High-speed and high-precision measurement of biaxial in-plane displacements: tens of nanometers principle error suppression in microprobe sensors.

When the microprobe sensor is faced with the demand of high-speed biaxial displacement measurement, due to the characteristics of phase generated carrier (PGC) technology, accompanying optical intensity modulation (AOIM) and unfavorable phase modulation depth (PMD) will bring about the tens of nanometer cyclic nonlinear errors, further hindering high-speed and high-precision measurement. Herein, a light source intensity stabilization system based on semiconductor optical amplifier (SOA) feedback control is achieved to eliminate the error caused by AOIM in the presence of high-frequency and large-amplitude laser modulation. Based on this, the reasons for large nonlinear errors in biaxial measurements and the inability to ensure the stability of the accuracy of multiple measurement axes are methodically examined, and an effective nonlinear error elimination methodology based on the normalized amplitude correction of active temperature scanning is proposed. The continuity and linearity of the temperature scanning are also discussed. The performed experiments show that the above approach is capable of reducing the displacement demodulation error from the nanometer scale to the sub-nanometer scale. Further, the nonlinear error is reduced to within 0.1 nm for both measurement axes and the performance becomes consistent. The dual-axis measurement resolution of the microprobe sensor reaches 0.4 nm and the measurement speed is better than 1.2 m/s with the standard deviation of lower than 0.5 nm.

Analysis and Design of Fiber Microprobe Displacement Sensors Including Collimated Type and Convergent Type for Ultra-Precision Displacement Measurement.

In this paper, a fiber optic microprobe displacement sensor is proposed considering characteristics of micro-Michelson interference structure and its components. The principal error of micro Fabry-Perot interferometric structure is avoided, and high-precision interferometric displacement measurement is realized. The collimated microprobe and convergent microprobe are analyzed, simulated, and designed for the purposes of measuring long-distance displacement and small spot rough surface, respectively. The core parameters of the probes' internal components are mapped to coupling efficiency and contrast of the sensor measurements, which provides a basis for the probes' design. Finally, simulation and experimental testing of the two probes show that the collimated probe's working distance and converging probe's tolerance angle can reach 40 cm and ±0.5°, respectively. The designed probes are installed in the fiber laser interferometer, and a displacement resolution of 0.4 nm is achieved.

Accurate and Comprehensive Spectrum Characterization for Cavity-Enhanced Electro-Optic Comb Generators.

Cavity-enhanced electro-optic comb generators (CEEOCGs) can provide optical frequency combs with excellent stability and configurability. The existing methods for CEEOCGs spectrum characterization, however, are based on approximations and have suffered from either iterative calculations or limited applicable conditions. In this paper, we show a spectrum characterization method by accumulating the optical electrical field with respect to the count of the round-trip propagation inside of CEEOCGs. The identity transformation and complete analysis of the intracavity phase delay were conducted to eliminate approximations and be applicable to arbitrary conditions, respectively. The calculation efficiency was improved by the noniterative matrix operations. Setting the maximum propagation count as 1000, the spectrum of the center ±300 comb modes can be characterized with merely the truncation error of floating-point numbers within 1.2 s. More importantly, the effects of all CEEOCG parameters were comprehensively characterized for the first time. Accordingly, not only the exact working condition of CEEOCG can be identified for further optimization, but also the power of each comb mode can be predicted accurately and efficiently for applications in optical communications and waveform synthesis.

Embedded micro-probe fiber optic interferometer with low nonlinearity against light intensity disturbance.

A novel low-nonlinearity Michelson microprobe fiber interferometer against light intensity disturbance for high-precision embedded displacement measurements is introduced. To analyze the influence of light intensity disturbance on the microprobe and measurement accuracy of the integrated fiber interferometer, an equivalent model of micro-probe sensing with the tilted target is established. The proposed PGC demodulation and nonlinearity correction method with simple principle helps avoid DC component varying with light intensity. The experiments show that residual displacement errors of the micro-probe fiber interferometer are reduced from 4.36 nm to 0.46 nm, thus allowing embedded displacement detection with sub-nanometer accuracy under low frequency light intensity disturbance.

Phase modulation depth setting technique of a phase-generated-carrier under AOIM in fiber-optic interferometer with laser frequency modulation.

The phase modulation depth (PMD) in phase-generated-carrier demodulation is determined by the laser frequency modulation amplitude and working distance of a fiber-optic interferometer and must be set at a certain value. Active setting of the amplitude is unsuitable, especially for high-speed modulation, owing to variations in the laser source tuning coefficients. Existing calculation schemes for passive setting cannot work both owing to carrier phase delay (CPD) and the accompanied optical-intensity modulation (AOIM). Herein, a modified phase modulation depth calculation and setting technique is proposed. Double photoelectric detection and signal division are optimized to eliminate AOIM using a fiber delay chain and phase-locked amplifier module. Fast Fourier-transform and look-up table methods are used to calculate phase modulation depth without adding the carrier, which is unaffected by CPD. A fiber-optic Michelson interferometer is constructed to verify the feasibility of the proposed method. The experimental results show that AOIM can be eliminated; moreover, PMD can be calculated and set precisely. The displacement deviation is less than 1.03 nm. The resolution of measurement is considerably lesser than 1 nm and nanoscale accuracy is achieved in displacement measurement.

Correction of nonlinear errors from PGC carrier phase delay and AOIM in fiber-optic interferometers for nanoscale displacement measurement.

In fiber-optic interferometers with laser frequency modulation, carrier phase delay and accompanied optical intensity modulation (AOIM) in phase-generated-carrier (PGC) demodulation inevitably produce nonlinear errors that can seriously hamper displacement measurement accuracy. As for the existing improved PGC scheme, they are only capable to compensate for one of these effects. As the only method that is effective in eliminating the two effects simultaneously, typical ellipse fitting methods require target movements λlaser/4, and fail when the PGC carrier phase delay is proximate to certain values (e.g., nπ +π/4, nπ +π/2). Herein, a modified nonlinear-error correction method for errors due to PGC carrier phase delay and AOIM is proposed. Active laser-wavelength scanning by constant variation of the laser drive temperature is used to replace the target movement. A fiber-optic Michelson interferometer is constructed and experiments are performed to verify the feasibility of the proposed method. The experimental results show that after correction, the nonlinear error is reduced to less than 1nm, and nanoscale displacement measurement is achieved.