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Re: Pinhole camera





On Fri, 27 Jun 1997, roger haar wrote:


Hi,

Several of us have been discussing the pinhole camera. We
disagreed on using the terms "image" and "focus" in conjuction with
pinhole optics. I claim a pinhole does not focus and thus there is no
image in the sense of an image formed by a system of lenses. My point is
that one should be able to treat the image formed by one optic system as
the object of another system, and that the formation of an image should
not depend of a viewing screen.

Ah, yes, another example of a technical term which is not carefully
defined in textbooks, yet freely used *as if* everyone understood it.

Students often *are* confused when shown a real image cast on a screen
from a lens. Take away the screen and ask students whether the image is
still there. I prefer to say that it is still there, independent on the
presence of the viewing screen, but I admit that textbooks are not helpful
on this point.

I suspect that this is one of those slippery points and I am being
a bit picky, but I looked at a few text and did not find an optical
image defined other than if an object is in plane x and an optical
sytem is at point y with optical characteristics q than the the image is
at z.

Advanced optics text refer to the mapping from the image space to
the object space and imply a one-to-one mapping. A pinhole camera is a
many-point-to-many-point mapping and is either some extreme limiting case
of the acceptable mapping or it just does not form an image.

To clarify (or muddy the waters) note that even in the case of the
lens-formed image, only in the ideal-lens case is the mapping one-to-one.
Aberrations ensure that a point object maps not to a point image, but a
"region" which, on a flat surface, is within a "circle of confusion". From
a practical view, is this not similar to the small circle produced by the
pinhole camera? The pinhole camera produces a "diffuse" mapping onto
whatever plane you want. A lens gives a diffuse mapping of similar
character onto planes at different positions, only one position gives
better-defined images than the others.

Or, on another level, can a pinhole camera be thought of as a lens of
infinite focal length stopped down to a very small aperture? :-)

Can the fuzzy-detailed picture on the surface of a cathode-ray screen be
properly called an "image"?

How about the image formed without lenses by a coherent fiber optic
bundle?

An anamorphic lens produces a stretched or distorted version of the
source? Should this be called an image? One aspect of information
(lengths) from the source is *not* rendered one-to-one.

Does the image formed by a single lens even deserve to be called a
one-to-one mapping? After all it loses 3-D depth information. A hologram
does depth, but has limitations of resolution, and other problems that
lens images do not.

So, as in so many other cases, the term "image" can have a broad meaning,
to describing mappings which preserve spatial arrays of distributed light
sources, at least preserving enough information to give a recognizable
reproduction of the source. Some distortion is allowed; some loss of
information is allowed. And it can have more specific uses, as in "optical
image", "holographic image", "cognitive image". Call it a "diffuse
mapping" if you like. But is there ever a "sharp" mapping, except in the
idealized realm of mathematics?

Does not a pinhole camera produce such a diffuse mapping, in any viewing
plane you choose?

By the way, I can't understand why I am having so much difficulty getting
funding for my proposal of an anamorphic pinhole camera. I had the same
problem getting support for my researches to find a transparent solid or
liquid substance whose index of refraction was exactly 1 for all
wavelengths. I thought I had succeeded in making some once, but I lost the
sample in the lab and can't find it. [Good "conceptual question" for
students. Ask them to discuss these two research proposals, including the
physics as well as the possible applications of the proposals for optical
instruments. Example: would the unit-index transparent solid material be
a useful improvement over ordinary glass for auto windshields, lenses,
spectrometer prisms, wine glasses, etc. Would any physical law or theory
suggest the possibility of such material? Would any physical law or
theory suggest the impossibility of such material?]

The image formed by a lens is sometimes called an "optical image" to
distinguish it from others and indicate that this is a more limited use of
the word "image".

-- Donald

......................................................................
Dr. Donald E. Simanek Office: 717-893-2079
Prof. of Physics Internet: dsimanek@eagle.lhup.edu
Lock Haven University, Lock Haven, PA. 17745 CIS: 73147,2166
Home page: http://www.lhup.edu/~dsimanek FAX: 717-893-2047
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