How the NPF rule works
Because the earth turns, stars draw short lines on the sensor during an exposure. The NPF rule (Nightscape Photography Formula) was developed in 2010 by Frédéric Michaud of the Société Astronomique du Havre. It gives the exposure time at which the movement of a star stays within the size of its own blur spot. It replaces the rule of 500, whose results the author considers too uncertain.
The blur spot has three parts: diffraction at the aperture, atmospheric turbulence (assumed at 3 arcseconds) and the colour reconstruction of the sensor (2 pixels). The rule and its formulas are the work of Frédéric Michaud and the Société Astronomique du Havre.
Formula
The exposure time t in seconds follows from the full rule or from the simplified rule:
t = k × (16.9 N + 0.10 f + 13.7 p) ÷ (f × cos δ)
t = (35 N + 30 p) ÷ f
- t: exposure time in seconds
- N: f-number
- f: focal length in millimetres
- p: pixel pitch in micrometres
- δ: smallest declination of the photographed sky region in degrees (0° if unknown)
- k: between 1 (point-like stars) and 3 (slightly elongated stars); the star moves by k times its radius
The simplified rule assumes k = 2 and a declination of 0° and neglects turbulence, so it is on the safe side for wide-angle photos of the Milky Way. The full rule pays off when the declination of the sky region is known, for example around Polaris.
NPF exposure times for common settings
Full frame sensor with 24 megapixels, declination 0°, k = 1. The rule of 500 is shown for comparison.
| Focal length | f/1.8 | f/2.8 | f/4.0 | Rule of 500 |
|---|---|---|---|---|
| 14 mm | 8.1 s | 9.4 s | 11 s | 36 s |
| 20 mm | 5.7 s | 6.6 s | 7.6 s | 25 s |
| 24 mm | 4.8 s | 5.5 s | 6.3 s | 21 s |
| 35 mm | 3.3 s | 3.8 s | 4.4 s | 14 s |
| 50 mm | 2.4 s | 2.7 s | 3.1 s | 10 s |
| 85 mm | 1.4 s | 1.6 s | 1.9 s | 5.9 s |
Pixel pitch 6.0 µm. For other sensors use the calculator above.
Limits of the rule
The NPF rule describes an average camera system under normal conditions: atmospheric turbulence of about 3 arcseconds, a real lens with moderate residual aberrations and a colour sensor with a Bayer filter. With very calm air, a lens close to the diffraction limit and a sensor without a low-pass filter, stars can be finer than the rule assumes, and the same movement then looks more elongated.
The rule is made for photos of the night sky with a fixed camera. It does not apply to telescopes, planets or tracked exposures. The star movement shown is the shift of a point-like star on the sensor, calculated from the sidereal day of 86,164 seconds.
More tools
Frequently asked questions
What is the NPF rule?
A formula by Frédéric Michaud (Société Astronomique du Havre) for the longest exposure time without noticeable star trails when the camera is fixed. It takes the pixel size, the aperture, the focal length and the declination of the sky region into account.
How is the NPF rule different from the rule of 500?
The rule of 500 divides 500 by the focal length, multiplied by the crop factor. It ignores aperture and pixel size. According to the author of the NPF rule, it dates from the film era and rests on a circle of confusion of 0.029 mm for 35mm film.
Which value of k should be used?
k = 1 gives point-like stars, k = 2 a slight trail and k = 3 a visible trail. The simplified rule corresponds to k = 2 (with declination 0°).
How is the pixel pitch found?
It is the sensor width divided by the number of pixels along the width. The calculator derives it from the sensor format and the megapixels: a full frame sensor with 24 megapixels has a pixel pitch of about 6.0 µm, one with 45 megapixels about 4.4 µm.
Why do long lenses and high resolution give short exposure times?
A star crosses more pixels per second the longer the focal length is and the smaller the pixels are, while the blur spot stays about the same size. A smaller f-number reduces the diffraction part of the blur spot and shortens the time as well.
Sources
- Société Astronomique du Havre (F. Michaud): Règle NPF ou Nightscape Photography Formula (formulas, parameters, credit). https://sahavre.fr/wp/regle-npf-rule/
- Société Astronomique du Havre (F. Michaud): Les coulisses de la règle NPF (derivation, limits). https://sahavre.fr/wp/les-coulisses-de-la-regle-npf/