The twilight factor of binoculars is a function of the objective lens diameter and the magnification and is between around 5 and 20. The higher it is, the better the resolution (performance) in twilight. A distinction is made between the performance factors for twilight, night and day.

The twilight factor D is defined as:

• D = square root of (O x V)
• O: objective lens diameter in millimetres
• V: magnification

The twilight performance L_T takes into account the quality of the optics and is often estimated by means of [1]:

L_T = D * 0.3

The daytime performance depends only on the magnification and the quality of the optics:

L_D = 0.6 * V

The night-time performance is primarily determined by the lens diameter:

L_N = 0.1 * O

The entrance pupil of the eye, AP, limits the beam of rays. The product of the pupil aperture and magnification defines the usable aperture of binoculars:

O_effective = AP * V

Night glasses are usually designed for a pupil aperture of 5 mm. Used in the above equation leads to the approximation:

D = V * 2

For this reason, it makes little sense to compare the twilight factor of night glasses with normal binoculars. As can be seen from the lack of a unit specified, the twilight factor is an empirical measure that says little about the performance of an optical device.

A 25x30 scope and a 9x63 binoculars have almost the same twilight factor of 25. Nevertheless, the scope is unsuitable for the night-time, as it only uses a diameter of 1.2 of the eye pupil. Night glasses are usually optimised for a pupil aperture of 7 mm.