Low-complexity velocity estimation in high-speed optical Doppler tomography systems

Optical Doppler Tomography (ODT) is a noninvasive 3-D optical interferometric imaging technique that measures static and dynamic structures in a sample. To obtain the dynamic structure, e.g. blood flowing in tissue, a velocity estimation algorithm detects the Doppler shift in the received interference fringe data with respect to the carrier frequency. Previous velocity estimation algorithms use conventional Fourier magnitude techniques that do not provide sufficient frequency resolution in fast ODT systems because of the high data acquisition rates and hence short time series. In this paper, we propose a nonlinear algorithm that uses the phase shift between two successive scans of interference fringe data to give a high-resolution estimate of the Doppler shift. The algorithm detects Doppler shifts of 0.1 to 3 kHz with respect to a 1 MHz carrier. In processing 5 frames/s with 100×100 pixels/frame and 32 samples/pixel, i.e. 1.6 million samples/s, the algorithm requires 26 million multiply-accumulates/s. The algorithm works well at 4 bits/sample. The low complexity and small input data size are well-suited for real-time implementation in software. We provide a mathematical analysis of the Doppler shift resolution by modeling the interference fringe data as an AM-FM signal.