Microlenses, f-numbers and vignetting (ultra techy thread)

Started Aug 12, 2010 | Discussions thread
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Tyrone Wellhung Contributing Member • Posts: 980
Microlenses, f-numbers and vignetting (ultra techy thread)

This thread is in a response to a few discussions on a few forums and also a challenge by the Great B.

The aim is to begin to understand the relationship between f-number and vignetting, and whether the optical theory of sensor microlenses gives us a good prediction of what people actually observe, and maybe lie to rest some preconceptions on things like telecentricity, offset microlenses and so on.
So first, the theory - you can find it in this paper:
the relevant bit being section 3.3, page 9.
The outcome for microlens design is summarised on page 10:

'In summary, the microlens should have an f/# that is smaller than that of the imaging lens by a factor that depends on the desired concentration.'

Here, the 'concentration' desired is the raw fill factor of the silicon - i.e. how much of a pixel is optically active. So, if the sensor silicon has a fill factor of 0.5, and we require to use f/1.4 lenses, we need microlenses of f/0.7 or lower.
So, a few points, speculations, questions, etc

  1. This theory predicts that each sensor is fully usable with lenses of a minimum f-number - if used below that, there will be no brightness advantage (although there will be the usual DOF properties associated with that f-number). Has anyone noticed this effect using very fast lenses?

  2. The microlens image of the exit pupil of a minimum f-number lens just fills the photosensitive part of the pixel. At the edge of the frame part of it will miss the photoreceptor which causes vignetting. Reviewers such as DPR routinely test lenses for vignetting but the above results suggest that the degree of vignetting will depend on the f-number of the microlenses on the camera. Has anyone noticed a difference in falloff of the same lens used on different cameras (comparisons between things like a 5D and 5DII would be interesting).

  3. This theory explains why vignetting becomes less severe as a lens is stopped down (the simple 'angle of incidence' explanation doesn't). Again, has anyone observed a difference in rate of improvement for the same lens used on different cameras?

  4. Some sensors approach the vignetting problem by offsetting the outer microlenses so the project the exit pupil image squarely on the photoreceptor (obviously, assuming some distance of exit pupil) - sensors designed like this would, paradoxically, show vignetting with very fast lenses with the exit pupil a long way from the sensor (typically long focus lenses). Has anyone observed this? Is it not noticeable simply because there are few such lenses?

Any response welcome, particularly with example images.
Any more questions and speculations also welcome.
Really, this is an invitation just to chat around the subject!

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