Based on dpreview's resolution figures for various cameras, I wanted to find out whether there was a relationship (or rather a correlation) between the sensor's pixel size and the measured resolution in 'lines per mm'.
The table in the attached pdf shows an almost linear relationship for APS and FF sized sensors. Picked as an example, a small digicam achieved the highest resolution (again lines per mm on the sensor).
Neglecting other image quality factors and considering only resolution, current sensor designs do not need high-resolving lenses (100 lines per mm for a Nikon D2x, that is 50 line pairs per mm. A coke bottle can do that.) As the pixels become smaller though, higher resolving lenses and a more precise AF are required.
The theoretical full frame sensor using a pixel pitch of 2 micrometers would need lenses resolving 250 lines per mm. Even this is achieved by good current lenses (as demonstrated on high-contrast BW film). Yes the lenses will need to be redesigned to take into account sensor caracteristics. This sensor would have close to 247 MPix for a 24x36 mm size.
Noise will be invisible as it will not be magnified a lot even for large prints.
Obviously such a design is utopical today, if only due to the computing power required to post-process.
The table shows that small sensors and adequate lenses have better resolution than large sensors with bigger pixels. Experience and physics show that per-pixel quality is better for larger sensors.
Point is: do not believe that limiting a sensor size to X megapixels has other reasons than economics and feasibility. 4/3 sizes, APS sizes, FF all still have *a lot* of potential.
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