Popular Target Scopes - Spec Comparison

[Fred Bohl]

I offer the attached Popular Target Scopes.pdf file for your review and reference to stimulate the understanding and a discussion of the optical design decisions made by the manufactures and their impacts on the specifications of several popular target scopes.

Click Here

For those of you that have had the opportunity to use or at least try two or more of these scopes, it would be particularly informative if you could relate the optical differences that you observed to the data presented and share that knowledge with all of us.

 

[rstreich]

Alright, Fred, you inspired me to go and study a bit. I found this web page to be quite helpful in helping me understand some of the bits you were throwing around.

Your emphasis on what seemed to be more dimensional characteristics of the scopes got me started thinking that something was missing,and I usually try to avoid thinking when I get home). It sort of reminded of the numbers that you hear thrown around at some stereo shops.

It seemed like the quality of the glass itself was being overlooked and that's when I started digging around a bit. On the page above, I came across a mention of the Strehl Ratio and then found this helpful page.

So, how can we tell that any of these optics are really diffraction limited when in fact the glass quality could be the limiting factor? Let me take it one step further: Are there even sufficient measures for glass quality? For example, can you quantify color correctness or any of the multitude of things that a human ocular system depends on to correctly discern images?

I hope I don't sound like I'm being critical of what you've written here,'cause I'm not. I'm just trying to put the measurements into perspective and I'm using my experiences of shopping for audio equipment as a basis. For example, in the audio world, there don't seem to be any useful numbers for a qualitative comparison of components, at least, none that are published. So, I was just wondering if much the same were true of optics.

 

[Fred Bohl]

Dave,gunamonth)

Thank you for your comments. I purposely avoided any comparisons of functionality of scope mechanics. My choice of scopes was for those of higher power to get into the realm where the designers had chosen to to use magnification and objective size combinations that were operating above the normally recognized diffraction limit. Your last paragraph on "comparison of optics" is the kind of input I was hoping for.

Robert,rstreich)

I just love it when a plan comes together. I'm glad that you are at least challenging my assertions,if not criticizing) based on your independent research and deductions.

Quality of glass and coatings was not what I was comparing and with intent. As you point out quality comparisons are difficult to define with objective testable criterion.

Even the Dawes limit for diffraction is a subjective test based on observations,although long accepted due to agreement by observation of many observers over many years with many instruments). Note that the formula I gave is for the wavelength of green light,at the peak of the normal human visual response spectrum) by long mutually agreed convention. It would be very different for filtered light, illumination by artificial light,at night) or for an observer with impaired vision,such as color blindness).

The practical resolution or quality characteristics as experienced by various observers have almost unbounded variability. Visual abnormalities,deviations from "normal visual acuity" and "normal" color response) can give optics designers nightmares. That is why I attempted to provide data based on the accepted "normal" standards as a reference.

May be we will see replies like the one from Dave on optics comparisons that will also include the observers notations of visual limitations. For example: I have astigmatism and some old damage to my right retina,too close to an RPG 40 years ago) that means I have to do any serious qualitative comparisons with my left eye and use correction for the astigmatism.

Keep challenging me though. Maybe we will all learn to be discerning users and consumers.

 

[rstreich]

...The practical resolution or quality characteristics as experienced by various observers have almost unbounded variability. Visual abnormalities,deviations from "normal visual acuity" and "normal" color response) can give optics designers nightmares. That is why I attempted to provide data based on the accepted "normal" standards as a reference....

Thanks, Fred. I kind'a thought that would be the case.

I think I'm a long way from challenging any of your assertions here, however. Quite the contrary, I've learned that those big bell objective lenses that I'm fond of are useful for a whole lot more than "enhanced light gathering" or some of the other useless info I hear when shopping for scopes.

The Dawes Resolution Limit seems like an excellent tool to use for selecting optics. Now I have something I can quantify when I'm trying to decide between various configurations.,This is probably also true of match magnification, but I only skimmed the calculations and haven't absorbed exactly what is being quantified in it.) For example, in looking at your chart, I can now quickly see that I just might not gain any greater resolution by selecting a 45x Leupold over the 40x. I also know that I still have to compare both of them visually to determine if that is true or not, but I can be more critical in my comparison and not fall into the "more must be better" trap.

Could you put something else into perspective for me? Based on your observations of consumer-grade optics, are we in fact diffraction limited? Using the case of the two Leupolds for example, is the glass that we typically see in commercial rifle scopes at or above that 80% Strehl Ratio where the DRL really comes into play? If not, how far do you think we are from it?

robert

p.s. I'm really hoping Paul can convince you to collect up all this info into a primer to add to his ever increasing library. It's great stuff that I haven't seen addressed on any of the shooting-related sites that I frequent.

 

[Fred Bohl]

Robert,

It is my carefully considered opinion that even the best of today's high end telescopic sites and spotting scopes are operated diffraction limited at high magnifications. Part of the reason I selected the scopes for this data set is that either I or others that I trust,except for the March/Koto scope) have verified by testing under controlled conditions on calibration targets that they are in fact diffraction limited to values very close to those calculated for resolution.

Having said that, I do not believe that the quality of the glass used is the limiting factor. There are too many combinations of variables: glass, lens grinding, lens polishing, coating formulation, coating application, lens mounting and optical alignment in the manufacturing process particularly for relatively low cost,these scopes have very high mark-up/margin) and fairly high volume. Dawes was working with extremely simple uncoated selected lenses made in low volume one at a time by a craftsman. As our technology has advance to aid in perfecting automated methods and materials, we have also complicated our telescopes to achieve ever higher performance goals and expectations. We are asking a lot more than to resolve the existence of two stars,a binary pair) versus a single blurry spot of white light in a black sky. History seems to suggest that the Dawes Limit still holds as complexity and expectations keep pace with technology.

I'm found of the pair of Leupolds in the comparison chart to illustrate some of the potential value of understanding the optic design parameters impacts. We can safely assume that the two share identical component and manufacturing methodology quality. In fact the only difference appears to be a very slight change in curvature and position of the objective lens to achieve a slightly longer objective focal length and consequently a slightly higher magnification,45x versus 40x). The negative consequences of this are reduction of Exit Pupil Diameter,1.13mm to 1.00mm) and Relative Exit Pupil Area/Brightness,1.28 to 1.00) as well as an increase in Magnification Ratio,1.72 to 1.93) which is farther beyond the the resolution limit. The actual resolution limit stays the same. Therefore the only justification for using the 45x model would be that the 12% larger image size versus the field of view allows the user to perceive some important information that justifies the lower brightness and slight increase in feature edge blurring.

For your amusement, of the 8 shooters using the Leupolds queried on that selection, 4 chose the 45x and 4 chose the 40x. One of the 40x users tried using the 45x but after one season swapped for a 40x. Also of note, all 4 using the 45x are primarily long range,600 and 1000 yard) shooters. All gave a similar reason for their selection that boiled down to their selection "worked better for me". It would appear that you still need to try it before you buy it but I hope this discussion will provide help in knowing what to look for in your visual comparison.

I would like to add some further comments on the Diffraction Limit and Magnification Ratio impact. Borrowing from the testing I have done and reports from the tests of others relative to the other thread about spotting scopes, there appears to be a sharp dividing line on the impact of crossing the Dawes limit on two distinct groups of observers. For those of us that come from a background of astronomy, we are used to the effects of diffraction limited optics at higher magnifications and as a consequence seem more inclined to accept those effects in pursuit of the images useful to our purposes. However those who are experienced with typical spotting scopes operating at magnifications below or just above the Dawes limit seem far more offended by blurr effects in their perception of image quality.

Re your p.s. - I can't speak for Paul, but your thoughtful responses and questions and those of the others on this and the spotting scope thread are encouraging my expanded testing and work on these threads. Thanks to all.

 

[Fred Bohl]

Robert

I will assume that you have been busy or are off doing your own testing and/or further research rather than the alternative - that I have bored you to death. I would like to revisit your post of 7/02/07 and take another go at more direct answers to the questions you have posed.

First be assured that there are in fact quite objective and very exacting testing methods and equipment for the lenses, assemblages of lens and complete optical devices,like telescopic sights) to verify most of the design parameters intended. Also be assured that most optical products we buy are in fact tested to insure some measure of compliance with the intended result,more testing and tighter compliance values for the better quality devises).

All real optical devises are diffraction limited by definition since the objective lens diameter or other aperture restriction is of finite rather than infinite size. As you read in your cited links the question is what value should be used for the diffraction limit. The cited values include:

Raleigh's Resolution Limit,MOA) = 2.33/Objective Diameter,mm), approximate 1/4 wave error, Strehl Ratio = 0.82
Dawes's Resolution Limit,MOA) = 1.93/Objective Diameter,mm), approximate 1/5 wave error, Strehl Ratio = 0.88
Sparrow's Resolution Limit,MOA) = 1.17/Objective Diameter,mm), approximate 1/8 wave error, Strehl Ratio = 0.95

All three are based on observational experiments reflective of the time frame and quality of instruments used by the experimenters. I chose to use the Dawes value in my calculations as being the most representative of amateur level optics of today. Sparrows very optimistic value has only been verified by the very big and super quality major observatory all mirror telescopes using high end cameras or digital image sensors not human eyes. Note, excellent individual mirrors and lenses are being made at 1/10 wave error, Strehl Ratio = 0.97, but actual telescopes have more elements so that an overall 1/5 wave error is very good. For example, even the simplest fix power telescopic sight has 4 lenses so 0.97 x 0.97 x 0.97 x 0.97 = 0.88 overall. Also all mirror telescopes with direct film or digital image sensors have at least 2 mirrors so 0.97 x 0.97 = 0.94 overall.

Modern optical test equipment uses either high resolution film or high resolution digital imagers for the observation,minimum imager resolution is 10 times better than the required device resolution). When us mere humans test optical instruments we use our own visual system as an imager . As wondrous as that is, it is not very consistent or predictable individual to individual or even with a single individual observer from observation to observation. That is the reasons for my defining my observer as having "normal" human visual acuity. For a more meaningful description of human visual resolution and acuity, see http://webvision.med.utah.edu/KallSpatial.html to get a sense of the variables involved and why we are not dependable test standards.

 

[rstreich]

I will assume that you have been busy or are off doing your own testing and/or further research rather than the alternative - that I have bored you to death....

Actually, it wasn't really any of the above, Fred. I have been struggling with a few gnarly technical problems at work this week that have left me a little short on brain juice, but I think your previous post just left me without any questions. Apart from a fair bit of digesting, about the only thing I was intending to add was a spreadsheet with your equations in it. I was hoping to get the time and ambition to put that together this weekend. I thought it might make a convenient tool.

BTW, I see that you're a Cheesehead. What part of the state? Ever get to the Twin Cities? If so, let me know when and I'll buy you your choice of beverage.

robert

 

[Fred Bohl]

Robert

I've been known to get to your Twin Cities on occasion so if I do I'll look you up. I'm in the northeast part of Wisconsin. Neenah specifically which is on northwest shore of Lake Winnebago about 40 miles SSW of Green Bay and 10 miles north of Oshkosh,site of the Experimental Aircraft Association). Don't you love those nice Anglo Saxon place names.

The EAA convention is in a couple of weeks,biggest civilian air show in the world). If you would like to come to visit that some time you could stay with us,all the motel and hotel rooms for many miles around it are booked for years ahead). There is no beer or booze on the grounds of the show,these folks are pilots) but this being Wisconsin I think we could find you a libation to savor.

Enjoy your spreadsheet building that would be a very nice tool to publish here. I'm off to the Wisconsin State Hunter Rifle Championships at the Van Dyne Sportsmens Club this weekend.

It looks like this topic laid a egg so far. Just you and Dave,gunamonth) responding. I had hoped for more but maybe it is just my style.

 

[chuckw2]

Hell Fred, you didn't lay an egg....This is a GREAT post.

It cleared up a lot of doubts for me...

Very,very interesting, all of your post interesting.


Chuck Wetherington


PS Thanks for your take on Wipe-Out.

 

[Fred Bohl]

The article on the main site, Nielson's 6.5x47 Nationals Winner, contains a section entitled 600 – Yard Optics. That section includes the following excerpt:

- - - - - - - -
However, during the course of the match, Don noted that his friend Lou Murdica, shooting in the same relay, was able to see bullet holes quite reliably until the mirage came up in the afternoon. Lou was using the new March 40X scope. Don noted that Lou was definitely able to resolve 6mm and 6.5mm bullet holes in conditions where the Leupold,or even the Nightforce) could not.

"Seeing is believing" according to Don, and at the end of the match, Don purchased Lou's March 40X. Lou, who finished third overall, said his March scope definitely offered an advantage: "Most of the time I had no trouble seeing 6mm bullet holes at 600 yards in both the white and blue areas of the target. Most of the other guys had trouble seeing their bullet holes with other scopes. This made it easier for me to make a call to hold off on a shot." Lou and Don also both believe that the new March scope offers unrivaled reliability. Don tells us "I'm confident in the scope--that it will hold zero and maintain consistent click values."
- - - - - - - -

When I started this thread I was particularly hoping for input from Lou Murdica and other users of the new March 40x – 52mm and comparisons to the other scopes in my table for real performance. I will have to use the above to hopefully keep the discussion going. One can hardly get more authoritative input than from Lou Murdica and Don Nielson.

The fact that the March 40x – 52mm out performed the Leupold was expected from the data in my comparison table. However the same comparison data would suggest a slight edge to the Nightforce 12-42x – 56mm at 42x but Don and Lou reported better usable results for the March over the Nightforce.

Previously Dave,gunamonth) had reported less than optimum image quality of the Nightforce variable compared to the fixed Leupold but better usable resolution for the Nightforce. These reports are similar to comments in the thread BEST spotting scope? in which several posters noted lower image quality of zoom versus fixed power eyepieces used at the same power.

I believe that these observations are consistent with my discussion of the quality challenges inherent in more complex designs with more elements presented in my 7/6/07 post. The variable power Nightforce as with Zoom eyepieces must of necessity add additional elements to accomplish the variable power,zoom) function as compared to simpler fixed power designs. Therefore with otherwise comparable specifications, the performance edge will probably continue to favor the fixed power scope.

 

[rstreich]

Fred, My brother-in-law and nephew have been attending that airshow forever. So, it wouldn't surprise me if I wound up taking you up on your very kind offer. Thank you.

I'm with Chuck. I don't think this thread laid an egg at all. However, I think there is a little bit of distillation of all of the concepts that you introduced us to in these threads. That's one of the reasons I want you to write a full article. It'd give you a chance to explain more fully some of these measurements and what they mean.

For example, I didn't really get what you meant by diffraction limited until I went to another site and saw the waveform illustration. You might have said it, but if you did, it didn't sink in when I read it. I think if you were able to pull it all together in an article instead of a series of posts, it would be much easier to grasp.

...The fact that the March 40x – 52mm out performed the Leupold was expected from the data in my comparison table. However the same comparison data would suggest a slight edge to the Nightforce 12-42x – 56mm at 42x but Don and Lou reported better usable results for the March over the Nightforce.....

This is the sort of result that made me wonder if we were truly diffraction limited with the scopes that we typically use. For example, I don't own a NightForce yet,my scope purchases can't seem to keep up with my gun purchases and gunsmith bills), but I've heard that they can be bluish in color or a bit washed out as gunamonth describes. Both of these could describe chromatic aberration. Also, considering the number of additional lenses and surfaces in a variable power scope, could it be that diffraction isn't the major limitation? Just a thought.

robert

 

[Fred Bohl]

Robert

You have suggested that I write an article rather than posts to threads such as this one a couple of times now. While I appreciate your confidence that I could write such an article I'm not sure that is true. For example in the other thread,Pat's BEST spotting scope?) I included a link to a brief paper that I wrote to explain the interrelationship between Magnification and Diffraction limits and introduce the concept of Match Magnification. It seems clear that it did not accomplish the intended objective. I have attached it here for your convenience to review and assess its effectiveness.

Part of my career included teaching new skills and concepts to practicing engineers,such as: Project Management, Process Analysis, Failure Mode & Effects Analysis, Design of Experiment). It was my experience that while the text versions of these courses were very good, the give and take of a seminar style presentation was the quickest path to understanding of new concepts. The ability to ask questions and discuss concepts while they are presented was very efficient and well received.

You are correct in that if the scope designer lets the sales department overrun good judgment so that you wind up with too big a zoom ratio, side controlled parallax,objective focus), reticule clutter blocking too much of the light path and cropped objective shape you could easily introduce enough optical aberrations that the resolution limit imposed by diffraction could become a secondary issue. Let us also remember that the altered light path used for internal adjustments causes its own aberrations by directing the light through refracting lenses off angle to the optical axis of the lenses. This is also aggravated by our demands for more range of internal adjustment which in turn means light paths still further off the lenses and system optical axes.

You are also correct that the more lenses and surfaces needed the more sophisticated coatings are required to reduce internal reflection losses and the harder it becomes to avoid chromatic aberrations. That is probably why there are reports of bluish color cast and washed out images of the Nightforce variable when compared to the fixed Leupolds or March. Note however that Dave reported the Nightforce to have more usable resolution than his Leupolds while Don and Lou gave a slight edge to the March over the Nighforce in resolution.

 

[rstreich]

Jeez, Fred. Now I feel kind'a stupid. Somehow I must have skimmed over the reference to that paper. It covers things pretty well.

The one part that lost me was the concept of the Airy Disk from the illustration I equated the Airy Disk with the aperture. But that obviously isn't true. These are the two sentences I didn't grasp:

The Airy Disk is getting smaller when the diameter of the aperture is getting bigger. On the other hand the Airy Disk is shrinking with smaller wavelengths.

I also didn't grasp the equation for the radius of the Airy Disk as I don't know what lambda or "D" represent in this context. OTOH, I'm not sure that I care as I'd rather leave that part up to you .

I especially liked the food for thought on the bottom of page 5. I might have to rethink getting a variable power scope for long range comp.

As to Dave's observation that his NF has better resolution than his Leupold, I can't really say. I wonder, however, if it isn't related to a couple of experiences I've had. For example, I was comparing the Zeiss T*Fl binoculars with Swarovski ELs last year. I had an immediate preference for the Zeisses in the store 'cause they just seemed brighter and clearer. However, when I compared them to the much warmer Swarovskis against a chart they had in the store, I couldn't discern any greater resolution with the Zeisses. Any thoughts on how color rendition might play into our perception of resolution--real or imagined?

If I had unlimited funds, I'd just buy one of each and take them all on some extended hunts, but, I don't foresee that happening any time soon.

 

[Fred Bohl]

Robert

The background of the discussion of diffraction limited optics is the science of astronomy and more specifically that of the analysis of telescope optical properties as they impact our visual observations of celestial objects. Setting aside nearby planets and very large aggregations of objects such as galaxies and nebula,gas clouds), all that we observe with astronomic telescopes are stars that are so far away as to be point sources,too small to have measurable size). What we instead actually see is the interference pattern created by the inbound light wave front and the limiting aperture of the telescope,usually the objective lens for our discussion). If you look at the example images on page 4 of my paper this is how a star appears,or a binary pair of stars) that have size,or separation distance) below the resolution limit and using sufficient magnification. The central disk is what is known as the Airy Disk named for Sir George Biddell Airy British astronomer,1801–1892) who discovered and described the phenomenon.

The minimum diameter of a detectable Airy Disk,or the minimum resolvable separation between similar diameter pairs) is what defines the resolution limit of the telescope. In the equation you mentioned, q ang = 1.22 * lambda/D,for angular resolving in arc sec), the lambda is the wavelength of the incoming light and D is the diameter of the restricting aperture,objective diameter in our case). Hence the problem lines: "The Airy Disk is getting smaller when the diameter of the aperture is getting bigger. On the other hand the Airy Disk is shrinking with smaller wavelengths."

By long convention the 550 nanometer,green) peak of the normal human visual spectral response is used in calculations. But we note that light at the shorter wavelength blue,400 nm) will yield better resolution,smaller disk and separation) were as the longer wavelength red light,700 nm) will yield lower resolution,larger disk and separation). Therefore when comparing two otherwise comparable scopes or binoculars the one that has the slightly cool blue cast will probably deliver slightly better resolution than one with the warmer red cast although the latter may be a more pleasing image.

Color rendition does in fact have a real and predictable impact on actual resolution. However, our perception of the resolution effects is not nearly so predictable. Not everyone has the same normal color response and many suffer from a learned prejudice for a pleasing color balance that may overwhelm a rational assessment of the more important resolution,for our purposes).

We may both take some flak over questioning using variable power scopes for long range target shooting. I have seen some mirage so bad that I was wondering if I was even looking a real target much less the correct target. But I still would rather see the mirage effects and deal with them rather than dial down and pretend that I know what I'm looking at. I'm working on some very interesting tests to better deal with and understand mirage but that is for another topic or article.

 

[rstreich]

...The central disk is what is known as the Airy Disk named for Sir George Biddell Airy British astronomer,1801–1892) who discovered and described the phenomenon....

Stupid me. You'll get a kick out of this: I took Airy Disk to mean perfect optics,or whatever you'd use for a good term to describe the lenses, mirrors, prisms and what not that the light has to pass through or over), i.e., optics with no wave error. Sigh. Someimes I just tend to skim way too much when reading stuff on the computer screen.

Now the rest makes sense. Thanks for filling in the variables in the equation. I guess I'm still missing one bit, however,'cause I can't figure out how to get to 1.933 at a wavelength of 550 nm.

...Color rendition does in fact have a real and predictable impact on actual resolution. However, our perception of the resolution effects is not nearly so predictable. Not everyone has the same normal color response and many suffer from a learned prejudice for a pleasing color balance that may overwhelm a rational assessment of the more important resolution,for our purposes)....

When I was comparing binos, I wound up picking Swarovski over Zeiss, mostly on the advice of a buddy who has been using them for a long time and who has also owned Zeiss before. But, I was also considering the fact that the color rendition might be an aid in game spotting,their intended purpose). I may never know for sure,'cause it seems like it would require a fairly elaborate experiment to prove it one way or another.

OTOH, I know that in the field, I have a fairly strong preference for the view from the seemingly brighter,whiter? skewed slightly more to the shorter wavelengths?) S&B scopes over the view from a warmer Swarovski. I'll pay more attention to this,now that I'm better educated on the subject) the next time I have both out in the field again.

....I'm working on some very interesting tests to better deal with and understand mirage but that is for another topic or article.

I'm looking forward to hearing about this. I'm going to have to make a decision here on a comp scope pretty soon.

BTW, I'm sorry if I gave you the impression that you should write a paper in lieu of all of your wonderful posts. What I was suggesting was that a paper would be in addition to the posts. I just thought it would be easier to digest all of this info if it were presented in a collected manner. If I hadn't missed the attachment in the other thread, I would have seen that you had already done that.

Thanks again for these last few threads and all the education therein, Fred. It's been a real pleasure.

robert

 

[Fred Bohl]

Robert

Re the missing one bit -

Dawes Resolution Limit

Dawes found out by his own observations that he could resolve a binary star with both stars having a magnitude of 6 slightly better than Lord Rayleigh claimed. The Dawes limit is hence an empirical one and can be written as:

Dawes's resolution limit [arc sec] = 116 / Aperture Diameter [mm],for green light) = 0.2109 x Wavelength [nm]/Aperture Diameter [mm]

Or more usefully to rifle scopes and spotting scopes, since 1MOA = 60 Arc Seconds

Dawes's resolution limit [MOA] = Dawes's resolution limit [arc sec] / 60

Dawes's resolution limit [MOA] = 1.933 / Objective Diameter [mm],for green light) = 0.003515 x Wavelength [nm]/Aperture Diameter [mm]

A note of caution:

We are starting to drift into a complicated area of optical design when we talk about the chromatic performance of optical systems. I'm particularly cautious about binoculars because they are burdened by having to use prisms to correct image orientation, deal with collimation of what amounts to two systems, provide means to adjust for two different eye acuities,usually one eyepiece diopter/focal adjust) and provide common focusing for both eyes. Many consumer optical systems are now having to include UV and IR protection,insurance companies don't just worry about trigger pull forces!). All of these demands make for some difficult compromises in the chromatic corrections and protections which often conflict with best optical performance for a particular end use purpose.

Then we are seeing the introduction of filters for telescopic sights,Leupold's Alumina Intensifier) and Gene Davis's Screw-in Optical Boosters for target scopes. These have potential benefits but also add some restrictions to optical performance that need to be understood for the user to determine if the net outcome of the use is perceived or is actually beneficial to his task at hand.

 

[Fred Bohl]

The two threads on Spotting Scopes and Rifle Scopes have both at times used visibility of bullet holes at different ranges as a measure of desired performance. I have therefore put together a simple calculator Click Here to help identify needed performance specifications.

You enter your bullet diameter in inches and range in yards, click on the update button and it will calculate the angular size of the bullet hole in MOA, minimum required magnification for a normal,or corrected to normal) eye to resolve that bullet hole and the minimum size of objective in millimeters for the Dawes Limit of Resolution to be smaller than that bullet hole size.

 

[rstreich]

Pretty cool, Fred. I didn't even think of doing the spreadsheet that I put together in JavaScript. Didn't have a place to host it. Could we put it up on your gun club's site also?

 

[Fred Bohl]

Robert,

Yes I could arrange for the posting on the TCR&GC site,I'm the webmaster). But since you have gone to all the work on the Excel version why don't you just finish it as per our email exchange and attach it to a reply here. That would be more in the spirit of this forum. Also that one is more focused on bench rest target shooters and the audience of this site.

Those little Java Script calculators I use are made from simple Excel spreadsheets with a conversion program,only simple functions are supported) but are handy for site viewers that do not have Excel. May be we could get Paul to allow those,HTML page - htm extension) to be attachments here?