The Pleasure of the Pin Hole Camera and Its Relative the Pinspeck Camera

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.

When an object is photographed with a pinhole camera, each point of the object facing the camera casts a corresponding spot of light onto the film (or photographic paper). The composite of the spots is the image recorded by the film. If the image is to be clear, the adjacent spots should not overlap. Therefore they should be as small as possible.

Part of the design of a pinhole camera lies in choosing a size for the pinhole and a distance between the hole and the film that will make the individual spots of light cast on the film remain discrete and as bright as possible. In principle the pinhole can be of unlimited size. The larger it is, however, the farther it must be placed from the film and the larger the film must be, so that in practice the size of the hole is limited. There is also a theoretical limit on how small a pinhole can be.

Consider a camera in which the pinhole is a reasonable distance (several centimeters) from the film. Suppose the pinhole is relatively large (too large for the distance to the film) and the camera faces a distant point source of light. The rays of light from the source arrive at the pinhole essentially parallel to one another and to the central axis that passes through the hole and is perpendicular to the screen. The radius of the circular spot of light cast on the film is equal to the radius of the hole. Since the pinhole is large, the spot of light is large. If many point sources of light were being photographed, the spots on the film would overlap and the individual point sources would not be recognizable.

The size of the spot of light from a single point source is reduced if the size of the pinhole is reduced. The scope of this improvement is- limited, however, because eventually the pinhole is so small that the light passing through it diffracts into an interference pattern. A point source of light creates not a single small spot of light on the film but a circular pattern consisting of one central bright spot surrounded by dimmer rings. If the size of the pinhole is reduced further, the diffraction pattern gets larger, with a resulting loss of resolution in the photograph.

Figure 2: A wide-angle view made by John M. Franke's camera with a glass hemisphere behind the pinhole 

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 screen.

Consider a family of circular zones on that plane and concentric on the camera's central axis. The zones are distinguished by their path lengths to a point at the center of the film that is also on the central axis. The distance between the central zone and the center point on the film is the distance that was between the pinhole and the film. The second zone is farther from the center point by half a wavelength of light, the third by an additional half wavelength and so on.

All the zones send light waves to the center point, but because of the differences in the path lengths the waves interfere when they arrive. For example, the wave from the second zone arrives half a wavelength out of phase with the wave from the central zone. If the amplitudes of the two waves were equal, the waves would cancel each other. Indeed, if all the contributions were equal in amplitude, they would all cancel at the center point.

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.

What one seeks, then, is not a particular size of pinhole but rather a particular relation between the size of the pinhole and the distance from the hole to the center point on the film. When an object to be photographed is relatively distant, the optimum radius of the pinhole is approximately equal to the square root of the product of the wavelength of the light and the distance between the pinhole and the film.

Figure 3: An arrangement for pinhole photography 

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 a film 

Assume for the sake of demonstration that the final photograph is the same size as the film and that it will be viewed at a distance equal to the distance between the pinhole and the film. You are to photograph two adjacent point sources of light whose angular separation is at the limit of resolution (.001 radian) of your eye. The camera should cast two spots of light on the film that barely touch or overlap slightly. When the photograph is viewed, you will just be able to resolve the spots. The angle. between the spots in your field of view can be calculated by dividing the diameter of the pinhole into the wavelength of the light. Suppose the wavelength is 500 nanometers (about in the middle of the visible range). If the angle for the limit of resolution is .001 radian, the pinhole's radius should be .25 millimeter.

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 below.

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.

A severer problem with the pinhole camera is its low light-gathering ability. Since the aperture is usually tiny, relatively long exposures are required. For example, if the film is at the pinhole's focal length and if that distance is a few centimeters, the f number of the camera is approximately 200. Although the small aperture makes the system slow, it is responsible for the camera's large depth of field.

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 limit to the field of view is that an object sufficiently off the central axis may not reflect light to the film unless the film is quite wide or fairly close to the pinhole. The usual solution to the problem has been to move the film closer to the pinhole so that a wide-angle ,a photograph can be made. The trouble is that this stratagem reduces the resolution of the photograph because the film is no longer at the right distance from the pinhole for optimum resolution.

Another way to increase the field of view is to design a film holder that is hemispherical with respect to the pinhole. Then any light entering the pinhole, even light from an object that is almost 90 degrees off the central axis, will reach the film. Another result would be less of a decline in the exposure far from the center of the film because the light would always strike the film perpendicularly. The resolution of the objects off the central axis would also be improved, since all sections of the film would be at the same distance from the pinhole. Unfortunately a hemispherical film holder is not very practical. A cylindrical one might be an adequate compromise.

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.

Franke's glass hemisphere is made from BK-7 glass and is 25.4 millimeters in diameter. Its index of refraction is about 1.5. The diameter is not critical, but different results are obtained with glass that has a different index of refraction. You might like to experiment with other glasses or even with plastic of good quality. If you want a field of view of 180 degrees, you will encounter some distortion of the image toward the edges of the photograph.

Figure 7: Adam Lloyd Cohen's setup for pinspeck photography 

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 dust.

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.

I chose to follow a procedure outlined by Young. On the base of his 35-millimeter camera he mounted an extension tube, which is available for most cameras with removable lenses. At the outer end of the tube he attached his pinhole assembly. Lacking an extension tube, I used a cardboard mailing tube that I attached to my camera base with several layers of black tape. The advantage of this type of pinhole camera is that an entire roll of film can be exposed. Since my camera is a single-lens reflex model, I could actually see a dim image of the scene I was to photograph before I made a picture.

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 object.

A photograph made with a pinspeck displays poorer contrast than a pinhole photograph because the pinspeck arrangement allows nearly all the light from a scene to reach the film. Most of it is a uniform illumination that is of no value and merely reduces the contrast of the image. It is the remainder of the light, the nonuniform portion, that carries the information about the object. Contrast would be improved if somehow the uniform illumination were diminished or the proportion of the nonuniform light carrying the information about the object were increased.

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 image. 

Some of the uniform illumination results from parts of the scene that are not important to the photograph. To decrease this unimportant illumination Cohen places a field stop (a screen with a hole larger than the pinspeck) in front of the pinspeck. The hole is large enough for the extreme parts of the object to illuminate the edges of the film but small enough to prevent the rest of the scene from reaching the film.

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.

Some of the properties of a pinhole camera are displayed equally well by a pinspeck camera. The field of view is large, the adjustment to the magnification of the camera is made by changing the distance between the pinspeck and the film, and there is no linear distortion Astigmatism can be avoided with a pinspeck camera if the pinspeck is spherical. Then any light traveling from the object to the film intercepts an obstacle with a circular cross section even if the object is well off the central axis of the camera.

One other difference in the two types of photography is that a series of pinholes aligned between the object and the film will not produce a photograph but a series of pinspecks will. The screens perforated with the pinholes keep the light from falling on the succession of pin- holes closer to the film. In contrast the pinspecks barely interfere with one another's ability to form an image of the object. The illustration at the bottom left is a photograph Cohen made from a series of pinspecks that he positioned between a single bright ring and the film. Each pinspeck produces its own negative image of the ring.

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.

Much more can be learned about pinhole and pinspeck photography than I have set out here. A description of Cohen's work will appear soon in Optica Acta under the title of "Anti-pinhole Imaging." Some of the most thorough work on pinhole photography, both experimental and theoretical, can be found in a series of papers by Connors in Interest, a journal he edits. It is available from him at the School of Pharmacy, University of Wisconsin, Madison, Wis. 53706. His recent papers have dealt with the conditions for optimum resolution and definition, the calibration of a camera for contrast control and the relation between a pinhole camera and the optics of a zone plate.