Brightness of scene, time, film rating, and aperture. Three of those four variables are needed to solve the exposure question.
So for example a sunny 16 front lit scene (EV 15), the normal setting for FP4 (ISO 125) at f/16 would be 1/125th of a second.
You are changing the aperture and need to apply the f/ number indicated. F/158 for the pinhole or f/55 for the zone plate.
To get close you can just count stops. From f/16 1-stop less light is f/32, 2-stops f/64, 3-stops f/125, 4-stops f/256.
The corresponding times count from 1/125 1-stop brighter is 1/64th, 2-stops 1/32, 3-stops 1/16, 4-stops 1/8.
So for the pinhole (f/158) in "sunny 16" (EV 15) with FP4 (ISO 125) somewhere just longer than 1/16th of a second would be the target.
The zone plate's target time would be a hair shorter than 1/32nd.
If you move from the sunny 16-EV 15 situation to something darker, say EV 10; you will need to adjust the speed 5-stops to let in more light.
So in an EV 10 lighting situation the time would adjust from the sunny setting at 1/32nd to about 1-second. (1/16, 1/8, 1/4, 1/2, 1)
Here's a good reference for EV numbers to estimate with.
Doh!
Note to self: finish coffee before doing photographic Maths.
The best way to determine the proper exposure for any pinhole film and camera combination is to test. It will use up a roll of film; but the time and money initially expended will pay off in a future of good exposures.
The exposure calculator that is built into my Zero 6x9 gives a good indication of proper exposure, and provides a good starting point for the test. It is easiest to do the test on a bright sunny day with a subject that includes a full range of tones (both lights with detail and darks with detail). Make five exposures ranging from two stops below to two stops above what the calculator indicates. When the film is processed, evaluate visually on a light table to see which exposure best captures the full range of tones in the subject. This is the proper exposure on a bright sunny day (the EV 15 situation noted above). This exposure time is a "magic number" for your camera and film.
As mentioned above, in darker lighting situations, subtract the EV of the ambient light (EV 15 above) to determine how many extra stops of exposure to give. Let's say your magic number is 5 seconds and the ambient EV is 12, you'd need to make a 40 second exposure.
5" = magic number
10" = one extra stop
20" = two stops extra
40" = three stops extra
Doing the test to determine the proper exposure on the pinhole camera itself eliminates the need to factor in the film's reciprocity failure characteristics since the test exposure was so long. In practice, I've found this approach to work great up to six or seven extra stops of exposure.
The testing can continue by doing prints or scans to determine the best film exposure; but doing the visual examination suffices.
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