A Study of Pinhole Photography - Erratum Page

Since writing my article on pinhole photography, I have discovered a number of errors and shortcuts in the calculations used to design an optimum pinhole camera. I have created a small java script calculator which will allow you to enter some basic information about your camera and automatically work out the hard bits.

Image Forming Cone

The light projected through the pinhole forms a cone whose base diameter increases by 1.3 inches for every 1 inch in depth. This figure was found by experiment and differs greatly from the figures quoted by Eric Renner which were used in my original article. Diagram 6 should therefore look as follows -

Figure 6 - Pinhole Image Forming Cone

Figure 6 - Pinhole Image Forming Cone

If the diagonal measurement of the film material used in the camera is less than the diameter of the cone formed for your depth of camera, the resulting image will cover the whole paper. For example a sheet of 6"x4" paper has a diagonal of 7.2". To ensure that the resulting image covers the whole of the sheet, the camera must be at least 5.6 inches deep (7.2 divided by 1.3 inches). Using a smaller depth will cause vignetting and produce a circular image on the paper.

Exposure Factor

The exposure correction formula which I quoted was very complex and partially inaccurate. Further research uncovered an old method of using exposure values (EV) to compare shutter/aperture combinations. The exposure value is defined as follows-

                  N2   
  EV = 3.32 log  ---   
                  t     

As the exposure value calculated from a meter reading is the same as that required to expose the image through the pinhole camera, the Exposure factor can be calculated as follows -

        N2   
  Ef = ---   
        n2

Where N is the aperture of the pinhole and n is the aperture used for the meter reading. Multiplying the exposure time given by the meter by the exposure factor gives the exposure time required by the camera.

The following table uses the formulas to calculate the optimum pinhole and exposure factor for a variety of camera sizes. Note how the exposure times start to get very long when using large cameras with their optimum pinhole size. The benefits of high resolution need to be weighed up against practicality as a 4 second exposure time at f/16 translates to a 38 minute exposure for a 12" camera.

Depth (hole to film) 1.5" 3.0" 6.0" 9.0" 12"
Optimum Pinhole Diameter 0.3mm 0.4mm 0.6mm 0.7mm 0.8mm
Aperture (N) f/127 f/191 f/254 f/327 f/381
Exposure Factor for f/16 63 142 252 417 567
Image Diameter 2.0" 3.9" 7.8" 11.7" 15.6"

I hope you find these corrections useful. If you have any feedback then please mail me at bobm@photostuff.co.uk

Pinhole Calculator