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Pinhole Optics: Musing Upon...

Date: Fri, 27 Jun 1997 19:13:47 -0700 (PDT)
From: William Beaty 
Subject: 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.)

Also see:

EXPLORATORIUM: Bob Miller's "Light Walk"

> 	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".

fig. 1

       \                    /
         \                /
           \            /
            _\|       /

     _________        _______
     HHHHHHHH||      ||HHHHHHH

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.") If the extra light overloads the sensor, a neutral density filter might be required.

fig. 2

       \                    /
         \                /
           \            /
            _\|       /

     ____________   __________
     HHHHHHHH||      ||HHHHHHH

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 below is the result.

fig. 3

        \                     /
          \                 /
            \             /
             _\|        /
     HHHHHHHH||       ||HHHHHHH

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 any tiny misalignments of the lens/retina distance, or tiny aspheric shape in the retina or lens both result in total blurriness of the perceived image.

This applies to the fight over lens-image versus pinhole-image. 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!

fig. 4

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

        |  |-
        |  | -
        |  |  -         Reduce the pinhole effects by increasing the
        |  |   -        dimeter of the lens, and the "image" becomes
        |  |    -       blurred except at a very small region at
        |  |   -        the focal plane.
        |  |  -
        |  | -
        |  |-

        |  |     -
        |  |     -
        |  |     -
        |  |     -      An infinite lens has no pinhole at all.
        |  |     -      It also has a focal length but no image.
        |  |     -
        |  |     -
        |  |     -
        |  |     -
        |  |     -
        |  |     -
        |  |     -


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 photograph. Do real or virtual images exist at all *except* when one 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 small 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 at the correct distance 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". The shadow is a projected image of the light source, not an image of the opaque object. And the complex shape of the shadow? That's just a strange form of blurriness caused by using too big a pinhole! (An inverse pinhole camera is a transparent plate with a tiny opaque spot, which produces dark images on a bright background).

When a pinhole camera is used to make a photograph, the resulting film contains a shadow of the front of the camera. What does this mean? 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. Bright spots in the scene (e.g. christmas lights at night) produce sharp shadows of the pinhole, and if the pinhole is square, the christmas lights will be recorded and little squares.

When shadows have fuzzy edges, the "fuzz" is actually a projected image of the illuminating source. If the illuminator is a point source such as a welder's arc or a very tiny light bulb, the shadow will be almost perfectly sharp. If the illuminator has a complex shape, then the fuzzy shadow edge will have complex features.

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.

Another: stand under a fluorescent tube on the ceiling. Hold a pencil or ruler out so that it's shadow is cast on the floor. Slowly rotate your object until it aligns with the fluorescent tube, and you'll find that it's shadow suddenly becomes sharp. (As a magic trick, you can claim that your "special" object has a magnetic shadow which points North!)

>  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 wave-type image into the particle type, and a lens system can transform the particle-image into the waves.
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