Twilight factor

The twilight factor is an indicator that we encounter when choosing binoculars or a spotting scope. It reflects the ability of an optical device to show a detailed image in low light conditions. Theoretically, the higher the twilight factor, the more the binoculars can perform twilight observations. Twilight factor of 17 or higher is considered optimal for evening observations. Does this mean that you can choose any binoculars based on this parameter and that’s it? No, it is not.

Equation of Twilight Factor

Twilight Factor table

How to calculate Twilight Factor

What is the twilight factor? Multiplying the magnification by the diameter of the aperture and then calculating the square root of this product. For example, for 8×30 binoculars, the twilight factor would be:

Does this mean that such binoculars are not suitable for us? Not necessarily. Looking ahead, I will say that the ability to form a high-quality image in twilight is influenced by several other factors. First of all, this is the diameter of the exit pupil. If it is not large enough, no twilight factor will help you.

Twilight factor and Exit Pupil

Here’s the thing. Pupil of a human eye in daylight is 2-3 mm in diameter, and in low light it expands to 4-8 mm to let more light onto the retina and see better. Binoculars, spotting scopes and telescopes also have an exit pupil. It can be seen as a white circle inside the eyepieces. So, if the diameter of the exit pupil of binoculars is smaller than the diameter of the pupil of our eye in the dark, then such pair of binoculars will transmit less light to our retina than is necessary to form a detailed image. Thus, the picture will be dark.

For observations in twilight, binoculars with an exit pupil diameter of 5 mm or more are suitable.

According to their light intensity, binoculars can be divided into three types:

• Low-light – with exit pupil diameter of up to 3 mm;
• Medium-light – from 3 to 4.5 mm
• High-light – 4.5–6 mm.

The diameter of an exit pupil can be found using the formula:

So, is Twilight Factor that important?

Thus, twilight factor itself would determine light transmission of binoculars if we were limited to theory and did not take into account other details.

This is evident even from the formula for it’s calculating:

The fact is that this formula will give the same product for both 8×40 and 40×8 binoculars (although such binoculars are not made, but we will assume it in theory). Obviously, the second version of binoculars is not capable of forming a bright image, since this is affected by the diameter of its’ objectives.

Twilight factor was indeed important in old binoculars produced until about the middle of the 20th century. With the invention of anti-reflective coatings, everything changed.

Twilight Factor and Optic coatings

In 1935, scientist Katherine Blodgett invented a method for producing mono- and polymolecular layers of modified barium stearate. She found that a 44-layer coating of optical surface increase the light transmission of a lens to more than 99%. Considering that before the overall percentage of light loss in binoculars reached 50%, Blodgett’s invention turned the world of optics upside down and made it possible to create optical devices that transmit a bright image even in low light.

During World War II, glass with an anti-reflective coating was widely used in optical sights, rangefinders, and cameras for aerial photography. In the second half of the 20th century, they also appeared in civilian optics: binoculars, telescopes, cameras, etc. Almost all modern binoculars have anti-reflective lens coatings that compensate for the low twilight factor. The quality of optics and its coating have a greater impact on the brightness of the image.

Twilight Factor and Relative Brightness

There is another parameter that goes hand in hand with twilight factor and diameter of exit pupil – relative brightness. This parameter also indirectly indicates ability of the binoculars to form image in low light, but it is closer to the diameter of the pupil and in this sense is more suitable for a real assessment than twilight factor.

How to calculate relative brightness? Equation

The relative brightness of binoculars (or a spotting scope) is calculated simply: you need to square the diameter of it’s exit pupil. For example, for 10×42 binoculars, the calculation will be as follows:

1. Find out the diameter of the exit pupil: 42/10 = 4.2.
2. Find out the relative brightness: 4.2×4.2 = 17.64.

Relative Brightness table

For clarity, let us provide a comparative table with the relative brightness index for different binoculars:

What is a good relative brightness for binoculars?

For low-light observations, binoculars with relative brightness of 16 or higher are recommended. To achieve this value, the exit pupil must be greater than 4. But again, as with twilight factor, do not forget that in real life, a pair of expensive binoculars with high-quality optics will most often give a brighter image with equal relative brightness values.