Diffraction Characteristics of the Connes-Apodized Aperture in the Presence of Tertiary Spherical Aberration

Abstract The diffraction behavior of a Connes-apodized circular aperture in the presence of tertiary spherical aberration (TSA) and defocus is investigated using the Fourier–Bessel diffraction formulation. Normalized and unnormalized amplitude point spread functions (PSFs) were computed for various values of the TSA coefficient and defocus parameter, and the corresponding Strehl ratios were evaluated to quantify image-quality degradation. The results show that increasing TSA and defocus progressively broaden the diffraction profile, reduce the central amplitude, and redistribute optical energy toward the outer diffraction regions. Strehl-ratio analysis reveals a monotonic decrease in optical performance with increasing aberration magnitude, although the degradation remains gradual due to the higher-order nature of TSA. A comparative study involving Connes, Bartlett, Hanning, and Blackman apodization functions demonstrates that the Connes filter provides the narrowest central diffraction peak and superior energy concentration near the optical axis, while the Blackman filter offers the strongest sidelobe suppression. The findings indicate that Connes apodization maintains favorable diffraction characteristics and exhibits good tolerance to tertiary spherical aberration, making it suitable for high-resolution optical imaging applications affected by higher-order wavefront distortions.