We have developed a polarization-independent reflection-type silicon photodiode trap detector and characterized its performance by laser beam-based measurement. Three dimensional CAD-based modeling enables us to optimize its interior design, resulting in minimizing each distance between centers of adjacent photodiodes by rotating each photodiode by 45° along each normal axis. It is expected by a simple ray-tracing simulation and also confirmed experimentally that the trap detector incorporating a photodiode with a large active area exhibits the largest acceptance angle ever proposed as the polarization-independent trap detector for the convergent incident beam. This is suitable for the national standard detector to realize and disseminate the cryogenic radiometer-based spectral power responsivity with high accuracy. It is also applicable to various kinds of working or transfer standard detectors for collimated or non-collimated monochromatic radiation. In addition, a history of development of trap detectors at national laboratories is reviewed.