A sparsification and reconstruction strategy for compressed sensing photoacoustic tomography.

Compressed sensing (CS) is a promising approach to reduce the number of measurements in photoacoustic tomography (PAT) while preserving high spatial resolution. This allows to increase the measurement speed and reduce system costs. Instead of collecting point-wise measurements, in CS one uses various combinations of pressure values at different sensor locations. Sparsity is the main condition allowing to recover the photoacoustic (PA) source from compressive measurements. In this paper, a different concept enabling sparse recovery in CS PAT is introduced. This approach is based on the fact that the second time derivative applied to the measured pressure data corresponds to the application of the Laplacian to the original PA source. As typical PA sources consist of smooth parts and singularities along interfaces, the Laplacian of the source is sparse (or at least compressible). To efficiently exploit the induced sparsity, a reconstruction framework is developed to jointly recover the initial and modified sparse sources. Reconstruction results with simulated as well as experimental data are given.

Remote mid-infrared photoacoustic spectroscopy with a quantum cascade laser.

We demonstrate non-contact remote photoacoustic spectroscopy in the mid-infrared region. A room-temperature-operated pulsed external-cavity quantum cascade laser is used to excite photoacoustic waves within a semitransparent sample. The ultrasonic waves are detected remotely on the opposite side of the sample using a fiber-optic Mach-Zehnder interferometer, thereby avoiding problems associated with acoustic attenuation in air. We present the theoretical background of the proposed technique and demonstrate measurements on a thin polystyrene film. The obtained absorption spectrum in the region of 1030-1230 cm(-1) is compared to a spectrum obtained by attenuated total reflection, showing reasonable agreement.

Characterization of the spatio-temporal response of optical fiber sensors to incident spherical waves.

In this study a theoretical framework for calculating the acoustic response of optical fiber-based ultrasound sensors is presented. The acoustic response is evaluated for optical fibers with several layers of coating assuming a harmonic point source with arbitrary position and frequency. First, the fiber is acoustically modeled by a layered cylinder on which spherical waves are impinged. The scattering of the acoustic waves is calculated analytically and used to find the normal components of the strains on the fiber axis. Then, a strain-optic model is used to calculate the phase shift experienced by the guided mode in the fiber owing to the induced strains. The framework is showcased for a silica fiber with two layers of coating for frequencies in the megahertz regime, commonly used in medical imaging applications. The theoretical results are compared to experimental data obtained with a sensing element based on a pi-phase-shifted fiber Bragg grating and with photoacoustically generated ultrasonic signals.

Design, implementation, and analysis of a compressed sensing photoacoustic projection imaging system.

Significance: Compressed sensing (CS) uses special measurement designs combined with powerful mathematical algorithms to reduce the amount of data to be collected while maintaining image quality. This is relevant to almost any imaging modality, and in this paper we focus on CS in photoacoustic projection imaging (PAPI) with integrating line detectors (ILDs). Aim: Our previous research involved rather general CS measurements, where each ILD can contribute to any measurement. In the real world, however, the design of CS measurements is subject to practical constraints. In this research, we aim at a CS-PAPI system where each measurement involves only a subset of ILDs, and which can be implemented in a cost-effective manner. Approach: We extend the existing PAPI with a self-developed CS unit. The system provides structured CS matrices for which the existing recovery theory cannot be applied directly. A random search strategy is applied to select the CS measurement matrix within this class for which we obtain exact sparse recovery. Results: We implement a CS PAPI system for a compression factor of 4:3, where specific measurements are made on separate groups of 16 ILDs. We algorithmically design optimal CS measurements that have proven sparse CS capabilities. Numerical experiments are used to support our results. Conclusions: CS with proven sparse recovery capabilities can be integrated into PAPI, and numerical results support this setup. Future work will focus on applying it to experimental data and utilizing data-driven approaches to enhance the compression factor and generalize the signal class.

Two-photon absorption-induced photoacoustic imaging of Rhodamine B dyed polyethylene spheres using a femtosecond laser.

In the present paper we demonstrate the possibility to image dyed solids, i.e. Rhodamine B dyed polyethylene spheres, by means of two-photon absorption-induced photoacoustic scanning microscopy. A two-photon luminescence image is recorded simultaneously with the photoacoustic image and we show that location and size of the photoacoustic and luminescence image match. In the experiments photoacoustic signals and luminescence signals are generated by pulses from a femtosecond laser. Photoacoustic signals are acquired with a hydrophone; luminescence signals with a spectrometer or an avalanche photo diode. In addition we derive the expected dependencies between excitation intensity and photoacoustic signal for single-photon absorption, two-photon absorption and for the combination of both. In order to verify our setup and evaluation method the theoretical predictions are compared with experimental results for liquid and solid specimens, i.e. a carbon fiber, Rhodamine B solution, silicon, and Rhodamine B dyed microspheres. The results suggest that the photoacoustic signals from the Rhodamine B dyed microspheres do indeed stem from two-photon absorption.

A webcam in Bayer-mode as a light beam profiler for the near infra-red.

Beam profiles are commonly measured with complementary metal oxide semiconductors (CMOS) or charge coupled devices (CCD). The devices are fast and reliable but expensive. By making use of the fact that the Bayer-filter in commercial webcams is transparent in the near infra-red (>800 nm) and their CCD chips are sensitive up to about 1100 nm, we demonstrate a cheap and simple way to measure laser beam profiles with a resolution down to around ±1 µm, which is close to the resolution of the knife-edge technique.

Sensitive and high laser damage threshold substrates for surface-enhanced Raman scattering based on gold and silver nanoparticles.

Surface-enhanced Raman scattering (SERS) is a sensitive and fast technique for sensing applications such as chemical trace analysis. However, a successful, high-throughput practical implementation necessitates the availability of simple-to-use and economical SERS substrates. In this work, we present a robust, reproducible, flexible and yet cost-effective SERS substrate suited for the sensitive detection of analytes at near-infrared (NIR) excitation wavelengths. The fabrication is based on a simple dropcast deposition of silver or gold nanomaterials on an aluminium foil support, making the design suitable for mass production. The fabricated SERS substrates can withstand very high average Raman laser power of up to 400 mW in the NIR wavelength range while maintaining a linear signal response of the analyte. This enables a combined high signal enhancement potential provided by (i) the field enhancement via the localized surface plasmon resonance introduced by the noble metal nanomaterials and (ii) additional enhancement proportional to an increase of the applicable Raman laser power without causing the thermal decomposition of the analyte. The application of the SERS substrates for the trace detection of melamine and rhodamine 6G is demonstrated, which shows limits of detection smaller than 0.1 ppm and analytical enhancement factors on the order of 104 as compared to bare aluminium foil.

Downstream Fabry-Perot interferometer for acoustic wave monitoring in photoacoustic tomography.

An optical detection setup consisting of a focused laser beam fed into a downstream Fabry-Perot interferometer (FPI) for demodulation of acoustically generated optical phase variations is investigated for its applicability in photoacoustic tomography. The device measures the time derivative of acoustic signals integrated along the beam. Compared to a setup where the detection beam is part of a Mach-Zehnder interferometer, the signal-to-noise ratio of the FPI is lower, but the image quality of the two devices is similar. Using the FPI in a photoacoustic tomograph allows scanning the probe beam around the imaging object without moving the latter.

Remote photoacoustic imaging on solid material using a two-wave mixing interferometer.

We report on remote and contactless photoacoustic imaging (PAI) for the inspection of solid materials using a two-wave mixing interferometer. In this Letter, a semitransparent sample was excited with picosecond laser pulses. The local absorption of the electromagnetic radiation led to generation of broadband ultrasonic waves inside the sample. Ultrasonic waves arriving at the sample surface were detected utilizing a two-wave mixing interferometer. After data acquisition, the initial pressure distribution was reconstructed using a Fourier space synthetic aperture technique algorithm. We show the potential of PAI for the inspection of semitransparent solid materials.

Extension of the Thermographic Signal Reconstruction Technique for an Automated Segmentation and Depth Estimation of Subsurface Defects.

With increased use of light-weight materials with low factors of safety, non-destructive testing becomes increasingly important. Thanks to the advancement of infrared camera technology, pulse thermography is a cost efficient way to detect subsurface defects non-destructively. However, currently available evaluation algorithms have either a high computational cost or show poor performance if any geometry other than the most simple kind is surveyed. We present an extension of the thermographic signal reconstruction technique which can automatically segment and image defects from sound areas, while also estimating the defect depth, all with low computational cost. We verified our algorithm using real world measurements and compare our results to standard active thermography algorithms with similar computational complexity. We found that our algorithm can detect defects more accurately, especially when more complex geometries are examined.

Laser excited super resolution thermal imaging for nondestructive inspection of internal defects.

A photothermal super resolution technique is proposed for an improved inspection of internal defects. To evaluate the potential of the laser-based thermographic technique, an additively manufactured stainless steel specimen with closely spaced internal cavities is used. Four different experimental configurations in transmission, reflection, stepwise and continuous scanning are investigated. The applied image post-processing method is based on compressed sensing and makes use of the block sparsity from multiple measurement events. This concerted approach of experimental measurement strategy and numerical optimization enables the resolution of internal defects and outperforms conventional thermographic inspection techniques.

Resolution Limits in Photoacoustic Imaging Caused by Acoustic Attenuation.

In conventional photoacoustic tomography, several effects contribute to the loss of resolution, such as the limited bandwidth and the finite size of the transducer, or the space-dependent speed of sound. They can all be compensated (in principle) technically or numerically. Frequency-dependent acoustic attenuation also limits spatial resolution by reducing the bandwidth of the photoacoustic signal, which can be numerically compensated only up to a theoretical limit given by thermodynamics. The entropy production, which is the dissipated energy of the acoustic wave divided by the temperature, turns out to be equal to the information loss, which cannot be compensated for by any reconstruction method. This is demonstrated for the propagation of planar acoustic waves in water, which are induced by short laser pulses and measured by piezoelectric acoustical transducers. It turns out that for water, where the acoustic attenuation is proportional to the squared frequency, the resolution limit is proportional to the square root of the distance and inversely proportional to the square root of the logarithm of the signal-to-noise ratio. The proposed method could be used in future work for media other than water, such as biological tissue, where acoustic attenuation has a different power-law frequency dependence.

Acoustic Reconstruction for Photothermal Imaging.

Pulsed illumination of a sample, e.g., of a biological tissue, causes a sudden temperature increase of light absorbing structures, such as blood vessels, which results in an outgoing acoustic wave, as well as heat diffusion, of the absorbed energy. Both of the signals, pressure and temperature, can be measured at the sample surface and are used to reconstruct the initial temperature or pressure distribution, called photoacoustic or photothermal reconstruction respectively. We have demonstrated that both signals at the same surface pixel are connected by a temporal transformation. This allows for the calculation of a so-called acoustical virtual wave from the surface temperature evolution as measured by an infrared camera. The virtual wave is the solution of a wave equation and can be used to reconstruct the initial temperature distribution immediately after the excitation pulse. This virtual wave reconstruction method was used for the reconstruction of inclined steel rods in an epoxy sample, which were heated by a short pulse. The reconstructed experimental images show clearly the degradation of the spatial resolution with increasing depth, which is theoretically described by a depth-dependent thermographic point-spread-function.

Exact and approximative imaging methods for photoacoustic tomography using an arbitrary detection surface.

Two universal reconstruction methods for photoacoustic (also called optoacoustic or thermoacoustic) computed tomography are derived, applicable to an arbitrarily shaped detection surface. In photoacoustic tomography acoustic pressure waves are induced by illuminating a semitransparent sample with pulsed electromagnetic radiation and are measured on a detection surface outside the sample. The imaging problem consists in reconstructing the initial pressure sources from those measurements. The first solution to this problem is based on the time reversal of the acoustic pressure field with a second order embedded boundary method. The pressure on the arbitrarily shaped detection surface is set to coincide with the measured data in reversed temporal order. In the second approach the reconstruction problem is solved by calculating the far-field approximation, a concept well known in physics, where the generated acoustic wave is approximated by an outgoing spherical wave with the reconstruction point as center. Numerical simulations are used to compare the proposed universal reconstruction methods with existing algorithms.

Fiber-optic annular detector array for large depth of field photoacoustic macroscopy.

We report on a novel imaging system for large depth of field photoacoustic scanning macroscopy. Instead of commonly used piezoelectric transducers, fiber-optic based ultrasound detection is applied. The optical fibers are shaped into rings and mainly receive ultrasonic signals stemming from the ring symmetry axes. Four concentric fiber-optic rings with varying diameters are used in order to increase the image quality. Imaging artifacts, originating from the off-axis sensitivity of the rings, are reduced by coherence weighting. We discuss the working principle of the system and present experimental results on tissue mimicking phantoms. The lateral resolution is estimated to be below 200 µm at a depth of 1.5 cm and below 230 µm at a depth of 4.5 cm. The minimum detectable pressure is in the order of 3 Pa. The introduced method has the potential to provide larger imaging depths than acoustic resolution photoacoustic microscopy and an imaging resolution similar to that of photoacoustic computed tomography.

Thermoacoustic tomography with integrating area and line detectors.

Thermoacoustic (optoacoustic, photoacoustic) tomography is based on the generation of acoustic waves by illumination of a sample with a short electromagnetic pulse. The absorption density inside the sample is reconstructed from the acoustic pressure measured outside the illuminated sample. So far measurement data have been collected with small detectors as approximations of point detectors. Here, a novel measurement setup applying integrating detectors (e.g., lines or planes made of piezoelectric films) is presented. That way, the pressure is integrated along one or two dimensions, enabling the use of numerically efficient algorithms, such as algorithms for the inverse radon transformation, for thermoacoustic tomography. To reconstruct a three-dimensional sample, either an area detector has to be moved tangential around a sphere that encloses the sample or an array of line detectors is rotated around a single axis. The line detectors can be focused on cross sections perpendicular to the rotation axis using a synthetic aperture (SAFT) or by scanning with a cylindrical lens detector. Measurements were made with piezoelectric polyvinylidene fluoride film detectors and evaluated by comparison with numerical simulations. The resolution achieved in the resulting tomography images is demonstrated on the example of the reconstructed cross section of a grape.

Thermodynamic Limits of Spatial Resolution in Active Thermography.

Thermal waves are caused by pure diffusion: their amplitude is decreased by more than a factor of 500 within a propagation distance of one wavelength. The diffusion equation, which describes the temperature as a function of space and time, is linear. For every linear equation the superposition principle is valid, which is known as Huygens principle for optical or mechanical wave fields. This limits the spatial resolution, like the Abbe diffraction limit in optics. The resolution is the minimal size of a structure which can be detected at a certain depth. If an embedded structure at a certain depth in a sample is suddenly heated, e.g., by eddy current or absorbed light, an image of the structure can be reconstructed from the measured temperature at the sample surface. To get the resolution the image reconstruction can be considered as the time reversal of the thermal wave. This inverse problem is ill-conditioned and therefore regularization methods have to be used taking additional assumptions like smoothness of the solutions into account. In the present work for the first time, methods of non-equilibrium statistical physics are used to solve this inverse problem without the need of such additional assumptions and without the necessity to choose a regularization parameter. For reconstructing such an embedded structure by thermal waves the resolution turns out to be proportional to the depth and inversely proportional to the natural logarithm of the signal-to-noise ratio. This result could be derived from the diffusion equation by using a delta-source at a certain depth and setting the entropy production caused by thermal diffusion equal to the information loss. No specific model about the stochastic process of the fluctuations and about the distribution densities around the mean values was necessary to get this result.

On the crossing points of the Lamb modes and the maxima and minima of displacements observed at the surface.

This article elaborates on the crossing points of the frequency-wavenumber branches for the symmetric and anti-symmetric Lamb modes in a homogeneous plate. It is shown both theoretically as well as experimentally that at these crossing points either the normal or the longitudinal components of modal displacement attain an extreme value, i.e. a maximum or it vanishes. This behavior is assessed herein using a method due to Mindlin, who showed that the dispersion curves for a plate with mixed boundary conditions - which are associated with uncoupled shear and dilatational modes - provide bounds to the spectral lines of the free plate. Therefore, a subset of the crossing points of the symmetric and antisymmetric Lamb modes for a free plate coincide with the crossing points for a plate with mixed boundary conditions.

Deblurring algorithms accounting for the finite detector size in photoacoustic tomography.

Most reconstruction algorithms for photoacoustic tomography, like back projection or time reversal, work ideally for point-like detectors. For real detectors, which integrate the pressure over their finite size, images reconstructed by these algorithms show some blurring. Iterative reconstruction algorithms using an imaging matrix can take the finite size of real detectors directly into account, but the numerical effort is significantly higher compared to the use of direct algorithms. For spherical or cylindrical detection surfaces, the blurring caused by a finite detector size is proportional to the distance from the rotation center (spin blur) and is equal to the detector size at the detection surface. In this work, we apply deconvolution algorithms to reduce this type of blurring on simulated and on experimental data. Two particular deconvolution methods are compared, which both utilize the fact that a representation of the blurred image in polar coordinates decouples pixels at different radii from the rotation center. Experimental data have been obtained with a flat, rectangular piezoelectric detector measuring signals around a plastisol cylinder containing various small photoacoustic sources with variable distance from the center. Both simulated and experimental results demonstrate a nearly complete elimination of spin blur.

Limits of Spatial Resolution for Thermography and Other Non-destructive Imaging Methods Based on Diffusion Waves.

In this work the measured variable, such as temperature, is a random variable showing fluctuations. The loss of information caused by diffusion waves in non-destructive testing can be described by stochastic processes. In non-destructive imaging, the information about the spatial pattern of a samples interior has to be transferred to the sample surface by certain waves, e.g., thermal waves. At the sample surface these waves can be detected and the interior structure is reconstructed from the measured signals. The amount of information about the interior of the sample, which can be gained from the detected waves on the sample surface, is essentially influenced by the propagation from its excitation to the surface. Diffusion causes entropy production and information loss for the propagating waves. Mandelis has developed a unifying framework for treating diverse diffusion-related periodic phenomena under the global mathematical label of diffusion-wave fields, such as thermal waves. Thermography uses the time-dependent diffusion of heat (either pulsed or modulated periodically) which goes along with entropy production and a loss of information. Several attempts have been made to compensate for this diffusive effect to get a higher resolution for the reconstructed images of the samples interior. In this work it is shown that fluctuations limit this compensation. Therefore, the spatial resolution for non-destructive imaging at a certain depth is also limited by theory.