Quadrant photodetector sensitivity.

A quantitative theoretical analysis of the quadrant photodetector (QPD) sensitivity in position measurement is presented. The Gaussian light spot irradiance distribution on the QPD surface was assumed to meet most of the real-life applications of this sensor. As the result of the mathematical treatment of the problem, we obtained, in a closed form, the sensitivity function versus the ratio of the light spot 1/e radius and the QPD radius. The obtained result is valid for the full range of the ratios. To check the influence of the finite light spot radius on the interaxis cross talk and linearity, we also performed a mathematical analysis to quantitatively measure these types of errors. An optimal range of the ratio of light spot radius and QPD radius has been found to simultaneously achieve low interaxis cross talk and high linearity of the sensor.