Development of a Robust Digital Lock-in Algorithm using a Closed Form Least Squares Method

摘要

Digital lock-in algorithms are routinely used to detect and measure very small AC signals acquired through digital signal analysis equipment, even if the signal may be obscured by coherent or incoherent noise sources many thousands of times larger. Unfortunately, these algorithms are iterative, normally quite complicated in functionality, and utilize digital filters which require large time constants if operating at low frequencies. We have developed passive millimeter-wave imaging systems which have application in defense, security and safety applications. Passive millimeter-wave imaging is challenging in that the amount of energy measured from a scene at these wavelengths is 10~8 times smaller than energies emitted from terrestrial objects when viewed in the infrared region. As a result, the small measured signal is buried deep in the noise floor. Our imaging systems rely on single pixel rasterizing, where it is desired that the computational time per pixel be small and fixed to avoid spatial resolution problems, but iterative algorithms create spatial registration problems and large time-constant digital filters result in greater than desired total scan times due to longer pixel acquisition periods. A digital lock-in algorithm utilizing a closed form least squares method was developed to resolve these issues. The result was the elimination of digital filtering with their time constants and the replacement of iterative routines with a fixed time computational model where the overhead per pixel was shortened by more than 10~3. This novel algorithmic approach is portable and can be used wherever digital lock-in is currently utilized.