The heterodyne signal of a grating interferometer is formed by the interference of two coherent light beams with a frequency difference. The frequency of the heterodyne signal is equal to the frequency difference of the two light beams. When one beam undergoes Doppler frequency shift, the heterodyne signal experiences a corresponding frequency change. By calculating the phase difference between the reference and measurement heterodyne signals of the grating interferometer, the displacement of an object can be determined. The accuracy and real-time performance of solving this phase difference affect the overall performance of the grating interferometer. Multi-degree-of-freedom grating interferometers play a crucial role in high-precision fields such as lithography machines and astronomical telescope mirror alignment. The phase calculation of interference signals is an important component. Current algorithms hard to balance real-time performance and accuracy effectively. Therefore, to enhance both the precision and real-time performance of grating interferometers, this paper proposes using an extended Kalman filter (EKF) method to solve the phase difference. In the EKF model, the state variables are set as the phase, frequency, and amplitude of the sinusoidal signal, and the calculation is performed through prediction and correction steps. Since the Kalman filter algorithm only uses the current sampling point data for model calculation, it has lower latency. The algorithm was deployed on an FPGA to test the signals generated by a signal generator, achieving a measurement accuracy of 0.03° and a resolution of 0.01°. This research contributes to improving the real-time performance and accuracy of grating interferometers.
In order to solve a series of application problems caused by the difficulty of adjusting prism collimation and the short working distance of small period gratings in current collimation solutions, this paper proposes a six-degree-of-freedom measurement scheme that uses a combination of large period gratings and long focus plano-convex lenses. This solution can achieve six degrees of freedom measurement at a working distance of more than 80mm. The main principle is that the displacement is calculated using the phase information formed by the interference of the four diffracted lights of the two-dimensional grating. The angle is based on the principle of autocollimation. According to the propagation direction of the diffracted light caused by the change of the grating diffracted light with the grating angle changes, thereby changing the angle obtained based on the location changes in the detected diffraction spot, ultimately forming a measurement of six degrees of freedom.
The heterodyne grating interferometer, based on the interference effect of gratings, has achieved widespread applications in the field of high-precision measurements. Its output optical signal, after phase measurement processing, allows for the acquisition of displacement data of the measured object. Among the phase measurement methods, the orthogonal lock-in method obtains two signals containing phase difference information through mixing and filtering. However, the orthogonal lock-in method faces various challenges in practical applications, such as significant sensitivity to filter performance and poor generalization capability. In particular, the need to adjust filter parameters according to changes in the measurement signal frequency limits its practicality and flexibility.
To address these challenges, this study proposes an enhanced lock-in method that utilizes pulse counting techniques to roughly estimate the frequency of the measurement signal and generates orthogonal signals for mixing with the measurement signal. Implementation and experiments on the FPGA platform demonstrate that the improved orthogonal lock-in method can achieve a resolution error of tens of picometers, with a maximum measurement speed exceeding 1 m/s. This research outcome effectively enhances the robustness of the lock-in method, aligning more closely with engineering requirements for high-precision phase measurement.
In order to solve the problem of the mutual limitations of large measurement range and high precision of absolute grating encoders, this paper employs absolute codes to individually number each spliced grating section on the substrate, leveraging the asymmetric code arrangement. With the light splitting ability of beam splitter, the light source is divided into dual beams and inputted into the encoder to form a dual beam reading head. At least one beam of light can always generate a stable signal within the travel range, and then the serial number of this grating area is determined through absolute codes. The signals generated by gratings with different numbers can be calibrated using calibration parameters. With the help of the data splicing principle and the structure of dual-beam, a nanoscale positioning accuracy scheme with a meter-level measurement range is proposed.
In this work, a solution based on sub-sampling technology for heterodyne signals is proposed. While achieving higher measurement resolution and measurement speed, the performance requirements for the analog-to-digital converter and microprocessor are greatly reduced. The heterodyne signal is a sparse signal with a single frequency at each moment, only its phase offset contains displacement information. We use the pulse counting method to obtain the periods of the signal, and a sampler with a sampling rate well below the frequency of the heterodyne signal. The phase of the sampling point can be restored through sub-sampling technology and extended Kalman filtering. In the experiment, we used 16-bit ADCs with a 600 Ksas sampling rate to sample the heterodyne signals with a center frequency of 10 MHz and the dynamic range from 1 MHz to 19 MHz. The simulation results indicate that our method can effectively calculate the phase information of the interference signal.
This paper presents a study on the spot location method and system based on QPDs. We construct a mathematical model of the relationship between spot position variations and detector responses, systematically analyzing the impact of the spot size and detector parameters on spot location accuracy. We propose an ultra-precision Gaussian spot location algorithm based on QPDs, along with a common-path laser light source fluctuation error compensation structure and method, and validated the method through simulation experiments. The experimental results show that this scheme can achieve submicron level spot positioning accuracy. In the measurement range of 1 mm, the measurement error after compensation is reduced by 97% compared to before compensation. Additionally, the repeatability and stability demonstrate excellent performance. This study provides a laser light source fluctuation error compensation method and an ultra-precision Gaussian spot location algorithm based on QPDs for laser measurement technology, significantly improving measurement accuracy and environmental interference resistance.
Grating encoder is a sinusoidal encoder based on grating diffraction principle, which is currently utilized in many high-precision displacement systems because of its advantageous characteristics: low cost, simple structure, works in harsh environments, high reliability, and so on. The output signal of grating encoder usually contains noise interference error, amplitude inconsistency error, DC bias error, harmonic error and quadrature phase error. These non-ideal factors are the main reasons for affecting the precision of subdivision.
In the traditional signal subdivision system, it is usually necessary to compensate each kind of error separately, which will consume many hardware and computing resources and cause a significant output latency, especially in the filtering section and normalization section. In this paper, a non-linear Kalman filter-based sin-cos wave subdivision method is proposed. Compared with the traditional filtering methods, non-linear Kalman filter has higher dynamic response and can provide instantaneous phasor estimation. In addition, it can simultaneously achieve filtering, amplitude normalization, decoupling DC bias, harmonic suppression, and phase compensation functions, which significantly reduces the computational burden and facilitates the implementation on low-cost processors.
In this study, a non-linear Kalman filter-based signal segmentation system is implemented on an FPGA platform and verified on a six-degree-of-freedom grating ruler platform. The results show that the single-channel output delay is only 1.8us at a 50MHz clock, which has a very high real-time ability. When the frequency and amplitude of the input signal varies, the non-linear Kalman filter can track instantaneously and has high dynamic characteristics. Experimental results show the effectiveness of this method.
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