# Poll on *Really* Wide Angle Lenses

Discussion in 'Digital Photography' started by BC, Aug 5, 2005.

1. ### BCGuest

Let me know if you need me to re-send. Its only a 300k document, so

Brian

BC, Aug 21, 2005

2. ### David LittlewoodGuest

You still haven't explained why you don't have to quadruple the exposure
for a wall if you move twice as far from it.

David

David Littlewood, Aug 21, 2005

3. ### David HarmonGuest

On Sun, 21 Aug 2005 18:45:52 +0100 in rec.photo.digital, David
Because you are receiving light reflected from four times as much wall
area.

David Harmon, Aug 21, 2005
4. ### kasheGuest

Aren't the various curves plane figures? If so, the planes can
be considered to be parallel if the separation between them is
constant at all points. This could still apply if the actual curve on
each plane was oriented in a different direction (i.e. rotated within
its plane.

If so, it would be just a special case when two curves in
separate, parallel planes happened to be congruent and oriented so as
to have uniform separation at all points.

kashe, Aug 21, 2005
5. ### David LittlewoodGuest

This is true, for an overall luminance measurement such as that obtained
from an extended light source by a reflected light meter (as long as the
source fills the meter's FoV). But for the image on a photo, each square
mm, or even square micron, is still correctly exposed and shows the
corresponding little bit of wall. The light from other bits of wall does
not contribute to the image of the little bit in question (unless it's a
^very^ fuzzy image!).

The answer is, of course, that the loss from each point on the object
due to inverse square law geometry is cancelled out by the reduction in
the area of the image formed as you move away. Thus the illuminance of
the corresponding area of sensor (and also the corresponding cone of
solid angle at the front of the lens) remains constant.

For a point source, this does not apply, since by definition the angular
projection of the object is too small to be resolved, and the size of
the image is fixed by the Airey Disc calculation (which effectively
means, for example, that all star images are the same size on film or
sensor, except for the effects of halation). Thus, moving further away
does actually reduce the illuminance of the image area by the inverse
square law. If you could move a star to twice its distance the image
would indeed be 1/4 as bright as predicted by the inverse square law.
(Let me know if you try this and it doesn't work.)

David

David Littlewood, Aug 21, 2005
6. ### NostrobinoGuest

BTW, David, my original choice of words was probably not the best. When I
wrote:
"You are trying to apply some special definition which just does not fit the
general case. Lines of latitude have been called parallels for centuries,
still are today and I'll bet they always will be. If your wife were a
navigator instead of a mathematician I'm sure she would understand this
better."
--I did not mean to suggest that your wife's understanding was deficient,
certainly not within her own sphere of expertise. I should have said "would
understand this differently" rather than ". . . better." I apologize if any
misunderstanding resulted from my carelessness in language.

I have to tell you I just don't have the foggiest notion of what "Rieman
2-space" means. It's been years since I studied any flavor of geometry, and
that term I don't recall ever having seen prior to this thread.

I never even heard or saw the term "2-space" before a few days ago. I gather
it refers to the treating of a sphere's three-dimensional surface as though
it were two-dimensional, for purposes of geometric calculation.

It does all sound very interesting, but at present leaves me scratching my

Can you refresh my memory: why were we doing that? I don't really have any
opinion, or anything to say, about "the projection of straight lines on a a
spherical surface in 2-space." Is this in connection with the image formed
on the retina? Because my opinion about that has been, and remains, that the
exact form or nature of the retinal image is of little if any importance
beyond the fact that it is the source of signals along the optic nerve that
the brain sorts out to create visual perception. All the retinal image has
to be is some form that the brain can make use of in that way, in other
words. I presume that the image of a square, say, must be at least somewhat
square-like on the retina, but I doubt that it has to follow any rules of
spherical geometry.

The same dictionary also gives a definition I know you will like better:
2.a. "Designating two or more straight coplanar lines that do not
intersect." On the other hand, of course, that is Euclidean and violates the
"Rieman 2-space" rule you appear to be endorsing above. Ergo, when you speak
of "a term rigorously defined in science" in this connection it's a term
that you yourself are using in at least two mutually exclusive ways.

N.

Nostrobino, Aug 21, 2005
7. ### NostrobinoGuest

The planes would be, but the curves would not, in that case.

In that case the curves would be parallel, sure. As long as the separation
between homologous parts of the curves remains the same, they are parallel,
it seems to me. But this does raise another question: What if the curves
remain equally spaced but are not on the same or parallel planes? For
example, the strands of the DNA helix diagrammed in the usual way. The
curves remain equidistant, but twisted. Are they still parallel? I think
they are, but it's quite a departure from the way we usually think of
"parallel."

N.

Nostrobino, Aug 21, 2005
8. ### NostrobinoGuest

Just got it, finally. Probably the difficulty was because it's Sunday and
there's a lot of traffic.

Thanks again!

N.

Nostrobino, Aug 21, 2005
9. ### NostrobinoGuest

Easy one, I think.

If I'm twice as far from the wall, I *am* getting only one-fourth the
photons from each point, but I'm getting them from four times as many
points.

N.

Nostrobino, Aug 21, 2005
10. ### Brian BairdGuest

I tried moved Alpha Centauri A back but it burns!

Brian Baird, Aug 21, 2005
11. ### NostrobinoGuest

Reduced to 1/4 the area on the negative (in the example). So you have 1/4
the illumination condensed to 1/4 the area, = no change in overall
illumination.

Doesn't need to.

Isn't that essentially the same thing he said? (And I said?)

N.

Nostrobino, Aug 21, 2005
12. ### David LittlewoodGuest

No problem - I did not take it as a personal attack. However, I still
assert that mathematics is the right tool for discussing geometry.
"2-space" simply means 2 dimensions. Rigorously. You are not allowed to
even imagine that there is a third. However, there is no reason to think
that, for a hyper-dimensional being, he would see our restricted world
as a plane. It could be a sphere, or some other surface. The important
thing is that we, the earthlings, don't even imagine the "other"
dimensions. It should be quite easy for us earthlings, as until flight
(and ignoring miners and mountaineers) we were mostly constrained thus.
Well, you got it about right. A straight line is the shortest distance
between two points, which, on a spherical 2-space, even navigators
(ahem, sorry) acknowledge means a great circle. Any other route
(including a line of latitude other than the equator) is a curve.
I thought (and I accept it got so confusing I may be wrong) we were
talking about rectilinear projection. If a sensor is a spherical
surface, and ignoring brain or other processor algorithms, then only a
great circle line on that sphere will be recognised as "straight";
anything else will record as a curve. I've almost forgotten why this
mattered though...
Classical (Euclidean) geometry is based on a series of postulates by
Euclid (Greek philosopher ca. 300BC). They are not something which can
be proved, they just have to be assumed. The final one was "parallel
lines continue to infinity and never meet, but continue to be the same
distance apart". Rieman and Lobachevsky (19thC German and Russian
respectively IIRC) each postulated an alternative: (a) parallel lines
always meet eventually, and (b) parallel lines continuously diverge.
Perfectly credible geometries result, and the former happens to coincide
with what we experience here on earth: a straight line is a great
circle, step a few feet away and generate another great circle in the
same direction, produce them and they will meet half way round the
earth. Straight lines, parallel, inevitable meet.

lexicographers can be forgiven for not knowing it. I'm sure you have
experience yourself of general dictionaries being completely in the dark
for higher technical matters.

BTW, I guess a more general definition of parallel would be "two or more
straight lines for which a line perpendicular to one of the lines at any
point is also a perpendicular to the other(s). I must ask my wife if she
agrees, but we just shared a bottle of wine with dinner and I'm not sure
how receptive she would be!

David

David Littlewood, Aug 21, 2005
13. ### NostrobinoGuest

I called the local towing company but they charge by the mile, and the cost
would have been literally, well, uh, astronomical.

N.

Nostrobino, Aug 21, 2005
14. ### David LittlewoodGuest

Not what he said - he was using light from the whole wall to generate
exposure at any point (if I understood correctly) which would make for a
rather low contrast picture.

David

David Littlewood, Aug 21, 2005
15. ### David Dyer-BennetGuest

At least in theory, yes. I've got lenses out to 17mm for my 35mm now;
there's *some* evidence that the 17mm was out towards the wide end of
what I seem to make good use of. But pushing somewhat past that is
the only way to know for sure . (I got a 24mm to push myself a
bit, and then a 20mm, and now a 17mm -- which also gets a LOT of use
on a 1.5x crop factor digital, as being an actual wideangle lens!)

(Theory vs. practice includes what money I have at any given moment
for that kind of not-guaranteed payoff, either artistic or commercial,
expense.)

David Dyer-Bennet, Aug 22, 2005
16. ### ASAARGuest

I don't know if he deserves the credit or if he deserves the
blame, but as anyone with more than a passing familiarity with
Harvard (or a certain Mr. Lehrer) knows, Nikolai Ivanovich
Lobachevsky was his name.

I've never studied that geometry but something doesn't seem right
Another similar great circle can be produced on the moon such that
it is completely parallel to the great circle on the earth. But the
two great circles you've described on earth are parallel at only two
points, which occur midway between where they intersect. So if
these are considered to be parallel curves in Rieman 2-space, does
that geometry recognize different degrees of parallelism? The two
great circles described above (one on earth, one on the moon) would
seem to be infinitely more parallel. Somewhat like the parallel
circles produced by the contraptions that slice hard boiled eggs
into a stack of little disks.

That makes sense to me, but it also seems to describe my two
"parallel" great circles, not yours!

ASAAR, Aug 22, 2005
17. ### PrometheusGuest

How can two points( . . ) be parallel? They change from diverging to
converging with the function going through infinity.

Prometheus, Aug 22, 2005
18. ### David J. LittleboyGuest

I've lost the context here.

Are you guys talking about an extreme wide angle _rectilinear_ lens imaging
a wall with the wall, lens, and film all parallel to each other?

David J. Littleboy
Tokyo, Japan

David J. Littleboy, Aug 22, 2005
19. ### ASAARGuest

Consider a steel wheel on a steel railroad track. The part of the
wheel in contact with the rail is parallel to it. An ideal
mathematical representation would be in contact in an
infinitesimally small, uh, point. Any other point on the wheel
(save for the point 180 degress away) would not be parallel with
the track. True, points are points and have no directions, but math
(calculus) deals with that quite effectively with its vanishingly
small epsilons and deltas.

ASAAR, Aug 22, 2005
20. ### NostrobinoGuest

<guffaw!>
Doesn't *that* take me back! I still have the LP, Tom Lehrer's first I
believe, a 10-incher! One of only two 10-inch LPs I ever owned.
Unfortunately I don't think it's as flat as it used to be.

N.

Nostrobino, Aug 22, 2005