Rifle Scopes optical spec on scopes?

[s002wjh]

just curious i never seen any manufacture provide detail spec of their optics. such as optical resolution/spatial frequency, focal length, optical cut-off frequency, field of view at min magnification vs max magnification etc. since I can't hold/see the optic, but if the manufacture provide these spec, it will tell me how good their optic is.



anyway, i thought would be good if manufacture can provide these detail. here is some definition for image system, these are use for any image system eg. cameras etc, but the optical definition for the optic should be same for both camera and scopes


f#=focal_length/aperture(mm).
Optical Resolution-Can be measured as limiting spatial frequency in focal plane (usually cycles/mm) or object plane (usually cycles/m). Bascially if you holding a card with different thickness of line separated by different distance, your will eventually see the line become blur or mesh up together thats the optical resolution.



Shorter focal length gives wider field of view
It also lowers the f# for fixed aperture, which increases the spatial cut-off frequency in the focal plane
Larger aperture (for fixed focal length) also lowers f/# increasing the spatial resolution
High FOV with high resolution requires a large aperture and short focal length (small f-number).
Optics
•–Lens or lens system on a camera in our application.
•Angular field of view
–Angle of coverage of the full focal plane array based on the focal length of the optics (radians or degrees).
•Spatial field of view
–Linear spatial dimension(s) of the field of view in the scene at a given distance that can be captured by the full focal plane array (e.g., 10 m at a distance of 200 m).
•Spatial cut-off frequency
–The highest spatial frequency in cycles per unit distance (e.g., cyc/mm) that can pass through an optical system without being completely eliminated.
–Depends on where you measure it (what distance from lens). Usually we measure in the focal plane or object plane.
•Angular cut-off frequency
–The highest angular frequency in cycles per unit angle (e.g., cyc/mrad) that can pass through an optical system without being completely eliminated.
–Independent of distance from lens.
•Object plane
–The plane in the scene that is to be focused by the optics onto the focal plane.
•Focal plane
–The plane behind the lens where the scene is projected and where we put our detector (focal plane array).
•Focal plane array (FPA)
–The detector array that is placed in the focal plane to sample the image and ultimately generate pixel values.
•Sampling frequency
–Number of samples per unit distance. It is one over the pixel pitch. Measured in samples/unit distance or equivalently in cycles/unit distance (if we think of a sampling cycle
•Nyquist frequency
–The highest frequency component present in a spectral analysis of a continuous signal. Usually equal to the cut-off frequency of the optics for us (and it can never be above the cut-off frequency). (usually measured in cycles/mm).
•Nyquist rate
–2 x the Nyquist frequency and the minimum sampling rate that can be used without aliasing.
–If you sample above the Nyquist rate, you are guaranteed to be able to recover the continuous information without loss. Exactly at the Nyquist rate, you may or may not be able to recover the signal depending on the particular signal and timing.
•Undersampling
–Sampling at a sampling rate that is below the Nyquist rate.
–Undersampling factor is the multiplicative factor by which our sampling frequency is below the Nyquist rate.
•Aliasing
–When you undersample, there are many possible continuous signals that would give rise to your samples. Thus, your samples do not uniquely specify one continuous signal, they only give you a wide range of possible “aliases” for that signal (you don’t know which is the correct one).
–Aliasing as a verb is the process of undersampling.
–Aliasing as a noun is the visual artifact you get when you undersample an image and display it through a D/A converter. It usually looks like a Moire pattern on quasi periodic structures or jagged diagonal edges.
•Pixel
–Picture element. The numerical value (or values for color) for one spatial location in a digital image. Each detector on the FPA produces one pixel.

 

[BALLISTIC]

Test equipment can be subjective, and eyes are definitely subjective. This has been brought up before, and no manufactures have decided to follow suit, and in reality it's not that important in regards to rifle scopes because even if you had all scopes tested on the same equipment within the same parameters few shooters could discern the meaning of the data. It's the same as some people think that USO has the best glass, others thinking that Nightforce does, and still others think that S&B does, or maybe it's Zeiss. The best way to find what your eyes view as the 'best glass' is to get behind different scopes, and 'see' what your eyes like. After that pick the configuration that suits your purpose and finally, get out there and shoot.

The information that is most pertinent when choosing a scope based on focal qualities when it comes to shooting are: Eye relief, Field of View, Exit pupil, and Parallax.

 

[s002wjh]

i agree that get behind the scope is the best ways, since human retinal act like an image system, each one is unique. but the place i live doesn't have all the scope i'm interest in, therefore the next best option is get as much data as possible for me to interpret. the data least will tell me some the important factor regarding glass quality, resolution etc. it can help to shorten the list.

i don't think test equipment can be subjective, since it really just output a set of data regarding the optic. in this case its using the same parameter and procedure to test the optic.
most manufacture give the eye relief, FOV etc. but it doesn't explain the glass quality, optical resolution, diffraction in the optic are parameters that indicate the glass quality.

 

[dcjs]

You are making a few simplified assumptions that about camera lenses (which only consist of an objective) that do not apply to scopes (which consist of an objective, an erector system with a certain (possibly variable) magnification and an ocular).

A few points in no particular order:

FoV at min/max magnification is specified in all spec sheets I've ever seen.

Focal length has no direct bearing on FoV in scopes since the angular FoV of a scope is small compared to camera lenses.

Lower f# does not necessarily mean higher resolution, that rule is a theoretical one for diffraction limited optics. To the best of my knowledge no scope has resolution that is practically limited by diffraction outside of extreme magnification ranges. Practically, optical systems with lower f# (within the practically important range) have better optical quality because of generally lower aberrations, and quite significantly so.

Publishing resolution/cut off frequency values would be either impractical or extremely demanding both on the testing procedure as well as the understanding of the potential customer. Although scientific data is not "subjective" as many would like to believe, interpreting the significance for the user is non-trivial. If for example max. resolution figures were published by all manufacturers and people started buying scopes based on the assumption that higher numbers equal better image, newley developed soptics would be optimized for max. central resolution, probably at the expense of higher performance throughout the FoV and low frequency contrast. The overall result would most probably be worse than a scope with well-balanced properties that may not look as impressive on a spec sheet that focuses on one number.

 

[s002wjh]

that is true, however, eye relief, and other parameter doesn't explain the quality of glass, diffraction, optical resolution does. for example how can you tell the optical clarity, quality of lens for different scope that has same eye relief, parallax, magnification etc without looking through it. when company design lens, they first has to have some kind requirements, that means diffraction/aberration, optical resolution, f# etc etc. these, all play into the quality of lens. no single parameter can be used for the overall system, in this case the scope.

if i'm purchase a nikon monarchy, a vortex pst, razor, elite or S&B that have similar eye relief, parallax and other parameter, then without looking through or know the price, i would assume the scope are the same, but when more data/information is given such as manufacture spec on lens resolution, aberration/diffraction and other optical parameter than least i would know the latter optics has higher quality lens.


its like purchasing a PC, i can't just look at the CPU frequency and ignore the spec for the rest system, but CPU frequency is an important factor.

 

[dcjs]

As for aberrations, there's about half a dozen different ones that would be interesting to an expert. You keep asking for "aberration" (singular) and seem to think that it is somehow related to diffraction (which usually doesn't play any significant role in a scope to start with). This is where the problems start, you would have to write a book to go with the specs for people to understand their meaning, and most still wouldn't. I don't pretend to really understand optics either, but I know just enough to know how little I know and how complex the subject is compared to the common "knowledge" about it.

There are indeed some theoretical design specs that are readily available to the optics designer and that would be interesting to an expert. The problem is, if a company started publishing those, it would be publishing data about "faults" of their scopes, because those data would all describe aberrations, which are deviations from a perfect image. The fact that the average customer isn't able to interpret this information correctly, together with the likely case that other companies (which may actually be selling an inferior product) would just stick to marketing their optics as "perfectly crystal-clear" instead of publishing their "faults" makes for a very unattractive environment for a company to start offering this kind of information, even if it has nothing to hide compared to the competition. On the other hand, if a company has something to hide, they wouldn't publish the data either.

 

[s002wjh]

well for basic optical resolution, looking at the diagram below, the optical resolution is how many line i can see before i can't distinguish the white space between each line or just too blur to see anything.
in other words if i draw 100 line/inch on a paper(from thick spaced line to narrow space) and hold it at arm length(object distance is another factor), and if i can just barely see the separation of the line, then my eyes resolution/cutoff optical frequency is 100cyc/inch.

the diagram show for lens, the distinction between line will eventually disappear. but for good quality well design lens, the spatial frequency is higher than lower one, might even higher than my eyeball.


anyway, would be nice if company would put their resolution spec out there. i know when i purchase a pc, i would need to know its frequency, for PC monitor i would definitely want to know the resolution.