02-06-2015, 09:26 PM
This lens contains CAF2, the patents preceding it contain CAF2 and the decision to use a material with anomalous partial(=order of 1000x price of normal material) occurs long before final tweaks are done to the design. The anomalous partial was probably necessary to attain the telephoto ratio they hit and CAF2 would be a natural choice because they already produce it thus the cost is lower.
Regarding making it f/2.8 this would not be "impossible" but rather impractical. The front portion of the lens would not grow by a factor of sqrt(2) since the chief ray (=FoV) already defines the front diameter vs the marginal ray essentially doing the leg work in e.g telephoto design. Coma grows by x^3 as the FoV grows so controlling it for such a massive field is already very difficult. Coma also grows by rho (= element diameter) but not too strongly; the reason stopping down some lenses doesn't "kill" coma too well is because the rays which contribute to the coma are being un-vignetted by stopping down just as fast as the worst offenders are being clipped by stopping down.
Astigmatism will be the greater problem and in modern designs is often the biggest challenge. It grows exponentially with element diameter.
In general we may examine the etendue of the systems to compare their design complexity, momentarily ignoring the difficulty dealing with the BFL >>> EFL problem.
Nikon 14-24: DFOV = 114.2deg | PUPIL AREA = 78.5mm
Canon 11-24: DFOV = 126.1deg | PUPIL AREA = 23.7mm
a rough lagrange invariant for the 14-24 is then 8965. For the 11-24 it is 2989. This definition doesn't truly work for wide angles (too much round off error) but gives a very rough estimate. The net meaning is that the 14-24 is the "better" or "harder" design, but then one must deal with the telephoto ratio which drives the 11-24 complexity as well as the radial projection problem. Note the shape of the following two curves, 11mm is further into the process of 'blowing up' as compared to 14mm.
http://i.imgur.com/Nnyz8C3.png
Plot focal length * tan(theta) in radians to see this for yourself. This is the source of so-called rectilinear distortion. The returned value is radial distance i.e "sensor height" for that AoE. To fit wider AoVs onto the same size sensor one adds barrel distortion - reduced magnification at the edge of the image. This counter-balances f*tan(theta) distortion.
More later, work soon.
Regarding making it f/2.8 this would not be "impossible" but rather impractical. The front portion of the lens would not grow by a factor of sqrt(2) since the chief ray (=FoV) already defines the front diameter vs the marginal ray essentially doing the leg work in e.g telephoto design. Coma grows by x^3 as the FoV grows so controlling it for such a massive field is already very difficult. Coma also grows by rho (= element diameter) but not too strongly; the reason stopping down some lenses doesn't "kill" coma too well is because the rays which contribute to the coma are being un-vignetted by stopping down just as fast as the worst offenders are being clipped by stopping down.
Astigmatism will be the greater problem and in modern designs is often the biggest challenge. It grows exponentially with element diameter.
In general we may examine the etendue of the systems to compare their design complexity, momentarily ignoring the difficulty dealing with the BFL >>> EFL problem.
Nikon 14-24: DFOV = 114.2deg | PUPIL AREA = 78.5mm
Canon 11-24: DFOV = 126.1deg | PUPIL AREA = 23.7mm
a rough lagrange invariant for the 14-24 is then 8965. For the 11-24 it is 2989. This definition doesn't truly work for wide angles (too much round off error) but gives a very rough estimate. The net meaning is that the 14-24 is the "better" or "harder" design, but then one must deal with the telephoto ratio which drives the 11-24 complexity as well as the radial projection problem. Note the shape of the following two curves, 11mm is further into the process of 'blowing up' as compared to 14mm.
http://i.imgur.com/Nnyz8C3.png
Plot focal length * tan(theta) in radians to see this for yourself. This is the source of so-called rectilinear distortion. The returned value is radial distance i.e "sensor height" for that AoE. To fit wider AoVs onto the same size sensor one adds barrel distortion - reduced magnification at the edge of the image. This counter-balances f*tan(theta) distortion.
More later, work soon.