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Dual femtosecond laser ranging (DFLR) is an enabling absolute distance measurement technique which is advantageous of high measurement precision, fast update rate, and large unambiguous range. Peak detection, which requires repeated online solution of nonlinear curve fitting, is a key module of the DFLR system and its performance affects the accuracy and real-time of the ranging system. In addition, for long baseline measurements based on satellite-borne platforms, the DFLR system has requirements in high integration, low cost, and small size. This paper presents a peak detection implementation on a field-programmable gate array (FPGA) that employs a Broyden-Fletcher-Goldfarb-Shanno (BFGS) method to handle nonlinear curve fitting. FPGA is used to explore the possibilities of parallel architecture for the acceleration of peak detection, and realize the miniaturization of the system. The detailed architecture design of the peak detection module using BFGS method (PD-BFGS) and two hardware structures are proposed. Then, the PD-BFGS module is applied to a DFLR system and evaluated with experiments on the absolute distance measurement. The experimental results indicate that the PD-BFGS based on FPGA effectively reduces the peak detection error by 42.81%, compared with the peak detection module using Caruana's method. For the DFLR system, the ranging error is reduced by 63.63% and the real-time updating of the ranging results is guaranteed. INDEX TERMS BFGS-QN method, femtosecond laser ranging, field-programmable gate array (FPGA), nonlinear curve fitting, peak detection.

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It is known that the collagen-rich and well-organized biological tissues have birefringent characteristics when presented to the light. Determination of collagen fiber organization in tissue is of paramount importance in clinical diagnosis. With the precise control of the polarization state of incident and reflected light, polarization sensitive optical coherence tomography (PSOCT) could be used to visualize the tissue birefringence. To understand this better, the mathematical treatment relying on rigorous polarization optics would be needed. This paper is primarily for this purpose. The emphasis is placed on the discussions of light reflected from within a sample using a point source beam and analytical derivations of the polarization properties of tissue based on quasi-Stokes parameters (I, Q, U, V) and Jones matrix formalism.