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 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.
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.
Fringe projection profilometry (FPP) has been widely applied in industrial 3D measurement due to its high precision and non-contact advantages. However, FPP may encounter fringe saturation in high-reflective scenes, consequently impacting phase computation and introducing measurement errors. To address this problem, an efficient exposure fusion method is proposed in this paper. We propose incorporating complementary gray codes into the multi-exposure fusion method to improve measurement efficiency for high-reflective scenes. After obtaining high-quality wrapped phase by the fused phase-shifting patterns, complementary Gray code patterns are used to assist phase unwrapping to achieve 3D measurement. This method takes advantage of the fast projection speed and edge error elimination capability of complementary Gray code patterns, requiring only one set of patterns to complete phase unwrapping. Compared to the common multi-frequency method, our method reduces the number of projected images and exposure time. Experiments are conducted to demonstrate the feasibility and efficiency of the proposed method.
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.
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