Before there were CCD and CMOS-sensors, there were Vidicon tubes.
Why to mention? These light receiving tubes influence till today the names for the sizes of our imaging sensors.
Vidicon tube (C) Wikipedia
The dark grey round area of the tube is the light sensitive part. Obviously the darg gray area can not reach the full diameter of the tube.
Lenses have a so called image circle, the round area on the image side of the lens that receives light. A lens has an image circle thats large enough to expose the dark gray part to light. if the dark area was 6mm in diameter, we talk of a 1/3″ lens, because the outer diameter of the Visicon tube is 1/3″ = 25.4/3mm = 8.467mm.
But has a 1″ lens an image circle which is 3x as large as a 1/3″ lens ?
A third inch lens has 6mm Image circle, so a one inch lens should have 3 times as much, say 18mm. It is 16mm only, A vidicon tube with 16mm diameter dark area had an outer diameter of one inch (25.4mm) however.
That’s why 1/3″ has 6mm and 1″ has 16mm image circle
Kinds of vignetting to distinguish:
A kind of vignetting which occurs exclusively with digital cameras.
In many sensors above the pixels so called microlenses are located, trying to capture and direct the light towards the light-sensitive parts of the sensor surface. This is but only up to certain angles with which the light passes to the sensor (eg 12 degrees off the vertical axis ). This can vary from sensor type to sensor type.
Micro lens vignetting can be avoided by a lens with a small angle of incidence (CRA Chief Ray Angle). Optimal is an image-side telecentric lens.
Some manufacturers try to avoid Micro lens vignetting by micro lenses that are shaped differently on the edge of the sensor than in the center.
To use such sensors with image side telecentric lenses, will result in (maybe unexpected) micro lens vignetting.
Some sensors have built an electronic correction of vignetting! (especially SOC (System on a Chip).
Using the software you can get rid of vignetting by so-called shading correction. However, this correction costs computing time and you may lose image dynamic by this correction.