I recently noticed that the software used in modern microscopes using CCD sensors apparently uses "deconvolution" processing to partially "undo" the blurring and resolution loss caused by diffraction. Olympus talks about it at the website Olympus on deconvolution

I want to read more on the mathematics, but at first glance, it makes sense: diffraction causes a spreading and "mixing" of light that does not necessarily totally lose information, but only rearranges it, so maybe sufficient post-processing can unravel this mixing and thus increase the resolution of a small aperture camera beyond the classical limits. For example, high end confocal microscopes apparently use "pinhole" apertures plus deconvolution to achieve high resolution.


P. S. I predict that Ray will be the first person to respond to this post.

The answer to your question is yes and maybe - yes in theory, maybe in practice.

A signal can only be deconvolved totally if there is no noise mixed in the signal - this noise could arise from imperfections in the sensor, photon noise, or variances between the actual and measured point spread function. Also, you would need to factor in a high enough sampling rate to ensure that you had sufficient sample points to recreate the original signal. In addition, I would assume (though this would need to be proven) that the point spread function would vary across the plane of the sensor as well as with zoom length (focal length) and aperture.

Given that there is a variability in the point spread function (the model would need several parameters to make it sufficiently accurate to show a difference), a noisy signal (relatively) and a low sampling rate (relative to the size of the point spread function/airy disk) the cost benefit ratio would be low. Though I am guessing that this is what DxO attempt to do with their algorithms for improving image quality.

I would suggest that deconvolution works in a system which is geared up to utilise such processes to improve image quality and where a stable predictable point spread function is designed in. However, your average camera has too many variables to realistically show a benefit across the limited number of situations that diffraction limitation is an issue. Though, obviously if you do shoot f/22 - f/64 frequently and want to make the best of the situation then this might be one way to eek out more performance - perhaps someone with DxO (or the trial) could demonstrate whether there is an improvment before and after their filters on a diffraction limited image (and whether it is better than any other method - USM for instance - for improving sharpness).

You can give it a try for free - there are a couple companies which make software for photography using deconvolution algorithms. One I find very useful is Focus Magic. This program lets you not only ameliorate up to a 15 pixel OOF condition, but also lets you correct for slight motion blur. As with any post process to "correct" deficiencies in image acquisition, it has its limits, but can definitely make some difference beyond what can be accomplished by edge contrast enhancement. Here's a link if you're interested in trying it:

http://www.focusmagic.com/

Lin

OK, I was wrong about Ray responding first! But thanks for the responses anyway!

About point spread functions, Olympus mentions the need for or advantage of working with three dimension point spread functions, and possibly this process only works with a sequence of images taken at a range of different focal distances (like with Focus magic?)

About software needing to know lens details, this could require either DxO type calibration data, or information like that which the Olympus E system lenses provide for each photo, stored in the EXIF data.

Focus Magic seems to apply deconvolution to another similar issue, OOF effects, but I can see similar software handling diffraction blurring due to the use of small apertures.

Indeed, deconvolution requires adequate sensor resolution: I was thinking primarily of the case where for the sake of high DOF and/or good control of lens aberrations, one ends up with an aperture so small (f-stop so high) that the diffraction spot size is significantly bigger than the photosites. You might then wish to recover the extra resolution potential of those smaller photosites, and deconvolution is one hope. It does seem likely to be useful only in slow work with a camera fixed in place (atop a tripod or microscope) and a stationary subject.

BJL,
Sorry to cause your predictions to be out , but the fact is I really don't know much at all about deconvolution and as you've probably realised by now, it would be totally out of character for me to waffle on about something I knew nothing about .

However, I would like to make some general points which passed through my mind when doing a web search on deconvolution, but I see that DiaAzul has pretty much covered this.

Anyway, at the risk of repeating what has already been covered, it does seem that deconvolution techniques work best in controlled, laboratory-like conditions, hence their application in microscopy. The variables in general photography would seem to be perhaps insurmountable, or at best allow an incremental improvement in some circumstances but not others.

This real world variability and unpredictability, which makes the design of general purpose robots so difficult, is I think the Achilles' Heel of the DXO system; variability amongst lenses of the same model.

I'd be happy if lens manufacturers were to thoroughly test all their lenses before shipping them and grade them and price them accordingly. Each lens needs to be accompanied by a set of MTF charts. Of course, that would increase the cost, but that increase in cost would at least partially be met by the higher price that keen photographers would pay for a premium grade lens.

Take the Sigma 12-24mm for example. This is a lens I would like to have for my next trip to Angkor Wat, but I know I'm not going to just take pot luck without testing the lens before buying. I'd even be prepared to find a retailer in Kuala Lumpur or Bangkok who might let me test 6 or 10 lenses during the course of an afternoon in the shop, on the condition of course that I paid a premium for the lens that I eventually selected.

But why should I have to go to that trouble? I'm willing to pay someone else to grade the lens for me, but no-one's offering the service.

I generally agree, and certainly if one aims to use deconvolution to deal with a wide array of optical problems from aberrations to OOF effects to diffraction. For example, OOF effects vary at different parts of an image according to subject distance, so correcting for that requires what Olympus calls "three dimensional image stacks": multiple images at multiple focal distances.

But correcting for just diffraction might be far simpler: diffraction effects are mostly controlled by a few optical parameters: effective aperture diameter and maybe focal length and the position of the diaphragm within the lens. So mitigating just diffraction effects by deconvolution might be possible from a single image and information about a few lens parameters.