Heterodyne grating interferometer is widely used in precision positioning due to its high precision and robustness. However, the polarization states of two frequency components in a dual-frequency laser are easy to overlap with each other because of the non-ideality of optical components. It will cause nonlinear error, which limits the measurement precision of the grating interferometer. To improve the frequency aliasing of heterodyne grating interferometer, a polarization adjustment module is proposed to adjust the polarization angle of the dual-frequency laser. The dual frequency system outputs two laser beams with different frequencies separately. The module realizes the polarization adjustment of the two frequency components through two groups of the polarizers and the half-wave plates (HWP). Finally, the polarization directions of two frequency components are orthogonal and combined by the beam splitter (BS). Thus, the nonlinear error caused by frequency aliasing is removed. The polarization adjustment module has the advantages of not changing the direction of the laser propagation and simple structure, which makes it easy to realize integration. It can provide a reference for the solution of frequency aliasing of heterodyne grating interferometer.
For solving the problem of sub-mirror installation and posture monitoring and compensation, an absolute four-degree-of-freedom (DOF) grating encoder that is able to monitor four degrees of freedom's absolute position and pose in the θx, θy, θz, and z-direction is proposed. In this grating encoder, a grating reflector and three quadrant photodetectors (QPD) are employed and an optical path is configured based on the laser autocollimation principle. A model for the solution of the four-DOF motions from outputs of the three QPDs is established. A calibration method for the identification of the relationships between the absolute positions and QPDs outputs is proposed. A prototype four-DOF grating encoder is constructed for verification of this proposal. Test results demonstrated that the method proposed in this research can achieve absolute position distinguishing with a sub-arcsecond and sub-micrometer accuracy in rotation angles and z-direction, respectively.
KEYWORDS: Field programmable gate arrays, Computer programming, Signal processing, Data conversion, Optical filters, Filtering (signal processing), Digital signal processing, Interfaces, Diffraction gratings, Logic
Compared with the four-phase optical structure, the grating encoder based on two-phase optical structure reduces the number of optical devices used in the system and makes the system more compact. Due to the high requirements for realtime and parallel processing of algorithm solution, the powerful parallel computing ability of Field Programmable Gate Array (FPGA) and customized hardware acceleration algorithm are needed to improve the real-time performance. In the previous research, the displacement signal generated by the grating encoder can be input into the FPGA through analog to digital converter (ADC) sampling, and then complete self-designed filter filtering, phase correction and displacement solution. In this paper, further, the ADC sampling rate adjustable interface is added to the FPGA, the global signal and the dc offset remove algorithm is added, and the displacement solution results in the form of fixed-point number are output to the host computer through the MicroBlaze (MB) soft core. MB core can realize process control and interface conversion on FPGA, and use a small amount of logic resources to replace the functions of MCU and DSP of traditional embedded measurement system, so as to further improve the integration of the instrument. A series of experiments are carried out on the two-phase FPGA platform. ADC sampling rate is 200ksps, 8-Channel synchronous parallel sampling, FPGA system clock frequency is 200MHz. The linear displacement table is set to drive the measurement grating at different displacement speeds, and the total stroke is set to 10mm. The FPGA real-time displacement solution platform is tested. The experimental results show that FPGA obtains accurate displacement solution results under different speed tests. In the test of 2 mm/s, the maximum cumulative displacement measurement error is 5um, which shows the real-time performance and accurate displacement solution performance of FPGA platform.
Laser interferometers and grating interferometers are typical optical measurement devices. The measurement resolution and range of the two devices are generally nanometers and meters, so they can meet the needs of high-resolution, largerange measurement. Whether it is a laser interferometer or a grating interferometer, it can be implemented based on a technical route based on the principle of homodyne interference or heterodyne interference. Heterodyne interference is not sensitive to changes in signal amplitude and DC offset, and can effectively avoid measurement errors. To design a highprecision displacement measuring device based on the principle of heterodyne interferometry, the key is whether it can accurately measure the phase change of the measured signal relative to the reference signal. The accuracy of the phase measurement determines the accuracy of the displacement measurement. Phase measurement methods can be divided into two categories: analog method and digital method. In this paper, a high-precision phase measurement system based on FPGA is designed based on the automatic digital phase detection method. The hardware part of the system includes FPGA, high-speed ADC module, signal conditioning circuit, the phase detection algorithm selects the automatic phase detection algorithm, and finally realizes the output display of the phase measurement results. The experimental results show that the deviation between the experimental data of all measurement points and the true value does not exceed 0.1°. Therefore, the accuracy of the phase measurement system designed in this paper is 0.2° and 0.018° resolution.
In this paper, we proposed a new reflection type heterodyne three-degree-of-freedom (three-DOF) grating interferometer for ultra-precision positioning of the worktable of the lithography machine. The grating interferometer is based on a 780 nm wavelength dual-frequency laser that can generate a 40 kHz beat signal through two acoustic-optical modulators (AOM). The reflected lights from the grating and the mirror are used to obtain the heterodyne interference signal in the z-direction, and the four beams of diffracted light from the two-dimensional planar grating are used to obtain the heterodyne interference signal in the x- and y-directions. By comparing the phase of the reference signal, the phase changes in the x-, y-, and z- directions are calculated to derive the three-DOF displacement. Based on optical subdivision and electronic subdivision, the analysis result shows that the resolutions in the x- and y-directions are 0.069 nm, and in the z-direction is 0.108 nm, providing a nanometer resolution for all three axes. In the experiment, the z-direction measurement optical path was constructed to test the static stability of the zero-crossing point of the heterodyne interference signal and the straightness of the z-direction displacement. The preliminary experiment result verified that this interferometer can simultaneously provide the static stability of the zero-crossing point of ±0.1 nm and high straightness. Due to the common optical path design of x-, y- and z-directions, the heterodyne three-DOF grating interferometer structure can be compact and allow a high-performance uniformity of the three axes.
KEYWORDS: Field programmable gate arrays, Signal processing, Computer programming, Digital signal processing, Optical filters, Data processing, Filtering (signal processing), Sensors, Phase measurement, Optical design
Six-degree-of-freedom (6-DOF) grating encoders have a wide prospect of application. Aiming at the requirement of real-time detection of 6-DOF grating encoders, this study designs and builds a real-time calculation system platform based on field-programmable gate array (FPGA). We realized a real-time parallel calculation of 16-path displacement signal and 24-path angular displacement signal, respectively. Specifically, the optical interference signals, generated by the translation and rotation of the motion stages, are firstly shaped by the front-end analog circuit. We further sampled the front-end analog circuit into an FPGA through a analog-to-digital convertor (ADC) for the realization of the digital filtering, amplitude normalization, phase correction, and phase-information calculation. Thus, the calculated signals on the 6-DOF motions can be displayed in real time. The established system was evaluated with the experimental parameters in terms of the translation with a 50 μm/s moving speed and an 18 mm stroke and the rotation with a frequency of 0.5 Hz, a step length of 100 micro-rad, and within a reciprocating rotation of 24 s. Finally, a linear-displacement error of <1 nm and an angle displacement error of <0.9 micro-rad were achieved, respectively. Furthermore, the system delay of <15 ms is obtained, exhibiting a high performance for the real-time measurement and high integration in the practical application.
The signal processing of the grating encoder has a great impact on its accuracy and resolution. We proposed a new type of signal processing method for a grating encoder using a two-phase differential algorithm based on the two-phase physical structure. The interference signal could be divided into two phases with 90 degrees phase delay, capable of effectively reducing the number of optical devices and the space occupied by the reading head. Owing to the rapid elimination of the DC component in the measurement signal, the measurement displacement was solved swiftly by the two-phase signal using the algorithm. In the experiment, a 660 nm laser and a 1 µm-period grating were used, and the scale grating was actuated at a speed of 1 µm/s by a linear stage. With a sampling rate of 20 kHz, the system resolution of the grating encoder was enabled to reach 50 pm. Simultaneously, there was a measurement error of ±1 µm at a stroke of 4 mm, and the error within a single cycle was 2 nm. Compared with the four-phase algorithm, our proposed two-phase differential algorithm exhibits a compact physical structure and fast solution without reducing the accuracy and resolution, which will be of great significance to the real-time measurement and miniaturization of grating encoders.
The signal filtering of the grating encoder is of great significance to the measurement accuracy, aiming at eliminating the background noise potentially from the temperature changes, airflow fluctuations, and mechanical vibrations. Compared with the traditional time-frequency analysis methods, including wavelet transform, fast Fourier transform (FFT), and time Fourier transforms (TFT), the empirical mode decomposition (EMD) algorithm owing to no basis functions and high adaptability, is widely applied for signal decomposition. Here, we extended the EMD algorithm for the background-noise-based signal filtering in a grating encoder, with the experimental parameters of 5 µm/s moving speed and ~19 mm stroke. Simultaneously, a laser interferometer, as a reference, was additionally assembled to calibrate the measurement results of the grating encoder. The measurement signal was collected by NI acquisition card with a 1000 Hz sample rate and processed by EMD algorithm. Here, EMD decomposed the signal into multiple intrinsic mode functions (IMFs), which were reconstructed by removing the noise and DC components according to the correlation coefficients. Compared with the measurement results of the laser interferometer, the measurement displacement with a 6.2 µm error was solved by the phase correction and arctangent calculation from the reconstructed signals. Finally, our proposed signal-filtering approach based on the EMD algorithm exhibits a stable, accurate, and real-time calculation performance applicable for the grating encoder with ultra-high precision positioning.
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