Optical Spatial Frequency Filtering of Image Sensors ?

Started Nov 20, 2012 | Discussions thread
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Optical Spatial Frequency Filtering of Image Sensors ?
Nov 20, 2012

I know just a little bit about analog (continuous) and digital (discrete) filtering systems. Was wondering if there may be someone who can help me better understand the combination of the various components involved in optical low-pass filtering of image-sensor photo-sites for the purpose of limiting spatial-frequencies at and beyond the Nyquist-Shannon sampling limit (at 1/2 the spatial sampling frequency). I read the following information published at a LumoLabs web-page:

... what everybody calls "AA filter" or "anti-aliasing filter" or "low-pass filter" isn't one. A low pass filter destroys the signal at high spatial frequencies. Every digital camera does have a low pass filter. But it is the finite photo-sensitive size of a sensel or pixel, typically enlarged to almost the full sensel's extensions by a microlens. The microlens array provides a better quantum efficiency (less photons get lost) but also provides a camera's true low pass filter. Assuming a fill factor of 100%, it destroys signal at twice the Nyquist frequency (the spatial frequency which sensels are placed at on the sensor) and dampens signal at the Nyquist frequency to 64%.

The problem is as follows: Assume a ray (e.g., from a star) reaches your camera and hits a single sensel. Above the sensel will be a green, red or blue filter from the Bayer filter array. This means that the camera will see a green, red or blue star. There is no way for the camera to detect the star's real color, and no smart software can recover the missing color information. This is the false color problem when demosaicing specular highlights ("stars") or contrast edges. If contrast edges form a regular pattern, the false color will vary slowly across the image forming what is called a false color moiré pattern ...

... the entire problem disappears if a ray hits more then a single sensel. Because then the color can be reconstructed by comparing the signal from neighboring sensels having different Bayer filter colors.

This is what a filter achieves which I call the "Bayer-AA filter". It actually isn't a low pass filter at all. It typically is a pair of lithium niobate crystal plates turned 90° with respect to each other. Lithium niobate is birefringent and splits a ray into two. The pair therefore splits a ray into four, designed to hit exactly one of each of the four Bayer color filters. In order to achieve this goal, the ray split distance must be equal to the sensel pitch (or pixel size). The result is exact color reproduction. Such a Bayer-AA filter is called to have 100% strength.

But the birefringent crystals interact with the microlens array and combine to a low pass filter of only half the spatial frequency: Now, the signal at the Nyquist frequency itself is destroyed.

Because vendors don't want to sacrifice the full sensor resolution, they typically design their Bayer-AA filters to be weaker where a 0% strength would correspond to their absence.

The Nikon D800E has such a 0% strength. However, it isn't achieved by replacing the birefringent crystals. This would require a re-calibration of the optical path, AF module, focus screen and color profiles. Rather, Nikon uses a pair of lithium niobate crystal plates turned 180° with respect to each other which happen to cancel each other (if aligned properly).

Source: http://www.falklumo.com/lumolabs/articles/D800AA/index.html

In your understanding, is the above quoted text an accurate description of what is going on ?

It sound like the microlens array assembly itself is (at least) as important of a component as are the lithium-niobate crystal plates themselves if it results in a zero response at the spatial sampling frequency, and up to a -3.87 dB (or -0.64 EV) attenuation at 1/2 of the spatial sampling frequency.

Thus, it sounds like when people say that a cameras has "no AA filter", there still nevertheless remains a significant optical low-pass spatial-frequency filter response which is implemented by the microlens-array assembly itself.

Any informative and interesting thoughts appreciated,

DM...

Nikon D800E
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