Photoacoustic imaging with limited diffraction beam transducers

Photoacoustic imaging with limited diffraction beam transducers

Guenther Paltauf*a, Sibylle Gratta, Klaus Passlera, Robert Nustera, Peter Burgholzerb aKarl-Franzens-Universitaet Graz, Austria;

bUpper Austrian Research, Linz, Austria

ABSTRACT

Photoacoustic imaging with a scanning, fixed focus receiver gives images with high resolution, without the need for reconstruction algorithms. However, the usually employed spherical ultrasound lenses have a limited focal depth that decreases with increasing lateral resolution due to the inverse relation between numerical aperture and Rayleigh length. In this study the use of an axicon detector is proposed, consisting of a conical surface onto which a piezoelectric polymer film is attached. The detector is characterized in simulations and in experiments, demonstrating the expected high resolution over an extended depth of focus. Simulated and experimental images reveal X-shaped artifacts that are due to the conical detector surface. Since the point spread function (PSF) of the detector is spatially invariant over the depth of field, a frequency domain deconvolution can be applied to the images. Although this clearly improves the image quality in simulations, the reduction of artifacts was not so efficient in experiments. However, the detector is able to produce images with accurate position and shape of objects. Moreover, the axicon transducer rejects signals from planar surfaces (e.g. the skin surface) and favors signals from small, isolated sources.

Keywords: photoacoustic microscopy, optoacoustic, Bessel beam, X-waves

1. INTRODUCTION Two main imaging modalities have emerged in photoacoustic or thermoacoustic imaging, depending on the type of detector used and the method for image reconstruction 1. The first modality uses small, unfocused detectors (ideally points) that scan a closed detection surface or curve around an object to be imaged. An image of the initial distribution of absorbed energy density is reconstructed by using some kind of back projection algorithm 2. A related method uses line instead of point detectors, giving a linear projection of the energy density after application of a two-dimensional (2D) reconstruction algorithm 3,4. The second modality uses a fixed focus transducer that is scanned across the surface of the object. Single time dependent signals are converted to gray levels and transferred to columns of an image without further reconstruction. With high numerical aperture spherical lenses extremely high image resolution has been achieved with this technique 5. In this kind of amplitude scan (A-scan) imaging the depth information is provided by the time axis and therefore the depth resolution is given by the temporal resolution. The lateral resolution is highest directly in the focus of the lens but deteriorates for objects lying out of focus in axial direction. Moreover, there is a trade off between lateral resolution and depth of focus, because the Rayleigh length of a spherical lens is proportional to the square of the lateral diameter of the focus. The problem of limited focal depth has been partly solved by using neighboring signals and synthetic aperture focusing, where the focal point of the lens acts as virtual point detector 6. However, it would be desirable to obtain constantly high lateral resolution over an extended depth of focus, which is not possible with conventional spherical lenses without the need for additional signal processing.

A possible solution is the use of an axicon, which is a focusing element that concentrates an incoming plane wave onto its axis giving a beam with constant, small lateral width over an extended depth. In optics, beams with such properties are called Bessel beams and are either generated by using an annular aperture in combination with a lens or a conical lens 7. Ultrasonic Bessel beams can be generated with narrow bandwidth, continuous ultrasound and similar focusing elements. However, due to its higher efficiency and broader applicability, pulsed ultrasound excitation is usually preferred, leading to focused pulses that are confined in space and time. Because a snapshot of such a pulse in a plane containing the axis looks like an “X”, they are called “X-waves” 8. In an experimental implementation, ultrasonic X-waves can be generated with annular transducer arrays 9. Because Bessel beams and X-waves seem to disobey diffraction, they are also called non-diffracting or limited diffraction beams.

* [email protected]

Photons Plus Ultrasound: Imaging and Sensing 2009, edited by Alexander A. Oraevsky, Lihong V. Wang,Proc. of SPIE Vol. 7177, 71770S · © 2009 SPIE · CCC code: 1605-7422/09/$18 · doi: 10.1117/12.808217

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Owing to the combination of extended depth of focus and high lateral resolution, axicon like receivers have already been used for photoacoustic imaging. A typical example is a piezoelectric ring 10 or even double ring 11. In the present study we describe a conical piezoelectric transducer. A cone (or funnel) forms the detector surface and acts as an axicon with characteristics very much like the X-wave transducer described previously 9. The performance of the axicon receiver will be first described theoretically, using simulations that demonstrate the focusing and imaging characteristics of such a detector. After that, we will show first experiments where phantoms were imaged with a linear scanner that contains an axicon receiver.

2. PIEZOELECTRIC AXICON DETECTOR For manufacturing an axicon receiver, the surface of a cone is covered with a piezoelectric film as shown in figure 1(a). As seen in the cross section (Fig. 1b), a point source of ultrasound located on the axis of the cone creates a spherical wave that touches the cone on a ring shaped area after a time

sc

zt αcos= , (1)

where z is the distance of the source from the tip of the cone, cs the speed of sound and α the axicon angle. This kind of constructive interference causes the focusing effect of the axicon. The focal depth is given by

αα cossinmax

Rz = (2)

where R is the radius of the axicon. It turns out that zmax is only determined by the geometry of the axicon but not by the wavelength of the ultrasound wave, as it is the case for the focal depth of a spherical lens.

Figure 1. (a) Schematic drawing of the axicon detector. A conical surface is covered by a piezoelectric film.

(b) Cross section of the axicon detector, showing the depth of focus zmax, which is a function of the axicon angle α.

To investigate the focusing and imaging capabilities of the conical transducer, we performed the following simulation. A small spherical photoacoustic source was assumed and its typical N-shaped pressure signal was integrated over the area of the detector for different source positions. A result of this calculation is shown in figure 2, displaying the positive amplitude of the received signal as a function of the position of the source in a plane containing the detector axis. Input parameters of the simulation were R = 8 mm, α = 45° and a source diameter of 100 µm. The amplitude, which is shown on a linear gray level scale, has a maximum on the axis (r = 0) over the length zmax.

piezoelectric film α

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Figure 2. Positive maximum of the signal received by a conical detector from a sphere with a diameter of 100 µm. The dashed lines indicate the cross section of the detector surface.

An example of an image is shown in figure 3(a). Three spherical sources with diameter of 0.5 mm were located at different distance from the axicon and scanned in x-direction across the detector axis. The received signals are converted to gray levels and are displayed as a function of axial and lateral distance. The depth axis was calculated from the time axis using Eq.(1). For comparison, part (b) of the same figure shows an image of the same object, simulated for a spherical lens transducer with a numerical aperture of NA = 0.6. The source centered at a depth of 10 mm was directly in the focus of the lens. This lens was simulated with an active layer (e.g. a piezoelectric film) deposited on a spherical surface with a radius of 10 mm. Finally, part (c) of figure 3 shows an image simulated with a ring detector. The inner and outer radii of the ring were chosen as R1 = 7.9 mm and R2 = 8 mm. All three detectors are sketched below the respective images. The images obtained with the conical and ring transducers show quite similar features. In both images all three sources are imaged with identical lateral and axial extensions, as a result of the extended focal depth of the detectors. However, there are quite strong X-shaped artifacts for both types of detectors. The spherical lens detector, on the other hand, creates a good image for the sphere located in the focal plane at z = 10 mm only. The two other spheres appear very blurred and with strong arc-shaped artifacts. These artifacts depend on the numerical aperture. A lower value of NA leads to a higher depth of field at the expense of lateral resolution. It has been demonstrated that the arc shaped artifacts for out of focus objects can be partly removed by using the virtual point detector concept 6. Although they appear very similar, there is a slight difference between the images obtained with the ring and conical detectors: The X-shaped artifact of the latter is independent of depth, whereas the angle between the two lines forming the “X” varies as a function of depth for the ring detector. This makes it possible to use a classical deconvolution of the image obtained with the conical detector using a spatially invariant point spread function (PSF). In the simulation such a PSF was calculated by scanning a smaller sphere across the detector axis. Deconvolution was performed in frequency space using

aH

HII+

=′2),(

*),(),(),(ζχ

ζχζχζχ , (3)

where I(χ,ζ) and H(χ,ζ) are the 2D Fourier transforms of the original image and the PSF, respectively, χ and ζ are the frequencies in x and z direction, and * denotes complex conjugation. A small number a is used to avoid division by zero at high frequencies and thus reduces noise. Figure 4(a) shows the image after deconvolution using Eq. (3), with

( ) 1000),(max ζχHa = . There is a clear reduction of artifacts compared to the original image. Moreover, the individual sources that appeared as positive-negative areas in the original image are seen now as structures with a bright area in the center with small negative patches below and above. These unphysical negative parts of the image can now be removed. The remaining bright areas clearly show the location and even the shapes of the spherical objects (Fig. 4(b)). Adding random noise (amplitude 10% of the maximum of the image) to the image before deconvolution leads to a very similar result (Fig. 4(c)).

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Figure 3 Images of three spherical photoacoustic sources lying on a line, calculated (a) for a conical detector, (b) for a

spherical detector and (c) for a ring detector. The detectors are scanned along a line perpendicular to its axis. The sketches below the images show the cross sections of the detectors and the three spherical sources.

(a)

(b)

(c)

Figure 4. Deconvolution of the image shown in Fig. 3(a) using a calculated PSF. Image (a) contains both positive and negative values, image (b) only positive values. (c) Is the same as (b) but with 10% random noise added to the image before deconvolution.

detector area detector areadetector area

scan direction

spheres

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3. EXPERIMENT Figure 5 shows a sketch of the imaging setup with the axicon transducer. The transducer was made of a cylindrical acrylic glass block into which a cone with an angle of α = 45° was cut. The diameter of the cone was 30 mm with a hole in the center for illumination of the sample. A 25 µm thick polyvinylidene fluoride (PVDF) film was glued onto the conical surface and acted as broad band sensing element for the ultrasound pulses. Pulses from an optical parametric oscillator (OPO) pumped by a frequency-tripled Nd:YAG laser were coupled into a 600 µm core diameter optical fiber and guided to the transducer. The fiber tip was imaged with a magnification ratio of 6 onto the surface of the imaging phantoms. A typical laser pulse energy for acquiring signals for the images shown in the next section was 2 mJ. For acquisition of images, the phantoms were placed on a plastic film on top of the water filled conical transducer and scanned in a plane perpendicular to the detector axis.

Figure 5. Setup of the scanning imager using the axicon detector.

Either an averaging over several shots was performed at each scanning position or the sample was scanned with constant speed without averaging. Especially in the latter case signal processing was necessary to remove low-frequency ripples and high-frequency noise. This was done by use of a digital band pass filter. To form an image, signals were arranged in columns of an image array and displayed on a linear gray scale.

The sample for the PSF measurement was the tip of a 100 µm diameter glass fiber coated with black color that was scanned across the axicon with a step size of 20 µm. More complex phantoms were fabricated by embedding absorbing objects in gelatin. The absorbers were either droplets of black paint mixed with castor oil, polyvinyl alcohol (PVA) spheres colored with red acrylic dye or a piece of a horse hair. Horse hairs and red spheres were embedded in scattering gelatin containing a diluted solution of Intralipid (1% fat content).

optical fiber

PVDF film water

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4. RESULTS Figure 6 shows the measured image from the 100 µm diameter black coated fiber tip that served as a PSF. In Fig. 6(a) the raw image is displayed and in (b) the image after band pass filtering with lower and upper cutoff frequencies of 0.5 and 20 MHz, respectively.

Figure 6. Image of a 100 µm diameter optical fiber tip coated with black color. This image served as point spread function

of the axicon detector. (a) Raw image, (b) image after band pass filtering.

Figure 7 shows images of a horse hair with a length of 2.4 mm and a thickness of 0.32 mm. The scan direction was parallel to the hair. After deconvolution (b) the hair appears thinner than before (a) and some blurring below the hair is removed. Only positive image values are displayed. A profile of pixel values along a line perpendicular to the hair is displayed in part (c). The full width at half maximum (FWHM) of the profile is 0.3 mm, corresponding well to the value obtained from direct microscopic measurement.

(a)

(b)

(c)

Figure 7. Image of a horse hair of length 2.4 mm and thickness 0.32 mm, oriented parallel to the x-axis. (a) Image after band pass filtering, (b) deconvolved image. (c) Vertical profile at x = 2 mm, before and after deconvolution. The signals are offset for better distinction.

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Figure 8 shows an image from a red sphere with a diameter of 1.5 mm irradiated with 566 nm wavelength laser pulses. The detector was scanned in x-direction with constant speed, without averaging. Again, the image contains only positive values, the negative values are set equal to zero. The dotted white circle indicates the circumference of the sphere. Only the lower part of the sphere is seen in the image due to the high optical attenuation in the red dye. Since for this sample the artifact level is already relatively low, no deconvolution was applied.

Figure 8. Image of a sphere made of PVA colored with red acrylic dye, embedded in scattering gelatin. The dotted white line indicates the size of the sphere.

The final example is an image of a black absorbing sphere embedded in gelatin with some background absorption (µa = 15 cm-1). In this experiment we want to demonstrate the difference in imaging of a layer boundary in comparison with a spherical source. Both features can be seen in the image. A vertical profile through the center of the sphere shows the relative amplitudes of the gelatin boundary and the sphere.

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Figure 9. (a) Image of a black sphere in absorbing gelatin (only positive values). (b) Vertical profile through the center of the sphere.

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5. DISCUSSION Photoacoustic images taken with the axicon detector are characterized by a constantly high resolution along its axis, but a high level of artifacts. The high depth of focus is due to the conical shape of the detector, providing equal focusing conditions for all points lying within the length zmax defined in Eq. (2).

An estimate of the axial and lateral resolution can be obtained from the analysis of a flat X-wave transducer as it is described by Lu and Greenleaf 8. A transducer transfer function

)exp()( 0kakB −= (4)

where k is the wave vector and a0 a constant, gives values of

αsin32

0awlat = αcos32

0awax = (5)

for the lateral resolution wlat and the axial resolution wax. The constant a0 can be interpreted as the minimum pulse width that can be resolved by the PVDF film. Considering the film thickness of 25 µm and the different speed of sound in PVDF and water, a0 in water is about 17 µm. With α = 45° this leads to wlat = wax = 83 µm. These values are compatible with the widths of the experimental pulse in Fig. 6(b), measured as FWHM values of 120 µm and 150 µm in axial and lateral direction, respectively. In this experiment the extended size of the source (100 µm) has to be taken into account.

Since the PSF is spatially invariant, a deconvolution in frequency space is possible. This worked particularly well in simulations, even when some noise was added to the signals. The main effect of the deconvolution is a reduction of the X-shaped artifacts and a restoration of the actual source dimensions. In experiments, the reduction of X-shaped artifacts was not as efficient as in simulations. However, the example of Fig. 7(c) shows the ability to turn positive-negative signal features in purely positive peaks.

A question arises how the plane wave signal that emerges from the boundary of the absorbing gelatin in Fig.9 leads to a defined temporal feature when registered by the conical sensor. The picture of a spherical wave shown in Fig. 1(b) is certainly not applicable in this case. However, the laser spot on the gelatin surface has a finite diameter of about 2 mm. Therefore the wave coming from this boundary is diffracted and parts of it are detected by the conical sensor. It can be expected that a point scanning parallel to the gelatin surface would have measured a much stronger signal from the surface than from the sphere. An estimation using a numerical integration of the wave equation for a sphere with its center 2 mm below the surface of gelatin with the same absorption as in the measurement gives a plane wave signal that is about a factor of 10 higher than the amplitude of the wave from the sphere. In this simulation a point detector was located 9 mm from the gelatin surface, exactly opposite to the sphere. The axicon detector therefore favors small, isolated sources and partly rejects signals from planar boundaries. A similar effect has the combination of dark field illumination with a spherical lens detector 12.

In conclusion, photoacoustic imaging with a conical axicon detector gives images with high depth of field but a relatively high level of artifacts. Due to the spatial invariance of the PSF the artifacts can be reduced by deconvolution. The axicon imager will be further investigated for the imaging of tissue samples.

ACKNOWLEDGMENT

This work has been supported by the Austrian Science Fund, project numbers S10502-N20 and L418-N20.

REFERENCES

1. Xu, M. H. and Wang, L. V., "Photoacoustic Imaging in Biomedicine," Review of Scientific Instruments 77, 041101 (2006).

2. Xu, M. H. and Wang, L. V., "Universal back-projection algorithm for photoacoustic computed tomography," Phys. Rev. E 71, 016706 (2005).

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3. Burgholzer, P., Hofer, C., Paltauf, G., Haltmeier, M., and Scherzer, O., "Thermoacoustic tomography with integrating area and line detectors," IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 52, 1577-1583 (2005).

4. Paltauf, G., Nuster, R., Haltmeier, M, and Burgholzer, P., "Photoacoustic tomography using a Mach-Zehnder interferometer as acoustic line detector," Appl. Opt. 46, 3352-3358 (2007).

5. Zhang, H. F., Maslov, K., Stoica, G., and Wang, L. V., "Functional Photoacoustic Microscopy for High-Resolution and Noninvasive in Vivo Imaging," Nature Biotechnology 24, 848-851 (2006).

6. Li, M-L, Zhang, H. F., Maslov, K., Stoica, G., and Wang, L. V., "Improved in vivo photoacoustic microscopy based on a virtual-detector concept," Optics Letters 31, 474-476 (2006).

7. Durnin, J., Miceli, J. J., and Eberly, J. H., "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).

8. Lu, J. Y. and Greenleaf, J. F., "Nondiffracting X-Waves - Exact-Solutions to Free-Space Scalar Wave-Equation and Their Finite Aperture Realizations," IEEE Trans. Ultrason., Ferroelectr., and Frequ. Control 39, 19-31 (1992).

9. Lu, J. Y. and Greenleaf, J. F., "Experimental verification of nondiffracting X waves," IEEE Trans. Ultrason., Ferroelectr., and Frequ. Control 39, 441-446 (1992).

10. Köstli, K. P., Frenz, M., Weber, H. P., Paltauf, G., and Schmidt-Kloiber, H., "Pulsed optoacoustic tomography of soft tissue with a piezoelectric ring sensor," Proc. SPIE 3916, 67-74 (2000).

11. Kolkman, R. G. M., Hondebrink, E., Steenbergen, W., Van Leeuwen, T. G., and De Mul, F. F. M., "Photoacoustic imaging with a double-ring sensor featuring a narrow aperture," J. Biomed. Opt. 9, 1327-1335 (2004).

12. Maslov, K., Stoica, G., and Wang, L. V., "In vivo dark-field reflection-mode photoacoustic microscopy," Optics Letters 30, 625-627 (2005).

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