Ray Diagram for an Experimental Lens Systems

[Ozen]

Hello,

I wanted to confirm a suspicion with how the Aimpoint optics work, but to do that I need to do some ray diagrams. I only ever did them with simple convex, concave, and spherical systems while at college.

From what I already know of how reflex sights work, the LED is placed at the focal point and is reflected off a spherical lens, typically a concentric spherical lens. The concentric nature of it permits light to be minimally distorted from the target. The goal is to get all the rays to reflect parallel with the gun bore axis.

My limited understanding is that while it is at the focal point this is true; but gun sights are adjustable. Aimpoint claims their two lens system is parallax free (below is their diagram), so I am assuming the second lens (correct lens) has to do with making the rays be parallel no matter where the LED moves (to an extent). However I want to prove this with ray tracing it at maximum and minimum adjustment values.

If anybody could help guide me with how you would do a ray tracing diagram for this type of system, it would be really appreciated!

 

[Drakkith]

Do you have any specifications on the lenses used? The lens on the rear of the sight appears to just be a flat piece of glass, which wouldn't have any effect on the light coming through after it reflects off of the mirror. So that wouldn't do anything to help the sight.

My limited understanding is that while it is at the focal point this is true; but gun sights are adjustable.

In what way are they adjustable?

 

[Ozen]

Do you have any specifications on the lenses used? The lens on the rear of the sight appears to just be a flat piece of glass, which wouldn't have any effect on the light coming through after it reflects off of the mirror. So that wouldn't do anything to help the sight.
In what way are they adjustable?

Thank you for the reply!

I do not have any specifications gathered on the lenses in question; I was going to mess around with different radii and look at some patents for this type of device. The rear optic is indeed a flat lens; i believe it is used to keep rain water out of the tubular scope and is coated with a polarizing coating along with an anti reflection coating for glare.

As for how they are adjustable: the source of the ray's in the diagram is the LED positioned as shown. But that is only in 1 case; that LED can move up, down, left, and right typically up to 80 Minute of Angle clicks. Doing that changes the ray diagram. That is why I wanted to see if a corrective lens is able to make the ray's parallel at both the maximum, minimum, and ideal positions. Since the lenses are symmetrical in the X and Y directions, I only have to look at it in terms of one axis. Unfortunately the patents I have found and read do not say anything on whether the correction lens does this or not.

If doing the ray diagram is too difficult to do by hand, I have been trying to learn the original Synopsys(TM); so if anybody is familiar with the software, an explanation with that would work too.

 

[Drakkith]

Well, I wish I could help you more. I only did 2 semesters in Optical Engineering and that was several years ago, so I've forgotten most of it. My only thought on this is that if the LED can only move a small amount compared to the focal length of the mirror, then there may not need to be any special corrective actions taken, as the deviation from perfectly parallel rays would be relatively small.

 

[Ozen]

Well, I wish I could help you more. I only did 2 semesters in Optical Engineering and that was several years ago, so I've forgotten most of it. My only thought on this is that if the LED can only move a small amount compared to the focal length of the mirror, then there may not need to be any special corrective actions taken, as the deviation from perfectly parallel rays would be relatively small.

I appreciate you taking the time to read and give my question some thought. The LED does move only a small amount as 80 MOA is very small; typically the focal point of these devices is no larger than 2 inches. Aimpoint and others in the industry adopted the setup because any variation with the rays not being parallel can result in a miss at 300 yards.

 

[Ozen]

I have a lens system that I want to see the ray diagrams for (mentioned in my other post) and I have considered using a software to do it. I found that Synopsys(TM) is a decent one to use and does not cost money. I began reading the tutorial manual, doing the examples I could, and following the starting guide. But to me, a mechanical engineer, all of it is vague. For instance, they use so many different abbreviations to run the MACros. And the concepts behind some of them make no sense to me; like the Pupil Wizard. Why is that needed? All I want to do is create a spherical mirror on surface 1 and have surface 2 be the corrective part of the lens so the rays emitting from an LED will be parallel upon reflecting and exiting the lens when placed within a certain defined region. Below is a picture of what I am trying to test. The LED I want to be able to adjust where it is relative to the optical axis in the Y direction. The first lens shown I am ignoring because it isn't needed and I know the outcome of combining the two lenses. So surface 1 would be the front of lens 2 and surface two is the back of it. the lens on the right side can be ignored as well.

But the software is anything but easy to learn. I have a bit of experience with professional software, primarily with CREO (which I am best with), Mathcad, MATLAB, and ANSYS. but compared to those, this is a nightmare. When I input my lens data, it doesn't describe where the thickness of the lens will be; is it always at the center or is it the tops? I imagine thickness does corresspond with the below image, but I am not 100% sure of it. And what determines how tall the lens will be (D)? Where can I find this value? I also want to try changing the Z direction of the light as well, from being at the focal of surface 2 to surface 1 or somewhere in between to see the results. The lens I am creating is the negative meniscus lens shown below. Then I want to use the software's optimization to ensure accuracy, but I haven't the slightest idea on how I would even write a MACro for it. As for the LED, I briefly read in the manual you can place the LED's but from what I saw it doesn't make sense, it is a funnel and the rays will bounce around in it? All I need is the light source to have rays from the center to the ends of the lens, that way I can confirm if the rays are parallel.

If anybody is familiar with this software, or has another easier software in mind (that doesn't cost, I don't have much money to drop on this stuff) I would greatly appreciate the help. Or if you know how to do the ray diagrams by hand, stop by my other thread and we can discuss it there. Thanks!

 

[Drakkith]

Aimpoint and others in the industry adopted the setup because any variation with the rays not being parallel can result in a miss at 300 yards.

I assume the sight is adjustable so as to allow you to correct for different ranges and mounting errors. Also note that if the reflecting lens is spherical, then the rays are absolutely not parallel after reflection. That would require a parabolic shape and an infinitely small LED, not a spherical shape and a real LED. So we're already dealing with a system that doesn't use parallel rays, despite what diagrams may say. Luckily the aberrations are likely small enough not to matter.

Aimpoint claims their two lens system is parallax free

I doubt it. Their sights most likely suffer the same small parallax error that other reflex sights suffer from. I expect that 'parallax free' actually means 'much less parallax than conventional gun sights'. However, according to what I read, some sights are set to be truly parallax free past a single distance, with a small amount of parallax being introduced at closer distances. For example, the Aimpoint M68 is supposedly parallax free beyond 50 yards, with a maximum parallax equal to the sight's optical window at close ranges. Source here.

Whether this is true or not, I don't know.

In any case, if we simplify this down to a spherical lens and a point-source of light placed at the focal point, you don't even need to raytrace. All the light will be parallel after reflection. So as you move your eye around the optical window the dot or reticle always appears to be directly along the sight's optical axis, just offset slightly, with the amount of offset equal to the distance your eye is away from the axis. The sight's optical axis being the middle of the window and parallel to the lens' true optical axis, which runs along the top of the sight.

Basically, imagine putting your eye up to that diagram. The incoming rays will always come in from the same angle, no matter where you put your eye. Since this angle points along the optical axis, which is either parallel to, or at at set angle to the gun barrel's axis, the sight always points very close to where the barrel is pointing, regardless of your eye placement. Moving your eye around the sight doesn't change the angle of the sight compared to the barrel, unlike what happens with iron sights, so, at worst, you've only introduced perhaps an inch or two worth of error in your shot, even if you move your eye all the way from one edge of the sight to the other.

I'm guessing that proper shooting technique essentially eliminates almost all of this parallax by keeping the eye in nearly the same place at all times, so distance shooting is easily possible even though some parallax remains. Any variations in eye placement between shooters is easily compensated by adjusting the sight.

That's my limited understanding of it all. As always, someone correct me if I'm wrong.

 

[Ozen]

I assume the sight is adjustable so as to allow you to correct for different ranges and mounting errors. Also note that if the reflecting lens is spherical, then the rays are absolutely not parallel after reflection. That would require a parabolic shape and an infinitely small LED, not a spherical shape and a real LED. So we're already dealing with a system that doesn't use parallel rays, despite what diagrams may say. Luckily the aberrations are likely small enough not to matter.

In my opinion and my university's professor on lens design, we both think that spherical aberrations will be small enough to neglect like you say. Although in all of the patents I've read they specify aspherical lenses in their system, which seems to just drastically increase costs for minute benefits.

In any case, if we simplify this down to a spherical lens and a point-source of light placed at the focal point, you don't even need to raytrace. All the light will be parallel after reflection. So as you move your eye around the optical window the dot or reticle always appears to be directly along the sight's optical axis, just offset slightly, with the amount of offset equal to the distance your eye is away from the axis. The sight's optical axis being the middle of the window and parallel to the lens' true optical axis, which runs along the top of the sight.

Basically, imagine putting your eye up to that diagram. The incoming rays will always come in from the same angle, no matter where you put your eye. Since this angle points along the optical axis, which is either parallel to, or at at set angle to the gun barrel's axis, the sight always points very close to where the barrel is pointing, regardless of your eye placement. Moving your eye around the sight doesn't change the angle of the sight compared to the barrel, unlike what happens with iron sights, so, at worst, you've only introduced perhaps an inch or two worth of error in your shot, even if you move your eye all the way from one edge of the sight to the other.

This part I understand. The problem that I don't understand is when you move the LED to align the bullet impact point with the reticle. The rays won't be parallel like when it is at the focal point, so the parallax is formed. One of my friends who builds firearms thinks it is negligible; on the other hand the newest sight designs coming out feature that corrective lens system shown in the first picture. Although they don't state the corrective lens redirects the LED's light to all be parallel upon bouncing towards the users eye, I assume that is what it does, or it would seem pointless to add another expensive lens to the system? And that is why I wanted to do the ray tracing to see if my suspicion is right or if they are correcting something else that seems negligible with the corrective lens.

 

[Drakkith]

The problem that I don't understand is when you move the LED to align the bullet impact point with the reticle. The rays won't be parallel like when it is at the focal point, so the parallax is formed.

You're sure the adjustment knobs move the LED and not the sight as a whole?

 

[Drakkith]

When I input my lens data, it doesn't describe where the thickness of the lens will be; is it always at the center or is it the tops?

It's almost certainly the center of the lens.

And what determines how tall the lens will be (D)? Where can I find this value?

The software that I've used before has a radius or diameter input that you specify for each surface.

I also want to try changing the Z direction of the light as well, from being at the focal of surface 2 to surface 1 or somewhere in between to see the results.

Might I suggest starting with a thin-lens design first? That way you don't have to worry about all these details. All we're really interested in is how the rays behave as you change the position of the LED. A parabolic or spherical thin-lens should work just fine to start with.

 

[Ozen]

You're sure the adjustment knobs move the LED and not the sight as a whole?

Yes, at least to my knowledge. US Pat. No. US8099897B2 shows their design for it. As you can see in the diagram the LED is directly incorporated in the adjustment mechanism. I tired inserting their diagram but it seems like the file keeps getting rejected...here is the link: https://patents.google.com/patent/US8099897B2/en

Might I suggest starting with a thin-lens design first? That way you don't have to worry about all these details. All we're really interested in is how the rays behave as you change the position of the LED. A parabolic or spherical thin-lens should work just fine to start with.

I am unsure how to even create the thin lens design in Synopsys(TM). I imagine it would just be a reduced thickness; but the other parameters don't make much sense to me. Like the pupil wizard as I said makes no sense, for reference the coding line for it in the tutorials is "OBB 0 5 12.5". I know OBB is selecting the dimensioning method and 0 makes the object at infinity, but 5 and 12.5 seem like random inputs to me (units are degree and mm).
https://www.osdoptics.com/files/SYNOPSYS(TM)%20Lens%20Design%20Software%20Starting%20Guide.pdf
Here is the link to the guide I've been following if that helps. On page 12 it shows the Lens Spreadsheet where I can change data and enter fresh data. As you can see there is no (D) dimension listed, only radii for the surfaces and thickness. As for the LED, I haven't the slightest idea on how to put that into the software.

 

[Drakkith]

Hmmm. I see what you mean. I don't think the dimensions matter to be honest. Whether it's millimeters, inches, or miles the geometry is the same. I remember seeing a couple of options for choosing dimensions as I browsed through the manual, but these shouldn't change the results of the ray trace.

As for the LED, I haven't the slightest idea on how to put that into the software.

You probably just treat it as a light source coming from the left side, like normal. There should be some way to move it closer than infinity. Check page 55 of that manual. I think I see something about an LED array.

 

[Ozen]

Hmmm. I see what you mean. I don't think the dimensions matter to be honest. Whether it's millimeters, inches, or miles the geometry is the same. I remember seeing a couple of options for choosing dimensions as I browsed through the manual, but these shouldn't change the results of the ray trace.
You probably just treat it as a light source coming from the left side, like normal. There should be some way to move it closer than infinity. Check page 55 of that manual. I think I see something about an LED array.

Okay I think I understand what you're saying to do; I'll give that a shot tomorrow night. If I am understanding what you are suggesting correctly, I would use something instead of OBB (object at infinite) and give all of the radii a negative value. That way the lens curves to the left instead of right, where the rays are coming from. I only question how I would be able to adjust the light source from off axis then? I remember reading how to turn a surface into a reflector, so I only see adjusting the light source off axis as a problem.

 

[Drakkith]

If I am understanding what you are suggesting correctly, I would use something instead of OBB (object at infinite) and give all of the radii a negative value. That way the lens curves to the left instead of right, where the rays are coming from.

That might work.

I only question how I would be able to adjust the light source from off axis then?

That I don't know. I don't think I can help you much further unfortunately.

 

[Ozen]

That might work.
That I don't know. I don't think I can help you much further unfortunately.

I appreciate you helping me with this. I found the software WinLens3D and was able to come up with the lens below.

The only thing left I don't understand is how to figure out where the focal point of this is. Maybe you can help me with this? I see the spherical aberrations this lens causes, but it is negligible. I want to find the distance from the mirror surface (right surface) to that spot where most of the rays converge. I am aware of the f=R/2; but my system has the light bending upon entering the lens at surface 1 (left). Wouldn't that through off that calculation for the focal point?

 

[Drakkith]

Not sure. I'll try to find some info for you tomorrow if I can.

 

[Tom.G]

According to the patent, any parallax created by moving the light source is compensated for by also moving the reticle.
If you download the patent PDF and use your PDF reader, look on pg.23, Ln.12.41 et seq. for a description.

Cheers,
Tom

edit:
p.s. That's why I generally go directly to the Patent Office website, Google strips and rearranges information for their online display.
US Patent Number Search: http://patft.uspto.gov/netahtml/PTO/srchnum.htm
US Patent and Trademark Office: http://patft.uspto.gov/netahtml/PTO/srchnum.htm

 

[Drakkith]

@Ozen
What were the specs for your lens and mirror? Focal lengths/curvatures, thickness of the lens, and refractive index?