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Re: Pinhole camera



On Fri, 27 Jun 1997, roger haar wrote:

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.

This is one of those fascinating places where decades of physics teaching
have failed to illuminate a grey area. ;)

(I apologize for non-brevity. An emergency at work has resulted in lack
of sleep and lots of coffee, and opened my floodgates.)

I suspect that this is one of those slippery points and I am being
a bit picky

Not at all. I suspect that the lack of detailed treatment of exactly this
point has seriously hobbled our understanding of optics at the intuitive
level. One might say that we suffer from unsuspected universal blindness
regarding what is meant by "image". Extensive intuitive treatment of
pinhole physics is missing from our education, and optical concepts suffer
as a result. See the Exploratorium's material on "Image Walk" for more on
these concepts.

Years ago I attempted to design an explanation of simple optics at the 5th
grade (general public) level using a set of cartoons, and I immediately
ran into Roger's above problem. If we build a visual/intuitive concept of
the operation of common optical devices (cameras, etc.), we immediately
discover that real-world optical devices are a mingled combination of
pinhole optics and lens optics.

For example, take the evolution of the eye. If a creature has a photo-
sensitive skin patch, it can detect the motion of shadows which fall
across the skin, but it cannot sense from what direction the light comes.
But if that skin patch is sunken into a slight concavity, the creature
gains the ability to "see". The perceived image is stunningly blurry, yet
every point in the external scene is mapped as a different large blotch on
the photosensitive area. The boundary of the concavity acts as a pinhole,
and the skin patch acts as the screen. This can be simulated with a CCD
camera and a portable video monitor by removing the lens entirly so that
the CCD element is exposed. Try it, you'll find that you can navigate a
room using this camera, you can "see" colored walls, large moving
objects, etc. The recessed CCD array constitutes a pinhole camera (with
very large pinhole and very blurry "images.") A neutral density filter
might be required.

If the creature eye's concavity is made progressively deeper, the
"sharpness" of the perceived image improves, until we arrive at the sharp
(yet very dim) image made by a pinhole camera. If we now install a crude
lens over the pinhole aperture, and enlarge the pinhole diameter a bit,
the image projected on the retina remains sharp, yet it becomes much less
dim. Modern eye is the result. Think we've eliminated the pinhole?
Think again! If we enlarge the aperature too much, we lose the image to
increasing blurriness because the depth of field becomes too small, and
tiny misalignment of the lens/retina distance, and tiny aspheric shape in
the retina and lens both result in total blurriness of the perceived
image.

This applies to the lens-image versus pinhole-image fight. In a
real-world instrument, one could say that a pinhole image is not really an
image because it lacks a focus location. But conversely, one could say
that a lens-image is not really an image because, if the lens has no
"pinhole" character, if the lens has infinite diameter, then the depth of
field is therefor infinitely small, and a real-world film or retina cannot
receive any image from such a lens!


------/\--__
| | --__
| | --__ A real camera is both a lens and
| | __-- a pinhole.
| | __--
------\/--



------/\-
| |-
| | -
| | - Remove the pinhole by making the D/F ratio
| | - infinite, and the "image" is infinitely
| | - blurred except at a uselessly infinitesimal
| | - region at the focal plane.
| | -
| | -
| |-
------\/-



Troublesome thought: If the "ariel" real image behind a convex lens is
viewed with a *pinhole* camera rather than with an eye, the pinhole camera
records it. But if the same image is viewed with a theoretical camera
having infinite lens diameter, the camera records only a blur. It seems
that an aperature (a pinhole) is needed if one wants to perceive a real
image or virtual image, or if one wants to record a 2-D pattern. Do real
or virtual images exist at all *except* when part of an optical system
contains a camera? When no one is looking, do virtual/real images exist?

Another troublesome thought: if "image" is defined as involving lenses,
never pinholes, then we are forced to conclude that cameras cannot
photograph "images". This is because there is always a finite amount of
blur in the resulting photograph, and a "blurred image" is no "image" at
all, it is intimately connected with the pinhole-character of the optical
system. If the camera film is not at the focal plane, if the photographed
scene has depth, or if the lens has spherical aberration, then the
recorded pattern of light is a "pinhole pattern" akin to a shadow, and is
not a "real image".

Place a diffusing screen behind a lens, and focus a complex scene on the
screen. What happens when the lens/screen distance is altered? Most
people would observe that "the image becomes fuzzy." But if we insist
that "image" can only mean "real image" or "virtual image", then when the
screen is moved we are instead forced to say "the image vanishes, and is
replaced with a 'pinhole pattern' ".

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.

The best term I have is "optical projection".

I call it "projected image". As opposed to "real image" and "virtual
image".

If a diffuser screen (or film) is installed behind a convex lens, then the
recorded pattern is *almost* the same as the real image. But it is
actually composed of little blur-disks (like the round shadows of the
pinhole in a pinhole camera), and is not a real-image. A real-image is
composed of points, not disks. If a photograph is examined carefully, we
find that the recorded pattern is always composed of little hexagons (or
whatever shape the camera iris has.)


Similarly is a shadow an image?

I'd say yes. A shadow is simply a projected image of a small light
source, using an inverse pinhole camera which employs a complex shape of
inverse pinhole. The object which generates the shadow is the "pinhole".
(an inverse pinhole camera is a transparent plate with a tiny opaque
spot).

When a pinhole camera is used to make a photograph, the resulting film
contains a shadow of the front of the camera. The front of the camera is
an opaque plate containing a hole. If the camera is used to photograph a
pointsource illuminator, the film records the shadow of the pinhole. If
the camera is used to record a scene, the resulting image is actually just
a very complicated shadow of the pinhole.

When shadows have fuzzy edges, the "fuzz" contains a projected image of
the illuminating source.

Suggested demonstration: build a large wall-mounted spinning disk having a
3ft. fluorescent tube fixture mounted upon it. Provide slip rings for
power. Light the tube and spin the disk. All the shadows in the room
will exhibit dark rotating arms. The shadow of a falling ball will appear
as a dark rotating stripe.


How about a diffraction pattern?
And rainbows?

Hmmm, this suggests an additional physicist's definition of "image."
Suppose we say there are two sorts of images: those containing phase
information (such as real images and virtual images) and those containing
only spatial information (such as shadows, photographs, projected movies,
etc.) These correspond to simple QM of electromagnetism. The first is
probability function, the second is collapsed. The first is a wave
pattern, the second a particle pattern. The second is a photograph, the
first a hologram. A piece of film or a diffusing screen can transform the
first type into the second type, and a lens system can transform the
second into the first.



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