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Vignetting: A Quick Overview
It's important to understand how pixel vignetting operates in the broader context of vignetting, first. There are many causes of vignetting, from those inherent in the design of cameras to those intentionally manipulated by photographers.
One type, optical vignetting, is caused by the design of the lenses as the light tends to refract more towards the center than towards the edges, and is exacerbated by the use of multiple lens elements. A related type, natural vignetting, is triggered by the slightly different angle at which light hits the image. Another type, mechanical vignetting, is triggered by a physical impediment to the light entering the lens barrel, such as a poorly fitted lens hood, or a filter that intentionally adds a vignette.
Also, photographers may choose to add a vignetting effect in post-processing work in digital image editing software. After all, even if vignetting can be an unwanted addition to your photograph, it can also be used to exquisite artistic effect by centering attention in the image on the subject. This is a matter of personal taste, as some photographers love it, while for others it's a pet peeve.
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Angle Dependence & Image Sensors
Consider the lens barrel. When you compose your image, the light at the center of the scene enters the lens barrel from directly ahead, and strikes the image sensor at a right angle. However, around the periphery of the image sensor, the light will be hitting ever-so-slightly off from 90 degrees. With the design of current image sensors, any light that hits at an angle will register as being less bright than that which strikes it head on. Thus, the edges will appear ever-so-slightly darker and desaturated as compared to the center, creating a subtle vignetting effect.
This differs subtly from another type of vignetting, natural vignetting, which is also a function of the oblique angle at which light hits the edge of the image sensor. However, the mechanism of natural vignetting also may occur with film cameras, whereas pixel vignetting specifically refers to the vignetting effect that only occurs due to the angle dependence of the image sensors. Think of it as an extension of natural vignetting, as opposed to something completely different.
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What You (Can't) Do About It
Really... there's not a whole lot that can be done, on your part. Pixel vignetting is something that is, for the moment, more-or-less inherent in digital cameras.
Because the amount of pixel vignetting that occurs is constant given a certain camera design, there has been some effort to create automatic processing techniques to remove the pixel vignetting effect when the image is being converted from a RAW to a JPEG or other file format.
There has also been an effort by camera companies to design microlenses that fit over the image sensor that will refract light so that it strikes head on across the entire image sensor. This could, in theory, alleviate all angle-dependent types of vignetting, including not only pixel vignetting but also natural and optical vignetting. However, as of the writing of this article, this is neither commonplace, nor entirely perfected. Stay tuned!
While pixel vignetting tends to be subtle, and often only detectable when compounded by other types of vignetting such as optical and natural vignetting, you can still try to amend it. Careful use of digital editing software can help alleviate the effects of pixel vignetting, either by darkening the center of the image to match the edges, or the opposite, by lightening the edges to match the center.
Check out Types of Vignetting: What are The Different Causes of Vignetting? to learn more about vignetting as it relates to photography.