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Re: Fresnel Lenses

I wrote:

I'm still confused about several other applications.
I've seen Fresnels 10 inches on a side, sold for affixing to windows
or glass doors, to create fisheye views. That's image quality, not
collimation quality.

Then at 08:27 AM 4/16/00 -0700, Leigh Palmer wrote:

Correct, but you have been fooled into thinking that the whole lens
forms the image you see with your eye. As a matter of fact only the
bundle of rays that enters your pupil forms that image, and that
bundle comes from a very small region of the lens.

For any point in the image, the "very small region" in question is on the
order of the size of my pupil, right? In the case of a Fresnel with
thousands of rings per inch, that still suggests that things would work a
lot better if the rings were properly phased, doesn't it?

No. If you could resolve the rings with your eye then it would
make a difference. You would see a separate image for each ring,
but you would see it *through* that ring; the separate images
would not overlap. If you can't resolve the rings then the image
overlap results in confusion which is also too small to be
resolved. Hold the lens close to your eye and you will see my
meaning clearly.

Aperture ratio is the critical parameter in burning glass
function, not sharpness of focus.

That's true, in any reasonable situation; see exception below.

The burning glass example may make my point a bit better. If you
hold a burning glass by hand you can certainly light paper (or burn
ants, etc.) with great ease. If you now take a mirror and a second
burning glass, and you form a hot spot (an image of the sun) at the
point of the first burning glass's image, but using the mirrored
Sun as your object, you will find that you deliver roughly twice
the power to the spot. The two lenses, at least one of which is
hand held, probably are not phased to within a fraction of a
wavelength,

That's all correct.

but the superimposed images of the Sun are certainly
mutually coherent.

Coherent? Really, over relevant timescales? That claim is not needed to
support your previous points. Even incoherent superposition will result in
additive power, and unless I'm hopelessly confused your notes have
consistently argued for the _lack_ of ring-to-ring coherence. I'll pretend
you didn't say "coherent".

Mutual coherence pertains to the sources, nothing else. The Sun
and its mirror image are mutually coherent.

In any practical situation, the peak temperature created by a burning glass
depends on aperture ratio and not much else. That is easy to see from a
Liouville-style argument (phase space, 2nd law of thermodynamics). You are
forming an image of the sun, and you can't produce an image temperature
hotter than the sun.

It may be easy to see, but I wasted a month on trying to beat
the second law of thermodynamics while designing a mirror
scheme to increase the far infrared output of a mercury arc
source. Once I saw that I was trying to squeeze the phase
space and defeat the second law I gave up. It was an important
lesson which I never forgot.

I started reading the second law article in Physics Today (PT
arrived in Canada on Friday). While apparently discarding the
classical development of the second law and the resulting
classical definition of entropy, it appears that this article
is really advocating a preference for the classical view over
the statistical view, a Good Thing in my opinion.

Exception / digression: The situation is different if you try to burn
something using the image of a star. The surface temperature of the star
is just as great, but you don't have enough resolving power to form a sharp
image. In this case, increasing the aperture size (even without increasing
the aperture ratio) is a huge win, because it creates a sharper image.

I see. I think that you will find Fresnel lenses to be poor
devices for high resolution imaging (such as astronomical
imaging). That was my original point.

Leigh

Leigh