Poll on *Really* Wide Angle Lenses

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

  1. BC

    BC Guest

    Let me know if you need me to re-send. Its only a 300k document, so
    I'm surprised you've had difficulty downloading it.

    Brian
     
    BC, Aug 21, 2005
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  2. 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
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  3. BC

    David Harmon Guest

    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. BC

    kashe Guest

    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. 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. BC

    Nostrobino Guest

    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
    head.

    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. BC

    Nostrobino Guest

    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. BC

    Nostrobino Guest

    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. BC

    Nostrobino Guest

    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. BC

    Brian Baird Guest

    I tried moved Alpha Centauri A back but it burns!
     
    Brian Baird, Aug 21, 2005
  11. BC

    Nostrobino Guest

    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. 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.

    However, this is not found in high school geometry books, so
    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. BC

    Nostrobino Guest

    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. 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. 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. BC

    ASAAR Guest

    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
    about your construction. Take the first great circle on earth.
    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. BC

    Prometheus Guest

    How can two points( . . ) be parallel? They change from diverging to
    converging with the function going through infinity.
     
    Prometheus, Aug 22, 2005
  18. 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. BC

    ASAAR Guest

    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. BC

    Nostrobino Guest

    <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
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