Exit Pupil – The Complete Guide

Optics & Binoculars 101:

Exit Pupil

In optics, the exit pupil is a virtual aperture in an optical system. On a pair of binoculars it can be seen as the bright circle in the center of each eyepiece when you hold them about 30cm away from your eyes and with the objective lenses pointed toward a bright light.

Another way to visualize the exit pupil is to first fully retract the eye-cups and focus the binoculars onto a bright area. Then hold a white card up to the eyepiece, this projects a disc of light onto the card. Now move the card closer to or further away from the eyepiece until you get the smallest possible diameter of the projected disc. The diameter of this bright disc is the diameter of the exit pupil.

Note: The exit pupil must always be circular and supply uniform brightness. If shadows are visible, this is an indicator of poor quality.

Why is the Exit Pupil Important?

It is important because the only light rays which pass through this virtual aperture can exit the system and enter your eyes. Therefore with all else being equal, the larger the exit pupil diameter, the more amount of light will be delivered to your eye. It is therefore and important aspect when comparing the theoretical brightness of two optical instruments and something to consider when choosing binoculars, especially for use in poor light conditions like at dawn or dusk or for astronomical observation.

How is the Exit Pupil Calculated?

Exit pupil = The effective diameter of the objective lens ÷ Magnification

8x42 binoculars
The formula is 42 ÷ 8 = 5.3 – Therefore, the diameter of the exit pupil is 5.3mm

10x42 binoculars
The formula is 42 ÷ 10 = 4.2 – Therefore, the diameter of the exit pupil is 4.2mm and this shows that all other things being equal an 8x42 pair of binoculars would be a better choice than a 10x42 pair in poor light conditions.

8x56 binoculars
56 ÷ 8 = 7 – Therefore, the diameter of the exit pupil is 7mm – Incidentally, this corresponds to the maximum pupil aperture of the human eye.

That is the maths, but to demonstrate how magnification affects the size of the exit pupil, take a look a the series of photos below that I took using a pair of Nikon EagleView 8-24x25 Zoom Binoculars set at a range of different magnifications. You will notice that the higher the magnification, the smaller the exit pupil gets (assuming the objective lens stays the same size):

The Exit Pupil at 8x Magnification The Exit Pupil at 12x Magnification
The Exit Pupil at 8x Magnification The Exit Pupil at 12x Magnification
   
The Exit Pupil at 16x Magnification The Exit Pupil at 24x Magnification
The Exit Pupil at 16x Magnification The Exit Pupil at 24x Magnification

 

But wait, there is more…

The relationship between bright/low-light conditions & a binocular’s exit pupil

From what we have learnt so far, you could be forgiven for thinking that for the brightest image possible, you should just choose a binocular with a really large exit pupil, but this is not necessarily the case and indeed sometimes a large exit pupil will make no difference at all:

The pupil in the human eye varies in diameter with viewing conditions:

  • In daylight, with good lighting conditions it opens about 2mm to 4mm
  • In dark and poor light conditions, the maximum pupil size of a human eye is typically between 5mm to 9mm for people below 25 years of age (usually about 7mm) – this maximum size will also decrease slowly with age

So if you were to use a pair of 7x50 Binoculars:

In bright conditions (7x50 binoculars)
Pupil diameter: 2-3mm
Exit pupil of binoculars: 50 ÷ 7 = 7.1mm
So because the binoculars’ exit pupil is larger than your pupil, over half the light will be blocked by your iris and will not reach the retina. However, the loss of light in the bright conditions is generally not significant since there is so much light to start with. Thus the result is you will perceive the image as being as bright as when seen with the naked eyes.

Ok, so what about if you were to use a much smaller 8x20 pair of binoculars:

In bright conditions (8x20 binoculars)
Pupil diameter: 2-3mm
Exit pupil of binoculars: 20 ÷ 8 = 2.5mm
So because the binoculars’ exit pupil is about the same size your pupil, the emergent light at the eyepiece fills the eye’s pupil, meaning no loss of brightness (assuming perfect transmission). The result is you will still perceive the image as being as bright as when seen with the naked eyes and with all other things being equal, they will seem just as bright as the 7x50 binoculars above.

So in this case the large exit pupil makes no difference to image brightness, but what about in poor light conditions:

In low light conditions (7x50 binoculars)
Pupil diameter: 7mm
Exit pupil of binoculars: 50 ÷ 7 = 7.1mm
So because the human pupil is about the same size as the binoculars’ exit pupil, the emergent light at the eyepiece then fills the eye’s pupil, meaning no loss of brightness in low light conditions due to using these binoculars (assuming perfect transmission). Thus the result is that you will perceive the image as being as bright as if you were to see it with the naked eyes.

And what about if you were to use a much smaller 8x20 pair of binoculars in low light conditions:

In low light conditions (8x20 binoculars)
Pupil diameter: 7mm
Exit pupil of binoculars: 20 ÷ 8 = 2.5mm
Because the 2.5mm exit pupil of the binocular is smaller than the 7mm human pupil, you will perceive the image as being dark.

So as you can see from the two demonstrations above, the ideal exit pupil diameter depends on the application with large exit pupils are only really being an advantage in low light conditions. Whilst most compact binoculars with smaller exit pupils are sufficient to fill a typical daytime eye pupil, making these binoculars better suited to daytime than night-time use.

This is why an astronomical telescope or binoculars designed for astronomy require a large exit pupil because they are designed to be used for looking at dim objects at night, whilst on the other extreme, optical devices like microscopes require a much smaller exit pupil because the object you are observing is brightly illuminated.

To sum up

  • The average healthy human pupil normally opens about 2mm in daylight, and 7mm in the dark.
  • If you use binoculars with an exit pupil of over 2mm in daylight, you won’t perceive dark images. Brightness will also not improve if you use binoculars with an exit pupil or more than 2mm
  • However, if you use binoculars with a small exit pupil in the dark, the image will not appear as bright as when seen with the naked eyes or as bright with large exit pupil binoculars.

Further Reading

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