Use of a transmission trap detector with four silicon photodiodes for absolute radiometry is described. The photodiodes are arranged in a three-dimensional array so that the small amount of light not absorbed after four reflections is transmitted in a direction coaxial with the input direction. The transmittance of the trap is measured for each application to determine the correction to the ideal photodetector response. Results at a wavelength of 633 nm show consistent power measurements for transmission losses in the range 0.3 % to 3 %, depending on the orientation of the trap detector relative to the polarization direction of the input beam. Trap power measurements are compared with a cryogenic radiometer.