Metrology

This paper introduces a constraint-aware optimization framework for designing spherical multi-camera rigs that achieve complete panorama coverage while adhering to physical and field-of-view limitations. The approach assesses coverage using solid-angle geometry and calculates the sampling density in pixels per steradian, providing a measurable, traceable basis for panoramic optical measurement. By viewing panoramic imaging as a directional measurement challenge, the framework aligns with principles of optical metrology and guarantees uniform, non-contact optical sensing around the sphere. The optimization process includes capsule-based collision constraints, soft coverage losses, and field-of-view intersection modeling to produce physically feasible rig configurations. Experiments show that the optimized rigs provide improved coverage uniformity and less redundancy, with validation through Blender-generated synthetic panoramas confirming the practical performance of the designed optical systems. The proposed approach allows for systematic, measurement-driven design of spherical camera rigs for use in immersive imaging, robotic perception, and structural inspection.

Many fields or disciplines (e.g., uncertainty analysis in measurement science) require a combination of probability distributions. This technical note examines three methods for combining probability distributions: weighted linear pooling, geometric pooling, and the law of combination of distributions (LCD). Although these methods have been discussed in the literature, a systematic comparison of them appears insufficient. In particular, there is no discussion in the literature regarding the potential information loss that these methods may cause. This technical note aims to fill this gap. It provides insights into these three methods under the normality assumption. It shows that the weighted linear pooling method preserves all the variability (including heterogeneity) information in the original distributions; neither the geometric pooling method nor the LCD method preserves all the variability information, leading to information loss. We propose an index for measuring the information loss of a method with respect to the weighted linear pooling method. This technical note also shows that the weighted linear pooling method can be used as an alternative to the traditional random-effects meta-analysis. Three examples are presented: the combination of two normal distributions, the combination of three discrete distributions, and the determination of the Newtonian constant of gravitation.

Photoacoustic (PA) velocimetry offers a promising solution to the limitations of conventional techniques for measuring blood flow velocity. Given its moderate penetration depth and high spatial resolution, PA imaging is considered suitable for measuring low-velocity blood flow in capillaries located at moderate depths. High-resolution measurements based on PA signals from individual blood cells can be achieved using a high-frequency transducer. However, high-frequency signals attenuate rapidly within biological tissue, restricting the measurable depth. Consequently, low-frequency transducers are required for deeper measurements. To date, PA flow velocimetry employing low-frequency transducers remains insufficiently explored. In this study, we investigated the effect of the concentration of particles that mimic blood cells within vessels under low-concentration conditions. The performance of flow velocity measurement was evaluated using an ultrasonic transducer (UST) with a center frequency of 10 MHz. The volume fraction of particles in the solution was systematically varied, and the spatially averaged flow velocity was assessed using two different distinct analysis methods. One method employed a time-shift approach based on cross-correlation analysis. Flow velocity was estimated from PA signal redpairs generated by particles dispersed in the fluid, using consecutive pulsed laser irradiations at fixed time intervals. The other method employed a pulsed Doppler method in the frequency domain, widely applied in ultrasound Doppler measurements. In this method, flow velocity redwas estimated from the Doppler-shifted frequency between the transmitted and received signals of the UST. For the initial analysis, numerical simulations were performed, followed by experiments based on displacement measurements equivalent to velocity measurements. The target was a capillary tube filled with an aqueous solution containing particles at different concentration levels. The time–domain method tended to underestimate flow velocity as particle concentration increased, whereas the pulsed Doppler method yielded estimates consistent with theoretical values, demonstrating its potential for measurements at high concentrations.