> True diffractive optical elements do not look anything like
> Fresnel lenses!! 
>

A DOE that is meant to behave as a normal lens will have the same type of
concentric rings that a Fresnel lens has.  The major difference is that it
will have much finer (smaller) features.  If the DOE is doing something very
odd, it will look nothing like a classical Fresnel lens, regardless of
scale.

>
> The Canon DO elements (or the
> schematic pictures of them) looked very much like Fresnel elements. Of
> course it might have just been a marketing photo to explain something that
> is far harder to explain... but at least it confuses me to doubd what they
> are saying/doing. 
>

There is no way to draw the micron size features  without greatly
exaggerating the drawing.  When simplified in this fashion, a DOE that is
intended to mimic the functions of an ordinary lens look like an ordinary
Fresnel lens.

>
> I've done some calculations around difractive optics a
> few years back... while you can do many strange things with diffractive
> optics, but one thing stuck to my mind - because I thought about making
> camera lenses with them - was that they work for only one wavelength at a
> time. 
>

Correct - they work most efficiently at one wavelength and tend to scatter
more light at other wave lengths.  

>
> ... maybe what Canon is doing is using very small scale Fresnel lens
> with somekind of diffractive optics stuff (at least loosely) to correct
> for the problems (that are caused by diffraction, but very much unwanted)
> that arise in the borders of the "rings".
>

One problem with a classical Fresnel lens is that each ring acts as its own
separate lens - the light from each ring is incoherently added together.
This means that the resolution of a Fresnel lens is limited to the
resolution of the individual rings.  If the rings are made smaller, the
resolution is worse.  The DOE acts as a single large ring that can
theoretically resolve up to its diffraction limit.

>
> Anyways, the lens was painted white... but that doesn't yet mean it has as
> good optical quality as L lenses. 
>

I believe that the two DOEs are positioned with respect to each other with
micron type tolerances.  The white lens would help hold these tight
tolerances when used in direct sunlight by reducing the amount of heat
absorbed.

>
> Or maybe one of it's main reasons is to correct the handling of different
> colors. (You know, the first one makes a rainbow out of the colors and the
> next one tries to correct it... same as with classical elements.)
>

Yes, I expect that this is correct.  I have not seen references to this in
the literature, but I have not paid a lot of attention since I stopped
working directly in this field.  I did look up a couple of Canon's patents
that seemed to be related, but my eyes glazed over and time ran out before I
found anything of interest.
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