Letter of the Week: The Full Frame Decision continues

To: Editor, Pop Photography RE: I had been thinking about this issue since I bought a D200 back when it first came out, and have since gone on to add a D300 based on the PopPhoto evaluation.

To: Editor, Pop Photography
RE:  fullframe vs. aps-c camera – which to choose?

I enjoyed your article in the April PopPhoto on full frame vs. APS-C sensors.  I was wondering when Pop Photo was going to address this question since it is obviously going to become a matter of contention among photographers.  I thought you addressed the issues well and the article really made some good points.  I had been thinking about this issue since I bought a D200 back when it first came out, and have since gone on to add a D300 based on the PopPhoto evaluation. Of special importance to me was the issue of effective resolution (image quality) for a real lens on a real camera, where the pixel density and pixel noise combine to create a valuable quantifier of image quality, independent of lens quality.

Practical Photography your UK competition mag said (when they tested the Nikon D3x) that the large format sensors are inherently superior to full-frame sensors even if they have fewer pixels and following this logic, full-frame must be superior to aps-C sensors and so forth.  I was not sure I agreed with this statement so I thought about this a bit and – if I can bend your eye a little – maybe there is a simple technical way to see this.

NOISE
•  The individual pixels in the sensor intercept a number of photons n for any exposure time that depends directly on their area Ap = Dx2  (where Dx is the dimension of assumed square pixel)  (No quantum efficiency considerations here.) 
•  The statistical variation in this number varies as the square root of n = n∏.  If you consider n as the signal and n∏ as the random variation expected in a steady signal then it behaves as a component of noise (no attention paid to inescapable background signal noise components due to external radiation or temperature-related noise.) 
•  A measure of purely statistical signal/noise ratio then is: S/N µ  n/n∏  µ n∏  µ  Ap∏  µ Dx.

So the obvious emerges – bigger Dx = more light = cleaner pic because the signal is relatively less noisy, and the signal to noise ratio goes directly with pixel dimension Dx. This means that your example Canon 50D 15.1 Mp camera with 4.7 micron Dx would be about 20% noisier right out of the gate than Nikon D300 5.5 micron Dx. (Presuming same quantum efficiency, etc. for Canon and Nikon sensors, and no attention paid to pixel wall thickness.)

RESOLUTION

The sensor resolution for the Dsensor is computed as the inverse of Dx or Dsensor µ 1/Dx, (geometry only, no lens, no noise, assumed zero pixel wall thickness, a significant factor when Dx ® 0).

NOISE-RESOLUTION BATTLE

Since the pixel noise and resolution are basically independent of one another, multiplying them together is a reasonable measure of the combination’s effect.  The sketch below (attached jpeg) shows that doing this gives a lens-less image quality that is basically constant over a wide range of pixel dimensions Dx.

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