Thoughts on Sensor Resolution

Originally posted to the “Nikon SLR Forum” on the DPReview site.

Moon wrote:

> DMillier wrote:
> > Yes when the frame enlarges, the pixels enlarge. But SO DOES THE
> > SIZE OF THE OPTICAL IMAGE!

> > If your one pixel on a small sensor is positioned so it covers say
> > 1 sq inch of the subject and you enlarge the pixel by say x10 what
> > happens? Absolutely nothing if you use a different lens matched to
> > the new sensor size. This is because the new optical image will
> > also be x10 larger so your one (x10 enlarged pixel) will still
> > cover 1 square inch of your (now x10 enlarged) subject...

> I follow what you are saying, but my presumption is that we were
> discussing a 35mm system. The D/1/x/h/100/30/60, 1D, etc. are based
> on 35mm systems and, as such, use the same lens system. Assuming
> the same lens is used from one sensor size to the next and the
> frames were compositionally identical, resolution would be lost.

IIRC, the formula for working out resolution with film is

1/res_total ~= 1/res_lens + 1/res_film

where resolution is given in lines/mm or some similar units.

So lets say we’ve got a lens with res_lens = 60 l/mm, and calculate numbers for CCD pixel density given Ron’s sensor sizes. For 6MP on a 15x23mm sensor, we get 1.71e5/mm, and for a 24x36mm sensor we get 6.94e3/mm. I’m going to just equate pixel spacing with lines/mm here; since this is just a before/after comparison this shouldn’t be a problem. So we have res_small = 132 l/mm and res_large = 83.3 l/mm (square root of the pixel density figures).

res_total_small ~= 1/60 + 1/132 = 41.2 l/mm

res_total_large ~= 1/60 + 1/83.3 = 34.9 l/mm

That’s a distinct drop in resolving power, yes?

But that wasn’t the whole claim made. The whole claim concerns how well an *identical composition* is resolved under the two different scenarios. And that takes us to a slightly different concept of resolution, one that is common in videography, which is the total number of lines of resolution that the system is capable of. This we can approximate by taking into account the sensor sizes and the lines/mm figures we just calculated. Again, we’re just looking at a before/after comparison, so this should also not be a problem.

total_lines = l/mm * mm

total_lines_small = 41.2 l/mm * 23mm = 948 lines

total_lines_large = 34.9 l/mm * 36mm = 1,256 lines

Hmm. It seems to me on the math that the larger sensor has the edge over the smaller sensor given the same number of pixels in both. This also explains why lenses that were adequate for use with 35mm film may not be adequate for the small sensors of the current [posted around 2003, IIRC] crop of DSLRs (D100, S2, D60). In order to get comparable performance, one needs a res_lens that is significantly higher. (To get the same total lines figure for the case above, for instance, one needs a lens capable of resolving 93 lines/mm on the smaller sensor to match the performance of a lens that resolves 60 lines/mm on the larger sensor.)

But perhaps I’ve remembered the formula wrong or messed something up in applying it. If so, I’d appreciate a correction.

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