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Optics and Night glasses

    Before IR viewers, NVD's, and even portable spotlights, people used optics to see better in the dark. Though there are limitations, it is surprising just how much of an aid a pair of night glasses can be on a dark night. Night glasses have the advantage of showing color, rather than the green of the modern NVD, and can reveal a fair amount of resolution. They also have the advantage of not requiring power supplies, and are considerably less fragile than today's electronic wonders. Optical systems are also completely passive, though other light sources can be used.
    This was the original form of what we would today call a passive NVD. It takes advantage of the fact that large lenses can gather and concentrate light. Within their limitations, night glasses are valuable aids to using the night, and reached their peak during the Second World War, where night glass equipped sailors would often spot enemy ships before they were detected by radar. The glasses used tended to be huge binoculars with objective lens diameters of 80mm or more. These pulled in huge areas of light, and concentrated it upon the watchful eyes of the night lookout.
    Before going too much into detail about the workings of night glasses, perhaps a basic overview of some optics, and of the optics of the eye are in order, along with some definitions.

Definitions Determined By
Focal length Length from lens at which an object at infinity is clearly projected
Aperture Diameter of lens or lens opening.
Objective Light gathering lens located at front of scope
Ocular Viewing lens located at back of scope (eyepiece)
Magnification Focal length of objective divided by focal length of ocular
F-stop Determined by dividing the focal length, by the aperture.
Exit Pupil Bright disc visible in ocular. determined by dividing objective lens diameter by the magnification

                                                        How optical systems work
     The optical system with which we are most familiar, is that of our own eyes. The optics of our eyes are pretty simple. A lens focuses an image upon our light sensitive retina. The amount of light that gets in is a product of the diameter of the opening in our eyes, the focal length of the lenses of our eyes, and the actual intensity of the light to which they are exposed. The image size is determined by the focal length of the lens, which in the case of the human eye is around 17mm (actually 16.67mm; but who's counting?). The maximum aperture of the human eye is around 7mm. This works out to an F ratio (f-stop) of around 2.1. This is discussed in more detail, in my page on The Human Eye. The human eye uses a simple, single lens system, which projects an image directly, and does not magnify.
     A telescope, or pair of binoculars, works a bit differently. These types of systems magnify the image, before projecting it, and use two lenses, commonly called the objective (up front), and the ocular (eyepiece). The objective gathers the light, and sends the image down to the ocular, where it is magnified and projected into the eye. There are essentially five limits, determined by the optical system. They are magnification, resolution, field of view, depth of field, and brightness. This page will only concern itself with magnification, and brightness, as relevant to the subject. It should also be noted that the system sets the limits. These limits would only be achieved in a perfect system. As a general rule, the higher the quality of the optics, the closed these limits are to being realized.
     The basic raw material for the system is light. The more light gathered, the better. Because of the way that light travels, the further away you get from an object, the smaller and dimmer is the image that can be created from it. The rule which expresses this fact is the inverse square law. The inverse square law has many applications in physics. It states that energy (including light) falls off according to the inverse of the square of it's distance. This sounds more complicated than it is. In real world terms this simply means that every time you double the distance between an observer and an object, you reduce the amount of light by a factor of four. So at twenty feet, and object will only seem about a quarter as bright as it did at ten feet. The inverse square law, when applied to light explains why objects which loom as great dark shadows in the night, suddenly resolve themselves into vague shapes, and then into recognizable objects as the observer draws closer.
     The inverse square law is a bit disheartening at first glance. It seems to indicate that light falls off much more rapidly than distance; but there is a corollary which offers some hope, for the intrepid night watcher. The same rule applies, in reverse, for the light gathering power of a lens. Every time you double the diameter of a lens, it gathers four times as much light. Now if you consider that the average human eye has a lens opening which is 7mm in diameter, then a one inch lens would gather 13 times as much light. This is a rule of thumb, which has been used by astronomers for decades, as they seek to view dimmer and dimmer night sky objects. I have stated the rule below, and have used the rule to calculate light gathering capacity of various popular sizes of lenses.

The aperture A of a telescope divided by the diameter of the human eye's entrance pupil squared will give us the amount of light it could detect as compared to the human eye. This means that (A/7)2 = K where K is the number of times brighter the scope can see.
Objective Aperture in Inches Light gathering power over human eye Objective Aperture in Millimeters
1 13 25
2 52 50
2.4 75 60
3.1 126 82
4 210 105
4.25 237 111
5 329 125
6 473 150
8 842 200
10 1216 250
12.5 2057 312

     It would be nice if we could, as the above table seems to suggest, take an 8 inch lens, attach it to an eyepiece, and have ourselves a passive NVD with a gain of 842 times that of the unaided eye.  Obviously, we can not do this, or there would be few electronic NVD scopes available, since the lower end devices offer a true user gain of about 90, making them inferior to even a 3 inch passive scope, while the upper end devices offer a gain of perhaps several thousand. The chart above has some relevance for astronomers, because they use large aperture lenses to see very faint objects; but they use a combination of brightness, and magnification to detect very dim objects. It should also be noted that, as a general rule, astronomers are looking at objects which are very bright at their source; but have dimmed, due to distance and the inverse square law. The first thing to understand, about optical night glasses, is that they can not break the laws of physics, by gathering more light than is actually reflected by a given scene, to make a scene appear brighter than it actually is. What they can do, is restore some of the brightness lost, from viewing a scene at a distance.  So let's look at what these glasses actually can do.
      A good set of night glasses will both magnify, and brighten the image being viewed. Both the brightening, and the magnifying of the scene use up some of the light gathering power of the objective lens. The magnification is determined by dividing the focal length of the objective, by the focal length of the ocular. As an example, let's take an average pair of 7 x 35 binoculars. The designation, 7 x 35, indicates a 35 mm objective lens diameter, and a magnification of seven power. To make calculation easier, for this example, let's assume an objective lens focal length of 350 mm. the would give the objective an F ratio (f-stop) of 10. magnification is determined by dividing the focal length of the objective, by the focal length of the ocular. Giving the ocular a focal length of 50, would give a power of seven magnifications. Notice that we are talking about magnification here, and not about brightness. So how much brighter would a 7 x 35 power pair of binoculars make a scene?
     Brightness and magnification both require the use of some of the light gathered by the objective lens. Lowering the magnification of a scope will make the image appear brighter, to a limit; while increasing the power will make it appear dimmer. In truth, any lens which gathers more light than the human eye, will make the image brighter than it would be from the observer's point of view; but the image may still be dimmer than it would be at the site being observed. The reason for this has to do with the inverse square law. In nature you don't get something for nothing.
     The inverse square law tells us that not only will an object appear smaller, at distance; it will also appear dimmer. a 35mm objective has, roughly 30 times the light gathering power of the human eye. When you use such a lens to provide a magnification of seven power, you are cutting the brightness possible from this lens by seven. This would seem to indicate that the lens should be able to increase the brightness of the scene being viewed, by a factor of four, which indeed it can; but this is not enough. If the scenes being viewed, is being magnified by a factor of seven, but is only being brightened by a factor of four, it will appear dimmer than it actually is. A 35 mm lens does not have enough light gathering ability to magnify a scene, and brighten a scene, both by a factor of seven. During the day this is not a problem; but at night, it limits the usefulness of a 7 x 35 mm binocular. This is where night glasses come into play.
     A pair of night glasses is a pair of binoculars with a somewhat lower power than normal, for a give objective diameter. The most common and popular is the 7 x 50 mm. If you do the math, you will discover that dividing the aperture by the power (50 divided by 7) will give you a result of seven, just enough to make a scene magnified by seven power, as bright as one viewed directly. If you look around at high powered night glasses, you will note that they never reach a higher ration than seven to one. So you may see 8 x 56 mm, and 10 x 70 mm; but you will never see a 7 x 70mm, or a 10 by 100 mm. Though it would be possible to make such an optical system; there would be no point. There is a reason for this.
     You may have noted that the number seven seems to play a role here, as in the 7 x 50, 8 x 56, and 10 x 70. You will always see this ratio in night glasses, because it is the limit at which a night glass can brighten an image. This is the result of the fact that, as mentioned above, you do not get something for nothing. It is not possible, by optical means, to put more light into a scene than the scene is reflecting. You can not make a scene brighter than it actually is, without amplification, and optical systems do not amplify, they merely gather and magnify. The actual limit is related to the exit pupil of the optical system, and the aperture of the human eye.
     A three dimensional cone of light is projected by the ocular of a telescope or binocular, into the eye. It is visible as a bright circle in the eyepiece of the telescope or binocular. This bright circle is called the exit pupil. The exit pupil determines how bright the image will be, when projected into your eye. The larger the exit pupil, the brighter the image will be. The exit pupil will kind of float around in the ocular; if you view from different angles, the bright circle of the exit pupil will seem to move around. The exit pupil will have a certain size, which may be determined by dividing the objective lens diameter, by the system magnification. Thus a 7 x 35 binocular will have an exit pupil of 5mm, while a 7 x 50 binocular will have an exit pupil of just over 7 mm. This 7 mm exit pupil will be found in all night glasses, because it is the diameter of the opening of the completely night adapted human eye.
     Still, it may seem like a good idea to make the exit pupil even larger, and thus make the image even brighter; but this will not work. Because the human eye has a light opening of 7mm, when fully dark adapted, an exit pupil larger than 7 mm will not be able to enter the eye. This extra light gathered will simply be wasted. So at best, an optical system is able to increase the brightness of a far off scene, to a level equal to that of an observer nearer by. Though this may seem to limit these devices, the improvement can be significant, as many a WWII ship commander could attest. At 10 feet away, objects which appeared as black or gray blobs, may suddenly be resolves as trees, people, animals or vehicles. A 7 x 50 pair of night glasses will give close to the same affect. A standard 7 x 35 pair of binoculars will simply make the black blobs into larger black blobs.
     Modern optical systems are considerably better than those from just a few decades ago. Modern lens coatings can increae light transmission to 80% - 90%, or even better. Though modern optical systems may be pasive, and not amplify the light that they gather, it is pretty amazing what you can see at night, through a pair of modern night glasses.