Comparative investigation of coherence factor weighting methods for an annular array photoacoustic microscope

The PA micro-imaging system used in this study (Hadatomo^TM Z WEL5200 prototype developed in a joint effort by Tohoku University and Advantest Corporation) consisted of a PA transmitter/receiver unit with a laser optical fiber placed in the center of an annular array transducer, an XY stage that allows mechanical two-dimensional scanning in an imaging field, and a unit for control and signal processing as shown in Fig. 1.

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The annular array transducer had a concave surface with a geometric focus of 6 mm and a center hole (ϕ1 mm) for the laser outlet. The concave geometry was divided into four ring-shaped PZT elements (a center frequency of 60 MHz $\pm \,\,$20%) with a minimum diameter of 1 mm and a maximum diameter of 6 mm as shown in Fig. 2. The Nd:YAG laser was selected to irradiate 532 nm pulsed beams at a repetition rate of 1 kHz and a pulse width of 1.2 ns. The emitted pulse energy was measured to be 16 μJ pulse⁻¹. While the PA transmitter/receiver unit was raster-scanned by the XY stage, an event of emitting a laser pulse and receiving PA signals was repeatedly performed to acquire the three-dimensional distribution of the optical absorbers in the imaging field. In each receiving event, the PA waves generated at the object by the laser irradiation were received by each element of the annular array transducer and recorded at a sampling frequency of 500 MHz.

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The theoretical axial resolution of our AR-PAM system, ${R}_{{\rm{A}}{\rm{x}}{\rm{i}}{\rm{a}}{\rm{l}}}$ is determined by the receiving bandwidth ${\rm{\Delta }}f$ of the ultrasonic transducer and is expressed by the following equation, ^5,6)

$$\begin{eqnarray}&&\begin{array}{c}{R}_{{\rm{A}}{\rm{x}}{\rm{i}}{\rm{a}}{\rm{l}}}=0.88\times \displaystyle \frac{c}{{\rm{\Delta }}f},\end{array}\end{eqnarray} \tag{ 1 }$$

where $c$ is the speed of sound. Also, the theoretical lateral resolution of AR-PAM system, ${R}_{{\rm{Lateral}}}$ is expressed by the following equation, ^5,6)

$$\begin{eqnarray}&&\begin{array}{c}{R}_{{\rm{L}}{\rm{a}}{\rm{t}}{\rm{e}}{\rm{r}}{\rm{a}}{\rm{l}}}=0.71\times \displaystyle \frac{c}{{\rm{N}}{\rm{A}}\times {f}_{c}},\end{array}\end{eqnarray} \tag{ 2 }$$

where ${\rm{N}}{\rm{A}}$ is the numerical aperture of the ultrasonic transducer, and ${f}_{c}$ is the center frequency in the receiving bandwidth. According to these equations, the theoretical axial and lateral resolutions were calculated as 56.1 and 36.2 μm, respectively.

The obtained PA signals were first beamformed with a DAS algorithm (described in Sect. 2.2) and then the beamformed signals were weighted by a coherence factor method to suppress the off-axis signals (described in Sect. 2.3). In Sects. 2.2 and 2.3, the description focuses on a set of channel-domain PA signals acquired in one receiving event. Subsequently, in Sect. 2.4, the processing was applied to PA signals at each XY position in the mechanical scanning field and the B-mode and C-mode images were generated. All signal processing and visualization were performed on MATLAB (Ver. 2020b, Mathworks).

First, the signals received by each element were converted to complex analytic signal data by the Hilbert transform as follows,

$$\begin{eqnarray}&&\begin{array}{c}{S}_{n}\left(t\right)={s}_{n}\left(t\right)+j\mathrm{Hilbert}\left({s}_{n}\left(t\right)\right),\end{array}\end{eqnarray} \tag{ 3 }$$

where ${S}_{n}(t)$ is a series of analytic signal of nth channel, ${s}_{n}(t)$ is the signal received by the nth element at $t\,\,$seconds after laser irradiation, and Hilbert() is the Hilbert transform operator that generates the quadrature signal of the input in-phase signal.

Second, for the nth element of the annular array transducer, the delay time ${t}_{n}$ has to be taken into account to receive a signal from an optical absorber at depth $d$ and expressed by the following equation, ¹⁹⁾

$$\begin{eqnarray}&&\begin{array}{c}{t}_{n}\left(d\right)=\displaystyle \frac{{a}_{n}^{2}\left(1/R-1/d\right)}{2c},\end{array}\end{eqnarray} \tag{ 4 }$$

where ${a}_{n}$ is the average radius of the nth element, and $R$ is the geometric focus. In this study, the speed of sound was respectively set as 1480 m s⁻¹ for the phantom study and 1530 m s⁻¹ for the skin microvascular imaging. ²⁰⁾ The delay time ${t}_{n}$ considers only the one-way delay of the PA signal since the time the laser reaches the object is negligible.

Third and finally, the receive beamforming was performed by synthesizing the PA signal ${S}_{{\rm{DAS}}}(d)$ from the depth $d$ from the PA signals obtained from each channel using the following formula,

$$\begin{eqnarray}&&\begin{array}{c}{S}_{{\rm{DAS}}}\left(d\right)=\displaystyle \sum _{n=1}^{4}{S}_{n}\left(d/c-{t}_{n}\left(d\right)\right).\end{array}\end{eqnarray} \tag{ 5 }$$

Essentially, DAS beamforming enhances in-phase PA signals among active elements by summing time-delayed channel-domain signals; however, since the pulsed laser broadly irradiates the target area, PA signals from other than the imaging axis (off-axis signals) may interfere with some of the channel-domain signals. Coherence factor weighting techniques have been proposed to suppress those off-axis signals by taking the coherency and phase differences among the signals to be summed in DAS process. Here, at each beamformed depth $d,$ the time-delayed signal value of nth channel (${S}_{{\rm{delay}}}\left(n,d\right)$) can be expressed as,

$$\begin{eqnarray}&&\begin{array}{c}{S}_{{\rm{delay}}}\left(n,d\right)={S}_{n}\left(d/c-{t}_{n}\left(d\right)\right).\end{array}\end{eqnarray} \tag{ 6 }$$

To compute a coherence factor for each beamformed depth, four complex values were extracted from each channel PA signal. Five coherence factor methods tested in this study (coherence factor, sign coherence factor, phase coherence factor, circular coherence factor, and vector coherence factor) were described in the following sections. Each coherence factor method derives its coherency index that takes values between 0 and 1.

2.3.1. Coherence factor (CF)

The CF is the ratio of the energy of the coherent component to the energy of the entire received signal, and is defined as follows, ^9–12)

$$\begin{eqnarray}&&\begin{array}{c}{\rm{C}}{\rm{F}}\left(d\right)=\displaystyle \frac{{\left|\displaystyle {\sum }_{n=1}^{N}{S}_{{\rm{delay}}}\left(n,d\right)\right|}^{2}}{N{\displaystyle {\sum }_{n=1}^{N}\left|{S}_{{\rm{delay}}}\left(n,d\right)\right|}^{2}},\end{array}\end{eqnarray} \tag{ 7 }$$

where $N$ is the number of the element ($N=4$ in this paper).

2.3.2. Sign coherence factor (SCF)

The SCF binarizes the phase of the signal and is defined as follows, ^9,13–15)

$$\begin{eqnarray}&&\begin{array}{c}{\rm{S}}{\rm{C}}{\rm{F}}\left(d\right)=1-\sqrt{1-{\left[\frac{1}{N}\displaystyle \sum _{n=1}^{N}\mathrm{sign}\left({S}_{\mathrm{delay}}\left(n,\,d\right)\right)\right]}^{2}},\end{array}\end{eqnarray} \tag{ 8 }$$

where

$$\begin{eqnarray}&&\begin{array}{c}{\rm{sign}}\left({S}_{{\rm{delay}}}\left(n,\,d\right)\right)=\begin{array}{c}+1\,{\rm{if}}\,{S}_{{\rm{delay}}}\left(n,\,d\right)\geqslant 0\\ -1\,{\rm{if}}\,{S}_{{\rm{delay}}}\left(n,\,d\right)\lt 0\end{array}.\end{array}\end{eqnarray} \tag{ 9 }$$

2.3.3. Phase coherence factor (PCF)

The instantaneous phase ${\varphi }_{n}\left(d\right)$ of the signal acquired by each element is defined as follows, ^13–15)

$$\begin{eqnarray}&&\begin{array}{c}{\varphi }_{n}\left(d\right)={\tan }^{-1}\left(\displaystyle \frac{{\rm{Im}}\left({S}_{{\rm{delay}}}\left(n,\,d\right)\right)}{{\rm{Re}}\left({S}_{{\rm{delay}}}\left(n,\,d\right)\right)}\right).\end{array}\end{eqnarray} \tag{ 10 }$$

The PCF is based on the measurement of the instantaneous phase dispersion of a delayed signal, assuming that the signal phase is distributed in the $\left(-\pi ,\,\left.\pi \right]\,\right.$interval, and is defined as follows, ^13,14)

$$\begin{eqnarray}&&\begin{array}{c}{\rm{P}}{\rm{C}}{\rm{F}}\left(d\right)={\rm{\max }}\left(0,\,1-\displaystyle \frac{{\rm{SD}}\left({\varphi }_{n}\left(d\right)\right)}{\pi /\sqrt{3}}\right),\end{array}\end{eqnarray} \tag{ 11 }$$

where ${\rm{SD}}$() is the standard deviation operation. The standard deviation of phases is normalized to the standard deviation of the uniform distribution between $-\pi$ and $\pi$ ($\pi /\sqrt{3}$).

2.3.4. Circular coherence factor (CCF)

The CCF is a weighting function that considers the phase of the signal as a circular distribution and is defined as follows, ^14,16)

$$\begin{eqnarray}&&\begin{array}{c}{\rm{C}}{\rm{C}}{\rm{F}}\left(d\right)=1-\sqrt{{\rm{var}}\left(\cos \left({\varphi }_{n}\left(d\right)\right)\right)+{\rm{var}}\left(\sin \left({\varphi }_{n}\left(d\right)\right)\right)},\end{array}\end{eqnarray} \tag{ 12 }$$

where ${\rm{var}}$() is the variance operation. Since the phase of the signal is regarded as circular, discontinuities around $\pm \pi$ can be avoided.

2.3.5. Vector coherence factor (VCF)

The VCF is a function that weights the phase difference of a signal by defining a unit vector in the complex plane, and is defined as follows, ^17,18)

$$\begin{eqnarray}&&\begin{array}{c}\begin{array}{l}{\rm{V}}{\rm{C}}{\rm{F}}\left(d\right)\\ \,=\,\displaystyle \frac{1}{N}\sqrt{{\left(\displaystyle \sum _{n=1}^{N}\cos \left({\varphi }_{n}\left(d\right)\right)\right)}^{2}+{\left(\displaystyle \sum _{n=1}^{N}\sin \left({\varphi }_{n}\left(d\right)\right)\right)}^{2}}\end{array}.\end{array}\end{eqnarray} \tag{ 13 }$$

The VCF method measures the concentration of the phases; if all the phases are aligned, the VCF is 1, and if they are uniformly distributed within the unit circle, the VCF is 0. As well as the CCF method, discontinuities around $\pm \pi$ can be avoided.

The aforementioned DAS and coherence factor calculations for PA signals acquired in a receiving event were repeatedly performed for the data acquired at each horizontal position (x, y) during the two-dimensional mechanical scanning. As a result, a three-dimensional beamformed PA signal data ${S}_{{\rm{DAS}}\_3{\rm{D}}}\left(x,\,y,\,d\right)$ and a coherence factor matrix ${x}{\rm{C}}{\rm{F}}\left({x},\,y,\,d\right),$ which was derived from one of five coherence factor methods, were achieved. Finally, a weighted PA signal data ${S}_{{\rm{weighted}}}\left(x,\,y,\,d\right)$ can be expressed as follows,

$$\begin{eqnarray}&&\begin{array}{c}{S}_{{\rm{weighted}}}\left({x},\,\,y,\,\,d\right)={x}{\rm{C}}{\rm{F}}\left({x},\,y,\,d\right)\,\circ \,{S}_{{\rm{DAS}}\_3{\rm{D}}}\left({x},\,y,\,d\right)\end{array}\end{eqnarray} \tag{ 14 }$$

here, $\circ$ symbol denotes the element-wise multiplication.

The weighted PA signal data was visualized in B-mode and C-mode by applying the maximum amplitude projection (MAP) method. The B-mode MAP image shows the maximum amplitude received from an arbitrary range of positions at the corresponding axial position (y, d). Similarly, the C-mode MAP image shows the maximum amplitude received from an arbitrary range of depths at the corresponding horizontal position (x, y). In this study, the maximum amplitude values projected on a selected plane were normalized by the maximum value of each image, and then color-encoded in the decibel scale.

For objective and quantitative evaluation of the efficacy of the five types of coherence factors on MAP images, a blood vessel phantom was made by filling a 100 μm inner diameter PFA microtube with red ink mimicking blood. The inner diameter of the phantom was set as to resemble a representative size of the skin microvasculature. ⁴⁾ PA imaging was performed in water by acquiring data from a blood vessel phantom attached to a spacer (Fig. 3). The spacer was fixed in front of the tip of the annular array transducer, and the distance between the phantom and the tip of the transducer was set to be 5.0, 5.5, 6.0 (geometric focus), 6.5, and 7.0 mm. The image size was 3.0 $\times \,\,$6.0 ($d\times y$) mm in B-mode and 6.0 $\times \,\,$6.0 ($x\times y$) mm in C-mode, and the step widths in the vertical and horizontal axes were 30 $\times \,\,$15 ($x\times y$) μm.

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In each B-mode and C-mode MAP image, the phantom diameter visualized by each method was calculated as the average of the widths of the phantom within −6 dB of the maximum intensity value in each Y-axis. The sharpening ratio by applying each coherence factor method to the DAS beamformed signals was calculated by the following formula

$$\begin{eqnarray}\begin{array}{c}\begin{array}{cc}\mathrm{Sharpening}\,\mathrm{ratio}\left( \% )\,\right) & =\,\frac{\mathrm{FWHM}\,\left(\mathrm{DAS}\right)-\mathrm{FWHM}\,\left(x{\rm{C}}{\rm{F}}\right)}{\mathrm{FWHM}\,\left(\mathrm{DAS}\right)}\times 100,\end{array}\end{array}\end{eqnarray} \tag{ 15 }$$

where ${x}{\rm{C}}{\rm{F}}$ represents one of the images applied by each coherence factor method.

To evaluate the efficacy of the five coherence factor methods on in vivo imaging, we performed PA imaging of cutaneous microvessels on the inner forearm of a healthy male in his 20 s. In the B-mode image, the image size was 3.0 × 9.0 ($d\times y$) mm and the measurement depth was 4.0–7.0 mm from the transducer. In the C-mode image, the image size was 9.0 × 9.0 ($x\times y$) mm and the measurement depth was 0.2–2.0 mm from the surface of the skin (5.29–7.00 mm from the transducer) to exclude the melanin in the epidermal layer. The focal point was set at the center of the dermal layer (1.1 mm from the skin surface). The step widths in the vertical and horizontal axes were 60 × 30 ($x\times y$) μm.

In each C-mode MAP image, the vessel of interest was set as a blue line, and the full width at half maximum (FWHM) of the vessel was calculated by Gaussian fitting. The sharpening ratio of the target vessel by applying each coherence factor method was calculated by the same Eq. (15).

As indices of image quality improvement, the contrast ratio (CR) and the contrast-to-noise ratio (CNR) were defined as the following, ^21–25)

$$\begin{eqnarray}&&\begin{array}{c}{\rm{C}}{\rm{R}}\,\left({\rm{d}}{\rm{B}}\right)=\left|{\mu }_{{\rm{s}}{\rm{i}}{\rm{g}}{\rm{n}}{\rm{a}}{\rm{l}}}-{\mu }_{{\rm{n}}{\rm{o}}{\rm{i}}{\rm{s}}{\rm{e}}}\right|,\end{array}\end{eqnarray} \tag{ 16 }$$

$$\begin{eqnarray}&&\begin{array}{c}{\rm{C}}{\rm{N}}{\rm{R}}=\displaystyle \frac{\left|{\mu }_{{\rm{s}}{\rm{i}}{\rm{g}}{\rm{n}}{\rm{a}}{\rm{l}}}-{\mu }_{{\rm{n}}{\rm{o}}{\rm{i}}{\rm{s}}{\rm{e}}}\right|}{\sqrt{{\left({\sigma }_{{\rm{s}}{\rm{i}}{\rm{g}}{\rm{n}}{\rm{a}}{\rm{l}}}\right)}^{2}+{\left({\sigma }_{{\rm{n}}{\rm{o}}{\rm{i}}{\rm{s}}{\rm{e}}}\right)}^{2}}},\end{array}\end{eqnarray} \tag{ 17 }$$

where ${\mu }_{{\rm{s}}{\rm{i}}{\rm{g}}{\rm{n}}{\rm{a}}{\rm{l}}}$ and ${\mu }_{{\rm{n}}{\rm{o}}{\rm{i}}{\rm{s}}{\rm{e}}}$ are mean amplitude of the signal from vessel and noise, and ${\sigma }_{{\rm{s}}{\rm{i}}{\rm{g}}{\rm{n}}{\rm{a}}{\rm{l}}}$ and ${\sigma }_{{\rm{n}}{\rm{o}}{\rm{i}}{\rm{s}}{\rm{e}}}$ are the variance of vessel signal and noise, respectively. In the generated images, we confirmed that the signal from the microvessels had a signal intensity of approximately −15 dB or higher. Hence, the above equation was calculated by thresholding the signals, assuming that the intensity above −15 dB are the signals of blood vessels and the other values are the noise.

As one of the results of the phantom study, the images generated when the phantom was 5.0 mm away from the annular array are shown in Fig. 4. Figure 5 also shows the visualized phantom diameters in each MAP image of the phantom study visualized at all depths. Furthermore, Table I shows the sharpening ratio by applying each coherence factor method to the DAS beamformed signals.

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In the B-mode image, the phantom image visualized with the DAS method was thicker than the original diameter, especially at depths of 5.0–6.5 mm, which was more than twice as thick as the original diameter of 100 μm. In contrast, all types of coherence factors showed a high effect of sharpening. However, in the case of the CCF method, the diameter of the phantom was thinner than 100 μm at all depths. At a depth of 7.0 mm, the diameter of the visualized phantom was thinner than the original diameter when several types of coherence factors were applied.

In the C-mode image, the phantom image visualized with the DAS method was thicker than the original diameter, which was more than twice as thick as the original diameter of 100 μm, similar to the B-mode. On the other hand, the effects of sharpening by all types of coherence factors were confirmed at all depths. The CCF method showed the highest sharpening effect as well as B-mode. However, the effect of sharpening by the SCF method was small than the other coherence factors. The width of the phantom visualized by C-mode tended to be thicker in the deeper position.

Figure 6 shows the B-mode images generated by imaging microvessels with each method applied. Figure 7 shows closeup images of the area enclosed by the yellow square in each B-mode image. In the image generated by the DAS method, the entire signal intensity was high, thus the vascular structure was unclear. On the other hand, the images generated by applying several types of coherence factors to the DAS method showed that the entire signal intensity was suppressed and the structure of the blood vessels could be clearly seen. However, in the image generated by applying the CCF method, the visualized vessel structure was partially discontinued (the white arrow in Fig. 7).

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Figure 8 shows the C-mode images of microvessels generated by each method. In the image generated by the DAS method, the running of the vessels was clear, but the vessels were visualized as being spread out. Table II shows the FWHM of the target vessel indicated by the blue line, the sharpening ratio by applying each coherence factor method to the DAS beamformed signals, and the CR and CNR calculated for each image. It could be seen that all types of coherence factors had the effect of sharpening the target vessel. In particular, the PCF method and the VCF method showed more than 20% sharpening effect and the CCF method showed 31% sharpening effect. However, in the image which applied the CF method, the CR decreased and the noise was emphasized compared to the other method. There was no significant change in the CNR between each type of coherence factor compared to the DAS method. The image obtained by applying the CCF method showed the highest CR and CNR, but the continuity of the vessels was partially lost, resulting in a rough image.

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In the phantom study, the improvement effect for image quality by applying the five coherence factors was evaluated by calculating the sharpening ratio of the phantom diameter at different imaging depths. In the B-mode and C-mode MAP images of the phantom study, the results suggested that the five coherence factors had a high effect of sharpening. However, in the B-mode MAP images at a depth of 7.0 mm, the phantom diameter visualized by applying the DAS method suddenly decreased and was confirmed to be around 100 μm. This may be attributed to the decrease in SNR of the PA signal in the deep region due to laser attenuation. In particular, the depth of 7.0 mm is deeper than the acoustic focal length of 6 mm, which is affected by both the influence of the laser attenuation and the decrease in the receiver sensitivity outside of the ultrasound focal length. Therefore, it is suggested that the phantom was not properly reconstructed due to the rapid degradation of signal reception sensitivity caused by these factors.

In the C-mode MAP images of the phantom study, the visualized phantom diameters were found to be larger than the true diameter at all depths and they were increased according to the depth. The reason for the lineally overestimation may be the linear degradation of the resolution and the measurement error due to the mechanical scanning. In the former case, the DAS method made the focal length variable, resulting in a linear change in the phantom diameter with a small ${\rm{N}}{\rm{A}}$ at deeper depths. In the latter case, the original phantom diameter is approximately three pixels in size, which means that the phantom is visualized at a depth of 5.0 mm with a spread of two or three pixels at both edges of the phantom. This indicates that the phantom was overestimated due to the measurement error caused by the mechanical scanning.

In microvascular imaging of human skin, we qualitatively and quantitatively evaluated the effects of applying five coherence factors to improve the image quality by calculating the sharpening ratio, CR, and CNR. In the same way as the phantom study, it was confirmed that the five coherence factors had a sharpening effect on the target vessel in the C-mode MAP images. The CR increased in the four coherence factors applied images and suggested an improvement in image quality except for the CF.

However, in the microvascular imaging of human skin, where the measurement range was set to 0.2–2.0 mm depth from the surface to match the thickness of the dermis layer, the maximum depth of evaluable blood vessels was only about 0.7 mm from the surface (about 5.8 mm from the annular array transducer) due to the absorption and scattering of laser in the tissue. Since the penetration depth of the laser varies depending on the optical characteristics and tissue structure of the target object, it is necessary to evaluate the imaging performance of this system in more detail using a small animal model, which is expected to enable imaging with higher penetration depth.

In this paper, we also qualitatively discussed the continuity of blood vessels. As the reason for the discontinuity of blood vessels, it can be considered that there are influences such as differences in hemoglobin concentration, blood vessels structures, etc. However, in vascular imaging, the correct vascular image is unknown, and it cannot be determined that it is the original vascular running even if the continuity of blood vessels is confirmed. In the future, it will be necessary to establish a method to quantitatively evaluate the continuity of blood vessels.

Since the CF method quantifies the phase difference of the signal by the ratio of the coherent energy to the total energy of the received signal, the phase differences among the channel-domain signals were not considered accurately. In addition, each element of the annular array transducer used in this system had different sensitivity. Consequently, in the case of vascular imaging, the signal in both vessels and the background area was excessively suppressed, resulting in noise-enhanced images. Hence, the CF method was not suitable for our system.

The SCF method is a weighting function that binarizes the phase of the signal. The results of the phantom study indicated that the SCF method was effective in sharpening for B-mode images, but not effective in sharpening for C-mode images. The results in Sect. 4.2 showed that the SCF method improved the CR value of the images, suggesting that the method was effective for noise suppression against C-mode, but not for sharpening. In addition, the SCF method might cause local variations due to the phase binarization process, so that the PCF, CCF, and VCF methods were more advantageous for this system. Instead, the SCF method may be an effective method for devices that perform real-time imaging because the computational complexity of the SCF method is relatively lower than that of other coherence factors due to the phase binarization.

The CCF method had the highest effect of sharpening than the other methods in both phantom study and microvascular imaging, indicating that was the most sensitive method to phase differences. However, in the B-mode MAP images of the phantom study, the diameter of the phantom was thinner than 100 μm at all depths. Furthermore, in microvascular imaging of human skin, the continuity of the vessels was partially lost, resulting in a rough image. That was because even a small phase difference could cause excessive signal suppression in the CCF method for transducers with a small number of elements, such as the annular array transducer used in this system. In particular, in the case of microvascular imaging, the system was more influenced by the noise from the surrounding tissue, which might cause excess phase differences. ^26,27) The CCF method might have a positive effect on multi-element transducers because of its high sensitivity in capturing the phase differences.

The results in Sects. 4.1 and 4.2 suggested that the PCF and VCF methods were effective methods for sharpening and noise suppression for our system. In a previous study, ¹⁸⁾ the PCF method was reported to have no advantage over the CCF and the VCF methods as it assumes that the phase of the signal is between −π and +π, and a phase discontinuity near ±π may cause artifacts in the image. Nevertheless, such problem was not confirmed in our system performing MAP visualization, suggesting that both the PCF and the VCF methods were effective in suppressing noise components and clearly visualizing the vascular structure. In the future, it is necessary to evaluate the effects of the PCF and the VCF methods more precisely using a variety of in vivo data.