An FPGA-based Real-time Laser Interferometric Length Measurement System with Point-by-point Phase Computation

With the rapid development of precision manufacturing， semiconductor lithography， and aerospace engineering， ultra-precision machining and metrology have placed higher demands on micro-displacement measurement systems that combine nanometer-level precision with high-bandwidth real-time performance. In dynamic， high-speed motion scenarios， such systems not only need to achieve extremely high resolution but also provide low-latency data processing at high sampling rates. As a fundamental technology in modern length metrology， laser interferometry has inherent advantages in terms of accuracy and stability. However， traditional software-based processing architectures rely on CPUs and sequential execution models， often encountering severe computational bottlenecks when processing high-speed interferometric signals. These limitations make it difficult to simultaneously meet the conflicting demands of large measurement range， high resolution， and real-time detection. To overcome these challenges， this paper proposes a single-frequency laser displacement measurement system based on FPGA， which integrates an FPGA platform and a high-performance point-by-point phase calculation algorithm. By transferring the signal processing algorithm from software to a dedicated hardware logic platform and employing parallel computing and a pipelined approach， the system significantly improves real-time performance while maintaining nanometer-level measurement accuracy.First， this paper establishes a four-channel orthogonal laser interferometry structure and develops a real-time phase demodulation method based on the phase difference between adjacent sampling points. By introducing phase jump correction and cumulative phase compensation mechanisms， the algorithm effectively solves the problems of phase unwrapping ambiguity and displacement direction discrimination under high-speed motion conditions， thereby ensuring the continuity and robustness of displacement measurement. Meanwhile， to analyze the impact of non-ideal optical elements on nonlinear errors， this paper constructs a systematic error model using Jones matrix theory. This model quantitatively analyzes the effects of waveplate angle misalignment and Polarization Beam Splitter （PBS） splitting ratio imbalance on the interference signal， revealing their roles in introducing DC offset， amplitude mismatch， and non-orthogonality between orthogonal channels. Based on this analysis， this paper designs a vector-based error compensation algorithm to correct these defects， thereby significantly improving phase linearity and overall measurement accuracy. Based on the proposed algorithm， a complete experimental test platform was established， and a host-computer-based multi-threaded displacement measurement software was developed to evaluate the system performance. Experimental results demonstrate that， within a measurement range of 200 μm， the system achieves a statistical measurement accuracy better than 10 nm while supporting millisecond-level data update rates， thereby validating the effectiveness and practicality of the proposed method.Based on the validated theoretical and software framework， this paper further develops an FPGA hardware system integrating a high-speed multi-channel ADC to comprehensively enhance real-time processing capabilities. By employing a fully pipelined architecture and dedicated parallel processing units， key algorithms such as error compensation and phase demodulation are transformed into hardware logic. This hardware-oriented design ensures stable and predictable computational latency， which is crucial for real-time measurement. Experimental comparisons show that the results of the FPGA-based hardware processing are in high agreement with the results of the host multi-threaded software algorithm， with a Root Mean Square Error （RMSE） of only 9.16 nm and statistical accuracy consistently maintained within 10 nm. Real-time performance evaluation further validates the advantages of the proposed system. The initial processing latency is reduced to 10.4 μs， and the displacement data update cycle reaches 100 ns. Therefore， the system can reconstruct complete micrometer-level motion trajectories in real time within 1 millisecond， representing a significant performance improvement compared to traditional CPU-based processing architectures. These performance characteristics make the system particularly suitable for applications such as high-speed motion， dynamic vibration monitoring， and real-time feedback control.In summary， this paper proposes a laser interferometric real-time displacement measurement system by deeply integrating a point-by-point phase demodulation algorithm and FPGA-based hardware acceleration technology. This system simultaneously achieves high precision， high stability， and ultra-fast real-time performance. It provides a reliable and high-performance metrology solution for closed-loop motion control， dynamic vibration analysis， and nanometer-level precision positioning in ultra-precision engineering applications， demonstrating significant practical value and broad application prospects.