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.

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 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.

Sinusoidal phase modulating absolute distance measurement interferometer combining frequency-sweeping and multi-wavelength interferometry.

A sinusoidal phase modulating absolute distance measurement (ADM) interferometer combining frequency-sweeping interferometry (FSI) and multi-wavelength interferometry (MWI) is proposed in this paper. The swept frequency in FSI and the wavelengths for MWI are calibrated by an optical frequency comb, so the distance measurement can be directly traced back to the SI definition of a meter. With a simple optical structure, an ADM interferometer consisting of a measurement interferometer and a monitor interferometer is constructed without polarization optics. A near-infrared external cavity diode laser (ECDL) calibrated by an optical frequency comb is used as a work source of the measurement interferometer for frequency sweeping and hopping. The monitor interferometer using a He-Ne laser runs parallel to the measurement interferometer to monitor the fluctuation of the measured distance during the measurement. Experiments for absolute distance measurements in a range of 8.25 m were carried out to verify the feasibility of the proposed ADM interferometer. The experimental results show that the maximum measurement error is less than 1 µm compared with an incremental-type laser interferometer.

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.

Iterative compensation of nonlinear error of heterodyne interferometer.

In order to compensate the nonlinear error of a heterodyne interferometer caused by both frequency mixing and phase demodulating electronics in real time, a novel iterative algorithm with a digital lock-in phase demodulator is proposed in this paper. By using iterative translating and scaling transforms, the phase diagram of the two output signals from phase demodulator is corrected from an ellipse with center offset to a circle at origin. As a result, the correct phase can be obtained and the nonlinear error is compensated. The nonlinear error in heterodyne interferometer is analyzed, the digital lock-in phase demodulator is designed and the iterative compensation algorithm is presented. Simulation and displacement measurement experiments were performed to verify the effectiveness of the proposed method. The experimental results demonstrated that proposed method is able to reduce the nonlinear error obviously and realize nanometer displacement measurement.

Real-time phase delay compensation of PGC demodulation in sinusoidal phase-modulation interferometer for nanometer displacement measurement.

As the phase delay between the carrier component of the detected interference signal and the carrier has adverse effect for phase generated carrier (PGC) demodulation, it is essential to compensate the phase delay to improve the accuracy of precision displacement measurement in sinusoidal phase-modulation interferometer (SPMI). In this paper, a real-time phase delay compensation method is proposed by regulating a compensating phase introduced to the carrier to maximize the output of the low pass filter so as to make the carrier synchronize with the interference signal. The influence of phase delay for PGC demodulation is analyzed and the method for real-time phase delay compensation is described in detail. The simulation of the method was performed to verify the validity of the phase delay compensation algorithm. A SPMI using an EOM was constructed and several comparative experiments were carried out to demonstrate the feasibility of the proposed method. The experimental results show that the phase delay can be compensated accurately in real time, and nanometer accuracy is achieved for precision displacement measurement.