Impact of System Factors on the Performance of Photoacoustic Tomography Scanners

1 Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, Hefei, Anhui 230026, China 2 Key Laboratory of Precision Scientific Instrumentation of Anhui Higher Education Institutes, University of Science and Technology of China, Hefei, Anhui 230026, China 3 School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China


I. INTRODUCTION
Based on the energy conversion of light into sound, photoacoustic tomography (PAT) is an emerging noninvasive biomedical imaging technique that has experienced explosive developments in the past two decades [1]. As a hybrid imaging technique, PAT possesses molecular contrast due to optical absorption found in optical imaging, while maintaining high spatial resolution in deep tissue found in ultrasound imaging [2,3]. PAT can visualize biological samples at scales from organelles, cells, tissues, and organs to the small-animal whole body and can reveal multidimensional biological information, such as anatomical, functional, molecular, genetic, and metabolic data [1]. PAT has unique applications in a range of biomedical fields [4,5], such as cell biology [6][7][8][9], neurology [10][11][12], oncology [13,14], rheumatology [15], and ophthalmology [16,17]. Both basic sciences and clinical translations involving PAT are expected to grow in the future.
In PAT, nanosecond laser pulses are used to illuminate biological tissues and excite ultrasound emissions from optical absorbing chromophores. Ultrasound detectors are then employed to receive the ultrasound signal to form images through acoustic inversion. Since the light-tosound energy conversion efficiency is limited and the illumination laser fluence should be controlled within the safety standard [18], the resulting photoacoustic pressure is typically weak, on the order of tens of thousands of pascals [19]. To achieve high-performance imaging in practical biomedical applications, it is essential to properly design the PAT systems for optimal signal reception and image quality.
Several groups have performed pioneering studies in exploring critical system parameters, such as detector bandwidth and aperture size, on final image quality in PAT. Xu and Wang first proposed analytical relationships between image spatial resolution and ultrasound detector bandwidth, as well as aperture size, using the point spread function (PSF) theory [20]. Wang et al. further interpreted the relations in the Fourier domain and drew similar conclusions [21]. Xu et al. theoretically studied how limited detection angle would affect final image quality and defined the concept of the "detection region" for the optimal design of the geometry of the detector [22]. Later, Haltmeier and Zangerl derived analytical expressions of the PSF to deal with limited bandwidth and finite aperture size of approximate point and line detectors and showed that the PSF, due to limited bandwidth, was spatially invariant for both detectors, while the PSF due to finite aperture size was only spatially invariant for line detectors [23]. Most recently, Dima et al. demonstrated the imaging performance of PAT systems employing 64, 128, and 256 ultrasound detectors and concluded that images acquired using 256 detectors had significantly higher quality than those acquired using 128 or 64 detectors [24]. These studies lay the foundations of image-quality enhancement in PAT. However, most of the studies focus on theoretical aspects or only cover specific topics.
Here, we study eight system factors associated with a typical PAT scanner and demonstrate how they affect the image quality from numerical and experimental perspectives. The eight factors, namely, detector view angle, element number, center frequency, bandwidth, aperture size, focusing, orientation error, and scan step angle error, all relate to the acoustic reception process and influence the final image quality, to some extent. The study is carried out based on a prototype PAT scanner, where a single-element detector is rotated around the sample to capture generated photoacoustic signals. The method, results, discussion, and conclusions are presented below.

II. METHODS
The prototype PAT scanner ( Fig. 1) works as follows. Nanosecond-duration near-infrared light pulses emitted from the tunable laser system are used to illuminate the sample for photoacoustic signal excitation. The excited signals propagate in free space and are picked up by an ultrasound detector, which is driven by a step motor and rotates around the sample. The acquired photoacoustic projections are then digitized by an oscilloscope and transferred to a computer for image reconstruction. The sample and ultrasound detector are both immersed in water for optimal ultrasound coupling. This single-detector-based prototype PAT scanner was demonstrated to be a success in early photoacoustic studies [25,26]. Even today, it is still frequently used in many photoacoustic experiments for proof-of-concept studies due to its simplicity, low cost, and effectiveness [27]. Although imaging speed and resolution are greatly enhanced, modern PAT scanners work similarly to this prototype [24,28]. System parameters study based on this prototype PAT scanner is thus of general significance.
In the prototype system, if the sample is uniformly illuminated, the imaging performance will be mainly determined by the acoustic reception process. Eight system parameters associated with the ultrasound detector, namely, view angle, element number, center frequency, bandwidth, aperture size, focusing, orientation error, and scan step angle error, are studied to understand how they independently influence the final imaging performance. Among the eight parameters, the first two relate to the arrangement of the detector, the middle four define the properties of the detector, while the last two describe the alignment accuracy of the detector. The method used in this study is based on single-variable analysis, which means that, in each analysis, only one parameter is allowed to vary and all others are kept in ideal situations, unless otherwise stated. The single-variable analysis method allows us to individually study the effect of each variable on final imaging performance. Moreover, in all numerical studies presented here, forward and inverse acoustic processes, including signal generation, propagation, and reception, are simulated using the k-wave toolbox [29]. In all experimental studies, the inverse image reconstruction process is performed based on the filtered back-projection algorithm [30].
To better illustrate findings in the study, we design four different phantoms used in numerical and experimental analyses: a blood vessel pattern, a multidisk pattern, a dot grid pattern, and a human hair cross, as shown in Fig. 2 Table I.

A. Detector view angle ( )
The detector view angle, , refers to the angle enclosed by the detector during the measurement and has a profound impact on final image quality. Ideally, the detector should completely enclose the sample for perfect image reconstruction; thus, indicating a 4π steradian view angle ( = 4π ) for three-dimensional (3D) detection and a 2π radian view angle ( = 2π ) for two-dimensional (2D) detection are preferred. However, in real scenarios, such as breast imaging and skin imaging, the view angle is often limited and images need to be recovered from incomplete projections. The image reconstruction problem in limitedview PAT can be well illustrated by means of the detection region concept developed by Xu et al. [22], which is defined as the convex hull of the detector arc. As such, a photoacoustic source can be divided into two reconstruction parts: one inside the detection region and the other outside the detection region. The one inside the detection region is the area that any line passing through it intersects with the detection surface, as shown in Fig. 3. Otherwise, it is regarded as outside of the detection region. For photoacoustic structures inside the detection region or outside the detection region but with their normal intersecting with the detection surface, they can be stably recovered. Otherwise, details of the photoacoustic source will be lost. Figure 3 illustrates a numerical and experimental example demonstrating limited-and full-view PAT imaging. The blood vessel phantom is imaged using a point ultrasound detector, which rotates around the phantom for 90°, 180°, 270°, and 360°. It is easy to see that a larger view angle results in better reconstruction results. The 360°f ull-view detection scheme gives the highest reconstruction quality, as expected. In the 270°case, although the  blood vessels are not completely enclosed by the detection surface, they can still be stably reconstructed, since they are within the detection region defined above. This finding may inspire innovative designs of ultrasound detection schemes. Some modern PAT scanners adopt the 270°d etection strategy and can reduce the detector fabrication cost, while producing outstanding image quality [24]. In the 90°case, the blood vessels are totally outside the detection region. The vessels (e.g., vessel 1) parallel with the detection surface can be reasonably recovered, while those (e.g., vessel 2) perpendicular to the detection surface are lost after reconstruction; this is in agreement with the aforementioned rules. The numerical simulations in the second row of Fig. 3 are well supported by the experimental results in the third row.

B. Detector number (n)
Ideally, the number of detectors, n, should be as large as possible, to receive generated ultrasound signals from the sample for accurate image reconstruction. This will not only improve spatial resolution, but also enhance imaging sensitivity. However, in reality, it is impossible for a PAT scanner to employ an infinite number of detectors due to high cost, fabrication complexity, and limited detection space. Determining an optimal number of detectors is of great importance to achieve high-performance imaging at an affordable cost. Dima et al. observed the problem and studied the effect of transducer number [24]. Figure 4 illustrates a study showing the impact of the detector number, n, on the image quality. The first row is a group of simulations that demonstrate how the number of detectors correlates with the imaging performance. It is seen that with an increase of the detector number from n = 32 to n = 512, reconstruction artifacts produced at sparse detectors are well suppressed and the final image quality improves significantly. The second row shows the corresponding experimental results under similar measurement conditions, except with a 1 MHz detector (V303). The experimental results are consistent with the numerical simulations for most detector numbers, except for n = 256 and n = 512, where the image reconstructed at 512 detectors seems to have little improvement compared with that at 256 detectors. The justification is that, in real experiments, the physical size of the detector may make the signal reception surfaces at two consecutive scan positions overlap, resulting in significantly redundant information when the detector number is large. In this case, the aperture size of the detector is 12.7 mm and the overlap ratio is 90.3% for n = 512, as shown in the third row of Fig. 4. In practical applications, 256 detectors evenly distributed in a full circle is a good choice for the sensor number to balance the imaging performance and cost.

C. Detector center frequency ( f c )
The detector view angle, , and the detector number, n, discussed above both relate to the arrangement of a chosen detector and are critical to the imaging performance of a PAT scanner. In addition, the properties of the chosen detector, including the center frequency, f c ; the bandwidth, B; the aperture size, 2a; and the focusing characteristics, l n , are also of great importance. To achieve high-performance imaging, the center frequency of the detector, f c , should be selected based on two facts. First, the center frequency of the detector should match the desired spatial resolution [31]. Detectors with higher center frequencies generally have better spatial resolving ability, and thus, can produce images with greater detail, as demonstrated by Ku et al. [32]. Second, the center frequency should match the frequency contents of generated photoacoustic signals to achieve maximum signal reception sensitivity. Although photoacoustic signals are broadband, they have limited bandwidths in the Fourier domain and typically center at a certain frequency (called center frequency, f c ). Take a spherical absorber with a diameter of d as an example, the center frequency, f c , of its generated photoacoustic signals can be estimated as where v s is the speed of sound in the medium. A smaller absorber will result in a higher center frequency.  Fig. 6 is a group of simulations showing the blood vessel phantom imaged using ultrasound detectors (100% bandwidth) with center frequencies of 1, 2.25, and 5 MHz, respectively. The 1 MHz detector produces the brightest image, but the worst resolution, while the 5 MHz detector gives the best resolution, but the darkest image due to loss of low-frequency components. This is easy to understand because the center frequency of the photoacoustic signal of the blood vessels (single vessel width, 0.8 mm) is estimated to be around 1.25 MHz, which is closer to the frequency response of the 1 MHz detector in the simulation. Experimental results shown in the second row of Fig. 6 support this finding.
To further illustrate this point, we perform another set of simulations and experiments using the multidisk phantom and the human hair cross. The first row of Fig. 7 is the simulation showing that the multidisk phantom is imaged using detectors (200% bandwidth) with center frequencies of 1.5, 2.5, 5, and 10 MHz. Results reveal that a higher The results again illustrate that ultrasound detectors with higher center frequencies have better spatial resolving power.

D. Detector bandwidth (B)
As mentioned above, photoacoustic signals are typically broadband. However, an ultrasound detector used to receive photoacoustic signals usually has limited frequency response, as characterized by the lower cutoff frequency, f 1 ; the upper cutoff frequency, f 2 ; and the center frequency, f c , as shown in Fig. 8(a). The limited bandwidth characteristics of an ultrasound detector directly impact on the PSF and the spatial resolution of the detection system. According to the theoretical analysis by Xu and Wang [20], if the frequency response of an ultrasound detector is flat between f 1 and f 2 , the PSF can be formulated as where k 1 = 2π f 1 /v s and k 2 = 2π f 2 /v s ; v s is the speed of sound, and j 1 is the first-order spherical Bessel function of the first kind. Assuming that the frequency response of the detector is symmetric and using the relationships k 1 = (1-0.5B)k c and k 2 = (1 + 0.5B)k c , the PSF can be represented by the center frequency, f c , and the bandwidth, B, as where k c = 2π f c /v s . Since the spatial resolution is usually represented by the full width at half maximum (FWHM) of the PSF, Eq. (3) indicates that the spatial resolution of a PAT system is determined by the center frequency, f c , and the bandwidth, B, of the detector. For typical detectors with 80% bandwidth [( f 2 −f 1 )/f c = 80%], the spatial resolution limit is estimated to be 0.55λ c , where λ c is the center wavelength. Figure 8(b) plots the PSFs of three ultrasound detectors with bandwidths of 50%, 100%, and 150% ( f c = 3 MHz). It is easy to see that an ultrasound detector with a broader bandwidth has a narrower PSF, and thus, finer spatial resolution, while an ultrasound detector with a narrower bandwidth has a more oscillating PSF and more significant ring artifacts. Figure 9 presents two groups of simulations, showing how ultrasound detector bandwidth would impact on the final image quality. The first row shows the imaging results of the blood vessel phantom using ultrasound detectors (center frequency, f c = 1 MHz) with bandwidths of 50%, 100%, and 150%, and full bandwidth. When the bandwidth of the ultrasound detector is set to 50%, significant ring artifacts occur, which can be largely mitigated by increasing the bandwidth. The second row shows the imaging results of the multidisk phantom using ultrasound detectors with the same bandwidth setting. In addition to the conclusion that increasing bandwidth can mitigate ring artifacts, as described, we note two other interesting findings. First, ultrasound detectors with broader bandwidth provide better spatial resolution and sharper edges. Second, ultrasound detectors with broader bandwidth help to recover low-frequency components (the center parts of the disks) of the objects. Ultrasound detectors with broader bandwidths are favorable for PAT, which is consistent with previous results reported in Refs. [33,34]. In this example, only simulation is performed because physical detectors with different bandwidths (i.e., 50%, 100%, and 150% in this case) are not readily available.

E. Detector aperture size (2a)
In PAT, detectors used for ultrasound signal reception usually have a finite aperture size, rather than being a point sensor. The finite aperture size 2a impacts on the imaging performance of a PAT scanner mainly in two ways. First, it degrades the accuracy of the mathematical model used for image reconstruction. In the forward process [ Fig. 10(a)], ultrasound signals are actually detected by the entire surface of the detector. In the inverse process [ Fig. 10(b)], ultrasound detectors with a finite aperture size are typically regarded as a point detector to simplify the mathematical model used in most state-of-the-art image reconstruction algorithms, such as filtered back projection [30] and time reversal [29], which inevitably blurs reconstructed images. To ease this problem, Yang et al. proposed a ring-based ultrasonic virtual point detector to avoid potential image blurring [35]. Second, different from point detectors with an omnidirectional response, detectors with finite aperture size have directional responses; this means that they have different degrees of response to ultrasound signals coming from different directions. The response differences can be characterized by the directivity function, D(θ), which directly correlates with the aperture size of the detector 2a and can be formulated as where k = 2π /λ is the wave number, λ is the wavelength, θ is the angle, and J 1 is the first-order Bessel function of the first kind for cylindrical coordinates. Figure 11 illustrates an example showing the directivity patterns of four ultrasound detectors with different aperture sizes, when 2a/λ = 1, 2, 4, and 6.2. For a fixed ultrasound wavelength, λ, a larger aperture size 2a will result in a more directional detector. The final impacts of the detector aperture size on the lateral resolution of the PAT scanner in Fig. 1 are explicitly given by Xu and Wang [20] as where 2a is the aperture size; r 0 is the detection radius; r is the spatial coordinate of the image. The lateral resolution (LR) linearly degrades with the distance r between the object and the center of the detection surface, indicating that, in the prototype PAT scanner, the detector aperture size will degrade the image quality at the edge more significantly than that in the center. The first row of Fig. 12 is an experimental study demonstrating how the detector aperture size would impact on the image quality of the blood vessel phantom. The ultrasound detector used in the experiment is a 1 MHz sensor with an aperture size of 2a = 12.7 mm (V303) and a detection radius of r 0 = 25 mm. The reconstructed image displayed in the first column in Fig. 12 shows that, while the central region of the blood vessels is well recovered, the edge part is blurred significantly due to the aperture effect of the detector. To confirm that blurring is indeed caused by the aperture, the aperture size of the detector is equivalently halved via increasing the detection radius, r 0 , from 25 to 50 mm and 100 mm, for which the reconstructed images are shown in the second and third columns, respectively, of the first row of Fig. 12. Results reveal that, by decreasing the aperture size, the image quality can be greatly enhanced, especially at the edge. The second row of Fig. 12 is the corresponding numerical study under similar conditions ( f c = 1 MHz, 2a = 12.7 mm, r 0 = 25, 50, and 100 mm), which is consistent with the experimental results.
To further illustrate the detector aperture effect, we perform another group of simulations, to compare images produced by pointlike detectors and nonpointlike detectors. Figure 13

F. Detector focusing (l n )
The results presented so far are all based on unfocused detectors, which have a flat signal receiving surface, as shown in Fig. 14(a). In practice, focused detectors that exploit a curved surface or acoustic lens to detect ultrasound within a spatially confined region are also frequently employed in photoacoustic imaging. Examples of focused detectors include spherically focused detectors, which have maximum detection sensitivity at a point, and a cylindrically focused detector, which have maximum detection sensitivity at a line. Important parameters associated with focused detectors include the normalized focal length, l n ; the beam width at the focus, w; and the DOF. The normalized focal length, l n , is defined as where l f is the actual focal length and z 0 is the nearfield distance. For flat detectors, l n = 1 because l f = z 0 . For focused detectors, l n is always smaller than one. The normalized focal length, l n , is sometimes preferred, instead of the actual focal length, l f . The −6 dB beam width at the focus can be estimated as where 2a is the aperture size of the detector and λ is the ultrasound wavelength. In addition, the DOF of a focused detector can be written as Taking the 5 MHz spherically focused detector (Model: V309, 2a = 12.7 mm, l f = 50.8 mm) as an example, the normalized focal length, l n ; beam width, w; and DOF are 0.38, 1.2 mm, and 32.6 mm, respectively. Focused detectors are most frequently used in photoacoustic microscopy to detect sound waves within a spatially confined region for enhanced detection sensitivity.
One major consideration of employing focused detectors in PAT is to enhance elevational resolution in 3D imaging. After focusing, the ultrasound beam becomes much narrower compared with its aperture size and, therefore, could improve the elevational resolution significantly. Detector focusing will not significantly degrade the lateral resolution, which is determined by the center frequency, bandwidth, and aperture size of the detectors used. This is demonstrated in Fig. 15, where a human hair cross is imaged using an unfocused detector [ Fig. 15(a)] and a focused detector [ Fig. 15(b)]. The resultant images show comparable intensity profiles [ Fig. 15(c)]; this means that there is no significant lateral resolution difference.
Focused detectors may improve imaging sensitivity at the focus region compared with flat detectors (Fig. 16) in PAT, but it depends on the ratio of the detector aperture size, 2a, and the detection radius, r 0 . This is illustrated using a group of simulations based on a dot grid pattern (dot diameter, 250 µm), as shown in Fig. 17(a). When the detector aperture size, 2a, is relatively large compared with the detection radius, r 0 , the sensitivity enhancement in the central region of the sample by using the focused detector is significant, as shown in Figs. 17(b) and 17(c); however, this is at the cost of sacrificing sensitivity in the nonfocused region. When the detector aperture size, 2a, is relatively small compared with the detection radius, r 0 , the sensitivity enhancement by using the focused detector is not that significant, as shown in Figs. 17(d) and 17(e). In this situation, flat and focused detectors produce very similar results. It is necessary to point out that the tangential resolution produced by the focused detector is worse than that produced by the flat detector, especially when 2a/r 0 is relatively large, as in the case shown in Figs. 17(b) and 17(c). This is because, for a fixed detector aperture size 2a, focused detectors have a larger surface area, which will degrade the tangential resolution more significantly. In this example, only simulations are performed because it is difficult to fabricate the dot grid phantom (dot diameter, 250 µm) using conventional printing methods.

G. Detector alignment errors (dα and dθ )
Because a single element detector is used to rotate around the sample for signal acquisition in the prototype PAT scanner, correct alignment of the detector is essential for accurate image reconstruction. Two detector alignment errors, namely, the orientation error, dα, and the scan step angle error, dθ , are commonly present in real experiments. The detector orientation error means that the normal of the detector does not correctly point to the center of the detection surface and can be characterized by the angle dα between the surface normal and the radial directions, as shown in Fig. 18(a). The scan step angle error indicates that the actual position of the detector does not coincide with its ideal position during scanning and can be characterized by the angle dθ between the actual position and the ideal position, as shown in Fig. 18(b). The detector orientation error, dα, can blur reconstructed images because of directional responses of nonpointlike detectors, as discussed in Sec. III F. The scan step angle error, dθ, can also degrade the imaging quality because of inaccurate detector positions used for image reconstruction.   Fig. 19(e) is a comparison of intensity profiles of the vessel indicated by the arrows. It is seen that a larger orientation error, dα, results in a more blurred reconstructed image. In practical situations, the detector should be correctly aligned to minimize possible blurring artifacts. In this example, only simulations are performed because it is difficult to precisely control the orientation error for small angles in the experiments. performed because it is difficult to randomly control the scan step angle error in the experiments.

IV. CONCLUSION
Here, we numerically and experimentally study eight system factors, which have significant impacts on the imaging performance of the prototype PAT scanner. The eight system factors can be grouped into three categories, namely, the detector arrangement group, the detector property group, and the detector alignment group.
In the detector arrangement group, factors including the detector view angle and the detector number should be considered. To achieve stable image reconstruction, the detection view angle needs not to be 2π radian in 2D and 4π steradian in 3D. As long as the object is within the detection region, it can be stably recovered. For structures outside of the detection region, they can be recovered if the normal of the structure intersects with the detection surface. The detector number should be large enough to acquire sufficient projection data for image reconstruction in the inverse process, but the acquired projections may saturate if the detector number is too large. For 2D imaging, 256 detectors evenly distributed on a circle is expected to yield good image quality.
In the detector property group, factors including the detector center frequency, detector bandwidth, detector aperture size, and detector focusing effect should be considered. The detector center frequency should be chosen to match the frequency spectrum of the object being imaged to achieve maximum receiving sensitivity. Detectors with higher center frequencies produce sharper images. The bandwidth, together with the center frequency of a detector, determines the spatial resolving power of a PAT scanner. Broader bandwidth helps to recover both lowand high-frequency content of the object, while suppressing oscillation ringing artifacts. The aperture of a physical detector is not favored in practice because it degrades the accuracy of the mathematical model used for image reconstruction and endows the detector with a directional response. The final outcome is that the image resolution will be degraded, especially in the direction parallel with the detector aperture. In addition, compared with flat detectors, focused detectors can enhance signal detection sensitivity within focal regions and are commonly used in photoacoustic microscopy. When used in PAT, focused detectors could improve elevational resolution in 3D imaging, but have little impact on the lateral resolution.
In the detector alignment group, factors including the detector orientation error and the scan step angle error should be considered. Both errors can blur reconstructed images and produce artifacts, if large enough. Correct alignment of the detector is required to minimize reconstruction artifacts and produce high-quality images.
The conclusions obtained in this study are of general significance and can provide practical guidelines on the design of advanced PAT scanners with enhanced imaging performance.