## 6 Conclusions  
We investigated the performance of the PA velocity measurement of an object in one-dimensional motions. The PA signals were generated by irradiating the pulsed lasers with a pre-selected time delay. The object velocity was measured by calculating the time shift between the PA signal pairs using CC in the time domain. For the calibration experiment, the average velocity of the stationary object was calculated as \(v_{\rm{avg}}=-3.4\) mm/s, which was consistent with the minimum measurable velocity \(v_{\rm{lim}}=\pm 3.4\) mm/s of the measurement system. To evaluate the dynamic performance, we employed the linear sinusoidal motion of a single GC attached to an LS membrane. The periodic linear motions resulted in reproducible linear velocities with a range of \(-300\) to 300 mm/s. Motion was independently monitored by the LDS, which provided the reference velocity of the moving object. The PA measurement results provided the phase-resolved velocities of the object monitored by the LDS measurement. The results suggested that the measurement uncertainties were consistent with the values in the stationary case and remained almost constant over the investigated velocity range. Furthermore, the PA measurements revealed the local fine velocities of the object which were not resolved by the LDS measurements. A comparison of the LDS and PA results revealed deviations in the shape of the output waveform from the input signals. The nonlinearity in the LS output and distortions caused by arm bending contributed to these deviations. Despite these deviations, the PA results faithfully captured velocity variations in the range of \(-200\) to 100 mm/s, even during the folding back of the LS oscillation. The fold  
Figure 8: Comparison of velocities measured using the PA and LDS in the range of 0 to 100 mm/s. The input signal to the LS was a sinusoidal waveform, with the resulting displacement measured with the LS being a cosine waveform. The PA data showcase the maximum velocities at the theoretical phases. The folding back of the LS oscillation occurs at 0.05 and 0.15 s, where velocities approach 0 mm/s. The LDS data were internally averaged before the output. The PA data were moving averaged over 12 neighbor points to match the temporal resolution of the LDS data. As a result, the PA (averaged) data shifted 0.033 s to the right.  
ing back was acquired at 0.055 s and the maximum deviation between the LDS and PA was 26 mm/s at 0.031 s. This deviation was attributed to the temporal resolution determined by the sampling rate at the measurement. The deviation could be reduced by increasing the temporal resolution and/or applying interpolation to the correlation coefficients in the determination of the peak location. The uncertainty of the PA velocity measurements ranged from 0.86 to 2.1 mm/s for the maximum and minimum velocities, respectively. Furthermore, the PA measurements revealed the local fine velocities of the object, which were not resolved by the reference velocities of the LDS measurements. The capability of the PA velocity measurement is expected to be advantageous in blood velocimetry measurements with dynamic variations in both magnitude and direction. This offers the prospect of mapping in a multi-dimensional region, although the present study is limited to a single object in a one-dimensional case. Further investigation is necessary to ensure the feasibility of the clustered RBCs at a micrometer scale in the microvascular environment.  
Conceptualization, K.F. and K.S.; Methodology, K.F. and K.S.; Validation, K.F.; Investigation, K.F.; Writing--original draft, K.F.; Writing--review & editing, K.S.; Supervision, K.S.; Funding acquisition, K.S. All authors have read and agreed to the published version of the manuscript. This research received no external funding.  
Not applicable.  
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy.  
The authors declare no conflict of interest.