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 extraction of the +1 term spectrum with spurious spectrum elimination in off-axis digital holography.

In off-axis digital holography, spatial filtering is a key problem limiting the quality of reconstructed image, especially in the case of spurious spectrum generated by coherent noise in the hologram spectrum. In this paper, a new spatial filtering method with spurious spectrum elimination is proposed. Side band centering judgment is firstly implemented to locate the center point of the +1 term in the hologram spectrum. Then by roughly recognizing the region of +1 term spectrum, most of the -1 term, 0 term and the spurious spectral components are eliminated. Finally, Butterworth filtering is performed to extract the +1 term spectrum as enough as possible without introducing the spurious spectrum. Simulated hologram of E-shaped specimen with the spurious spectrum is generated to evaluate the performance of the proposed method. Experimental data of USAF 1951 resolution target, ovarian slice and microlens array are adopted to verify the effectiveness of the proposed method. Simulation and experimental results demonstrated that the proposed method is able to accurately extract the +1 term spectrum with spurious spectrum elimination and achieve a relatively good balance between the structural detail characterization and noise suppression.

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.

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.

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.

Three-degrees-of-freedom measurement system for measuring straightness errors and their position based on the Faraday effect.

A three-degrees-of-freedom measurement system based on the Faraday effect is proposed for simultaneously measuring two-dimensional straightness errors and their position. Thanks to the Faraday effect of the Faraday rotator, the direction of a linearly polarized beam can be changed by 90° when the linearly polarized beam passes through the same Faraday rotator back and forth twice. A novel optical configuration is designed that can integrate the interferometry and position-sensitive detection technology ingeniously and put their advantages together. The measurement principle is described in detail. The influence of angle error of the semitransparent mirror on straightness measurement is discussed. To verify the feasibility of the proposed system, the experimental setup for measuring three degrees of freedom was constructed, and a series of experiments were carried out.

Laser heterodyne interferometer with rotational error compensation for precision displacement measurement.

A laser heterodyne interferometer with rotational error compensation is proposed for precision displacement measurement. In this interferometer, the rotational error of the measured object is obtained by using an angle detecting unit which is composed of a semi-reflective film, a polarizing beam splitter, a quarter-wave plate, a convex lens and a two-dimensional position sensitive detector. And the obtained rotational angle is used for compensating its influence on displacement measurement result. The optical configuration of the proposed interferometer is designed, and the mathematical model for displacement measurement with rotational error compensation is established. The coupling effect of axial displacement on rotational angle measurement and the rotational angle range used for compensation on displacement measurement are discussed in detail. To verify feasibility of the proposed interferometer, the experimental setup was constructed and several verification experiments were performed.

Real-time normalization and nonlinearity evaluation methods of the PGC-arctan demodulation in an EOM-based sinusoidal phase modulating interferometer.

In order to reduce the nonlinearity caused by an error of phase modulation depth, carrier phase delay and non-ideal performance of the low pass filters in the sinusoidal phase modulating interferometer (SPMI), a modified EOM-based SPMI is proposed in this paper to realize real-time normalization of the quadrature components for the arctangent approach of phase generated carrier (PGC-Arctan) demodulation. To verify the effectiveness of the real-time normalization technique, a fixed-phase-difference detection method is presented to evaluate the periodic nonlinearity in real time. The modified EOM-based SPMI is consisted of a monitor interferometer and a probe interferometer. The two interferometers share a reference corner cube, which is mounted on a slowly moving stage, thus periodic interference signals are generated for real-time normalization of the quadrature components in PGC demodulation. Subtracting the demodulated phase of the monitor interferometer from the phase of the probe interferometer, the phase to be measured can be obtained. The fixed-phase-difference detection method is realized by detecting an interference signal with two photodetectors, which are placed at an interval of quarter fringe, and the variation of the fixed-phase-difference can reflect the nonlinear error in PGC demodulation. Experiments of real-time normalization, nonlinear error evaluation of PGC demodulation, and displacement measurement were implemented to demonstrate the effectiveness of the proposed method. Experimental results show that the nonlinear error of phase demodulation reduced to less than ± 1° with real-time normalization, and nanometer displacement measurement is realized.

Laser heterodyne interference signal processing method based on phase shift of reference signal.

A novel signal processing method based on phase shift of reference signal is proposed for heterodyne interferometer. The integer fringe counting method based on overflow judgment and compensation can realize longtime and correct integer number measurement. In order to eliminate the influence of jitter in measurement signals on combination of integer and fraction fringe counting, the reference signal with phase shift of 180° is used to obtain integer compensating number to compensate the unstable integer number in unstable phase zone, which guarantees the correct combination of integer and fraction fringe counting. The principle of the proposed signal processing was described in detail. The static and dynamic resolution of the proposed method were discussed. A signal processing board based on FPGA was developed, and three tests were performed to verify the feasibility of the proposed method. A displacement measurement experimental setup was constructed, and two experiments verified the effectiveness of proposed method in application of an interferometer to realize precision displacement and testing of a stage.

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.

Arcuate wrinkling on stiff film/compliant substrate induced by thrust force with a controllable micro-probe.

Wrinkling patterns are widely observed in nature and can be used in many high-tech applications such as microfluidic channel, self-assembly ordered microstructures and improved adhesives. In order to use the wrinkling patterns for these applications, it is necessary to precisely control the formation and geometry of the wrinkles. In this paper, we investigate the localized wrinkling of a stiff film/compliant substrate system subjected to a thrust force with a controllable micro-probe. A thin Au film is deposited onto a thick PDMS substrate attached to a glass to form the stiff film/compliant substrate system. And a micro-probe is controlled by a piezoelectric microrobotic system to exert a point force onto the stiff film/compliant substrate to demonstrate the evolution of the localized wrinkles. The experiments show that the film will wrinkle into orthoradial morphology spontaneously when it is deformed in the vertical direction, and then it will wrinkle into arcuate morphology with deformation in the horizontal direction. Since the compressive stress and tensile stress of the film are generated simultaneously, the evolution of the arcuate wrinkles is always accompanied by some radial cracks. The morphological characteristic, formation mechanism and dynamic evolution of the arcuate wrinkles are demonstrated and discussed in detail.

Evolution of local wrinkles near defects on stiff film/compliant substrate.

Disordered wrinkles are widely observed in stiff film deposited onto a thermally expanded polymer when compressive stress exceeds the critical wrinkling stress of the film. Highly ordered wrinkles can be fabricated by introducing regularly arranged patterns on the polymer before deposition. However, the study on the morphological evolution of localized wrinkling patterns near defects on the stiff film/compliant substrate is neglected. In this paper, we show two morphological transitions of the local wrinkles induced by defects on an Au film/PDMS substrate. The observation shows that the straight wrinkles form perpendicularly to the line defects and the radial wrinkles form near spot-like defects. We observe that the extended radial wrinkles tend to split and evolve into branching patterns, this limits the deviation of the local wrinkle wavelength from the equilibrium wrinkle wavelength and causes the wrinkle wavelength to be always maintained in a narrow interval. Because the herringbone patterns have the minimum energy state, the straight and radial wrinkles evolve into herringbone wrinkles spontaneously. The morphological characteristic and evolution mechanism of the local wrinkles are described in detail. The observation may provide some clues to the formation and evolution of some localized wrinkling patterns in nature and multilayer materials.

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.

Laser heterodyne interferometric system with following interference units for large X-Y-θ planar motion measurement.

A novel laser heterodyne interferometric system with following interference units is proposed for large X-Y-θ planar motion measurement. In this system, two interference units moved by two separate linear stages along x-axis and y-axis are used to follow the large movement of the measured stage so that the simultaneous measurement of three degrees of freedom X-Y-θ parameters of large planar motion is realized. The optical configuration of the proposed system is designed by using the orthogonal linearly polarized beam return method, the measurement principle is described and the mathematic model for simultaneously measuring X-Y-θ planar motion is derived. To verify the feasibility of the proposed system, the experimental setup was constructed and a series of experiments were performed.

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.

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.

Laser straightness interferometer system with rotational error compensation and simultaneous measurement of six degrees of freedom error parameters.

A laser straightness interferometer system with rotational error compensation and simultaneous measurement of six degrees of freedom error parameters is proposed. The optical configuration of the proposed system is designed and the mathematic model for simultaneously measuring six degrees of freedom parameters of the measured object including three rotational parameters of the yaw, pitch and roll errors and three linear parameters of the horizontal straightness error, vertical straightness error and straightness error's position is established. To address the influence of the rotational errors produced by the measuring reflector in laser straightness interferometer, the compensation method of the straightness error and its position is presented. An experimental setup was constructed and a series of experiments including separate comparison measurement of every parameter, compensation of straightness error and its position and simultaneous measurement of six degrees of freedom parameters of a precision linear stage were performed to demonstrate the feasibility of the proposed system. Experimental results show that the measurement data of the multiple degrees of freedom parameters obtained from the proposed system are in accordance with those obtained from the compared instruments and the presented compensation method can achieve good effect in eliminating the influence of rotational errors on the measurement of straightness error and its position.

Laser heterodyne interferometer for simultaneous measuring displacement and angle based on the Faraday effect.

A laser heterodyne interferometer for simultaneous measuring displacement and angle based on the Faraday effect is proposed. The optical configuration of the proposed interferometer is designed and the mathematic model for measuring displacement and angle is established. The influences of the translational, lateral and rotational movements of the measuring reflector on displacement and angle measurement are analyzed in detail. The experimental setup based on the proposed interferometer was constructed and a series of experiments of angle comparison and simultaneous measuring displacement and angle were performed to verify the feasibility of the proposed interferometer for precision displacement and angle measurement.