Field curvature of the lens is a law of physics, which is applicable to all simple lenses. The image focused at a certain distance is perpendicular to the axis of a lens. This perpendicular imaginary line, at which an image is focused, is not straight, but it is in a curved form. So if the focusing surface, on which the image is to be focused is flat, then the image focused in the middle part, is not sharply focused on the corners. When the distance is shifted to focus corners, middle part of the image goes out of focus.
In this case, there is nothing wrong in the lens design or its workmanship and machining. The law of physics is working, and the simple solution to solve this problem is to curve the film plane or the surface of the digital image sensor. However, this is not a practical solution as this curvature is different for other focal lengths and also different, when the focusing distance of a lens is changed.
So the practical solution for field curvature is to change the power of the lens in such a way, that the focusing distance is slightly more at the corners. This is achieved by a compound lens design, having aspherical lens elements.
Stopping down of aperture to smaller opening will reduce this lens aberration and we can get an image, which is perfectly focused in the middle as well as at the corners. However, a good lens must give a corner to corner sharp image at its widest aperture. Now when the widest aperture is f 2.8 or f 4, then it is easier to control this fault, as compared to the lens, which has the widest aperture of f 1.4 or f 1.2. And this is the reason, why these fast lenses are so expensive.
Read about these lens faults in detail:
Blur or defocus of lens: Blurring of an image due to lens fault
Chromatic aberration: How chromatic aberration or distortion affects the image quality
Diffraction: Scattering of light causing diffraction in an image
Lens flare: How to take care of a lens flare
Loss of contrast: How ability of capturing contrast of a lens is lost
Optical distortion: Physics of optical distortion and how to check it
Spherical aberration: Optics of spherical and asherical lens
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