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1, The shape factor is S = (r2
+ r1)/(r2 - r1)
(Jenkins & White) [S zero is a symmetrical double convex]
ALSA (Longitudinal spherical aberration) for object @ "infinity" is
: {S , ALSA} -2 , -1.0; -1 , -0.45;
-0.5 , -0.25; 0.0 , -0.18; +0.5 , -0.1; +1
, -0.12 ; +2 , -0.3 (from Nussbaum & Phillips '76 pp. 44-48)
HUGE DIFF. as LP points out. The inexpensive? way to obtain
low aberrations it to stack meniscus lenses with the proper S. Altering
the shape of a lens while holding other props. constant is know
as bending the lens.
2, One can, until recently, buy those TV lenses at thrift stores
-- I remember seeing one, long ago, on display at a retailer.
3, don't go out into the sun w/o your sun block or adequate clothing and a hat -- now that we're past the equin. Sunny days near zenith are melanoma days. My Dermatologist suggests < two hours of noon ("Sun time")
4, I suppose centrifugal or vacuum casting would get rid of bubbles, but I thought optical glass required stirring.
5, I consulted for several IOL companies during the '70/'80's both injection molded and ground from PMMA sheet mfg. We rejected lenses for optical quality using an Air Force target while checking their refractive power. Subjectively we found that the quality didn't have to be very good. Under 30X, bubbles and scratches would reject for cosmetic reason. What was very important was that the label had to reflect the power w/in ~ 1/2 D. Defocusing is much more important than lens quality -- (finding from someone who's done MTF measurements)
6. Even if only a small part of a lens is used, I find it quite
distracting if either there are defects or changes in power over a lens,
because I also scan using my eves in addition to moving my head.
If people only used their heads, glasses would be very small! Also
for short working distance, reading and watch repair, is not a larger region
of a lens used? BTW I always specify glass (at no extra cost) from
my optometrist.
7, Adaptive focussing? Probably not very necessary, otherwise we would have evolved it. I suspect that insects may have it, because they have multiple eyes. I always laugh at the science programs where they show (claim) that insects see multiple images because they have many eyes! We, and I'm sure the insects, fuse them into one image! Now the question is, why do insects have multiple eyes -- they do spend much time using a short working distance. What whoever, must be referring to the brain's ability to adapt; this is true for all of our senses.
8, an advantage of a "crummy" lens is that it imperfectly collimates when one doesn't want or need narrowly directed light. An example of a similar use (to auto lenses) is traffic signal arrows where one instead wants good collimation. They're invisible 'till one has driven into the appropriate lane -- Since they're of small size (4'?) they can inexpensively be of glass projection lens quality.
9, About what defects do: try comparing shaking pepper on a lens (projection photographic enlarger) and smearing grease. Immediately one understands why bubbles and scratches are only of cosmetic importance (they do reduce the "f") while figuring is relatively very important.
bc
Leigh Palmer wrote:
>I'm beginning to think there are two types of critter that go by the name
>Fresnel.
>
>*) In the lighthouses I've seen, the goal is evidently collimation not
>imaging, and the Fresnel has only about N=10 segments. The difference
>between something that scales like N and something that scales like sqrt(N)
>won't be completely overwhelming. Unphased rings must be OK in this case.
>
>*) OTOH there are Fresnels that have _thousands_ of rings and produce
>images, not just collimation. I don't see how unphased rings could
>possibly work in this case.You can produce an image with a condenser lens from a slide projector.
They are cast and are certainly not ground to optical tolerances.
Even a crummy Fresnel lens will produce an image of sorts, the crummier
the lens, the crummier the image. No great attention is paid to grinding
or polishing these things. The lighthouse lenses I have seen are usually
beautiful objects. They should produce rudimentary images as well, but I
have never had one in such a position that I could play with it in that
way. (I would have done so had it been possible.)>At 09:26 AM 4/15/00 -0700, Leigh Palmer wrote:
>
>>Lenses for application to collimation, as is
>>the case with most Fresnel lenses, are frequently cast instead of
>>being ground.
>
>1) I realize that collimation is not the same as imaging. For applications
>such as stage lighting, the task is to throw a lot of energy in the right
>general direction. Sharp focusing would be not only be an unnecessary
>complication, it would be counterproductive.
>
>OTOH I'm still confused about several other applications.
> 1a) 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.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.> 1b) 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.Perhaps it would be noticed over a smaller solid angle, however. I
have yet to see a hard-to-notice lighthouse, so it doesn't seem to
be a problem.> 1c) For burning-glass applications, one often wants the highest possible
>peak temperature, which calls for sharp focusing.No. Aperture ratio is the critical parameter in burning glass
function, not sharpness of focus. The larger the aperture (and the
smaller the numerical aperture) the greater the image temperature
attainable. If the target can conduct the heat away too rapidly
then that may also constitute o problem.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, but the superimposed images of the Sun are certainly
mutually coherent.>2) The cast-versus-ground argument is very weak. For years it has been
>possible to cast optically-perfect surfaces. Many eyeglass lenses are
>cast, and there are other important technological applications for
>precision casting.Take a good look at different cast Fresnel lenses. You will see
a lrge number with macroscopically identifiable nonidealities. As
for eyglass lenses, I don't believe they are "optically-perfect"
in any sense, and they have ground surfaces. In forming an image
with spectacles one only uses a piece of the lens which is about
the same size as the pupil. It is pretty easy to maintain the
required tolerance over that lateral extent. Surely bifocals must
suggest that the whole lens is not used.>>Any old piece of lumpy glass with a smooth surface (a cast drinking
>>glass, for example) ... After all, one can still see an image through a
>>cast drinking glass, though a distorted one.
>
>An excellent point. But I wonder how much of that has to do with the
>adaptive focusing powers of the eye? When I try to use a lumpy drinking
>glass to form a recognizable image on a passive image-plane (like an index
>card), it doesn't work very well.Now you are getting the point.
>> >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).
>>
>>As I have already explained, a) is a pretty good answer.
>
>Yes, (a) is the right answer. I missed that. That answers the physics
>puzzle that was bothering me.
>
>To see this in more detail, let's build up a Fresnel, ring by ring. Start
>with the light that comes from the central "bullseye" section of the
>lens. It focuses to form an Airy disk, which we will call disk #1. The
>contributions of the next ring, if added in ideal phase, will contribute
>strongly constructively to the middle of disk #1, contribute strongly
>destructively to the outer parts of disk #1, and contribute _weakly_
>everywhere else. Ideally this produces a smaller Airy disk, disk #2. If
>we add in the second ring with non-ideal phase, all the strong
>contributions are still within disk #1, but they might well produce a donut
>shape rather than any small disk. Additional rings will randomly dump
>energy into this general area. They won't sharpen the image nearly as much
>as they would in an ideal lens, but they won't broaden it beyond disk #1,
>and the energy will go up as we add more rings.
>
>> >>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?
>>
>>Well, that is a question you can think about if you know something
>>about creep or thermal expansion, or if you have ever seen a
>>Fresnel lens made of a flexible sheet material that, because it is
>>nonrigid, can't possibly be held to micron tolerances across its
>>lateral extent.
>
>I have thought about it, and the bending argument seems very weak. To
>first order, simply bending a lens doesn't change the amount of material
>(hence the amount of phase shift) that a given ray sees. As a well known
>example, putting a thin plano-convex lens in backwards makes very little
>difference.What?! It sure makes a difference in image quality on the
interference pattern scale. The spherical aberration will
likely change drastically when an asymmetrical lens is put into
an optical train backwards.What's this "to first order" business? If we are talking
about high resolution imaging we must at least consider the
standard third order aberrations, in this case spherical
aberration. If one considers off-axis aberrations thigs get
even worse.>Consider this:
> L
> LL
> LLL
> LLL
> LLL
> LL
> L
>
>which, if bent quite a bit, becomes this:
>
> L
> LL
> LLL
> LLL
> LLL
> LL
> LAnd if one considers the optical path length between object and
image this makes a difference which is appreciable. Consider the
central ray for an on-axis object and image. The two lenses have
exactly the same optical path lengths. Now consider a ray which
is inclined at an angle with respect to the axis. In the first
abd second cases the amount of refraction at the first surface
is different, and the subsequent distance the ray travels through
the lens will be different, and the point at which this ray
intersects the axis in the object space is dependent on on the
initial angle. A numerical example is called for, and perhaps you
will be good enough to construct one for us (I can't find my own
example).It turns out that a good rule of thumb for minimizing spherical
aberration in single thin lens imaging is to design the lens so
that about half the bending of the rays is done at each surface
of the lens. Thus when imaging a distant object (to the left) on
a nearby focal plane (to the right), the lower lens orientation
in the diagram above will produce less spherical aberration than
the upper orientation. In the upper orientation almost no bending
is done at the first surface.I once set the power pole in front of my house on fire with an
old TV Fresnel lens. I managed to blow it out, but that gave me
a tremendous respect for the idea of a solar furnace. The Fresnel
lens on an overhead projector is a good example of a collimator
you can show your students. Just place a sheet of white paper on
the projector and then raise it to the projector lens. The light
will intensify nicely as you go up.Whenever I teach a course in which there is an optical part I ask
my students if they have ever performed the burning glass tricks.
Astonishingly in every class where I've asked, there has been at
least one student who had never done it. Of course I did not let
that cultural deficiency persist. Childhood activities have
certainly changed over an amazingly short period.Does anyone else remember the mineral oil filled Plexiglas lenses
that we used to put in front of our four-inch television screens?I'm feeling particularly elderly this morning. I'd better get out
into that sunshine!73,
Leigh