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 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.

Note: Comparison experimental results of the laser heterodyne interferometer for angle measurement based on the Faraday effect.

A laser heterodyne interferometer for angle measurement based on the Faraday effect is proposed. A novel optical configuration, designed by using the orthogonal return method for a linearly polarized beam based on the Faraday effect, guarantees that the measurement beam can return effectively even though an angular reflector has a large lateral displacement movement. The optical configuration and measurement principle are presented in detail. Two verification experiments were performed; the experimental results show that the proposed interferometer can achieve a large lateral displacement tolerance of 7.4 mm and also can realize high precision angle measurement with a large measurement range.

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.

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.

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.

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.

Note: Laser wavelength precision measurement based on a laser synthetic wavelength interferometer.

A laser wavelength precision measurement method is presented based on the laser synthetic wavelength interferometer (LSWI). According to the linear relation between the displacements of measurement and reference arms in the interferometer, the synthetic wavelength produced by an unknown wavelength and a reference wavelength can be measured by detecting the phase coincidences of two interference signals. The advantage of the method is that a larger synthetic wavelength resulting from an unknown wavelength very close to the reference wavelength can be easily determined according to the linear relation in the interferometer. Then the unknown wavelength is derived according to the one-to-one corresponding relationship between single wavelength and synthetic wavelength. Wavelengths of an external cavity diode laser and two He-Ne lasers were determined experimentally. The experimental results show that the proposed method is able to realize a relative uncertainty on the order of 10(-8).

Precision measurement of refractive index of air based on laser synthetic wavelength interferometry with Edlén equation estimation.

A novel method for the precision measurement of refractive index of air (n(air)) based on the combining of the laser synthetic wavelength interferometry with the Edlén equation estimation is proposed. First, a n(air_e) is calculated from the modified Edlén equation according to environmental parameters measured by low precision sensors with an uncertainty of 10(-6). Second, a unique integral fringe number N corresponding to n(air) is determined based on the calculated n(air_e). Then, a fractional fringe ε corresponding to n(air) with high accuracy can be obtained according to the principle of fringe subdivision of laser synthetic wavelength interferometry. Finally, high accurate measurement of n(air) is achieved according to the determined fringes N and ε. The merit of the proposed method is that it not only solves the problem of the measurement accuracy of n(air) being limited by the accuracies of environmental sensors, but also avoids adopting complicated vacuum pumping to measure the integral fringe N in the method of conventional laser interferometry. To verify the feasibility of the proposed method, comparison experiments with Edlén equations in short time and in long time were performed. Experimental results show that the measurement accuracy of n(air) is better than 2.5 × 10(-8) in short time tests and 6.2 × 10(-8) in long time tests.

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.

An orthogonal return method for linearly polarized beam based on the Faraday effect and its application in interferometer.

Correct return of the measuring beam is essential for laser interferometers to carry out measurement. In the actual situation, because the measured object inevitably rotates or laterally moves, not only the measurement accuracy will decrease, or even the measurement will be impossibly performed. To solve this problem, a novel orthogonal return method for linearly polarized beam based on the Faraday effect is presented. The orthogonal return of incident linearly polarized beam is realized by using a Faraday rotator with the rotational angle of 45°. The optical configuration of the method is designed and analyzed in detail. To verify its practicability in polarization interferometry, a laser heterodyne interferometer based on this method was constructed and precision displacement measurement experiments were performed. These results show that the advantage of the method is that the correct return of the incident measuring beam is ensured when large lateral displacement or angular rotation of the measured object occurs and then the implementation of interferometric measurement can be ensured.

Laser heterodyne interferometric signal processing method based on rising edge locking with high frequency clock signal.

A novel phase measurement method composed of the rising-edge locked signal processing and the digital frequency mixing is proposed for laser heterodyne interferometer. The rising-edge locked signal processing, which employs a high frequency clock signal to lock the rising-edges of the reference and measurement signals, not only can improve the steepness of the rising-edge, but also can eliminate the error counting caused by multi-rising-edge phenomenon in fringe counting. The digital frequency mixing is realized by mixing the digital interference signal with a digital base signal that is different from conventional frequency mixing with analogue signals. These signal processing can improve the measurement accuracy and enhance anti-interference and measurement stability. The principle and implementation of the method are described in detail. An experimental setup was constructed and a series of experiments verified the feasibility of the method in large displacement measurement with high speed and nanometer resolution.

A laser interferometer for measuring straightness and its position based on heterodyne interferometry.

Not only the magnitude but also the position of straightness errors are of concern to users. However, current laser interferometers used for measuring straightness seldom give the relative position of the straightness error. To solve this problem, a laser interferometer for measuring straightness and its position based on heterodyne interferometry is proposed. The optical configuration of the interferometer is designed and the measurement principle is analyzed theoretically. Two experiments were carried out. The first experiment verifies the validity and repeatability of the interferometer by measuring a linear stage. Also, the second one for measuring a flexure-hinge stage demonstrates that the interferometer is capable of nanometer measurement accuracy. These results show that this interferometer has advantages of simultaneously measuring straightness error and the relative position with high precision, and a compact structure.