The large-scale equipment manufacturing represented by aircraft and ships continues to promote digitalization and gradually develops toward intelligence, which leads to a sharp increase in the geometric measurement missions on the manufacturing site and a more complex and changeable on-site environment. Therefore, measurement must take into account adaptability, efficiency, and accuracy. Frequency scanning interferometry (FSI) ranging technology can be applied to non-cooperative targets to tackle the low measurement efficiency problem in the manufacturing field. However, it also confronts some problems, such as weak interference signal strength, low signal-to-noise ratio (SNR), and a large amount of data. According to the characteristics of FSI signals of non-cooperative targets, the distance to be measured is usually calculated with the interference beat frequency resolved through the spectrum. However, the discrete spectrum is affected by signal truncation in the time domain, and its amplitude, phase, and frequency are subject to large errors. Hence, spectrum correction is required for higher accuracy. The existing signal processing methods are based on the fast Fourier transform (FFT)+spectrum thinning algorithm, which are inefficient and difficult to meet the requirements of manufacturing sites. Therefore, according to the characteristics of FSI signals of non-cooperative targets, this paper uses the sparse Fourier transform (SFT) algorithm to quickly solve the range spectrum and introduces the synthesized Rife (s-Rife) algorithm to precisely correct the range spectrum, which greatly improves the understanding efficiency while considering the accuracy of range calculation.

In this paper, a mathematical model is built to study the basic principle of FSI and the influence of the surface roughness, spatial distance, and incident angle of non-cooperative targets on FSI signal strength and SNR. A fast detection method for FSI signals of non-cooperative targets is proposed to overcome the shortcomings of existing processing methods in accuracy, efficiency, and adaptability. This method includes two processes: spectrum estimation and spectrum correction. For massive signal data (2×10⁶ points) after the correction of the nonlinearity of optical frequency scanning by resampling, the SFT algorithm is used instead of the fast Fourier transform (FFT) algorithm to ensure the effectiveness of the spectrum solution at the target position and shorten the running time. To correct the discrete spectrum affected by time-domain truncation, this paper selects the s-Rife algorithm to obtain the best estimation of the beat frequency. This algorithm has fast calculation speed, high correction accuracy, and strong anti-noise ability, and can adapt well to various measurement targets and measurement conditions. Finally, the whole algorithm is deployed on the field-programmable gate array-digital signal processor platform to achieve high-precision real-time calculation of the distance to be measured.

To verify the adaptability, timeliness, and accuracy of the fast detection method for FSI signals of non-cooperative targets proposed in this paper, an experimental device to measure the FSI signals of non-cooperative targets is built (Fig. 5). Different algorithms are used for spectrum estimation and correction of the collected interference signals. The feasibility of the SFT algorithm and s-Rife algorithm is verified by comparison (Figs. 6 and 7). For adaptability, the solution results can be obtained when non-cooperative targets with different roughness are measured at different spatial distances and incident angles, and the standard deviation of measurement results is less than 10 μm (Fig. 8). For timeliness, the distance calculation time is shortened from 2.8543 s to 0.1224 s compared with the case of the classical FFT+CZT method (Table 1). For accuracy, the comparison error with the measurement results by the commercial interferometer within the range of 12 m is less than 13 μm, and the standard deviation of measurement results is less than 10 μm (Fig. 9). The experimental results show that the design in this paper has good adaptability, timeliness, and accuracy and can meet the actual measurement needs.

This paper studies the method to rapidly acquire and calculate the range of FSI signals of non-cooperative targets, analyzes the time-frequency characteristics of FSI signals of non-cooperative targets, estimates the frequency spectrum of the resampled interference signals using the SFT algorithm, and interpolates the frequency spectrum using the s-Rife algorithm. The above methods are implemented and verified on the FPGA-DSP platform, and it is proven that they can realize high-precision and fast calculation of the distance to be measured. The experimental results show the fast detection method designed in this paper can effectively collect and process the FSI signals of non-cooperative targets with various roughness. Compared with the results of the classical FFT+CZT method, the distance calculation time is optimized from 2.8543 s to 0.1224 s. The comparison error with the measurement results by the commercial interferometer is less than 13 μm within the range of 12 m, and the standard deviation of the measurement results is less than 10 μm. This method has good adaptability, timeliness, and accuracy and can meet the needs of large absolute distance measurements in the industrial field.