I try all the time to improve my bag of pinhole camera design tools. As I like it easy and fast I was looking for a graphical solution instead of lists with numbers, calculator work or spreadsheets in the computer. I like to design a camera the old way with a piece of white paper, a pencil and not much more.

As I'm using a lot of different cameras, sometimes at the same time, I was looking how I could implement the f/stop as a design parameter as well. Different cameras with the same f/stop reduce the number of possible failures and makes it easier to take pictures.

The basic formulas are:

f/stop = focal length / diameter of the pinhole (correct f/stop for the center)

diameter of the pinhole = c * sqrt( focal length * wave length) (correct for infinite object distance)

If I set the wave length of the light as fixed then I can choose two out of the four variables. The other two are fixed by the equations above. In the real world there are more solutions as I have to take in account that all values can have variations. How precise can I measure a pinhole? What is the practical difference between f/128 and f/125? How well defined is the focal length? What is the correct c-value?

In the following picture I present a graph with all these parameters in. It is the c-value as a function of the focal length. Fixed f/stops and fixed pinhole diameters are shown as curves.

Focal length: In the graph you can easily see the influence of a slightly changed focal length. In very simple camera designs the focal length can vary by up to 0.5 mm or even more.

Pinhole diameter: Also variations of the pinhole diameter can be easily seen in the graph. If you can measure the pinhole diameter better than 0.05 mm then you are already good.

f/stop: I can guess light values in 0.5 EV steps. I can measure with my equipment differences of 1/3 EV. This is enough even for slide film. For more accuracy you have to bracket the exposures. So in the graph are main lines shown for f/128, f/152, f/181 and f/215 and for each curve + 0.25 f/stop and minus 0.25 f/stop.

c-value: the thicker black horizontal lines show the from my point of view usable range of c-values for standard applications: 1.2 until 1.9. For general purpose choose a c-value between 1.4 and 1.7 and you are save. For more dreamy pictures or portraits with longer focal lengths a value around 1.9. If you are mainly interested on closer object distances in the range of centimeters go with a c-value below 1.4

I hope this graph is also helpful for some of you.

The 100k limit doesn't allow me to show the graph in a larger size and/or better quality. But you can make easily your own graph in any spreadsheet program. Attached files