View Full Version : Correcting some optical misconceptions

03-25-2008, 06:56 PM
Inspired by an old "debate" (2006) about the FW190 Revi gun sight and the effect of the plane's very thick armoured glass up front.

I work in an optics shop, and as I write this I'm holding a thick plate of glass tilted at a rakish angle to "simulate" the FW's armoured glass. Moreover, I've used and even built telescope finders based exactly on the gun sight principle (which is what inspired their creation starting about 1980).

Optical Gun Sights

Many people mistakenly think that a gun sight's reticle is actually projected *onto* the angled reflector plate. Wrong.

CFS2 is a notoriously bad example of this improper representation, where the reticle is indeed drawn as a pattern right on the surface of the glass reflector.

In reality, the reticle's image is seen *through* the reflector, and appears to lie effectively at infinity. This is achieved by the collimating lens, collimation by definition being the making parallel of light rays of an imaged object. If the light rays from any object enter your eye parallel, that's exactly identical to the object being seen at infinity, regardless of its being collimated from only inches away.

If the reticle was indeed projected *onto* the reflector, a photo taken from a close distance (like the typical viewing distance in the cockpit) should show both the reticle and reflector plate assembly (as well as dirt on the glass) in focus at the same time. If someone could arrange to do this, he will find that the lens will always have to be set at infinity focus (or pretty close to infinity) in order to sharply image the reticle. (Note that a very wide angle lens and/or small aperture--large f/ratio--will to some extent compensate for differences in focus because of the larger depth of field.)

The optical gun sight was invented solely to offer the pilot a less stringent sighting arrangement than afforded by the old-fashioned ring and bead sight. The latter required exact alignment of the eye, whereas the modern gun sight allows the eye to wander around (due to shaking/buffeting/slumping under "G", etc.) and still be aligned properly. In other words, the optical gun sight eliminates parallax error in a zone as wide as the collimating lens's diameter.

Part of the aforementioned "discussion" centered around the effect of changing the line of sight if the pilot sat a little higher. One "debater" argued that the sight picture would worsen, his thesis being predicated upon the notion of the reticle being projected *onto* the reflector. Once again, wrong.

As long as the reticle is visible through the reflector, moving the eye's sight line higher would *technically* improve the view over the nose. In actuality, the somewhat small collimator/reflector size affords a too-limited range of eye displacement to make any significant difference in the view.

Now, if the collimator/reflector plate were to be made, say, 2 feet wide, the pilot would then have a similarly wide zone from which to aim. He could then move upward as much as 1 foot above the central sight line, with a definite improvement in the view over the nose. To understand this, always remember that the projected reticle *moves with* the pilot's eye, and always is seen at an infinite distance. What was just hypothetically described (the 2-foot diameter collimator) is exactly and precisely the same as re-mounting the existing Revi 1 foot higher than its current position.


Effects of Thick Armoured Glass

The incorrect properties ascribed to the thick, slanted screen in the FW190 were:

1) "Warping" of the view. Wrong. The view through a backward-tilted plane parallel optical widow is displaced *only*, in this case downward. The light rays entering the glass are refracted downward while traveling within the glass, but exit in the same direction at which they entered. All parts of the image appear perfectly normal.

2) Chromatic effects (color fringing). Wrong. A plane parallel plate is not a prism or lens, for which all or portions of the surfaces are not parallel. Even if constructed of materials having different indices of refraction all laminated together, the principle of plane parallelism applies.

3) View displacement of distant objects. Not entirely wrong, but the effect is quite small. For nearby objects, most certainly. But the more distant an object, the smaller the parallax caused by the redirected path through the plate. For objects effectively at infinity (more than, say, 200m), the parallax would be essentially zero, and the object seen directly and then through the thick glass would appear in much the same place. What leads to this misconception is photos taken from inside hangars or museums, where all objects are close enough that parallax in sufficiently significant to readily reveal refractive displacement.

03-25-2008, 07:19 PM
Originally posted by Lurch1962:
1) "Warping" of the view. Wrong. The view through a backward-tilted plane parallel optical widow is displaced *only*, in this case downward. The light rays entering the glass are refracted downward while traveling within the glass, but exit in the same direction at which they entered. All parts of the image appear perfectly normal.

Try changing the angle you look through the glass. Light from an object in front will refract
differently than from an object above and front. Light from an object high enough will not
refract at all.

Solution is to sit back far enough that it does not change *much*.

03-25-2008, 07:42 PM
[QUOTE]Try changing the angle you look through the glass. Light from an object in front will refract
differently than from an object above and front. Light from an object high enough will not
refract at all.[\QUIOTE]

Your're 100% correct, Gunz. This would more properly be called distortion, where the image scale changes with angle. But this is so subtle over the relatively large angle that by itself would be completely imperceptible.

The only way to see it would be to have a somewhat nearby grid pattern against which the view through the glass and some immediately adjacent perspex could be compared.

But again, for distant scenery the effect is rather reduced as compared to what occurs for nearby objects. The key to understanding what I'm driving at is that the light enters and exits the glass in the same direction, i.e., the original path is not deviated *in angle* upon exiting. The lateral translation induced in non-perpendicular light rays leads to the apparent displacement of objects which are sufficiently near that parallax is perceptible.

03-25-2008, 07:58 PM
So, in layman's terms you are saying that the armored glass would not reduce the visible lower framework ("bar") of the windscreen?

03-25-2008, 08:10 PM
So, in layman's terms you are saying that the armored glass would not reduce the visible lower framework ("bar") of the windscreen?

Didn't say that, or even address the issue specifically. But the answer was implied in a subtle way when I stated that the refraction operated in the downward direction when the plate is angled back. Furthermore, I elaborated at length on the fact that *nearby* objects are more displaced that those farther away, and the outer frame which is in actual contact with the glass would most certainly qualify as being close--as close as something on the outside could get.

Holding the thick glass plate in hand right now, this is amply verified. That is, the outside lower frame would be quite noticeably displaced downward, so that it would probably extend upward to one-half to two-thirds the un-refracted height.

03-25-2008, 09:06 PM
Just conducted an experiment, by making a crude "model" of the front of a plane to gauge the effect of the tilted thick glass plate. And it confirmed my thoughts on the matter.

In a nutshell, the thick plate has the effect of raising the pilot's viewing position by an amount equal to the lateral displacement of the refracted light path.

How did I conduct this experiment?

A flat piece of cardboard stood in as the the engine cowling, which I laid flat on the corner of a bench. An identical bench, some distance away, was to serve as a target which was centered in our gun sight, about to get blasted. So the cardboard and distant bench top were necessarily co-planar. (If the cardboard was long enough, it's far edge would have aligned exactly with the bench's edge at the top surface.)

Against the near edge of the cardboard I placed the glass plate so that its lower edge was *below* the cardboard and tilted back at a fairly steep incline. (In the FW the lower edge of the glass is *not* below the cowling's top surface, but I did this so that I could more clearly see the refraction in operation right up to the glass surface--think of this edge as the external frame "bar" we all gripe about.)

In this crude "model" the far end of the cardboard represents the farthest visible portion of the cowling, as might be seen from the cockpit.

What do I see when I sight *exactly* along the top surface of the cardboard, but just to one side of the glass plate, i.e., NOT looking through the glass? The cardboard's surface seems to merge into the top surface of the distant bench, because they are co-planar, as already stated.

But here's the neat part. Without changing my eye's position whatsoever, but now sighting through the glass, I see the following;
1) the edge of the cardboard in contact with the front surface of the glass is displaced downward quite noticeably,
2) the far edge of the cardboard is displaced downward by a smaller amount,
3) the distant bench top is hardly displaced downward at all, and
4) Where there was none visible before, there was now a very clear "gap" of empty space between the cardboard's far edge and the distant bench top.

It's as though, without actually moving a jot, my eye was raised upwards by a few millimeters. Through the glass, instead of sighting exactly along the surface of the cardboard, I'm seeing it from a slightly higher vantage point, looking *downward* onto its surface. And that's why the gap became visible, simulating the apparent lowering of the far end of the cowling.

Because the vertical *angular* displacement depends on the distance of the object, it's as though the "cowling", by some magic, became angled upward by what appears to be something like one degree.

To clarify... It's NOT as though the cowling has appeared to have been angled upward by a degree with respect to the rest of the visible scene. It's more accurate to say that the pilot seems to see it (and everything else visible through the glass) from an angle one degree higher than the real sight line.


The thicker the plate, the greater will be the effective raising of the pilot's viewpoint.

03-25-2008, 09:15 PM
What is this "parallax" that prevents distant objects from having light ray displacement?

03-25-2008, 09:23 PM
Originally posted by LEXX_Luthor:
What is this "parallax" that prevents distant objects from having light ray displacement?

It dosnt, just not nearly as much as close objects.

03-25-2008, 09:30 PM
Okay. Now, what is it?


Lurch -- cool setup there.

03-25-2008, 09:51 PM
What is this "parallax" that prevents distant objects from having light ray displacement?

Parallax is the term describing the direction difference between sight lines toward an object from two locations. For example, if you alternately blink your ayes, a nearby object will appear to "jump" back and forth against a more distant background. The angle through which the nearby object alternates is the parallax of that object as seen across the inter-ocular spacing of your eyes. Alternately, the angle subtended between your eyes as seen from said object is also that parallax.

Recall that a plane parallel glass plate deviates a light ray laterally, but not angularly (same direction leaving as when entering.)

Imagine a fly hovering 2 feet from your eyes. Interpose in your sight line a tilted FW screen (thick glass plate). A light ray which formerly went straight from the fly to your eye is refracted downward within the glass, then upon exiting is refracted upward by exactly the same amount--the *direction* is unchanged, but the path is translated laterally. Let's say for our FW plate this lateral displacement is 1 inch.

This now altered ray, when extended backward through space *undeviated as though the glass was not there*, and for the *same distance* at which the fly is hovering, will end 1 inch below the the fly's actual position, and hence present to you a noticeably different apparent direction of travel (parallax). One inch over 2 feet is a not small angle.

Remember, the distance to the fly appears basically the same whether the glass is present or not (in a rigorous treatment the small change in apparent distance would be accounted for, but for our purposes it's insignificant.) So if the deviated ray has a new path through space, it must necessarily appear that the object will be displaced *in angle*, depending on the parallax.

For a very distant object, the re-traced ray will still terminate the same 1 inch below the object. But if that object is 100 feet distant, you can see that 1 inch over 100 feet is a much smaller angle than 1 inch over 2 feet. The distant object's apparent position as seen through the glass will remain essentially unchanged from your point of view.

If I've been unclear, please ask more.

03-25-2008, 10:01 PM
I wish I had some lenses and glass to play with. http://forums.ubi.com/groupee_common/emoticons/icon_smile.gif

Food for thought.

03-25-2008, 10:13 PM
Here's how to mock up an actual functional gun sight.

1) Get a cheap magnifier, at least 2 inches in diameter. This will be the collimator.

2) Get a small picture frame and remove the glass. This will be the angled reflector plate.

3) Get a penlight, or flashlight with a small bulb (LED?). This will be the reticle.

4) Stand the flashlight on end, pointing up.

5) Hold the magnifier above the light, at a distance at which it appears in comfortable focus. This will be fairly close to the lens's focal length, and will thus work exactly like a real gun sight's collimator.

6) Hold the picture frame above the lens at a 45 degree angle, with one edge nearly touching an edge of the lens. Look through the flat glass to see the the re-directed image of the light bulb.

7) Fine tune the distance between the bulb and lens until, as you move your head around, the bulb's image appears to remain fixed in place when seen against a distant object. You'll then have eliminated parallax error by truly collimating the image, and your gun sight is complete!

OK, you might want to make a more proper device to hold the bits, but that's it in principle.

Cheap, easy and actually functional!

03-25-2008, 11:09 PM
cool thread Lurch,I just learnt me a WHOLE bunch of stuff http://forums.ubi.com/images/smilies/partyhat.gif

cheers http://forums.ubi.com/groupee_common/emoticons/icon_biggrin.gif

03-26-2008, 02:15 AM
What got me about the missing glass was getting PK'd by bomber gunner with 30 cal when the
bomber was totally within the front pane. What ain't there did not stop a bullet either.

The armor glass is over 2 inch thick and tilted to 29 degrees, so far back the revi just fits
under it. 30 cal should do no more than make a small pattern in it.

03-26-2008, 05:51 AM
Interesting read Lurch1962.
Thanks for sharing all the details with us.

03-27-2008, 12:07 AM
If I've been unclear, please ask more.
Pretend I'm a combat flight simmer. http://forums.ubi.com/groupee_common/emoticons/icon_smile.gif I think you are trying to say the light rays of an infinite distant point object are all parallel to the tilted glass, and when displaced, they are all displaced equally and are still parallel, so the direction of the image is the same with or without the glass. In other words, all the rays "look" the same whether they are the original ray or shifted ray.

However, the light rays of a near point object diverge along their approach to the glass. After displacement, these rays are still diverging. I can imagine a rising ray hitting the glass, displaced downward so it hits the eye instead of the original ray before the glass was set, and this new ray has the same rising slope it started with -- has a steeper slope than the slope of the ray the eye sees before the glass is in place. So, this displaced higher sloping ray seems to come from below -- trace back the line. The image is shifted downward for the near point object (but not for the infinite distant point object).

I think I can see this now, and it is a bit long winded.

03-27-2008, 10:00 AM
How much a light ray is refracted depends on the angle of incidence of light on the glass.
If your view through the glass covers much of an angle at all then it will be distorted by the
glass to match. That includes horizontal axis as well as vertical. Thick glass windows
generally have such width while it's harder to see in small samples.

The pilot sits back from the glass though, the system worked in practice even if you would
not want to use it for surveying or star mapping!

03-27-2008, 04:33 PM
You do indeed understand!

And as Gunz was indirectly alluding to, if the pilot looks perpendicularly through the glass (29 degrees from the vertical if the FW is in a level attitude), the light from an object is undeviated, and the apparent and true sight lines are identical. Maximum deviation of light rays occurs when the sight line through the glass is at near-grazing incidence (looking almost parallel to the *surface* of the glass.), at which point the sight line is translated by an amount essentially equal to the glass's thickness.

Another way to think of a thick armoured wind screen, at least when looking forward through it... it's a very subtle periscope. The pilot has a view from a position a little higher than his eyes actually are.


Has anyone tried to mock up a gun sight along the lines of my "prescription" given earlier?

Most of you will have at home (or the office) the three basic parts; magnifier, small piece of flat glass and small flashlight.


03-27-2008, 10:26 PM
The bar is reduced optically by the glass. The pilot sits back so the angle from the bottom
of the front windscreen is what, about 20 degrees? Light coming through the bottom of the
glass is shifted up more than light coming in through the top, the farther back he sits the
less difference bottom to top but the narrower his view *through that window*. Same thing
side to side except that in center there is zero refraction while at the side edges there
is some small amount.

I have a brother who is optician from optical school and over 20 years in the business.
What doesn't bother me much could drive him near to fits, LOL!
These refraction issues are why eyeglass inside curve is spherical set with center in the
proper place in your eye lens. Flat glasses are bad for your eyes but then the angle you
view that close is large and those are not tilted even.

It's not a big deal at all in the FW except to perfectionists, when CPU and videocard get
to the place where a combat flight sim can show distortion and if Oleg is still producing
new sims I'm sure he'll get a specialist in. Perspex bubbles have more 'interesting'
distortions depending on viewer POV, easy to tell from photos taken.

My problem is when the bullets come through unhindered! Or perhaps since the bomber was
Brit they had put some "English" on them?