Efficient Pattern Modeling Method for Parabolic Cylindrical Antennas Incorporating Multi-Source Structural Errors

Parabolic cylindrical antennas are characterized by their structural simplicity, high radiation efficiency, and low manufacturing costs. Consequently, they are widely used in Earth observation and serve as a viable option for spaceborne Synthetic Aperture Radar (SAR) systems. However, structural errors in the phased array feed and the parabolic cylindrical reflector are inevitable during manufacturing, assembly, and operation. These errors significantly degrade the accuracy of antenna pattern models. To address this issue, this paper proposes a comprehensive radiation pattern model that accounts for structural errors in both the linear feed and the reflector. This approach enables precise pattern prediction and efficient in-orbit calibration. Specifically, the reflected far-field pattern is first calculated using the field superposition principle and the Physical Optics (PO) method. Specifically, the combined phase effects resulting from feed and reflector structural errors are superimposed to establish a direct integration pattern model for the parabolic cylindrical antenna. Given the high computational complexity of the direct integration model, a simplified model based on Fresnel approximation is proposed. This approach significantly reduces integration complexity while preserving the quadratic phase characteristics of the main lobe, thereby substantially improving computational efficiency. Simulation results verify that the simplified model maintains high accuracy in both normalized amplitude and phase. Furthermore, a partitioned calibration method is proposed to compensate for the absolute gain deviation inherent in the simplified model. By integrating weighting relationships derived from sensitivity analysis of individual errors, an empirical parameter is defined to quantify the correlation between total structural errors, antenna performance, and the prediction accuracy of the simplified model. The results indicate that reflector structural errors are the dominant factor affecting the overall performance of the antenna. In contrast, the prediction accuracy of the simplified model is found to be more sensitive to feed structural errors. The simplified model exhibits tolerance to structural errors far exceeding the wavelength, enabling it to effectively replace the direct integration model. This work provides new theoretical foundations and technical methods for tolerance design, performance assurance, in-orbit testing, and calibration of parabolic cylindrical antennas.