Twilight number

The twilight factor  D - sometimes twilight factor (English Twilight Factor ) - is a measure for the resolution (power) of a binocular or spotting scope in the twilight , the greater the twilight factor, the better. The twilight factor is between approx. 5 and 25, its unit is not specified. ${\displaystyle {\sqrt {\mathrm {mm} }}}$

calculation

The twilight factor can be calculated as:

${\displaystyle D={\sqrt {V\cdot O}}}$

With

• the magnification  V
• the lens diameter  O in millimeters.

With night glasses

The entrance pupil  AP of the eye delimits the beam . Therefore, the product of the eye pupil and magnification determines the usable opening of a binocular:

${\displaystyle O_{\mathrm {eff} }=AP\cdot V}$

A night glass is usually designed for a pupillary opening of . Inserted into the formula for the twilight factor follows: ${\displaystyle AP\approx 5\mathrm {mm} }$

${\displaystyle \Rightarrow D\approx 2\cdot V}$

For this reason, it makes little sense to compare the twilight figures of night glasses with normal binoculars. As can also be seen from the lack of specification of the unit, the twilight factor is an empirical quantity that says little about the performance of an optical device . More precise statements about the performance of binoculars in different lighting conditions can be derived from the various models of the telescope performance .

Relationship with telescope performance

In some cases, a distinction is made between the telescope power  L for day, twilight and night:

• The daily output depends only on the magnification and the quality of the optics : ${\displaystyle L_{T}}$

${\displaystyle L_{T}=0,6\cdot V}$

• The twilight performance takes into account the quality of the optics and is often estimated using: ${\displaystyle L_{D}}$

${\displaystyle {\begin{aligned}L_{D}&\approx 0,3\cdot D\\&\approx 0,3\cdot {\sqrt {V\cdot O}}\end{aligned}}}$

• The night performance  is largely determined by the lens diameter: ${\displaystyle L_{N}}$

${\displaystyle L_{N}=0,1\cdot O}$

example

Exit pupils of a telescope (left) and a night glass

The 25x30 telescope on the left in the picture and the 9x63 telescope have almost the same twilight factor of approx. 25. However, the telescope is unsuitable for the night as it only uses 1.2 mm of the diameter of the eye pupil. The night glass is optimized for an eye pupil of 7 mm.

literature

• Dietrich Kühlke: Optics: Basics and Applications. Harri Deutsch Verlag, 2nd edition, 2004, ISBN 978-3817117413 , p. 148 ( online ).
• Optics and optical instruments - Test methods for telescopes - Part 1: Test methods for determining the basic parameters (DIN ISO 14490-1: 2006-08)

References

1. ↑ Performance figures