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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?

============

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".

========================

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.

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.

This digression serves as a warning _not_ to consider the light source
(e.g. light-bulb filament) in the lighthouse as a point source. (I think I
was implicitly making that mistake earlier.)

> I've seen quite a few lighthouses, green/white airport beacons, and
>suchlike that would IMHO benefit from sharper focusing. One would think
>that a shorter-and-brighter pulse would be much easier to notice.
>
I have yet to see a hard-to-notice lighthouse, so it doesn't seem to
be a problem.

Ummmmm.... If lighthouses hadn't had a noticeability problem, tell me
a) why did they spend money on powerful light sources, and
b) given a powerful light source, why did they spend additional money on
huge lenses (on the order of 2 meters in the instances I've seen)???

I claim that they had two requirements:
a) They needed a certain energy per pulse. This required a high-power
source.
b) They needed that energy to be concentrated in a reasonably _short_
pulse.

Alas, they didn't have lasers, so they had sources with limited surface
brightness; the high total power was spread out over a large surface
area. Therefore they needed a reasonably long focal length in order to
demagnify the source into a smallish beam.

I surmise that the image size is limited by the size of the source and the
focal length of the lens, not by optical quality or Airy-disk size
(contrary to my earlier implicit assumptions).

================

Bottom line: I'm quite convinced that many Fresnels have random
ring-to-ring phasing, and that this works just fine in many
applications. But I'm still suspicious that the
thousands-of-rings-per-inch critters are carefully phased.

=======

BTW, can anybody explain why lighthouses used lenses instead of mirrors???