Since its first application toward displacement measurements in the early-1960s, laser feedback interferometry has become a fast-developing precision measurement modality with many kinds of lasers. By employing the frequency-shifted optical feedback, microchip laser feedback interferometry has been widely researched due to its advantages of high sensitivity, simple structure, and easy alignment. More recently, the laser confocal feedback tomography has been proposed, which combines the high sensitivity of laser frequency-shifted feedback effect and the axial positioning ability of confocal microscopy. In this paper, the principles of a laser frequency-shifted optical feedback interferometer and laser confocal feedback tomography are briefly introduced. Then we describe their applications in various kinds of metrology regarding displacement measurement, vibration measurement, physical quantities measurement, imaging, profilometry, microstructure measurement, and so on. Finally, the existing challenges and promising future directions are discussed.

Reducing Variance in Hobson and Rogers Model for Option Pricing

Influence of acousto-optic frequency shifter's thermal-induced birefringence on laser frequency-shifted feedback system

A new signal processing method named orthogonal signal phase multiplication (OSPM) is proposed, which is used to improve the precision of vibration measurement in a phase-modulating self-mixing interferometer (SMI). The modulated signal is acquired by an electro-optic modulator, which is placed in the external cavity. Higher measurement precision is realized by performing the phase multiplication algorithm on the orthogonal signals extracted from the harmonic components of the signal spectrum. Theoretically, the displacement reconstruction precision of OSPM is higher than that of conventional modulation methods, and it can be continuously improved by increasing the multiplication times. The feasibility and performance of the proposed method are verified by simulated signals and confirmed by experiments; the absolute error is less than 11 nm, and relative error is less than 0.75%, within the amplitude range from 661 nm to 2013 nm. This method does not involve additional optical elements, and its effectiveness meet the requirements for real-time high-precision measurements.

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High-Precision Laser Self-Mixing Displacement Sensor Based on Orthogonal Signal Phase Multiplication Technique

Fast measurement method of defocused differential correlation-confocal microscopy

The dynamic response of single-mode a-cut Nd:YVO4 laser combined with linearly polarized oscillation and orthogonally polarized optical feedback is investigated. Under frequency-shifted of 2 MHz, the output laser exhibits amplitude and phase modulation with anisotropic feedback when arbitrary retarder is inserted in external cavity. Its response characteristics vary with both phase retardation and optical axis orientation of the retarder. The amplitude response coefficient (ARC) and the phase response coefficient (PRC) are introduced to describe the response characteristics. In the special case where phase retardation equal to π/2, there is the minimum value in ARC and jump in PRC. Based on the Jones matrix of birefringent external cavity and rate equations of micro-chip laser, theoretical analysis of the frequency-shifted dynamics is carried out, in which the amplitude and phase response coefficient bridge the measurement and simulation quite well. Under different feedback level, the response limit of micro-chip laser with anisotropic feedback is verified as low as 10-9 of the reinjected light. 

Li Zhang

Papers

High-sensitivity laser confocal tomography based on frequency-shifted feedback technique