[Scythels]

 

The PF lens, like the DO lens configurations used in Canon DO lenses, make the lens all on their own shorter

No, it doesn't.  What a fresnel lens does is use so-called microoptical structures to bend the light in lieu of a continuous curve as you would see with a normal lens.  The formula for the apex angle of each prism is given by A(ρ)=ρ/(f(n2-n1)).  In the case the fresnel surface lies along a curve so we must complicate the math mildly by converting what we want to optical power, as the curve itself gives power to the lens.  Optical power, is the measure of how strongly something focuses light. 

 

For any lens surface we have ϕ=(1/R)(n2-n1) where R is the radius of curvature, n2 is the refractive index of the medium to the right of the surface, and and n1 is the refractive index of the medium to the left of the surface.  For any optical system, uppercase phi (browsers do not draw phi correctly...) Φ=1/efl - the effective focal length.  In laymans' terms this is the focal length. 

 

Let's have a little thought experiment, shall we? 

 

The 300mm f/4 is a telephoto design.  This you must surely agree with.  It has a phenominal telephoto ratio of just .466, a ratio which i believe may be a world record of some kind. 

 

in its simplest form a telephoto lens is a positive lens followed by a negative lens.  There are two basic ways to increase the power of a lens, to make its radii of curvature shorter and thus steepen the slope of its surface, or to use a higher index material for the glass.  There are other methods such as using a fresnel lens or using a GRadient INdex (GRIN) material but they are (ironically) outside the scope of this bit here.

 

The fourth lens in the new 300/4 has a net negative power.  The first surface has positive power but it likely has been curved in the way it has simply to adjust the angle of incidence on the rear surface without a goal of having positive power there, or it is a concession to allow a thinner lens overall. 

 

Let us imagine that we want the rear surface of the fourth lens, considered in isolation, to have a focal length of -50mm.  I do not believe that is an unreasonable guess given how strongly curved it is and the fact that it has a fresnel lens. 

 

Now take a moment of basic theory with snell's law.  If a lens is curved, the angle of incidence with respect to the surface normal is not constant along the surface.  Because for non-GRIN lenses the refractive index is constant, the angle light is bent at is not constant.  Unfortunately, for basic spherical surfaces Δθ for the angle of refraction does not exactly mirror the angle of incidence with respect to the optical axis, so you get defocus when you utilize a lens.  This is the origin of all aberrations, but spherical is easiest to imagine. 

 

The stronger your curvature, the more you "aggrivate" the Δθ disagreement.  Ideally, you want very weak curvatures. 

 

Because the radius of curvature necessary to create a long focal length is very large, the slope of the lens surface is small.  This creates only weak geometrical aberrations and is why long focal length lenses tend to perform better than short focal length lenses.

 

Nikon has shown us in their diagram that they have combined a high dispersion lens with with whatever the fresnel "element" is cut into, it's probably NSF2 or a "neighbor" glass.  The material the fresnel element is cut into is most likely a crown.  Given that there will be manufacturing difficulty a nice cheap crown was likely chosen, either NBK7 or NSK4 or one of their neighbors.  I'll use NBK7 for an example, but in this thought experiment it doesn't truly matter.

 

NBK7 has a refractive index of 1.517.  Air has a refractive index of 1.  The radius of curvature necessary to achieve a focal length of 30mm can be calculated with -1/50=.517(1/x) = -25.85mm.  That is an extremely strong curvature and would induce absolutely monstrous aberrations.  But, if you add a fresnel component and say that the fresnel componenet will contribute 1/2 the power, now your radius of curvature must only be -51.7mm, which is still strong but nowhere near as bad as the value without a fresnel componenet.

 

Why do you want a short focal length - isn't this a telephoto lens?

 

Yes, it is.  But the adjustment of the telephoto ratio requires an adjustment of the Positive and Negative lens arrangement.  There is a "good zone" to be in regarding how close these two elements are to each others' centers of curvature that is developed in nodal aberration theory.  If you want to shrink the overall length you must get them close together, so they must have roughly complementary short focal lengths (for example 50 and -50mm). 

 

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There is a great deal of positive optical power in front of the fresnel element, the job of that surface is to reduce the power.  The very strong radius of curvature has unfortunately induced many aberrations which must be undone.  To undo them nikon has chosen to use additional elements, though they could have done it with aspheric surface(s) if they had wished to. 

 

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 without causing CA because it is combined by a single refractive lens and without the need of many more elements.

 

Elements are used to correct much more than polychromatic aberrations.  There are two basic techniques to address problem elements and improve the performance of a lens - splitting and compounding.  By splitting a lens you distribute its power across more surfaces and thus reduce the radii of of curvature, "piggybacking" off of the refractive index of the elements to provide the power.  This allows you to reduce geometrical aberrations.  One may also compound a lens into a doublet.  This allows the creation of an achromatic doublet if one wishes to correct axial and lateral CA, or the simulation of an element with very high refractive index if one wishes to reduce the curvatures at play. 

 

There are fifteen other elements in this lens.  There are other chromatic aberrations that must be addressed, and the monstrous geometrical aberrations created to achieve the exceptional telephoto ratio are being corrected through the addition of more elements.

 

 

And Canon does similar things, but with multiple DO elements bonded togethet without gap in the 400mm DO II to prevent the flaring the Nikon lens shows.

The only similarity between the third generation DO technology and nikon's new PF technology is the use of a fresnel surface.  They aren't even the same type of fresnel surface.  Flare from fresnel surfaces is caused by reflections off of the legs of the "triangles".  Canon has eliminated that by very precisely manufacturing two equal fresnel surfaces and cementing them together.

 

 

Like I pointed out before, the simple fact is that the 300mm f4E PF has the same number of elements as the 400mm f2.8E FL.... And the latter has no PF element.

I'm not sure what your point is.  Element count only directly affects cost, manufacturability, size, and weight.  It says nothing about anything else directly.  The 400mm's design is made easier by having a longer focal length.  It is made harder by having a wider aperture.  These two "fight" regarding design complexity, but the 400mm pursues a less aggressive telephoto ratio.

 

Now please, brightcolors.  Stop pretending you know so much about lenses.  You know far less than you think you do.