Atelier Bonryu(E)
pinhole photography
Laboratory: Pinhole Photography
Taking Pinhole Photographs
- Designing a Pinhole -
Design of a pinhole: How small is the optimum diameter of a pinhole? If the diameter of a pinhole is very small incident radiation is faint and necessary exposure time becomes long. But it may be imagined that clearer image could be attained by decreasing the diameter of the pinhole as small as possible. Is it really the case? When the diameter is large enough it is certainly true, i.e., clearer image is obtained by decreasing the diameter of the pinhole. However, if the diameter is decreased less than a certain value then the image becomes to blur. The cause of the blur is the ”diffraction phenomenon of the light“ which will be described at zone plate photography. In brief, decreasing the diameter of a pinhole decreases both the straight-traveling light and the diffracted light which sneaks into the backside of the pinhole plate, but the decrement of the straight light is far larger than that of the diffracted light. Therefore, the amount of the diffracted light relatively overwhelms the amount of the straight light and the image blurs. Thus decreasing the diameter needlessly does not help to make the image sharp.
Then how much is the pertinent size of the diameter (d) of the pinhole (*4)? Suppose the radius of an image of a point source at infinity by a pinhole with a radius of a (=d/2) is a’, where the image of the point source is enlarged to a circle with a finite area due to the diffraction. By setting the radius a equal to a’, and an equation for the optimum diameter of the pinhole is derived as 
. In this equation 
are the focal length and the wavelength of the light, respectively. Though the wavelength of the visible light ranges from 400 nm to 700 nm (1 nm = 0.000001 mm) and we cannot set down a single value strictly, 
( 
) is usually employed as a representative value of the wavelength of the light. For this value of the wavelength the size of the diameter of a pinhole is given in unit of mm as 
. In this way the optimum diameter of a pinhole is proportional to square root of the focal length. As this value is not very strict because of the above reason a pinhole with a diameter of 0.2 - 0.5 mm is usually adequate to take a photograph with a focal length of several ten centimeters.
