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.

A Two-Dimensional Precision Level for Real-Time Measurement Based on Zoom Fast Fourier Transform.

This paper proposes a two-dimensional precision level for real-time measurement using a zoom fast Fourier transform (zoom FFT)-based decoupling algorithm that was developed and integrated in an FPGA. This algorithm solves the contradiction between obtaining high resolution and obtaining high measurement speed, and achieves both high angle-resolution measurement and real-time measurement. The proposed level adopts a silicone-oil surface as the angle-sensitive interface and combines the principle of homodyne interference. By analyzing the frequency of the interference fringes, the angle variation can be determined. The zoom-FFT-based decoupling algorithm improves the system's frequency resolution of the interference fringes, thereby significantly enhancing the angle resolution. Furthermore, this algorithm improves the efficiency of angle decoupling, while the angle decoupling process can also be transplanted to the board to realize real-time measurement of the level. Finally, a prototype based on the level principle was tested to validate the effectiveness of the proposed method. The principle analysis and test results showed that the angle resolution of the prototype improved from 9 arcsec to about 0.1 arcsec using this angle-solution method. At the same time, the measurement repeatability of the prototype was approximately ±0.2 arcsec. In comparison with a commercial autocollimator, the angle measurement accuracy reached ±0.6 arcsec.

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.

Homodyne laser vibrometer modified by an LCVR for measurement at the nanometer level.

The existence of periodic nonlinear error restricts the performance of the homodyne laser vibrometer in sub-fringe amplitude vibration measurement. A homodyne laser vibrometer with nanoscale-amplitude detectability by using a liquid crystal variable retarder (LCVR) is proposed. The LCVR introduces an extra variation of optical path difference larger than the laser wavelength to acquire a full ellipse so that the nonlinearity correction parameters could be pre-extracted. The experiments showed that the nonlinear error could be well suppressed with the correction process based on the pre-extracted parameters, and the detectable minimum amplitude is less than 1 nm. In addition, measurement of vibration with the reflectivity of measured targets down to 0.048% was achieved with an automatic-gain-control module.

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.

Analysis of a highly efficient phase-locking stabilization method for electro-optic comb generation.

We theoretically show that a slightly modified Pound-Drever-Hall (PDH) stabilization scheme can lead to the optimum time-domain characteristics for electro-optic comb generators (EOCG). The ideal locking point is located by analyzing the EOCG output pulse width. By summing up the electrical field reflected by the EOCG front mirror, a model of the phase-locking error signal is derived with the Jacobi-Anger identical transformation. The simulation and experiment show that the zero-locking point of the error signal of the modified scheme coincides well with the ideal locking point in contrast with the direct application of the PDH scheme. Finally, a power efficiency of up to 2.9% is achieved with this EOCG stabilization scheme. A relative instability of better than 2.6×10-8 is demonstrated by a dual comb interferometer with fixed paths. The Allan deviations of the comb mode frequencies are smaller than 2.8×10-9 and 1.1×10-10 for average times of 1 and 100 s, respectively.

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.

Ultrastable Offset-Locking Continuous Wave Laser to a Frequency Comb with a Compound Control Method for Precision Interferometry.

A simple and robust analog feedforward and digital feedback compound control system is presented to lock the frequency of a slave continuous wave (CW) laser to an optical frequency comb. The beat frequency between CW laser and the adjacent comb mode was fed to an acousto-optical frequency shifter (AOFS) to compensate the frequency dithering of the CW laser. A digital feedback loop was achieved to expand the operation bandwidth limitation of the AOFS by over an order of magnitude. The signal-to-noise ratio of the interference signal was optimized using a grating-based spectral filtering detection unit. The complete system achieved an ultrastable offset-locking of the slave CW laser to the frequency comb with a relative stability of ±3.62 × 10-14. The Allan deviations of the beat frequency were 8.01 × 10-16 and 2.19 × 10-16 for a gate time of 10 s and 1000 s, respectively. The findings of this study may further improve laser interferometry by providing a simple and robust method for ultrastable frequency control.

Measurement Method for Nonlinearity in Heterodyne Laser Interferometers Based on Double-Channel Quadrature Demodulation.

The phase quadrature measurement method is capable of measuring nonlinearity in heterodyne laser interferometers with picometer accuracy whereas it cannot be applied in the new kind of heterodyne interferometers with bidirectional Doppler frequency shift especially in the condition of non-uniform motion of the target. To solve this problem, a novel measurement method of nonlinearity is proposed in this paper. By employing double-channel quadrature demodulation and substituting the external reference signal with internal ones, this method is free from the type of heterodyne laser interferometer and the motion state of the target. For phase demodulation, the phase differential algorithm is utilized to improve the computing efficiency. Experimental verification is carried out and the results indicate that the proposed measurement method achieves accuracy better than 2 pm.

Nonlinear Errors Resulting from Ghost Reflection and Its Coupling with Optical Mixing in Heterodyne Laser Interferometers.

Even after the Heydemann correction, residual nonlinear errors, ranging from hundreds of picometers to several nanometers, are still found in heterodyne laser interferometers. This is a crucial factor impeding the realization of picometer level metrology, but its source and mechanism have barely been investigated. To study this problem, a novel nonlinear model based on optical mixing and coupling with ghost reflection is proposed and then verified by experiments. After intense investigation of this new model's influence, results indicate that new additional high-order and negative-order nonlinear harmonics, arising from ghost reflection and its coupling with optical mixing, have only a negligible contribution to the overall nonlinear error. In real applications, any effect on the Lissajous trajectory might be invisible due to the small ghost reflectance. However, even a tiny ghost reflection can significantly worsen the effectiveness of the Heydemann correction, or even make this correction completely ineffective, i.e., compensation makes the error larger rather than smaller. Moreover, the residual nonlinear error after correction is dominated only by ghost reflectance.

Highly thermal-stable heterodyne interferometer with minimized periodic nonlinearity.

Heterodyne interferometers suffer from thermal drift of optics (TDO), which may introduce error even up to several micrometers. In this paper, we propose a symmetric heterodyne interferometer with spatially separated beams, which realizes completely balanced optical paths between probe and reference beams and simultaneously avoids the optical mixing, and thereby is theoretically capable of eliminating TDO and the periodic nonlinearity (PNL). To validate the performance of the proposed interferometer, first a special experimental setup is constructed, with which the TDO test can be conducted in vacuum, and the result shows that a thermal coefficient of 1.2 nm/°C is achieved. Next, the PNL of the proposed interferometer is measured by both the frequency domain method and the phase quadrature method, which demonstrates an undetectable PNL at a noise level of 13 pm.

Nonlinearity error in homodyne interferometer caused by multi-order Doppler frequency shift ghost reflections.

This paper reports a hitherto undiscovered cyclic error whose origin is different from that of conventional errors in homodyne interferometers. To explain this error, a model based on ghost reflections and the interference principle is developed. In general, in homodyne interferometers, multi-order Doppler frequency shift ghost beams participate in the final interference and generate multi-order cyclic errors. This "new" cyclic error is compared with conventional errors by means of Lissajous curves. And we establish a setup to validate our proposed model. We use a corner cube retroreflector to replace the mirror and we find the error is significantly reduced. We believe that our findings can contribute to the further development of highly accurate homodyne interferometers.

Nonlinear errors induced by intermodulation in heterodyne laser interferometers.

A striking abnormal harmonic is detected in the measurement signal spectrum of a heterodyne laser interferometer, which deviates from the conventional frequency-domain model. A nonlinearity model based on intermodulation is proposed to explain this abnormality and to analyze its influence. Analysis from this model demonstrates that the harmonics arising from intermodulation can result in not only nonlinear errors opposite in sign to the traditional first- and second-order nonlinearities, but also new third- and fourth-order nonlinearities; moreover, these periodic nonlinearities cannot be fully compensated anymore by the Heydemann correction.

Simple method for reducing the first-order optical nonlinearity in a heterodyne laser interferometer.

A simple method was proposed by using a tunable attenuator fitted in the reference or measurement arm of a heterodyne laser interferometer to adjust the values of mixing laser beams while the spectrum of the measurement signal is monitored using a signal analyzer. The effectiveness of the proposed method in reducing the first-order optical nonlinearity was verified through experiments. Results indicated that the peak value of the first-order optical nonlinearity could be reduced from 5.15 to 0.24 nm. It was therefore concluded that the proposed method was applicable to ultraprecision laser interferometry.

Both c-Myc and Ki-67 expression are predictive markers in patients with extranodal NK/T-cell lymphoma, nasal type: a retrospective study in China.

Extranodal natural killer (NK)/T-cell lymphoma, nasal type (ENKTL) is an increasingly recognized disease entity of aggressive tumor progression. The objective of this study was to investigate the clinical and prognostic significance of c-Myc and Ki-67 expression in ENKTL. Immunohistochemistry for c-Myc and Ki-67 was performed on tissue sections from 53 patients diagnosed with ENKTL, and their correlation with clinicopathologic variables was assessed. We also made a comparison between c-Myc positive and negative ENKTL on proliferation index (PI); and analyzed relationship between expression of c-Myc and Ki-67 index. The survival was analyzed by Kaplan-Meier product-limit method. Positive expression of c-Myc was shown in 64.2% of the patients, and high expression of Ki-67 was found in 66%. The PI in c-Myc-positive tumor cell was significantly higher than that in c-Myc-negative ones (P=0.005). The positive correlation between c-Myc expression and Ki-67 index was also found (r=0.454, P=0.001). Patients of c-Myc expression were shown to be associated with unfavorable overall survival (OS) and decreased progression free survival (PFS) (P=0.000 and 0.013, respectively). High expression of Ki-67 was also shown to be correlated with worse OS and PFS (P=0.014 and 0.016, respectively). And patients expression of c-Myc+/Ki-67 high had the worst OS and PFS (P=0.002 and 0.027, respectively). c-Myc may play an important role in the carcinogenesis of NK/T cell lymphoma by promoting cell proliferation. Both c-Myc expression and Ki-67 high expression in ENKTL patients may be valuable indicators for predicting the survival of ENKTL patients.