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Rifle Scope Design

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Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: October/24/2014 at 10:03
GarageShopIt View Drop Down
Optics Apprentice
Optics Apprentice

Joined: May/23/2014
Status: Offline
Points: 50
So I've bought or perused a few books on optics, ranging from SPIE materials to old post WW2 era home guides and I've decided that for my next machining project, I want to make a rifle scope. I've got the design more or less worked out but I wanted to check some of my conclusions and assumptions against some peer review.

The design itself is a three or four lens fixed power setup (I’ve got both written up), in the style of 3-gun/sport shooting optics (where the scope only has a "bell" shape on the eye piece end), a second focal plane BDC etched reticle, and is externally adjusted. There's more to it, but these are the relevant bits of info going forward.

The exit pupil. From what I've learned, the exit pupil diameter is the diameter of the column of light that leaves a scope. The image that the scope produces is contained within this column. Relative to the human pupil under any given lighting conditions, if the column's diameter is too small you end up with an image that is both sensitive to the brightness of the target and harder to locate in rapid shooting situations. On the other hand, if it is too big, your eye/pupil will have to rove the column of light in order to see the full image BUT you'll be able to acquire a sight picture relatively faster.

Based on those assumptions, I've decided to fix the exit pupil diameter to about 5 mm. Smaller the 7 mm of a fully dilated human pupil (i.e. like in extreme darkness) but greater than the 2 mm typical of target scopes. My BDC reticle design extends some of the reference lines to the edge of the field of view, and I don't want to have to physically re-position my eye in order to see them but I still wanted relatively forgiving eye placement under daylight shooting conditions.

This is a design aspect that I'm still a little iffy on, both in terms of my assumptions and in terms of my design choice - I maybe wrong about how the cone of light interacts with the eye and a larger than necessary exit pupil (even significantly larger) may not meaningfully affect a shooters ability to use corrective references at the extreme edge of the FOV or at extreme shooting angles. For example, it might be that in larger than necessary exit pupils, you don't have to re-position the eye, so much as look around the column of light, which would be much less inconvenient. My understanding here also plays a role in the next design consideration.

The objective. My current theory about the objective diameter is that it in rifle scopes it doesn't matter as much as it does in other applications. If you took physics at the high school or collegiate level you might recall that the magnification of a system of lenses is equal to the entrance pupil diameter divided by the exit pupil diameter. Assuming a fixed power scope, a fixed diameter exit pupil, and external adjustments, it seems to me that there is only one size diameter that will work. Any objective/entrance pupil larger than "magnification X exit pupil diameter" and you're wasting light or overshooting your magnification. Any smaller and you're hitting under your target magnification. For internally adjusting scopes, I'm half convinced that the only reason to have a larger than necessary lens is to give the internal lens setup room to move around without having the edge of the field compromised by the barrel/bell of the scope body.

If I'm understanding this correctly, an externally adjusted scope can be significantly smaller than an internally adjusted scope of the same optical design and yet still have the same image quality with a smaller objective. That seems too good to be true. Between that and the fact that image quality is partly dependent on objective diameter, I'm concerned that I'm misinterpreting something here and potentially losing out on some benefit. If I'm wrong about the large exit pupil being a problem, then I could potentially increase objective size for the image quality benefits. If I'm wrong about the practical limitations of objective diameter I want to know why so that I can weigh the pros and cons of a larger objective better. As it stand though, I don't see how you can design a scope for a specific exit pupil size and then get any benefit whatsoever from a larger than necessary objective.

Glass Types and Lens Cell Design. I've come across a couple of tutorials and primers on lens cell design for high shock applications (like field-use rifle scopes where the glass has to resist dislodging/shattering from repetitive recoil or multiple drops) but I'd love more info it, especially as it relates to MIL-STD 810. Something I haven't been able to find low hanging design fruit for though, is glass type selection. I'm no slouch when it comes to materials science, the professor that teaches it has some insane standards, but the material and optical properties of different glasses are waaaaaaaaaay beyond even the aggressive standard set by my school (where the emphasis is largely on steel and its alloys). So, if you know: what are the preferred glass blends or families for rifle scope lenses. The ones that strike a good balance between optical characteristics and resiliency.

Glass Purchasing. I've only managed to chase down two catalog lens suppliers from some Amateur Telescope Making resources and the prices they've listed for the diameters typical of rifle scopes are surprisingly reasonable. Those two are surplus shed and anchor optics, and once again, the "too good to be true" part of me worries that their quality is suspect for how good their prices are. They might not be, but if anyone has experience with their products or what typical price points for rifle scope lenses at the entry level are, that would help. Besides those two, does anyone know of any others? Or if someone has experience with it, how much more expensive is it to have lenses made to a specific set of diameter and focal length requirements (prescription lens style). Some ATM articles have suggested that custom made lenses are not that much more expensive. Having already asked about glass families, I'm perfectly willing to consider plastic lenses suppliers if they offer decent quality.

Other Considerations. The design, in so far as lens diameter, focal length, and spacing is concerned, is more or less set. I've got access to ZEMAX through my university, so if I can figure it out, I'll put my requirements into the program and run an optimization before I purchase BUT I'm not sure how realistic that is (its not exactly simple software) and I'm not technically in the class that uses it. As for the reticle, I'm putting it in the second focal plane since it'll be home brew and likely not as precise as factory reticles. By putting it in the second focal plane, I'm trying to avoid having any positioning or relationship errors magnified by the scope's power (or at least limit it). Also note that the scope is externally adjusted to simplify machining and assembly since I don't have the lathe tool for making ball shapes used in the spring loaded ball-joint of typical internal mechanisms. Stith style mounts will be used - you might have to google it, they’re ancient and have been out of style for a looong time - because they are highly adjustable and super easy to machine externally adjusted mounts.

Edited by GarageShopIt - October/24/2014 at 14:09
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: October/24/2014 at 10:09
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Optics Apprentice
Optics Apprentice

Joined: May/23/2014
Status: Offline
Points: 50
  • What is the affect of a larger than ideal exit pupil diameter on the scope's user? Does he have to physically re-position his head/eye-pupil within the exit column in order to see the full image, or can he simply keep his head in the same place and look up/down/left/right (by rolling the eye in the socket) in order to see the full image?
  • Is there any image quality benefit to using a larger than necessary objective lens (in terms of diameter) for a scope, if you have a specific magnification and exit pupil diameter in mind?
  • What are some of the glass type/families that are commonly used for rifle scope lenses?
  • What are some supplier of catalog lenses?
  • Is it significantly more expensive to buy custom diameter and focal length lenses (vs buying best-fit lenses from the existing catalog stock)?

Edited by GarageShopIt - October/25/2014 at 13:54
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