The job of the camera lens is to project an image of the outside world on the flat surface of film or digital sensor. What we want is a faithful image. To achieve, the lens projects a minuscule circle of light that corresponds to a tiny point on the subject. Thus the projected image consists of a collection of points of light, each so tiny that they are seen as a dimensionless point. That portion of the image that lies at the center of the projected image has the advantage. In other words, the center of the projected image is called the “circle of good definition”. That portion of the projected image outside the boundaries of the circle of good definition is substandard.
To explain; think about a flashlight aimed straight on. You see a circle of light. If you aim the flashlight at an angle at a wall, you see an oval spot, not a circle. The oval spot of light covers more surface, meaning it is bigger. It is the size of the tiny circles of light projected by the lens that determines the perceived sharpness. It is a fact of physics that the outlying periphery of the projected image is substandard. Additionally image brightness is greatest within the circle of good declination, and it dims as the distance from center increases. This phenomenon is called a vignette.
Again the vignette is due to the light rays arriving at the edges, project an oval and not a circle. This phenomenon is called cosign error. To mitigate, it has been common practice to mount a lens with a focal length about equal to the diagonal measure of the format rectangle. Such a focal length is termed “normal” as it delivers a view that corresponds to the perspective we see with our eyes. For the full frame camera format (24mm by 36mm) this is a lens with a focal length of about 50mm. For the compact digital (16mm by 24mm) the “normal” is a lens with a focal length of 30mm.
As we mount lenses that are shorter in focal length (wide-angle), the vignette becomes more difficult to control. As we mount lenses with super wide apertures, the task of the lens maker is challenged. These difficulties are mitigated by innovative lens design. The bottom line is, when we task lenses to zoom and cover a wide range of focal length and apertures, the complications mount and the costs go up. Somewhere, the camera/lens maker must make compromises or prices go through the roof.
The faithful image has never been achieved!