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Abstract
In this work, full-field detection of laser-induced ultrasound waves was performed with an off-axis LED-based Schlieren system. Sensing strobe light, pulsed laser dual light-sheet excitation, and CMOS sensor device were all synchronized to capture the pressure wave as it propagated through an elastic liquid surrounding the test sample. In addition, a reconstruction algorithm based on the Radon transform was applied to the digitally recorded field in order to obtain an image of the photoacoustic source. The proposed system is capable of retrieving the profile of cylindrical and hexagonal targets.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The photoacoustic (PA) effect consists in the generation of an ultrasound wave due to the optical absorption of, among others, a short laser pulse by a thermoelastic medium. [1] The electromagnetic energy deposited into a thin layer of the absorber induces a transient local increment of temperature, producing a sudden thermoelastic expansion-contraction response, which in turn causes ultrasound (pressure) waves that propagate through the sample and, after boundary effects, into the surrounding medium. [2,3] This unique optical-to-mechanical transduction process allows the fusion of the wavelength selectivity (contrast) of optical absorption with the high spatial resolution of ultrasound in photoacoustic imaging techniques. [4–6] The most widespread ultrasound detection technology is based on piezoelectric transducers, due to their design and manufacturing versatility. However, pressure detectors used to acquire photoacoustic signals demand special requirements in terms of sensitivity and bandwidth. For example, photoacoustic signals generated in living biological samples have amplitudes about a thousand times smaller than ultrasound signals emitted by standard medical probes. On the other hand, while ultrasonography operates within a narrow frequency range, laser-generated ultrasound has a wide bandwidth of up to hundreds of megahertz. [7] In this regard, optical sensing methods offer increased sensitivity over a much wider frequency range, this being the main reason for the growing interest in developing optical devices to sense pressure signals. [8] The working principles of optical ultrasonic detectors are mainly based on two fundamental phenomena: refraction and interference. In the former, an interrogation optical beam is used to sense pressure gradients through refractive index variations, which are induced by the ultrasound wave propagating through the elastic medium. [9] In the latter, the photoacoustic wavefront locally modifies the optical path length traveled by a light beam along the interferometer sensing arm; because of this, when superimposed on the unvarying reference light beam, the resulting interference pattern follows the propagation path of pressure wavefront. [10–12]
In photoacoustic tomography, a number of fluctuating pressure signals are usually acquired at discrete positions around the sample through rotational scanning when few detectors are available, or using specially designed sensor arrays when multiple acquisition is possible. All of these signal waveforms are arranged in a so-called sinogram with the aim of imaging the photoacoustic sources. This is achieved by solving an inverse problem through the implementation of a reconstruction algorithm, which may be based on a time-reversal propagation or backprojection. [13,14] Some optical methods reduce the need of multiple sensing points, and frequently, a charge-coupled device (CCD) camera is used to capture a two-dimensional image of the entire ultrasonic field at a given instant. Departing from this image, and applying a reconstruction algorithm, the spatial distribution of the photoacoustic sources can be retrieved. This technique is known as full-field detection method. [15] Several optical configurations are used in order to convert the pressure information into irradiance modulation so that it can be detected by a camera. In the early works reported, a test beam is reflected at an optical interface. The propagation of the ultrasonic wave slightly modifies the reflectivity of the surface and the intensity of the reflected beam, which is recorded in the camera. [16] Also, Fabry-Perot interferometers, Schlieren photography, shadowgraphy and optical phase contrast set-ups have been used as full-field optical detectors. [17–19] Particularly, the Schlieren technique allows visualizing the photoacoustic field thanks to the optoelastic phenomenon. The ultrasound wave propagating through the medium modifies its refractive index and, consequently, the phase of the test beam. By applying spatial filtering on the detection plane, the out-of-phase light is removed to generate a map of intensities representing the acoustic field, which is recorded by a digital camera. [7,20]
Given its efficiency in generating photoacoustic images of absorbing objects from a single capture, full-field PA acquisition techniques find potential applications in a sort of real-time imaging systems. For example, the Schlieren configuration presented herein is perfectly usable for nondestructive testing or biological studies where the sample can be fully immersed in a transparent liquid, but its use for in-vivo clinical testing is limited. In particular, this work presents an off-axis Schlieren system employing a LED stroboscope as light source that is used to capture the acoustic wave generated by the excitation of several optical absorbers immersed in a transparent medium with pulsed laser light. From the acoustic full-field captured, the numerical reconstruction of the spatial distribution of photoacoustic sources is accomplished using the Radon transform.
2. Theory
The theoretical analysis section is presented in two parts: the first one refers to the Schlieren detection system and the parameters influencing its sensitivity; the second one describes the fundamental aspects of the Radon transform and its application to the tomographic image reconstruction process.
2.1 Schlieren detection system
Let us propagate a bunch of light rays through a transparent medium subjected to transversal physical stress. Those rays traversing regions with induced refractive index changes deviate from the original trajectory. In the PA case, the mechanical force is exerted on the immersion fluid by the traveling pressure wave and light is locally deviated. The deflection angle $\varepsilon$ depends on the piezo-optic coefficient $C_{n_0}$ of the propagating medium, [21,22] and is described by
where $n_{0}$ is the refractive index of the medium, $\partial p / \partial x$ is the pressure change as a function of the distance, and $\omega$ is the path length across the ultrasonic field. $C_{n_0}$, also known as the Gladstone-Dale coefficient, quantifies the refractive index variations and provides a coupling measure between ultrasound and light. It is defined asIn an off-axis single-mirror coincident Schlieren system with a diverging/converging wavefront beam, in general, it is valid to assume that a light ray passes twice through practically the same inhomogeneous region on its round trip. [23] This system will separate the diffracted light from the undiffracted beam a distance $\delta$ that can be approximated according to
Here, $s$ represents the distance from the converging point to the inhomogeneous region (see Fig. 1). Assuming that the PA source sample is placed close to the parabolic mirror of focal length $f$, then
Now, $\tan \varepsilon \approx \varepsilon$ for small angles, and Eq. (3) can be rewritten as
Fig. 1. Off-axis Schlieren system (not at scale). LS: Light source, C: Condenser lens, ES: Entrance slit, P: Perturbation, M: Concave mirror. K: Knife, CCD: Camera
If we consider a Schlieren system with a rectangular entrance slit and a knife edge as a stop, the deviated rays will manifest themselves as an intensity change over the output image. Then, each variation of local image contrast corresponds to a region in the immersion fluid where the refractive index undergoes a change caused by the traveling pressure wave. Contrast is given as [23,24]
where $a$ is the height of the unobstructed beam that is not stopped by the knife edge at a given position, and thus reaches the detector.The sensitivity of the system gives a measure of the change in image contrast as a function of the angle of the refracted beam. Using Eqs. (5) and (6), sensitivity yields
This result shows that sensitivity depends on both the focal length of the mirror and the height of the unobstructed image. It is important to note that this sensitivity is four times higher than that in a Z-type Schlieren system, a configuration that uses two parabolic mirrors in a symmetrical distribution. [25–27]
2.2 Image reconstruction
Although the photoacoustic wave is generally a 3D problem, when a Schlieren probe and camera are used to carry out the recording, it is reduced to a two-dimensional projection. The detection method described above will provide an instantaneous 2D image representing the variation of the refractive index of the surrounding liquid in the direction perpendicular to the edge of the sheet. Then, it is a map of the pressure gradient caused by the traveling pressure wave after a time of flight $t$. Although this is technically the first derivative of the pressure, the image obtained depicts the wavefront profile and is sufficient to reconstruct pressure sources. [20,28]
Let us use the function $P(x,y,t)$ to designate the PA wavefront at the indicated fixed instant, and from which it is desired to retrieve the projection of 2D initial pressure distribution $P_0$, namely, the PA-wave source shape. This is possible by using the projection inversion method described in Ref. [15]. In that, the Radon transform of $P(x,y;t)$, denoted as $(R P_{\phi })(d;\phi ;t)$, integrates all function projections along lines defined by coordinate $u$ with direction ($\sin \phi$, $\cos \phi$) placed at a signed distance $d$ from the origin. In the previous transformation, $\tan \phi = y/x$ with a range for $\phi$=$[0,\pi ]$. Therefore, considering that each ($x,y$) coordinate can be rewritten as a function of $\phi$ involving $d$ and $u$,
Since $(R P_{\phi })(d;\phi ;t)$ fulfill wave equation and initial conditions, it can be expressed in terms of the initial pressure projection $P_0$. That is,
which is the d’Alembert solution to the inverse problem, where $s$ is the distance traveled by the acoustic wave and is determined by the medium sound speed $c$ and the time of flight.Then, if we take the captured data and apply the Radon transform to it, it is possible to recover the initial information by reversing the translation by an amount equivalent to $\pm s$. Applying the translation to Eq. (9) yields
Now, if we restrict the function to a sphere of radio $r$, the contribution given by the term $R\left [ P(d;\phi ;2t)\right ]$ is outside the interval, so it can be discarded. This results in an explicit inversion formula, as follows
At this point, the initial pressure distribution $P_0$ can be obtained by applying the inverse Radon transform to $R\left [ P(d;\phi )\right ]$.
3. Methods
3.1 Photoacoustic wave generation
A scheme of the PA imaging system developed in this work is shown in Fig. 2. The PA excitation source, an OPO-Nd:YAG laser (NT352C10, Ekspla), delivered a 4 ns pulsed laser beam centered at $\lambda$=670 nm, with an energy of 20 mJ per pulse, and a repetition rate of 10 Hz. The laser beam was propagated through a 50:50 beamsplitter, and the two resulting beams were manipulated (not shown in the schematic representation) in order to simultaneously illuminate both lateral sides of the sample along the $x$ axis, and perpendicularly to the Schlieren beam, which propagates in $y$ direction. Each beam was passed through a cylindrical lens ($f_S=100$ mm) to form a sheet of light with a Gaussian intensity profile (FWHM=12mm, Kurtosis=-1.4). The sample was immersed in a glass container filled with ethyl alcohol, since this immersion fluid has a piezo-optical coefficient ($3.612 \pm 0.02\times 10^{-10}$ Pa$^{-1}$) that is more than twice greater than the one for water ($1.466\pm 0.01\times 10^{-10}$ Pa$^{-1}$). According to Eqs. (1) and (6), larger deflection of perturbed light rays and contrast enhancement are to be expected. The container is placed in front of a convergent spherical mirror of focal length $f_M = 1.15$ m, so that the distance between the sample and the mirror surface is 20 mm, thus maximizing the sensitivity of the system.
Fig. 2. A Experimental set-up (not at scale). B, C, D: Top, angled ans front views, respectively, of the container with the sample and excitation light. LED: Pulsed LED, L: Condenser Lens, ES: Entrance Slit, S: Sample, M: Mirror, CL1 and CL2: Cylindrical Lenses, PL: Pulsed Laser, N: Blade, CCD: Camera
3.2 Stroboscopic illumination
In order to obtain a snapshot image of the traveling ultrasound wavefront, a digital camera with the ability to set very short exposures and to activate acquisition with a trigger signal is required. The minimum programmable exposure in the CMOS camera (Genie HC640) was 10 $\mu$s. Then, an alternative was to implement a stroboscopic type of illumination [29]. Here, a custom-built stroboscopic lamp based on a white LED (maximum power = 3 W, correlated color temperature =5000 K, viewing angle = 125$^{\circ }$) generated the detection light field. A power supply overexcited the LED with current pulses that had peaks of 5 A, with the aim of reducing the rise and fall times of LED emission. Pulses with a duration in the order of microseconds and synchronously triggered with the laser source signal were obtained, being the shortest a $2 \mu$s LED pulse. This parameter is key because it defines the effective exposure time to capture the instant profile of the propagating ultrasound wave. [30]
On the other hand, once the trade-off between the camera frame capture and the strobe flash to image the PA wavefront has been solved, both should be synchronized with the laser pulse that induces the photoacoustic wave. However, it is necessary to wait until all PA waves generated in any part of the sample have propagated sufficiently into the surrounding medium to capture the full pressure field. [15] Therefore, an optimized delay needs to be introduced to the laser pulse-triggering signal to activate the strobe pulse/frame capture. In this regard, the trigger signal is sent to an adjustable delay unit that allows setting a waiting time from 2$\mu$s to 100 $\mu$s in 1$\mu$s steps. The selected delay defines the time of flight of the wave, which will be used for the reconstruction process.
Finally, the divergent strobe LED beam was focused to pass by the system entrance slit (width=1 mm) with an aspheric condenser lens ($f_C=30$ mm). The slit was located at the frontal $2f_M$-plane of the convergent mirror. Light reflected by the mirror, and passing twice through the ethyl alcohol tank, was slightly off-axis focused with unitary magnification at the back $2f_M$-plane. A razor blade was placed in the conjugate plane of the slit in order to filter the deviated-by-photoacoustic-wave light. The undisturbed light fraction reaches the CMOS camera, which is placed beyond the blade edge, and it is recorded. The image of the acoustic field will be observed as shadow zones on a bright background.
3.3 System Calibration
Using a calibration target, the captured field of view was estimated as 50 $\times$ 50 $mm^2$ over 200 $\times$ 200 pixels. Let us assume that ultrasound speed in ethyl alcohol at $20$ $^{\circ }$C is $1152$ m/s. [31] Under these conditions, the traveling length of the PA wave during an exposure of $3$ (or $2$) $\mu$s is approximately $3.5$ (or $2.3$) mm, thus, approximately $14$ (or $9$) pixels are needed to detect the averaged profile. To estimate the sensitivity of the system, the knife was placed on a sliding holder, and its position was adjusted until the unobstructed image height was 500 $\mu m$. Then, considering the focal length of the mirror and using the Eq. (7), it was found that $S=9.2\times 10^3$.
In order to demonstrate the effect of detection LED pulse duration on image reconstruction fidelity, the PA signal wavefronts obtained from two cylindrical graphite absorbers with 0.5 mm diameters and placed 3 mm apart were acquired under the above-mentioned conditions. Figures 3(B) and (D) show the reconstructed cross-section of the absorbers using $2$ and $3$ $\mu$s strobe probe duration, respectively. In order to compare the full-width at half maximum of the reconstructed profile of the graphite cylinders, the grayscale profiles are shown in Fig. 3(E). For the 2 $\mu$s pulse duration, it was obtained that the sizes of the photoacoustic sources were FWHM$_1 =$ 510 $\mu$m and FWHM$_2=$ 440 $\mu$m. On the other hand, for the 3 $\mu$s pulse duration, obtained measurements were FWHM$_1=$ 620 $\mu$m and FWHM$_2=$ 610 $\mu$m. As it was expected, longer pulses generated wider profiles and a lower capacity to resolve small objects. The differences obtained in the diameter of the reconstructed sources for the same pulse are due to the inhomogeneous illumination intensity during PA wave excitation. However, reconstructed dimensions are close to the real ones because the time-of-flight of the PA wave is known with precision.
Fig. 3. Effect of the stroboscopic pulse width in the resolution of the image. A, C Schlieren image of PA wavefront for a pulse width 2 and 3 $\mu$ s respectively. B and D: Reconstructed images. E: Cross-section of the reconstructed images, showing the profiles
4. Results
4.1 Two cylindrical absorbers
Two pencil leads (2 mm in diameter and 3 mm apart) were placed inside the alcohol container and held in place with a stick of modeling clay. The stroboscopic pulse was triggered 15 $\mu$s after the excitation laser pulse. The knife was moved until the optimum position was found, where the image contrast was at its maximum. The snapshot of the acoustic field recorded by the camera is shown in Fig. 4(A).
Fig. 4. A: Captured acoustic wave pattern. B: Image after removing the clay support and normalizing. C: Reconstructed profile of the two cylindrical absorbers. The inset shows the sample
To apply the reconstruction algorithm described in section 2.2, the shadow of the clay support was first cut out of the image in order to avoid artifacts in the final image, Fig. 4(B). Here, we took a time of flight of the wave equivalent to the delay between the laser and LED pulses. The reconstructed profile is shown in Fig. 4(C) where the distribution of the absorbers is clearly visible. Among the reconstructed image features that it is important to discuss, the difference in the size of the two absorbers is key. Due to the Gaussian distribution of the light spot that induces the photoacoustic wave, it is expected that both elements were not uniformly excited, and therefore, the intensities of the two induced acoustic waves were different, which is manifested in the reconstructed image. Additionally, it is possible to observe artifacts in the image that are due to spurious reflections of the acoustic wave. Several optimizations can be proposed to eliminate these unwanted signals, such as moderating the intensity of the excitation.
4.2 Hexagonal absorber
A graphite rod was cut into a hexagonal shape to be used as an absorbent element in a second experiment, Fig. 5(A). The rod was held inside the container with a stick of modeling clay, as in the previous case. In this case, the delay between the laser and LED pulses was set at 7$\mu$s. The detected acoustic wave pattern presents a more complex and less defined structure due to the multiple reflections of the wave inside the object. Under these conditions, the reconstruction was applied, and the profile obtained is shown in Fig. 5(C). In the reconstructed image, the distance between opposite sides of the hexagon is approximately 5.5 mm, which is close to the real value of the sample (5.0 mm). As can be seen, the reconstructed image reproduces the profile of the specimen quite well, and there is concordance in the dimensions despite the limited resolution of the system.
5. Discussion and conclusions
The proposed Schlieren mirror-based system built to acquire the full PA wavefront generated by simple or complex structure absorbing elements has shown good sensitivity in reconstructing the PA source profile. Nonetheless, some technical limitations have been found that prevent the achievement of higher lateral spatial resolution in the wavefront capture. Firstly, with the aim of acquiring a reliable profile of the traveling 2D-omnidirectional PA wave, a shorter LED strobe pulse is needed to shorten the recorded path length and reduce pixel intensity averaging. However, this parameter depends on several semiconductor material growth conditions: efficient carrier injection, transport, relaxation, and radiative recombination associated with a stronger carrier localization and a low polarization effect. [32] In our case, decreasing response time and rising time of available commercial LED sources did not allow getting pulse durations shorter than 2 $\mu$s because the achieved luminance was not enough to obtain sharp images. Therefore, the use of fast, high-power LED systems or diode lasers in our experimental setup can be considered as a future optimization. [33–35]
On the other hand, the poor resolution of our CMOS camera, given as (640$\times$480) with a pixel size of (7.4$\times$7.4) $\mu$m, limited the spatial signal sampling. Besides, due to the impossibility of reaching an optimized combination between the focal lengths of the spherical concave mirror and the telephoto lens, it was not possible to image the region of interest over the entire sensor area. The size of the processed images in the reconstruction stage corresponds to one-third of the CMOS sensor area, reducing computational cost, but increasing uncertainty in sample dimensions. In addition, the image acquisition device that was used had a bit depth of 8 bits, affecting waveform sampling. Consequently, another possible improvement to increase the sensitivity of the system could be the use of a camera with a higher dynamic range. Although the light sheet has previously been used to perform PA images of thin objects, illuminating a human hair from only one side, [36] our setup induces the PA signal by using symmetrical dual-sheet pulsed laser lighting. This allows the sample to be uniformly excited and capture the entire acoustic field to image the structural elements of more complex objects.
However, it is possible to increase current axial resolution by reducing sheet-thickness and controlling intensity homogeneity using, for example, Powell lenses. Also, it is necessary to mention the importance of minimizing spherical aberrations in the optical system because these have a negative impact on the numerical reconstruction of PA images. In the first instance, they deform the spatial frequency spectrum at the image plane, complicating the filtering process of the light beams deviated by pressure waves. Also, they deform the image of the acoustic field, an effect that manifests itself in the reconstructed image. As the position of the knife has a definite impact on the sensitivity of the system, the use of dynamic elements to perform spatial filtering can be considered. For example, a spatial light modulator can be proposed. [37] Referring to the reconstruction algorithm, we can state that it adequately recovers the shape of the photoacoustic source. Work should be done to reduce as much as possible the artifacts in the final image.
In summary, the implemented full-field acquisition system is an effective method to image the ultrasound wave induced by nanosecond pulsed laser absorption. Because of the exciting illumination setting-up, the 2D-acoustic field captured in a single frame contains all the in-plane spatial information of the photoacoustically imaged object. This provides a viable alternative to the complex multiplexing systems required for PA-point detection while reducing acquisition times. Although the configuration discussed here can only be used for samples completely submerged, which limits biomedical applications, the technical details can be used as a basis for future complete field capture systems in a single exposure and applied to in-vivo samples. Hence, it has a potential application for real-time photoacoustic imaging systems.
Funding
Consejo Nacional de Ciencia y Tecnología (2019-000037-02NACF-20954, FC-612).
Acknowledgements
The authors acknowledge the technical assistance from Ricardo Valdivia and the optics technicians of the Center for Research in Optics, as well as the contribution of Mario Ruiz Berganza to proof-reading this manuscript.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time, but may be obtained from the authors upon reasonable request.
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