Apertia · Library
Why must the wavelength assumption stay visible in a diffraction comparison?
At f/11 the ideal Airy disc is 0.0121 mm for 450 nm, 0.0148 mm for 550 nm and 0.0174 mm for 650 nm; Apertia's warnings assume 550 nm green light.
The wavelength fixed in the app
The Airy-disc diameter is proportional to wavelength: d = 2.44 × λ × N. Apertia's calculator, hyperfocal table and shot planner all use λ = 0.00055 mm, which is 550 nanometres, green light near the peak of the eye's sensitivity. Every diffraction threshold in the app, such as f/22.35 and f/11.18 on full frame, comes from that single value.
The airy-disk-model tool in this library lets you change the assumed wavelength in millimetres. That is useful for seeing how the same f-number behaves for blue or red light, but each result is still a single-colour estimate, not the response of a colour sensor.
Worked example
At f/8, a 0.00065 mm wavelength gives an ideal diameter of 0.012688 mm. The 0.00055 mm comparison gives 0.010736 mm; both are stated monochromatic assumptions.
- Ideal disk diameter at the stated wavelength (mm)
- 0.012688
Compare wavelengths cleanly
- Convert the wavelength to millimetres: divide nanometres by 1000000, so 450 nm is 0.00045 mm.
- Keep the aperture and circle of confusion fixed while changing only the wavelength.
- Read the disc diameter and its ratio to the circle of confusion for each value.
- Note which wavelength each result used before you compare it with an app warning.
Worked example: three colours at f/11
Full frame, c = 0.030 mm, f/11. For 450 nm blue light the disc is 0.012078 mm, 0.403 of c, and the disc would equal c only at f/27.32. For the app's 550 nm the disc is 0.014762 mm, 0.492 of c, with equality at f/22.35. For 650 nm red light it is 0.017446 mm, 0.582 of c, with equality at f/18.92. Under the red assumption the equality point arrives about half a stop sooner than under the blue one.
- 450 nm (0.00045 mm)
- 0.012078 mm · 0.403 · f/27.32
- 550 nm (0.00055 mm)
- 0.014762 mm · 0.492 · f/22.35
- 650 nm (0.00065 mm)
- 0.017446 mm · 0.582 · f/18.92
Common mistakes
- Entering 550 instead of 0.00055; the disc becomes a million times too large.
- Entering 0.55, which treats micrometres as millimetres and is still a thousand times too large.
- Expecting the app's warning to move when you change the tool's wavelength; the app keeps 550 nm.
- Reading a red-light result as the camera's overall diffraction limit.
Single-colour scope
Real scenes contain many wavelengths and a sensor records them through colour filters, so no single value describes the whole image. The University of Arizona camera-systems notes listed below give the monochromatic formula used here.