## 1 Introduction  
The photoacoustic (PA) effect refers to the generation of ultrasound waves when a light absorbing material absorbs energy from light irradiated at a specific wavelength and undergoes volumetric expansion. This phenomena involves a conversion mechanism where heat energy is directly coupled to vibrational modes [1, 2]. This thermoelastic process is governed by thermal expansion, in which a pressure build-up is generated, releasing a stress wave. Thermoelastic mechanisms can efficiently convert the absorbed energy into acoustic pressure waves, particularly when the period of optical excitation is short. The resulting ultrasound pressure waves are known as PA waves [3]. The applications of the PA effect encompass in vivo three-dimensional visualization using PA imaging (PAI) [4, 5]. This imaging technique allows for the capture of vital information concerning blood vessels by employing a light source with specific wavelengths to determine the optical absorption properties of hemoglobin (Hb) [6, 7]. Notably, the difference in the optical absorption properties of Hb is used to measure the oxygen saturation by using light sources with wavelengths longer and shorter than the isosbestic point of oxy- and deoxyhemoglobin at 805 nm [8]. Currently, the majority of PA applications are related to morphological imaging, with the quantitative measurement of blood flow velocity yet to find widespread practical application. The twisting and turning of microvasculature within tumor blood vessels disrupt blood flow, hindering effective treatment. The quantitative measurement of blood flow velocity proves beneficial for identifying and assessing these disturbances in the blood flow [9]. Presently, the blood flow velocity is predominantly measured employing pulsed ultrasound Doppler velocimetry (UDV). UDV is widely used for medical diagnoses relatively deep inside the human body with its advantage of non-invasiveness without nuclear radiation [10]. [PERSON] et al. conducted UDV-based imaging of blood velocity in the rodent brain with a time resolution of 100 us and a penetration depth exceeding 10 mm [11]. However, the spatial resolution of UDV is restricted by the low contrast due to small differences of acoustic impedance between biological tissues. On the other hand, in PA methods, a higher resolution is expected with a higher contrast due to the wavelength-dependent optical absorption of different biological tissues [12]. [PERSON] et al. imitated UDV and developed PA Doppler velocimetry [13]. Another advantage of PA flow velocimetry is its signal enhancement capability with high repetition rate light sources. PA imaging has applied wavelength sensitivity to visualize lymphatic flow and oxygen saturation distributions [4], while signal enhancement was demonstrated by coding and decoding illuminations in PA measurements [14]. Notably, the PA method has the potential to determine the velocity of individual cells or particles using specific wavelengths. For instance, the ultrasound signals generated from red blood cells (RBCs) are not significantly affected by the refraction from the surrounding tissue. The PA method excels in measuring microvasculature velocity, which is challenging to measure accurately using conventional UDV due to low echogenicity [15]. Researchers have employed the PA Doppler effect to measure flow velocities using tracer particles [16; 17]. In such PA velocimetry, the cross-correlation (CC) of pairs of PA signals has been proposed [18; 19; 20; 21]. PA signal pairs generated from clusters of RBCs irradiated with pulsed lasers are measured at the ultrasound transducer (UST). The velocities of the clusters were measured by determining the time shift of the arrival signals with the peak of their CCs. One key advantage of the method is that, if the time delay between pulse irradiations is freely selected, it can measure a wide range of velocities compared to the Doppler method, which has limitations in the region of interest (ROI) and velocity range.