alundeb wrote:
I appreciate your demonstration of gaussian deconvolution, but I question the assertion that the airy disc has a hard frequency limit in theory. The point spread function does not have a flat top. In practice though, the difficulteis with diffraction deconvolution may arise from a non-perfect aperture and a non-perfect airy disc.
For the slightly more technical explanation of why this is true: the Fourier transform (think frequency spectrum) of an Airy disc is a circle (as per your Wikipedia citation, noting that this is equivalent to the statement that the Airy disc is the Fourier transform of a circle). Convoluting an image with a point-spread function is the same as multiplying an image's frequency spectrum by that of the point-spread (Convolution theorem, which I personally think is one of the coolest results in all of mathematics). This means convolution with an Airy disc is the same as putting a "circular window" on the frequency spectrum, keeping all frequencies inside and chopping off everything outside (note that the same logic applies not just to circular apertures, but any diffracting aperture blade shape).
A flat-topped point spread function might actually let some higher frequencies leak through that an Airy disc cuts off. In fact, convolving with a circular point-spread means the Fourier spectrum is an Airy disc, which has fringes and zeros going out forever. That means some particular frequency components will be completely zeroed out, while those between will still be there (but greatly diminished) for possible recovery.
Thanks, mpmendenhall !
I should have seen that at once. The sin x / x shape of the airy disc is of course the spatial function of a frequency spectrum step function. What was I thinking.
maxxevv wrote:
For best comparisons, copy and past a RAW file in the same directory. Process with DLO on one of them. I find the DLO slider at 50% and 75% is the best as there are some artifacts with 100%.
Then open up both files in DPP and view 100% side by side. The differences are more evident when you do that versus the preview window.
the difference seems to largely go away, and even seemed on the worse end of things, comparing it to ACR's best efforts though anywhere near the center of the frame (although I've only compared two images so far) but it was better at far edges on both
Joseph C J wrote:
Can someone please provide the version number of DPP that has DLO?
Thanks
Joe
It is version 3.11.10 and at this time is only available on the CDs that come with the 5DIII. It is not yet on the CanonUSA site even though the instruction manual for it is there.
This has been a fascinating discussion and I look forward to seeing the software (1) post beta, (2) available for the Mac, and (3) covering more lenses.
I commend Monito, Mendenhall, Pixel Perfect, and Wickerprints for their cogent and well written descriptions of what are truly topics of higher order mathematics. My own university math ended with the calculus sequence, but I was able to follow the discussion conceptually (wouldn't have a clue how to demonstrate any proofs) and have a clear grasp of what Canon is attempting. Given that their engineering has the data on mathematical compromises made in the design of a lens, I can see how Canon could "recreate" it to "correct" for the limitations of glass bending light to force a multi-dimensional world into 2-D.
I read periodically that FM is no better than the rants over at DPreview or something. This thread certainly gives lie to that claim.
OntheRez wrote:
This has been a fascinating discussion and I look forward to seeing the software (1) post beta, (2) available for the Mac, and (3) covering more lenses.
I commend Monito, Mendenhall, Pixel Perfect, and Wickerprints for their cogent and well written descriptions of what are truly topics of higher order mathematics. My own university math ended with the calculus sequence, but I was able to follow the discussion conceptually (wouldn't have a clue how to demonstrate any proofs) and have a clear grasp of what Canon is attempting. Given that their engineering has the data on mathematical compromises made in the design of a lens, I can see how Canon could "recreate" it to "correct" for the limitations of glass bending light to force a multi-dimensional world into 2-D.
I read periodically that FM is no better than the rants over at DPreview or something. This thread certainly gives lie to that claim.
Actually there is a thread over on DPreview on this subject that gets into the theory of this type of correction and is not heavy in the "rant" department.
DXO has been using deconvolution and providing for complex aberration correction for years. They have not however had an "inverse fitler" for the AA filter that Canon has provided with DLO. DXO has raw level noise reduction and I believe it performs this first. As mentioned here noise really balls up deconvolution. I wonder how DLO performs at high ISO's. I am staying tuned here.
skibum5 wrote:
the difference seems to largely go away, and even seemed on the worse end of things, comparing it to ACR's best efforts though anywhere near the center of the frame (although I've only compared two images so far) but it was better at far edges on both
Haven't tried ACR as I seldom go beyond the batch processing of CR2 with DPP. More for purposes of heavy editing work when I touch Photoshop.
Perhaps if that's the case, a post edit with a merge of ACR and DLO processed RAW images would make for the best results then Best of both worlds ?
mpmendenhall wrote:
Just FYI, a visual simulation of the "hard frequency cutoff" effect of diffraction.
Nice demo
There are still some high frequency residuals in the diffraction sweep, with phase reversal. You probably used a rectangular window to delimit both the diffraction funtion and the signal. For ultimate high frequency sidelobe suppression I would suggest applying a Blackman window on the sinc function
alundeb wrote:
There are still some high frequency residuals in the diffraction sweep, with phase reversal. You probably used a rectangular window to delimit both the diffraction funtion and the signal. For ultimate high frequency sidelobe suppression I would suggest applying a Blackman window on the sinc function
Yep, you're right. The frequency sweep at top (not even a sinc function, just linear interpolation between two wavelengths) was sampled with a plain old rectangular window. I could claim to be simulating an AA-less sensor response, but really it's because sometimes I'm exceedingly lazy.
In putting this together, I also realized that I have been somewhat wrong in my description of how the aperture shape cuts off the frequency spectrum of the image. It turns out that, when you aren't being too hasty to take into account that we aren't sensitive to the sign/phase but only the square magnitude (intensity) of the diffracted light, the correct falloff to impose on the frequency spectrum is not the shape of the aperture but the autocorrelation of the aperture with itself. So, from a circular aperture, you get more of a cone instead of a flat disc. It still has a complete cutoff of all information beyond its edges, but also partially attenuates the lower frequencies instead of having no effect below the diffraction limit (duh!).
Best of both worlds ? 
