assumed in the analysis above that the reflectors are perfectly reflecting with the modulus of the reflection coefficient |R| = 1. Assuming that the acoustic medium is water (c = 1500 m/s, p = 1000 kg/m³), a material with high density and sound speed, such as steel with a normal incidence reflection coefficient of 0.94, would be required to approach this. An alternative is silica (glass) with |R| = 0.8, which has the advantage of being optically transparent, thereby allowing the excitation light through to the sample to be imaged. This is not an essential requirement, as the sample may be illuminated from above, or even through the sensor in some cases, but it allows greater flexibility in the illumination geometry. Most common plastics, such as PMMA, would not be ideal as their reflection coefficients, at around 0.4, may well be too low for this application. In principle, a pressure release boundary, such as a water-air interface, with R close to -1 could be used. However, this will present a greater engineering challenge than using a solid boundary.

One difference between planar imaging with and without reflectors, is that in the former case the object to be imaged must fit between the reflectors. This still allows a wide range of potential uses, including breast tumour detection, whole body imaging of small animals, including vasculature visualisation, functional brain imaging and molecular imaging. Imaging of ex vivo tissue samples, monitoring the growth of engineered tissue and, perhaps, plant morphology should also be possible.

A technique for PAT without finite aperture effects has been described. Acoustic reflectors, placed at either end of the finite aperture sensor and perpendicular to it, introduce acoustic image sources which make the acoustic field spatially periodic. By exploiting the periodicity inherently assumed by the discrete Fourier transform, an existing and efficient method for reconstructing PAT images from planar measurements can be used to reconstruct images exactly from the measured reverberant field. This technique allows the acoustic data emitted over a solid angle approaching 2π steradians to be measured, whilst maintaining the planar measurement geometry for which there exists an efficient reconstruction algorithm. There are a number of benefits of this planar approach over circular, cylindrical and spherical geometries: planar sensor arrays (including optically-addressed arrays) are readily available, a large array is not required for high resolution imaging, the image reconstruction is exact and efficient, and the PSF of the sensor can be deconvolved straightforwardly from these images improving the image quality still further. These advantages offer the prospect of rapidly-acquired photoacoustic tomography images with high, spatially-invariant, resolution over larger samples than is possible with current techniques.

However, the invention is not limited to planar sensor devices. The invention essentially recognizes that reverberant fields can be used in imaging applications to enable a smaller sensor area to provide accurate imaging.

This concept may be applied to 3D sensors, in which the sensor surrounds the sample. However, the invention enables a 3D reflector to be used in combination with a smaller surface area sensor, or a number of discrete sensors (for example two or more). With mathematical modelling of the reflector surface shape and reflection properties, the analysis of emitted signals over a time period long enough to include the reception of reverberant fields makes it possible to reconstruct the source characteristics in the same way as explained above.

The invention is of particular interest for algorithms using a Fourier transform, as the reflectors create virtual sources which lend themselves to DFT analysis and improve the image quality resulting from the DFT signal analysis. However, the invention is not limited to signal processing using a DFT, and as mentioned above more generally relates to the processing of reflected reverberant fields so that additional signal data is captured and processed. The invention has particular application in photoacoustic imaging, but can be applied to other imaging modalities, such as ultrasound imaging.

As will be clear from the above, the reflectors in the example shown create a repeating pattern of pairs of virtual sources, but with each pair having mirror symmetry. The signals from the virtual samples need to be processed to provide a repeating (non-mirrored) sequence suitable for the DFT algorithm. Thus, some additional signal processing is required before the signals received over time can be processed (to implement the mirroring function explained above), but standard and known signal processing algorithms can then be used.

The invention can provide a benefit with only one reflector, providing a single virtual source, but it is preferred that an infinite array of virtual sources is provided for the planar case, as outlined above. This array may extend in one direction (i.e. laterally) using two reflectors, but it may extend in two perpendicular directions, so that a four-sided reflector arrangement can surround the sample.

In the 3D case, the reflectors may not be planar, for example a spherical reflector may be defined.

It will be understood that the invention as claimed is intended to cover the use of a single acoustic detector, or an array of detectors. The reverberant field can include anything from a single reflection to multiple reflections from any shape of cavity. Planar or other reflectors may generate the reverberant field.

Various other examples will be apparent to those skilled in the art.

Claims

1. An imaging system comprising: a sensor arrangement for detecting an acoustic signal which emanates from a sample; and means for analysing the sensor arrangement output signals to derive a property for different portions of the sample; and a reflector arrangement for reflecting a portion of the signal generated within the sample which is not directed to the sensor arrangement, such that it is reflected to the sensor arrangement, wherein the analysing means is adapted to process sensor arrangement output signals over a time period which covers the direct receipt of the signal generated within the sample by the sensor arrangement as well as the reflected portion of the signal generated within the sample.

2. An imaging system as claimed in claim 1 , further comprising an excitation source for exposing the sample to be imaged with an excitation signal, thereby to stimulate the emanation of the acoustic signal.

3. An imaging system as claimed in claim 1 or 2, wherein the sensor arrangement comprises a planar sensor device.

4. An imaging system as claimed in claim 3, wherein the reflector arrangement comprises at least one planar reflector perpendicular to the plane of the sensor device.

5. An imaging system as claimed in any preceding claim, comprising a photoacoustic tomography, magnetoacoustic tomography, electroacoustic tomography or thermoacoustic tomography imaging system.

6. An imaging system as claimed in claim 2, wherein the excitation source comprises an electromagnetic wave source.

7. An imaging system as claimed in claim 6, wherein the excitation source comprises a pulsed light source.

8. An imaging system as claimed in claim 6, wherein the excitation source 5 comprises a continuous light source modulated at an acoustic frequency.

9. An imaging system as claimed in any preceding claim, wherein the sensor arrangement comprises a piezoelectric detector array.

10 10. An imaging system as claimed in any one of claims 1 to 8, wherein the sensor arrangement comprises an optical ultrasound sensing device.

11. An imaging system as claimed in any preceding claim, wherein the means for analysing the sensor arrangement output signals comprises a processor which

15 implements an imaging algorithm.

12. An imaging system as claimed in claim 11 , wherein the processor implements an FFT algorithm.

20 13. An imaging method comprising: detecting an acoustic signal which emanates from a sample using a sensor arrangement; and analysing the acoustic signal to derive a property for different portions of the sample,

25 wherein the signal analysis comprises processing monitored signal data over a time period which covers the direct receipt of the signal emanating from the sample by a sensor arrangement as well as receipt of reverberant reflected fields by the sensor arrangement.

30 14. A method as claimed in claim 13, further comprising: exposing a sample to be imaged with an excitation signal, thereby to thereby to stimulate the emanation of the acoustic signal.

15. A method as claimed in claim 13 or 14, wherein monitoring a signal emanating from the sample comprises using a planar sensor device.

16. A method as claimed in claim 15, comprising generating reverberant reflected fields using a reflector arrangement which comprises at least one planar reflector perpendicular to the plane of the sensor device.

17. A method as claimed in any one of claims 13 to 16, comprising a photoacoustic tomography method, a magnetoacoustic tomography method, an electroacoustic tomography method or a thermoacoustic tomography method.