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Spherical aberration is a type of aberration (distortion) in the image of an optical instrument (such as a telescope) due to the shape of a mirror or lens. The image made by a parabolic mirror (i.e., paraboloid shaped) is truer than one with a spherical curvature, and the additional distortion of the latter is termed spherical aberration. Lenses of various shapes show the same issues.
A paraboloid mirror focuses light that's arriving perfectly parallel to its optical axis to a point (ignoring diffraction, i.e., the Airy disk), and has a characteristic aberration for point sources off the line of the axis. Near its vertex, the curvature of a paraboloid is quite close to that of a sphere, and a spherical mirror approximates what a paraboloid mirror accomplishes, but the further from the optical axis, the more the sphere-shape diverges from a paraboloid and focuses light to the point in space further from the mirror, which on the focal plane, turns a point source in the image into a finite-sized spot. This distortion is spherical aberration. The larger the percentage of a sphere that the mirror represents, the more it diverges from a paraboloid and the greater this aberration, and one way to limit it is to shape the mirror as only a small percentage of a large sphere, which is another way of saying "use a longer focal length". Spherical mirrors are easier to construct, so there is a quality trade-off regarding the resources you put into a telescope's construction. Schmidt cameras use a spherical mirror, compensating for it somewhat with a purpose-built lens (Schmidt corrector plate) but it creates its own problem: a non-flat focal "plane".
Though paraboloid mirrors do avoid some of the aberrations inherent to spherical mirrors, they still do produce some aberrations, the further from the optical axis, the more pronounced the aberration.