High-Speed Microscale Optical Tracking Using Digital Frequency-Domain Multiplexing

Position-sensitive detectors (PSDs), or lateral-effect photodiodes, are commonly used for high-speed, high-resolution optical position measurement. This paper describes the instrument design for multidimensional position and orientation measurement based on the simultaneous position measurement of multiple modulated sources using frequency-domain-multiplexed (FDM) PSDs. The important advantages of this optical configuration in comparison with laser/mirror combinations are that it has a large angular measurement range and allows the use of a probe that is small in comparison with the measurement volume. We review PSD characteristics and quantitative resolution limits, consider the lock-in amplifier measurement system as a communication link, discuss the application of FDM to PSDs, and make comparisons with time-domain techniques. We consider the phase-sensitive detector as a multirate DSP problem, explore parallels with Fourier spectral estimation and filter banks, discuss how to choose the modulation frequencies and sample rates that maximize channel isolation under design constraints, and describe efficient digital implementation. We also discuss hardware design considerations, sensor calibration, probe construction and calibration, and 3-D measurement by triangulation using two sensors. As an example, we characterize the resolution, speed, and accuracy of an instrument that measures the position and orientation of a 10 mm × 5 mm probe in 5 degrees of freedom (DOF) over a 30-mm cube with 4-μm peak-to-peak resolution at 1-kHz sampling.