Re: Fresnel Lens

[John Denker <jsd@MONMOUTH.COM>]

At 07:43 AM 4/15/00 -0500, brian whatcott wrote:

> There is one Fresnel-like lens that has not yet caught the
> imagination of engineers who specify such things.
>    This application *does* require precision at the wavelength
> level.
>
>  It's the hologram lens.

Yes.  BTW, in the simplest cases a hologram lens is essentially
indistinguishable from a Fresnel zone plate (which is not quite the same
thing as a Fresnel lens).

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

At 12:15 AM 4/15/00 -0700, Leigh Palmer wrote:
> John Denker supposes that Fresnel lenses are figured to within a
> wavelength of light or fraction thereof. That is not the case.

OK, I'll bite.  Yes, I thought all lenses and mirrors were figured to
within a fraction of a wavelength.  Multiply by (n2/n1 - 1) if you're picky.

1) Suppose we have a lens, any lens that deserves the name lens.
2) Suppose we divide it into a hundred or more regions (Fresnel-like rings
or otherwise) and introduce random phase shifts between regions.  The phase
shifts are large compared to 2pi.

Could somebody please explain the _physics_ of how this works?  Why do not
the randomly-phased contributions add to near-zero?

> M. Fresnel invented these devices to collimate lighthouse beacons,

OK.  But he is also credited with greatly advancing the wave theory of
light, and with inventing Fresnel zone plates (which absolutely depend on
proper phasing).  Why would such a person pass up the opportunity to
properly phase the rings in his lenses?

> not to make high resolution optical images, and they don't.

OK, but that doesn't prove that the rings are randomly phased.

Suppose we have one of these alleged lenses with randomly-phased
rings.  What happens to the energy that (because of destructive
interference) does not go into the main image?
  a) Does it go into "nearby" locations in the image plane, which might be
somewhat useful, or
  b) Does it go into random far-away side lobes, which are useless for
lighthouses and for every other purpose I can imagine?

I suspect (b).

> For a plastic lens this means it can be formed from sheet stock.

If the plastic is good enough to implement micron-scale figuring _within_ a
given ring, is it not good enough to implement micron-scale control over
the step height?