In optical imaging systems, the convex lens, as a core component, is affected by various aberrations, including spherical aberration, coma, astigmatism, field curvature, and chromatic aberration. These aberrations can cause blurring, distortion, or color distortion of image points, thus requiring systematic design for correction to improve overall image sharpness and fidelity.
Spherical aberration is one of the most common aberrations in convex lenses, stemming from the difference in refraction angles of light rays passing through different positions within the lens. The focal points of edge rays near the optical axis differ from those of the central rays, resulting in halos around the image point. To correct spherical aberration, aspherical lenses can be used instead of traditional spherical lenses. The continuously varying surface curvature of aspherical lenses allows light rays from different incident heights to converge precisely at the same point. Furthermore, combining positive and negative lenses can partially offset spherical aberration; for example, pairing a high-refractive-index convex lens with a low-refractive-index concave lens optimizes the optical path through the synergistic effect of materials and curvature.
Coma manifests as a comet-like tail after imaging from a point light source, especially noticeable in off-axis regions. Coma is caused by the asymmetry in the focusing ability of lenses for light rays of different apertures. Correcting coma requires optimizing the aperture stop position of the lens or using a symmetrical lens group design. For example, a double Gaussian lens structure uses symmetrically arranged convex and concave lenses to cancel out aberrations of off-axis rays. Furthermore, increasing the number of elements in the lens group and using multi-stage correction can further reduce the impact of coma on imaging.
Astigmatism and field curvature are related to the curvature of the imaging plane. Astigmatism causes the image to not be simultaneously sharp in the meridional and sagittal directions, resulting in a cross-shaped blur; field curvature causes the entire imaging plane to be curved, resulting in sharpness at the center and blurry edges. Correcting these two aberrations requires a curved imaging plane design or compensation through lens groups. For example, in microscope objectives, by combining multiple convex and concave lenses, the system's field curvature is matched to the curvature of the imaging plane, thus obtaining a uniformly sharp image on a curved image plane. Modern optical systems tend to use planar imaging designs, in which case complex lens groups are needed to completely eliminate field curvature.
Chromatic aberration is an imaging problem caused by the dispersion of materials in convex lenses. Different wavelengths of light have different refractive indices, causing a shift in the focusing position and creating colored edges. Chromatic aberration correction is divided into two categories: axial chromatic aberration and lateral chromatic aberration. Axial chromatic aberration is corrected through apochromatic design, which combines lenses with two different dispersive materials (such as fluorine crown glass and flint glass) to make the focal points of red and blue light coincide near the focal point of green light. Lateral chromatic aberration requires optimizing the aperture stop position of the lens group or using an asymmetrical structure to balance the aberrations of different wavelengths of light. For example, ultra-low dispersion lenses in photographic lenses can significantly reduce the impact of chromatic aberration on imaging.
Lens surface coating technology is also crucial for improving image quality. Anti-reflective coatings increase light transmittance and reduce ghosting by reducing light reflection loss at the lens surface. Multi-layer coatings can be optimized for different wavelengths of light, further suppressing chromatic aberration and glare. In addition, hard coatings protect the lens surface from scratches, extend its lifespan, and indirectly maintain image stability.
Modern optical design software (such as ZEMAX and Code V) optimizes lens parameters through computer simulation, rapidly iterating to find the best aberration correction scheme. Designers can set imaging quality targets (such as MTF curves and dot plot radii), and the software automatically adjusts lens curvature, thickness, and material combinations to achieve global optimization. This algorithm-based design method significantly improves the imaging performance of convex lens systems, especially in complex systems such as zoom lenses and endoscopes.
From single lenses to multi-lens groups, from spherical to aspherical surfaces, from simple coatings to multilayer optical films, aberration correction technology for convex lenses has continuously evolved. Through the integration of materials science, geometric optics, and computational optics, modern imaging systems can now achieve near-diffraction-limited imaging quality while maintaining a compact structure, meeting diverse needs from consumer electronics to aerospace exploration.
