quote:

The ability of a riflescope to form an image is called “definitionâ€. The quality of image definition in a scope, determines how clearly you can see the target, how accurately you can sight and how quickly you can aim and shoot.



How one arrives at the quality of definition in an optical system is dependent on three things;

1. Excellence of optical design,
2. Amount of correction present in that design,
3. Control of materials, precision of manufacturing and assembly to design specifications.

The way you determine excellence of definition is by resolution. This is a method of actually measuring what the eye can see in each system, and goes beyond that into the theoretical realm of possible resolution of the instrument. This is because most U.S. Optics “Hi Res†optical systems “see†better than the human eye on axis, some even off axis. All U.S. Optics “Ultra Hi Res†optical systems are better than the human both off axis and on axis.

Ultra High Resolution
Throughout the years, riflescopes have been made with one consideration; “design the optical system to the resolution specs of the human eye, and no better.†Most companies have not even gone that far.
The average eye will resolve about 40 line pairs per milliradian, which has become the industry standard for acceptance in determining the maximum resolution of a scope with the human eye. Problem is, their resolution falls off at the edge of field and will not typically do even 35 L.P.
Nine out of ten scopes one sees on the dealer’s shelf, will not resolve 50 line pairs per milliradian at the center of the field of view, let alone the entire field. Their justification for this has been thatâ€...you only aim with the center of the field, so why worry about the edge?†When reviewing riflescopes today, most editors are bright enough to use a proper resolution chart to determine full field resolution. Hopefully, they will soon learn to observe and be able to evaluate the other problems most scopes have, such as coma, chromatic aberrations, light transmission, fogproofing, adequate diopter adjustment, parallax and usable true eye relief, (true distance of use in which 95% of the field of view can be seen.) The term “Brightness†has no place in proper scope evaluation.

Resolution depends basically on two factors;

1. Correction of aberrations that degrade image quality,
2. All things being equal, a larger objective resolves finer detail than a smaller one.

Because the above items are apparent, it then becomes necessary to discuss aberrations in order to understand resolution. Once we understand this phenomenon, we then can understand the concept of ultra-high resolution.

Aberrations
Chromatic Aberrations -- The inability of a lens or a system to bring to a common focus light rays of different colors produces chromatic aberrations. Present when images formed by different colors of light, which make up “white†light, are at different distances from the lens or are of unequal size.
Result: These out of focus images form colored halos around the object you are looking at, and seem to blur them together.
Solution: Chromatic aberration is corrected by the optical design, combining different types of glass which will form several colors at the same point.

Spherical Aberration -- Inability of the different zones of a lens to form an image all in one plane at the same distance from the lens
Result: The middle portion of a convex lens has a longer focal length than the outer portions. Makes sharp focus impossible.
Solution: The designer must make sure the proper shapes of the lens to correct this problem does not upset the correction for chromatic and other aberrations.

Coma -- A spherical aberration that passes light obliquely through the lens.
Result: Comet shaped image of a distant point. The image appears blurred because each detail appears “smearedâ€.
Correction: Design must correct this problem.

Distortion -- Failure of the lens to form images of straight lines in the field as straight lines.
Result: Distortion occurs because the magnification of the lens system is not consistent throughout the entire field of view. A round object will appear oval, or a square will have a non-square geometric shape, etc..
Correction: The designer must design an orthoscopic prescription for the lens system.


Curvature of Field -- Occurs when the shape of the objective image is not formed on a flat plane, but on a concave area.
Result: The scope can be brought into sharp focus in the center of the field, but the edge of the field will be out of focus, and vice versa.
Correction: The erector lens system in particular, must be corrected properly to achieve necessary flatness of field image.

The U.S. Optics Ultra-HiRes series of optical prescriptions have been thoroughly optimized to make the proper corrections for all aberrations to achieve the highest resolution possible. Lenses are manufactured, (as all U.S. Optics systems are), to exact tolerances and quality control standards. Any deviations from tolerances in grinding/polishing of lens components or machining operations produce unwanted aberrations and deteriorated optical performance. The U.S. Optics Ultra-HiRes series of optics undergo extra steps in an already exacting manufacturing process, to ensure that these optical prescriptions are manufactured and assembled as perfectly as possible. These steps include the following:

1. Higher resolution optical design.
2. More color corrective glass of the highest quality necessary to achieve the conditions we need.
3. Extraordinary testing procedure insures the following to give the very highest quality.
4. Coating procedures above and beyond those necessary to achieve high resolution.

Optical Terms and their Definitions

Field of View
ANGULAR FIELD: Expressed in degrees of angulation diverging from the objective.
Example: 5° = 65 feet @ 100yds.
LINEAR FIELD: The angular field X power= distance from side to side of the area viewed through the eyepiece of the scope
How it works optically: Generally, decreasing the eye relief widens the field of view if properly designed.

POWER (Magnification)
In a telescopic sight, the first number indicates the power.
Example: 15x58, 15x is the power, 58mm the objective diameter (1mm = .0394in.) This means that the image is magnified 15 times the normal size, making an object that is 1500yds away appear to be 100yds away.

COATINGS:
Lens coatings reduce glare and the amount of light loss, and increase transmission and contrast.
Reflected light is a very important determining factor in scope optical systems. 3-5% of transmitted light is lost per each surface of glass throughout the lens system without any coatings being used. When 5-7 surfaces of a 10 or 11 lens system is uncoated, 50% or more of the light is lost from scatter and reflection.


The following is a breakdown on how this works;
COATING COATING TYPE LIGHT LOSS
N.C. NONE 40-42%
F.C. MgF2 18-22%
M.C. MgF2+BBC 11-15%
F.M.C. BBC 10-14%
U.S. OPTICS FSSBBC 5-8%
U.S. OPTICS FSSBBC .6% per lens

N.C.=No Coating
F.C.=All glass surfaces coated
M.C.=One or more lenses multi-coated
F.M.C.=All glass surfaces fully multi-coated
B.B.C.=Broad Band Coating
F.S.S.=Full Spectrum + Specialty Spectrum
U.S. Optics=All lenses and glass surfaces fully multi-coated for proprietary broad band spectrum, with specialty band emphasized for maximum contrast and resolution. Special top coat on eyepiece and objectives.*

BRIGHTNESS: (not a scientifically valid term) (Resolution) Definition or resolution is determined by;
A. Amount of light present at target,
B. Size, type and quality of glass used for lenses,
C. Amount and quality of light passing through the scope, determined by;
1. Coating type and quality,
2. Restriction of scatter in the interior of the scope,
3. Amount of correction in the design,
4. Magnification (a 2x increase in power, diminishes light and resolution by 1/2)


FACTORS TO CONSIDER:

1. Larger objective lenses admit more light into the system,
2. Larger objective increases optical performance,
3. Higher magnification decreases other optical performance, (in most cases),
4. Higher magnification decreases resolution, (in some cases),
5. Higher magnification and smaller objective decreases and limits exit pupil, or usable physical parameters of the optics.
6. Higher magnification increases susceptibility to mirage.
*7. A proprietary coat (last coat) on all objective and eyepiece lenses to help prevent scratching of coatings. In addition we have special proprietary optical glass covers available at extra cost. These can be replaced when scratched.



From "Optics Tech-Optical Design", US Optics Web Site