THE STAGGERING VARIETY OF SOPHISTICATED cameras now on
the market obscures the fact that quite acceptable photographs can be
made with nothing more than a pinhole between the film and the object
being photographed. The same is true with the optical complement of a
pinhole: a "pinspeck," which is a small, circular spot placed between
the film and the object. In discussing pinhole photography I shall be
following the work of Kenneth A. Connors of the University of
Wisconsin at Madison and Matt Young of the National Bureau of
Standards. The novel idea of pinspeck photography comes from Adam
Lloyd Cohen of Loyola University in Chicago.
Figure 1: A photograph made with pinhole optics by
Kenneth A. Connors
Pinhole photography relies on the passage of light
through a small hole in an opaque screen. The light falls on a piece
of film to construct an image of the object being photographed. Images
from pinholes were mentioned by Aristotle, explained in principle by
Leonardo da Vinci and analyzed formally by Lord Rayleigh. Simplicity
is only one of the advantages the pinhole camera offers over a camera
with a lens.
The optimum radius for the pinhole is related to the
distance between the hole and the film. The relation can be shown by a
theoretical argument that depicts light as being in wave form. Imagine
that the pinhole and the screen have been removed. A light wave from a
point source travels through the plane formerly occupied by the
In reality, however, the amplitudes are not equal, as is
shown in descriptions more precise than those I can supply here, so
that the cancellation is only partial. The net amplitude of the light
wave at the center point turns out to be half the amplitude the
central zone would have contributed on its own. Because the brightness
of the light is related to the square of the amplitude this result
means that the brightness at the center point is a fourth of what it
would be if only the central zone were contributing light.
One of the purposes of a pinhole is to block all the
zones except the central one. (Some investigators say it blocks all
but the first two zones.) A pinhole of optimum size allows only the
central zone to send light to the center point on the film. With a
pinhole of that size the spot of light at the center point will be
bright and small with a good distribution of light. If the pinhole is
smaller than this optimum size, only part of the central zone
contributes light at the film. The spot of light is dimmer and the
distribution of light is poorer. If the pinhole is too large, the
additional zones in it decrease the brightness of the spot and
increase its size.
From this relation a focal length for the pinhole can be
defined. The pinhole acts as a lens in the sense that it concentrates
an image of an object. The focal length is approximately the
wavelength of the light divided into the square of the radius of the
pinhole. The spot of light on the film is small and bright, with good
distribution of light, when the film is distant from the pinhole by
the focal length. Then only the central zone fill the pinhole and
contributes light to the center point.
Suppose the object is close. If you photographed it
through a lens, you could calculate the proper distance between the
lens and the film by applying what is called the thin-lens equation
which states that the inverse of the distance between the lens and the
film should be equal to the inverse of the lens's focal length minus
the inverse of the distance to the object. The same relation holds for
a pinhole if the focal length is defined in the way I have described.
Thus a pinhole camera can be focused in order to make a photograph
with the best resolution.
For example, if the object is far away, the best
position for the film is at the focal length of the pinhole. If you
walk toward the object and thereby decrease the distance between it
and the pinhole, you must increase the distance between the film and
the pinhole in order to maintain the optimum resolution. Such an
adjustment may not be very practical, since in a pinhole camera the
distance between the pinhole and the film is usually fixed. Instead
you could replace the pinhole with a smaller one so that the focal
length is smaller.
In practice neither adjustment is made because the
resolution in the photograph is usually acceptable even if the size of
the pinhole and the distance between the pinhole and the film are
suboptimal. If you photograph a scene in which objects are at a large
range of distances from the camera, most of them will be acceptably in
focus in the photograph. This large depth of field is a characteristic
of the pinhole camera.
From what I have said you could calculate either the
appropriate size for the pinhole or the distance between the pinhole
and the film once one of them has been picked. How do you make the
first choice? Practicality bears on the answer: you do not want a
pinhole camera that is several meters long. You also want to turn out
a finished photograph that has as much detail as you would see looking
directly at the scene. The desire for resolution is the starting point
in the initial choice of conditions for the camera.
The limit of resolution of your eye is measured in terms
of angle. Suppose your field of view encompasses two points. You can
distinguish them as long as the angle between them is larger than a
certain minimum value, approximately .001 radian. If the angle is
smaller, you see only a single, blurred object. For example, if two
adjacent points are separated by one millimeter and are one meter away
from you, they would be just at the limit of your ability to resolve
them. A camera with that degree of resolution would be sufficient;
improving its resolution would add nothing.
Figure 4: The zones contributing light to the center of
Once this choice has been made the optimum distance
between the pinhole and the film can be calculated (by the relation I
have already set out) to be 12.5 centimeters. If you made the pinhole
twice as large and adjusted the distance of the film from the hole
accordingly, the resolution of a photograph from the camera would be
twice as good. If the size of the photograph and the distance at which
you view it are unchanged, however, you would not be able to see the
improvement. Moreover, the camera would now be 50 centimeters long (in
order to have the proper distance between the pinhole and the film)
and larger film would be needed to capture all the light from the
pinhole. Clearly the improvement is not worthwhile.
When the pinhole is larger than it should be, the poorer
resolution can actually add erroneous detail to the photograph. This
effect, called spurious resolution, results from the overlap of the
images from several adjacent objects. Young's demonstration of the
spurious resolution of three vertical bars appears in the illustration
Figure 5: Three types of resolution
Most lens systems cause a linear distortion in an image
recorded on film. For example, a square object might appear to have
slightly curved sides. Most modern cameras incorporate corrections for
the problem. One of the advantages of a pinhole camera is that it is
virtually free of linear distortion.
The pinhole camera does have several types of
aberration, including chromatic aberration. Since the optimum radius
of the pinhole (and thus its focal length) depends on the wavelength
of light, the camera cannot be optimized for more than one wavelength.
The resolution for that wavelength can be optimized but the resolution
for the other wavelengths in white light will be poorer.
The result with color film is a blurring of the edges of
an image and perhaps some noticeable color along the edges. With
black-and-white film only the blurring of the edges is visible. One
way to eliminate the chromatic aberration is to use black-and-white
film with a color filter placed in front of the pinhole. Optimize the
size of the pinhole and the distance of the film from the pinhole for
the wavelength passed by the filter.
All other colors are eliminated and the edges of the
image are blurred less by chromatic aberration.
Another aberration with the pinhole camera is
astigmatism. It arises when an object being photographed lies off the
central axis of the pinhole. The shape of the pinhole perpendicular to
the object is elliptical rather than circular. If the object is a
point source of light, an elliptical spot is cast on the film. In
addition, the place on the film where the spot falls will not be at
the proper distance from the pinhole. If the center of the film is put
at the proper distance from the pinhole, any other point on the film
is too far from the hole, which means that the resolution is not
optimum anywhere but at the center.
Figure 6: Franke's setup for wide-angle pictures
For several reasons the intensity of the light cast on
the film is nonuniform. Suppose two point sources of light are being
photographed, one on the central axis and one off it. The light from
the off-axis point source encounters a pinhole that is effectively
elliptical. Therefore less light travels through the hole from the
off-axis source than from the point source on the axis. In addition
the light forming the off-axis spot must travel farther to reach the
film and so spreads more, thereby arriving at the a film with less
intensity. Moreover, this light reaches the film at an angle that
further spreads the exposure over more of the film, reducing the
intensity even more. These losses over the width of the film establish
a practical limit to the field of view.
Another solution to the problem was invented by John M.
Franke of the National Aeronautics and Space Administration's Langely
Research Center. Franke positions a glass hemisphere just behind the
pinhole of a camera in which the film is held in a normal flat plate.
As the light passes through the pinhole and into the glass it is
refracted. The full field of view, which occupies an angle of 180
degrees, is reduced to a cone of light occupying an angle of 84
degrees. When the light emerges from the glass, it is perpendicular to
the surface of the glass. Hence the angle of the cone of light is
unaltered. The reduction in the angle from 180 to 84 degrees enables
Franke to position the film at an appropriate distance from the
pinhole and still make a wide-angle photograph with a field of view of
approximately 180 degrees.
You can form a pinhole in several ways. Take care to
make a circular hole with smooth edges. Young has made clean pinholes
in brass shim stock 50 micrometers thick. He mounts a sewing needle in
a milling machine and then with the machine's vertical feed forces the
needle through the thin brass sheet. He puts a freshly smoothed lead
block under the brass to prevent distortion of the sheet. After
removing the burrs on the edge of the hole he reams it with a needle
point and cleans it again.
Connors uses brass shims .001 or.002 inch thick. Thicker
plates are undesirable because the hole is then more of a cylinder and
generates more internal reflection of the light rays. A square piece
of the shim is placed on firm cardboard or smooth soft wood. With a
needle point Connors gently pushes a dimple into the center of the
shim piece, being careful not to push the point entirely through. He
turns the piece over and rubs the small mound on the back of the
dimple with a fine emery cloth until it is removed. He repeats the
procedure, perhaps as many as 15 times, until a hole appears and gets
large enough for the shaft of the needle to go through it. He has
previously measured the diameter of the needle shaft with a microscope
that has a graduated reticle, and so he now knows how large the
pinhole is. If he wants a pinhole that is smaller than his smallest
needle, he stops the enlargement process before the needle fully
enters the hole.
Once the pinhole is complete Connors cements the shim to
a thicker brass sheet (.005 inch thick) for support. The pinhole lies
over a 1/4-inch hole drilled in the thicker piece. The side of the
assembly that is to face the film is painted with a flat black to
diminish any reflections of light inside the camera. Some people think
the interior of the pinhole should also be blackened, but Connors does
not want to degrade the symmetry of the hole he made, and so he paints
only to within a millimeter or two of it.
Connors notes that a pinhole should be kept free of
dust. He stores his pinhole assembly in a plastic bag until the
assembly is needed. Periodically he examines the pinhole with a
microscope to check for any degradation of the symmetry resulting from
Figure 8: Cohen's photographs by pinhole (left) and
pinspeck (right) of a P cut in paper
The assembly of the brass sheet and the shim can be
mounted on virtually any type of light-tight box. I have seen pinhole
cameras made with cereal boxes. Working in a darkroom, the
photographer mounts a piece of photographic paper at the back of the
box and slides on the lid. A piece of black tape is put over the
pinhole to prevent light from entering the box prematurely. When
everything is ready, the tape is pulled back from the hole for the
exposure and then put back over the hole. Although such a camera
functions as a pinhole camera, it has two disadvantages: only one
photograph can be made before the camera is returned to the darkroom,
and the removal and repositioning of the tape might shake the box too
much, blurring the photograph.
Whereas in pinhole photography light passes through a
hole to create an image, in Cohen's pinspeck photography a pinspeck
casts a negative image of an object. His setup is the optical
complement of the pinhole. The screen and hole are replaced with a
small obstacle of circular cross section. Now all the light that would
travel through a pinhole is blocked. All the light that would have
been blocked by the screen reaches the film, forming a negative image.
The final pinspeck photograph is similar to the pinhole photograph
except that bright and dark areas are exchanged.
Figure 9: A single bright ring photographed by Cohen
through a series of pinspecks
The image cast by Cohen's pinspeck does not depend on
the diffraction of light because the pinspeck is too large to give
rise to a significant diffraction pattern. The image is created by the
simple blocking of light rays from the object. Any particular spot on
the film records the shadow of a section of the object lying on a
straight line extending from the spot through the pinspeck and to the
The variation of light can be increased u if the
pinspeck is positioned closer to the film, but just as with pinhole
photography this arrangement decreases the resolution of the
photograph. Cohen says he does sacrifice some of the resolution to
achieve enough contrast in the photograph to create a recognizable
The coloring of pinspeck images can be strange. If a
small collection of colored objects is photographed, the image of each
object will probably be of a different color from that of the object.
The change depends on the combined colors of the objects in the
collection. If the combination is white, each color in the collection
is switched to its complement in the photograph. For example, a red
object will form an image in a color that is the subtraction of red
from white (be cause the pinspeck blocked the red from the object).
Therefore the color of the shadow is cyan, the complement of red.
Correspondingly, a green object creates a magenta shadow.
If you would like to make pinspeck photographs, Cohen
offers the following suggestions. For a pinspeck place a dot of black
paint on a piece of clear glass or acetate. The shape of the dot is
not critical. Instead of paint you could paste on a small circular
dot. (I find such dots in office-supply stores. They are for labeling
purposes.) Cohen recommends that the dot not be too small or the
contrast in the photograph will be too low. The scene photographed
should have high contrast so that the photograph will also. You could
begin your experiments with pinspeck photography by cutting figures in
a black, opaque sheet of paper and then illuminating the sheet from
behind with a diffuse source of light.
FIELD-WIDENED PINHOLE CAMERA. John M.
Franke in Applied Optics, Vol. 18, No. 17, pages 2913-2914; September,
*1986, Scientific American.
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