Quantitative phase image stitching guided by reconstructed intensity images in one-shot double field of view multiplexed digital holographic microscopy.

In digital holographic microscopy (DHM), achieving large field of view (FOV) imaging while maintaining high resolution is critical for quantitative phase measurements of biological cell tissues and micro-nano structures. We present a quantitative phase image stitching guided by reconstructed intensity images in one-shot double FOV multiplexed DHM. Double FOVs are recorded simultaneously through frequency division multiplexing; intensity feature pairs are accurately extracted by multi-algorithm fusion; aberrations and non-common baselines are effectively corrected by preprocessing. Experimental results show that even if phase images have coherent noise, complex aberrations, low overlap rate and large size, this method can achieve high-quality phase stitching.

Multi-heterodyne interferometric absolute distance measurements based on dual dynamic electro-optic frequency combs.

In multi-heterodyne interferometry, the non-ambiguous range (NAR) and measurement accuracy are limited by the generation of synthetic wavelengths. In this paper, we propose a multi-heterodyne interferometric absolute distance measurement based on dual dynamic electro-optic frequency combs (EOCs) to realize high-accuracy distance measurement with large scale. The modulation frequencies of the EOCs are synchronously and quickly controlled to perform dynamic frequency hopping with the same frequency variation. Therefore, variable synthetic wavelengths range from tens of kilometer to millimeter can be flexibly constructed, and traced to an atomic frequency standard. Besides, a phase-parallel demodulation method of multi-heterodyne interference signal is implemented based on FPGA. Experimental setup was constructed and absolute distance measurements were performed. Comparison experiments with He-Ne interferometers demonstrate an agreement within 8.6 µm for a range up to 45 m, with a standard deviation of 0.8 µm and a resolution better than 2 µm at 45 m. The proposed method can provide sufficient precision with large scale for many science and industrial applications, such as precision equipment manufacturing, space mission, length metrology.

Active linearized PGC demodulation with fusion of PGC-Arctan and PGC-DCM schemes for nonlinear error elimination in SPM interferometer.

To eliminate the nonlinear error of phase generated carrier (PGC) demodulation in sinusoidal phase modulating interferometer (SPMI), an active linearized PGC demodulation with fusion of differential-and-cross-multiplying (PGC-DCM) and the arctangent (PGC-Arctan) schemes is proposed. In this method, the periodic integer multiple of π (π-integer phases) of PGC-Arctan without nonlinear error and the corresponding PGC-DCM results recorded at the same time are fused to obtain a calibration coefficient for PGC-DCM demodulation. Combining the accurate π-integer phases of PGC-Arctan and the calibrated fractional phase in the range of π of PGC-DCM, a linearized PGC demodulation result can be achieved, effectively eliminating the nonlinear error caused by drifts of phase demodulation depth (m) and carrier phase delay (θ). The distinct advantage of the proposed method is that it actively and linearly calibrates the fractional result of PGC-DCM without needing to measure or compensate m and θ. Simulation and displacement measurement experiments with different m and inherent arbitrary θ are performed to validate the proposed method. The experimental results show that nonlinear error of the proposed method can be reduced to about 0.1 nm with real-time linearization.

Accurate EOM-based phase-shifting digital holography with a monitoring interferometer.

Phase-shifting digital holography (PSDH) can effectively remove the zero-order term and twin image in on-axis holography, but the phase-shifting error deteriorates the quality of reconstructed object images. In this paper, accurate PSDH with an electro-optic modulator (EOM) is proposed. The EOM is used to generate the required phase shift of on-axis digital holography, and the required phase shift is precisely measured with orthogonal detection of a homodyne interferometer and controlled with proportional-integral-derivative feedback in real time. The merits of our method are that it can achieve fast and accurate phase shifting without mechanical motion or sacrificing the resolution and field of view. The optical configuration was designed, an experimental setup was constructed, and real-time phase shifting was realized. Experiments of the phase-shifting accuracy evaluation, suppression effectiveness of the zero-order and twin image terms, and the specimen measurement demonstrate that the proposed method has significant application for precision topography measurement.

Absolute distance measurement using sinusoidal phase modulating frequency sweeping interferometry with a reference interferometer.

Frequency sweeping interferometry with reference interferometer based on sinusoidal phase modulating technique is proposed in this paper for absolute distance measurement. With the frequency of the external cavity diode laser (ECDL) swept continuously in sinusoidal, a HeNe laser was employed to monitor the drifts of the target and the reference length, and influences caused by drifts during the measurement were compensated in real time. Sinusoidal phase modulation with non-overlapping frequencies were applied to the two laser lights individually by two electro-optic modulators (EOM), and the interference phases corresponding to the two laser lights were extracted simultaneously using the phase generated carrier (PGC) demodulation based on frequency-division multiplex technique. Performance of the phase detection method has been verified by nanometer displacement measurements. Experimental results show that the measurement uncertainty can be considerably reduced by compensating the influences of drifts and by applying linear regression to get the ratio of interference phase changes between the measurement interferometer and the reference interferometer. Comparison of the absolute distance measurement with an incremental interferometer yields a measurement uncertainty of 10-5, which is in good agreement with the estimation of the measurement uncertainty.

Absolute distance measurement using laser interferometric wavelength leverage with a dynamic-sideband-locked synthetic wavelength generation.

Absolute distance measurement with laser interferometry has the advantages of high precision and traceability to the definition of meter but its accuracy is primarily limited by the phase demodulation. Among kinds of absolute distance interferometric measurements, the multi-wavelength interferometry is widely used but seriously limited by the generation of suitable synthetic wavelength and the stability of adopted synthetic wavelength. Inspired by the mechanical lever, we hereby establish a principle of laser interferometric wavelength leverage (LIWL) for absolute distance measurement. By keeping the phase difference in two single wavelengths constant, LIWL achieves the measurement of large distance with respect to synthetic wavelengths by detecting nanometer displacement with respect to a single wavelength. The merit of LIWL is eliminating the influence of phase demodulation error. And a dynamic-sideband locking method based on a high-frequency electro-optic modulator is proposed, which can flexibly and quickly generate variable synthetic wavelengths from tens of kilometer to millimeter with high stability. Experimental setup was constructed and absolute distance measurements were performed. Experimental results show that a measurement range of 100 m with residual error of less than 15 µm has been achieved by comparing the LIWL system and an incremental laser interferometer.

A phase modulating homodyne interferometer with tilting error compensation by use of an integrated four-photodetector.

The tilting error of the measuring reflector moving with the measured object influences the accuracy of displacement measurement in laser interferometers. To solve this problem, a phase modulating homodyne interferometer with tilting error compensation is proposed for precision displacement measurement. In this interferometer, the displacement and tilting angle of the measured object are obtained simultaneously by differentially processing the phase changes of four interference signals detected with an integrated four-photodetector, and the obtained tilting angle is used to compensate its influence on the displacement result. The optical configuration of this interferometer is designed, and the displacement measurement with tilting error compensation is presented. An experimental setup is constructed, and the feasibility and effectiveness of the proposed interferometer are demonstrated.

Precision PGC demodulation for homodyne interferometer modulated with a combined sinusoidal and triangular signal.

A precision PGC demodulation for homodyne interferometer modulated with a combined sinusoidal and triangular signal is proposed. Using a triangular signal as additional modulation, a continuous phase-shifted interference signal for ellipse fitting is generated whether the measured object is in static or moving state. The real-time ellipse fitting and correction of the AC amplitudes and DC offsets of the quadrature components in PGC demodulation can be realized. The merit of this modulation is that it can eliminate thoroughly the periodic nonlinearity resulting from the influences of light intensity disturbance, the drift of modulation depth, the carrier phase delay, and non-ideal performance of the low pass filters in the conversional PGC demodulation. The principle and realization of the signal processing with the combined modulation signal are described in detail. The experiments of accuracy and rate evaluations of ellipse fitting, nanometer, and millimeter displacement measurements were performed to verify the feasibility of the proposed demodulation. The experimental results show that the elliptical parameters of the quadrature components can be achieved precisely in real time and nanometer accuracy was realized in displacement measurements.

A heterodyne straightness and displacement measuring interferometer with laser beam drift compensation for long-travel linear stage metrology.

The laser beam drift seriously influences the accuracy of straightness or displacement measurement in laser interferometers, especially for the long travel measurement. To solve this problem, a heterodyne straightness and displacement measuring interferometer with laser beam drift compensation is proposed. In this interferometer, the simultaneous measurement of straightness error and displacement is realized by using heterodyne interferometry, and the laser beam drift is determined to compensate the measurement results of straightness error and displacement in real time. The optical configuration of the interferometer is designed. The principle of the simultaneous measurement of straightness, displacement, and laser beam drift is depicted and analyzed in detail. And the compensation of the laser beam drift for the straightness error and displacement is presented. Several experiments were performed to verify the feasibility of the interferometer and the effectiveness of the laser beam drift compensation. The experiments of laser beam stability show that the position stability of the laser beam spot can be improved by more than 50% after compensation. The measurement and compensation experiments of straightness error and displacement by testing a linear stage at different distances show that the straightness and displacement obtained from the interferometer are in agreement with those obtained from a compared interferometer and the measured stage. These demonstrate that the merits of this interferometer are not only eliminating the influence of laser beam drift on the measurement accuracy but also having the abilities of simultaneous measurement of straightness error and displacement as well as being suitable for long-travel linear stage metrology.

Laser homodyne straightness interferometer with simultaneous measurement of six degrees of freedom motion errors for precision linear stage metrology.

A laser homodyne straightness interferometer with simultaneous measurement of six degrees of freedom motion errors is proposed for precision linear stage metrology. In this interferometer, the vertical straightness error and its position are measured by interference fringe counting, the yaw and pitch errors are obtained by measuring the spacing changes of interference fringe and the horizontal straightness and roll errors are determined by laser collimation. The merit of this interferometer is that four degrees of freedom motion errors are obtained by using laser interferometry with high accuracy. The optical configuration of the proposed interferometer is designed. The principle of the simultaneous measurement of six degrees of freedom errors including yaw, pitch, roll, two straightness errors and straightness error's position of measured linear stage is depicted in detail, and the compensation of crosstalk effects on straightness error and its position measurements is presented. At last, an experimental setup is constructed and several experiments are performed to demonstrate the feasibility of the proposed interferometer and the compensation method.