Canon recently introduced its EOS-1D X Mark III Digital Single-Lens Reflex [Edit: and now also possibly the R5 Mirrorless ILC] touting a new and improved Anti-Aliasing filter, which they call a High-Res Gaussian Distribution LPF, claiming that

“This not only helps to suppress moiré and color distortion,
but also improves resolution.”

In this article we will try to dissect the marketing speak and understand a bit better the theoretical implications of the new AA.  For the abridged version, jump to the Conclusions at the bottom.  In a picture:

Aliasing & Moiré: Party Crashers at the Gate

Aliasing and Moiré are two potentially ugly byproducts of the sampling that digital cameras must perform in order to capture images in our files.  They may not be as noticeable in natural scenes, where straight lines and regular repeating patterns are few and far between, but they become a nuisance when photographing man-made objects like architecture or fabrics.  Worse there is little that can be done in post processing to mitigate the unwelcome effects once the image has been acquired.

Aliasing and Moiré are caused by spatial frequencies beyond the capabilities of a given sensor sneaking into the sampled image under the guise of lower frequencies (under an alias), therefore corrupting the capture.  Clearly, the larger the sampling pitch the more the potential existence of such frequencies with a given lens.  Therefore digital cameras with large pixel pitches have historically sported Optical Low Pass (aka Anti-Aliasing) Filters to attenuate the energy of potentially offending higher frequencies before the image is captured.

The classic AA implementation has historically taken the form of two simple birefringent plates placed just above the sensor back-to-back, with one rotated 90 degrees, to perform an optical low pass function.  For example in Figure 2 a beam is split four ways, displacement controlled by the choice of material and its thickness.  Such a 4-dot beam splitter does indeed reduce aliasing and moiré – at the expense of some overall sharpness, as described in this earlier article.

16 Candles

With the introduction of the 6.5um-pitch EOS 1DX Mark III Canon Japan’s site boasts that an optical

“low-pass filter has been newly developed to bring out the superior resolution of EF lenses. By separating the light reaching the sensor into 16 points, an MTF shape close to a Gaussian curve is realized, achieving higher resolution than conventional low-pass filters while effectively suppressing false colors and luminance moire.”^[1]

So reading between the Google-translated lines and looking at Figure 1 we can fathom that the Gaussian Distribution AA is obtained by first using two birefringent plates to generate a classic 4-dot beam splitter PSF with displacement ,  followed by two additional plates of different thickness to obtain the indicated High-res action with displacement : the first of the additional plates duplicates the four dots diagonally at a 45 degree angle and the second duplicates that result orthogonally, linearity and superposition implied.

The optical low pass filter resulting from such a four birefringent plate arrangement would be a 16 point (or equivalently dot) beam splitter.

MTF of Canon High-Res 16-dot AA

From the earlier article, the Modulation Transfer Function of  a  simple beam splitting operator is a cosine so a symmetrical 4-dot AA such as the one shown in Figure 2 can ideally be modeled as

(1)  

with spatial frequencies in the horizontal and vertical directions and sharing units with displacement .  The addition of the second set of splits to obtain the 16-dot AA can be thought of as the convolution of half the signal from the 4-dot AA above with a horizontal split, added to a separate convolution of the other half of the signal with a vertical split, resulting in the second factor with the sum of the two additional cosines below:

(2)  

with and as shown in Figure 3.  Formulas in hand, we can now simulate the spatial frequency response of the new and classic filters:

The 16-dot High-Res MTF on the left is based on displacement proportions measured off the Canon PSF rendering shown in Figure 3, with / about equal to 3.2 – if those are correct so should be the relative MTF shape. With proportions fixed,  actual x-y axis units depend on the absolute value of , which I eye-balled from Canon’s material to be about equal to one pixel (pitch, see Figure 5 below).

On the other hand displacement for the classic 4-dot AA on the right was set equal to 2/3 of pixel pitch, which results in a typical MTF null of 0.75 cycles/pixel pitch (c/p^[2]) in the horizontal and vertical directions, as explained in the earlier article.

These values were chosen to make the resulting plots look as much as possible like those published by Canon Japan on their site:^[1]

Seeing is Believing

To decipher the marketing speak we can take a helicopter view of the response of the low-pass filters, extending the analysis to a wider range of frequencies (+/- 8 c/p, the red square below corresponds to the +/- 1 c/p range shown in Figure 4^[2]).  When we do so it becomes clear that the new High-Res filter does indeed attenuate energy further from the MTF peak at zero frequency compared to a classic AA.

Note that the High-res pattern does not start repeating within the area shown, while the classic AA pattern is fully defined by its simpler single frequency cosine product and clearly repeats verbatim over 100 times in the same space.

Horizontal Response of AA by Itself

We can get a more familiar view of it in 1 dimension by extracting MTF plots from the center in the horizontal direction only (in this case equal to the vertical direction since both filters are symmetrical around the axes):

Through these simulations we can clearly see that the High-res 16-dot filter in isolation is much more effective at suppressing energy above about 0.8 c/p than the classic 4-dot version – as setup, in the horizontal direction.  An arbitrary Gaussian curve that approximately tracks the response down to Nyquist is also shown to validate the ‘Gaussian Distribution’ LPF moniker claimed on the Canon Japan site.

Recall that the limit beyond which spatial frequencies may start causing aliasing is pixel pitch, Color Filter Array and scene dependent.  In this context it is generally taken to be 0.5 c/p and referred to as the Nyquist frequency.  Ideally, we would like all frequencies below 0.5 c/p to be perfectly passed (i.e. show an MTF of 1) and all those above that to be blocked (MTF of 0).

No Free Lunch

The state of the art of the possible is instead far from perfection as you can see in Figure 7.  In this case the high frequency suppression comes at the expense of some lost ‘sharpness’ below the 0.5 c/p Nyquist frequency compared to a Classic AA of displacement 2/3 of a pixel pitch, a fairly typical value but not necessarily what Canon are comparing to.

And keep in mind that though the shape of the High-res AA curve should be correct based on the / ratio extracted from Figure 3, its units are arbitrarily chosen by me to make the results of the MTF simulation (Figure 4) and the pretty pictures on Canon’s site (Figure 5) look approximately the same.  So the blue curve that in Figure 7 shows a minimum around 1 c/p (determined by my initial choice of displacement = 1 px) could just as easily need to be scaled so that the minimum is instead, say, 1.14 c/p corresponding to = 0.88px – should Canon’s engineers have made that choice instead of that implied by the artist’s rendering.  In that case the plot would look as follows:

Now the High-Res filter no longer loses out  to the classic AA below 0.5 c/p (the Nyquist frequency) but the compromise is letting through more energy in the critical aliasing frequencies just above that.  Take your pick, until Canon tells us or someone reverse engineers the actual size and proportions of the 16-dots your guess is as good as mine.  I will use =0.88px for the rest of this article for reasons that will become apparent shortly.

So keep in mind that these are simulations based on my assumptions and until we get actual information the plots just represent an educated guess.

AA’s Interact with Pixel Aperture

Of course the optical low-pass filter’s response interacts with all other components in the imaging system, especially with pixel aperture which is an integral part of what is normally considered to be the ‘pixel’ when modeling the spatial resolution performance of an imaging system^[3]  .  Assuming efficient microlenses and a perfect, square, 100% fill factor, pixel aperture drives energy to zero horizontally at 1 c/p, compounding the effect of the OLPF.  This is the frequency response in the horizontal direction of the combination of Canon’s 16-dot High-Res AA and such a pixel aperture,  with displacement of 0.88 pixels:

On page 43 of the EOS 1D X Mark III Still Imaging white paper we read that with the new High-res LPF^[4]  

“risk of false colors or patterns in diagonal linear subject detail is significantly reduced (moiré is reduced to approximately 1/4th the level previously possible, without lowering visible image detail and resolution)”

Below, responses in the diagonal direction are shown combined with that of a perfect square pixel aperture with 100% fill factor:

With displacement of 0.88px, the High-res low-pass filter hits a first null in the diagonal direction at around 0.8 c/p – though it’s the classic AA that looks more Gaussian now.   We could tell this was coming from Figure 6 because it is evident there that the first null lines of the two LPFs are rotated 45 degrees with respect to each other.  This works in the High-res LPF’s favor because the corners of the AA and pixel aperture are cleverly counter-aligned, helping to quench wayward ripples.

Rotation Combination

It becomes then apparent that it makes more sense to compare the combination of Canon’s new 16-dot AA and the Classic 4-dot AA with pixel aperture after rotating the results of one or the other by 45 degrees: we can do that wantonly because we typically don’t know what direction detail in a capture will be aligned with a priori, so both orientations are equally likely and valid in practice.  Here is the High-Res LPF horizontally and the Classic diagonally:

The performance of the two AA configurations so aligned, in combination with the usual perfect square pixel aperture, is virtually identical up to about 1.7 c/p.   This is in fact the reason why = 0.88px was chosen for this analysis.  Below is instead the response of the High-Res LPF diagonally vs the Classic horizontally:

Here the two AA + pixel aperture responses are only similar up until 1 c/p – but that’s where the similarity ends: the much larger amount of energy that the classic 4-dot AA in combination with perfect, square, effective pixel aperture lets through above 1 c/p in the H/V direction is striking.  That’s where the new 16-dot LPF shows its mettle.

For reference this is how bare, square, 100% FF pixels without an AA perform in comparison.   Food for thought for those of us with AA-less digital cameras.

 Overall Spectral Performance of AA+Pixel

Below is a perspective view of both MTFs side by side in the +/-3 c/p spatial frequency range^[2]  to get a better intuition of the overall theoretical performance of the AAs in combination with a perfect, 100% fill factor, square pixel aperture.  Note how much more effective Canon’s new High-Res LPF is at suppressing side lobes away from working frequencies.

The psychedelic color map is unfortunately necessary because the others did not show lower energies as clearly and I was too lazy to make up my own.  It will serve to differentiate these plots from those in Figure 4 that were limited to +/- 1 c/p and did not include the effect of pixel aperture.  Here is a view of the MTF contours in Figure 15 seen from above:

The 45 degree rotation of the central cone is readily apparent.  Ideally we would just like to see a round circle in the center with 0.5 c/p radius (the Nyquist frequency) – and nothing else, a sea of orange.  Note the much smaller ‘waves’ away from the central solid in the High-Res LPF plots.  On the other hand there is a lot of stuff happening beyond that in the Classic AA plots, foreboding greater potential aliasing issues.

Preliminary Conclusions

It is evident that the real substantive differences between the old 4-dot and the new 16-dot optical low-pass filters as setup in this post are likely to occur beyond 1 c/p in the two directions roughly aligned with the pixel grid (horizontal and vertical).

1 c/p with a 6.5um pixel pitch corresponds to about 150 lp/mm.  Today’s better lenses, when used with good technique, are certainly capable of passing plenty of detail above that frequency, detail that could become the root cause of aliasing and moiré.  This simulation of Canon’s 16-dot AA configuration seems to suggest that it is in a good position to ensure that energy from those frequencies is attenuated, thus reducing the potential for consequent pollution of working detail.

As for Canon’s “higher resolution” claim for the new AA, well, let’s just say that it’s vaguely worded – and the question becomes ‘higher compared to what?’  From this simple analysis, and given the information at hand, it’s hard to see where higher resolution would come from within the hardware without forcing compromises elsewhere.  Perhaps taking processing into account?  An entirely different chapter of investigation that will need to be performed by folks who actually own cameras with this type of filter.

There are a lot of assumptions in this theoretical exercise, starting from the guesstimated plate displacements read off Canon’s artist rendition.  It will be interesting to complement it with hard data and properly processed real life captures by folks who own such cameras in order to see how well theory predicts practice in this case.

Notes and References

<sub>1. The Canon Japan Page with the pictures and description of the new AA can be seen here. It’s in Japanese, Google translate to the rescue.
2. This article explains the various units typically used in connection with spatial resolution.
3. The Simple Model for Sharpness Articles start here.
4. The Canon EOS 1D X Mark III Still Imaging White Paper can be downloaded from here.
5. The Matlab code used to produce plots on this page can be downloaded from here.</sub>