Optimized noise reduction scheme for heterodyne spectroscopy using array detectors.

In this work, we optimize and further advance a noise reduction scheme for heterodyne spectroscopy. This scheme linearly combines data from reference detectors to predict the noise statistics in the signal detector through an optimized coefficient matrix. We validate this scheme for visible white-light-continuum and 800-nm light sources using un-matched CMOS arrays and show that the signal-to-noise ratio can approach the noise floor of the signal detector while using only ~5% of the energy for reference detection. We also optimize the strategy for estimating the coefficient matrix in practical applications. When combined with elaborate algorithms to perform pixel data compression and expansion, our scheme is applicable in difficult situations, including when the sample position is rapidly scanned, when detectors exhibit nonlinear response, and/or when laser fluctuations are large. The scheme is generalized to scenarios with complex chopping or phase cycling patterns, and a simple approach is provided for the chopping case. Finally, a robust and computationally efficient method is devised to remove multiplicative noise.