How does an anti-alias filter affect image quality other than reducing Moire?

Question

The commonly stated trade-off for using an anti-alias filter or not is that it diminishes the risk of moire while also reducing potential sharpness. This is what I have seen myself and in many online demos.

Now what surprised me is that DxOMark which measure RAW sensor performance is now split halfway between improvements and setbacks, having tested 4 pairs of cameras with and without anti-alias filter:

Nikon D800 vs D800E:

95 vs 96 score based on 25.3 vs 25.6 bits of color-depth, 14.4 EV vs 14.3 EV of DR and Low-Light score of 2853 cs 2979. While I expected the D800E to do better in bit-depth, I also expected it to do better in DR.

Olympus OM-D E-M5 vs PEN E-PL5:

71 vs 72 score based on only a difference in low-light scores: 889 vs 826.

Pentax K-5 II vs Pentax K-5 IIs:

Both 82 score with bit-depth of 23.8 vs 23.9, identical DR and low light score of 1235 vs 1208. Again I was expected the lack of anti-alias filter to help with DR as well as bit-depth.

The Nikon D5200 vs D7100 do not use the same sensor but results are still surprising considering the D7100 is the newer model:

Score of 83 vs 84 with identical bit-depth, 13.7 vs 13.9 EV of DR and low-light score of 1256 vs 1284.

Thinking about the effects of an anti-alias filter, I would expect bit-depth and DR to be superior without the filter at low ISO when noise is virtually none.

Low-light should be the reverse because the anti-alias filter probably blurs shot noise while read-noise stays the same.

These are my intuition however the results do not correlate. So what is really going on here?

How can the presence or lack of an anti-alias filter explain these measurements?

Answer 1

Dynamic range should not be affected at all. Unlike, say, blur caused at the lens position, an optical low pass filter sits immediately above the sensor. The blur induced is at the pixel level, and there is essentially no flare (beyond the one-pixel or fractional-pixel spread). When testing dynamic range, normally one uses a step wedge with significantly lower resolution at the sensor than one or two pixels (more on the order of 5-6% of the sensor dimension), so areas that are black (or, rather, that crucial "minimally different from black") will not be affected by lighter tones except right at the border between that wedge and the next. For the same reason, you shouldn't expect to see bit-depth differences between two cameras with the same sensor modulo OLPF; the wells are still the same size, the photon capture has the same efficiency, and the same analog-to-digital converters are used.

The only effects that should be measurable (apart from ordinary camera-to-camera variation) are increased frequency response (which translated to increased sharpness, bearing in mind the effect of the Bayer mosaic) and, depending on how the camera is constructed, a slight increase in sensitivity (a fractional T-stop).

Answer 2

What you're seeing is most likely the result of variability in the experimental conditions.

Almost all the DXO mark scores relate to noise in some way. Dynamic range is measured by finding the difference in illumination between the saturation and the point where the signal to noise ratio drops to 1. The colour sensitivity score is the logarithm of the number of colours than can be distinguished, two colours are "considered distinguishable if their difference is larger than the noise". The low light score is the amount of gain that can be applied whilst retaining a certain signal to noise ratio, thus all three of the scores you mention are determined by how much noise the sensor is producing under certain circumstances.

Noise is influenced by the temperature of the sensor, which depends on how long the sensor has been active for, and the ambient temperature. Anything and everything could have affected the test results, including the weather.

There's also a smaller possibility of sample to sample variation in sensors. Or more likely batch to batch variation - Nikon will probably produce a thousand D800 units, then change over the filters and make a hundred D800E units then change back. So even if you compared two D800s and two D800Es you might find the same result.

You could also be seeing the variable effects of sensor calibration, there will be some steps performed on the production line to set the appropriate black level, amp power etc.

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I see no reason to expect dynamic range or colour sensitivity to be any different at the image level when using a camera with the AA filter cancelled out. The AA filter is not removed in these cameras, instead the two parts of the filter are aligned differently so they have no overall effect. Therefore light passes through exactly the same amount of exactly the same materials in either case. The only difference between cameras with an AA filter and those "without" occurs at the pixel level.

Optics cannot reduce noise (except by delivering more light), neither the AA filter, nor diffraction nor a soft lens reduce shot noise at the image level. With an AA filter, each photon will at random land on any one of four pixels.

I say at the image level, because a single point of light shining through an incredibly sharp lens will result in four noisy pixels in an AA camera image, but one less noisy, brighter pixel in an AA filterless image (on account of collecting 4 times as many photons). However by time you add up the effects for all points of light across the image, the results cancel out and you're left with the same overall level of noise.