Home Forums Hunting & Shooting Hunting Optics Need Help With Binocular Math...

I have seen various numbers tossed around regarding binoculars. Dividing objective lens size by the magnification produces something...twilight factor?<P>What are some of the other equations that people have come up with? What do they measure? How useful are they? Thanks for the insight.<P>Wade

<BLOCKQUOTE><font size="1" face="Verdana, Helvetica, sans-serif">quote:</font><HR>Originally posted by Waders:<BR><STRONG>Dividing objective lens size by the magnification produces something...twilight factor?</STRONG><HR></BLOCKQUOTE><BR>No, I think that would give you the "exit pupil"...ie an 8x32mm has an exit pupil of 4mm. I'm sure others here have much more binocular lore at their fingertips than I do, and I gotta hit the sack .... will check back here tomorrow, hopefully to find a load of optical insights!

Loud cloud is right about exit pupil. That is usually combined with the magnification to determine the twilight factor. 10X40's have a greater "twilight factor" then 8X32's even though they have identical Exit pupils. I do not know the formula to determine twilight factor.<P>From my experience the coatings that are applied to the lens are probably as important as the Exit pupil. Most important of all is the quality of the glass. Everyone seems to have a favorite european glass, probably why they are all still in business. I don't think once you get to the level of the big dogs(swarovski, Ziess, Leica, Kahles, Steiner) that the quality for the average guy with decent vision is going to matter as much as construction. <P>Are the Binocular bodies machined out of solid metal or a molded resin? Resin is much lighter, but not nearly as bump and fog proof. <P>I have Leica, Kahles, and Steiners here in my house right now. I have used most of the others. Most guides have their favorites after years of looking through so many high end glasses that clients bring to camp. Swarovski has a special arrangment with PH's and guides in NA to buy factory direct at very good prices. One reason you see lots of Swarovski glass in the hands of Professionals. There are many hoops to jump through for this price but it sells a lot of binoc's to people when they see a professional using them in the bush!<P>The One thing to remember about the "math" part of the choice is that is going to be a constant based on size. No matter who makes them. The Coatings and the quality of the glass has no number or "math" to rate it in a n easy answer. <P>Unlike a rifle scope binoculars need to be clear and high quality to the very edge of the glass not just the center. Rifle scope quality is much less critical because we only focus dead center on the crosshairs anyway when aiming. I doubt any intellegent hunter on earth would use a rifle scope as binoculars while trying to scan for game. To hard to hold steady, and much to dangerous to point a rifle at unknown targets. <P>In my opinion the quality of binoculars is far more important then the quality of the scope because you only look through the scope long enough to pull the trigger or pass on the shot. You're not studying the trophy quality and scouting for game with a rifle scope. <P>To see a good example of how different the coatings can change the price of optics look at the steiner glasses. They are the only company I know of using the same Binocular body for several different sets of glass. they have at least 3-4 different quality lenses in the same housing priced accordingly. All will have the same Exit pupil and structural integrity.

The formulas used are exit pupil size, and Twilight Factor. <BR> Exit pupil size is simply the objective lense size divided by the magnification. Therefore, your 8X32's have an exit pupil size of 4. The problem with this formula is that (a) not everybody's eyes can use the upper end, say 7, in pupil size, and (b) it says nothing concerning the quality of the glass, or the various coatings on lenses, or, in the case of binoculars, prisims. <BR> The other problem is one of low light, or twilight performance. A 4X scope with a 28mm objective lense has the same exit pupil as a 6X42. But even a quick glance through each at low light will reveal that the 6X has a much brighter image. Therefore the Twilight Factor. Again, this doesn't take into consideration glass, and coating quality. <BR> Twilight factor is determined by multipling the magnification times the objective lense size, and then taking the square root. Therefore an 4X28 has a twilight factor of 10.6 The 6X42 has a TF of 15.9. E

Thanks Fellas!<P>I knew you would come through! I was playing around with my binos after I got home from hunting and got to wondering about the numbers. I have Leica 8x32's and love them. I was comparing them to my buddy's Steiner Military Marine 10x50 and we couldn't tell much of a difference (mine were slightly clearer). Of course this was during the day with good light. We are going to do some comparisons at dusk and see what happens. <P>Thanks again,<P>Wade

Here's something I've wondered about ... is the twilight factor assigned to a scope equally meaningful to all of us, as an absolute, all else being equal?<P>Example: Let's say that while shooting in low light conditions, the pupil in my eye will open up to 5mm. (I wish!) If I were to compare the brightness of two scopes (same brand, same basic construction, same lens coatings), one being a 10x40mm (twilight factor of 20.0, exit pupil of <B>4mm</B>) and the other being a 7x42mm (twilight factor of 17.15, exit pupil of <B>6mm</B>), will the 7x42mm seem less bright because the pupil in my eye can't open up to 6mm, or simply because of the mathematical formula that determines the "twilight factor"? If my own pupil wasn't able to open beyond 3.8mm, would I be able to detect any difference in brightness between the two scopes? <BR> [img]images/icons/crazy.gif" border="0[/img]<BR>One more question ... Would it be accurate to say that this 10x40mm is 16.6% brighter than the 7x42mm? (20 minus 17.15, divided by 17.15)

Loud Cloud. I'm not sure. Basically, if your eye won't open to the 6 mm size, then the additional light is wasted. So, theoretically your 7X42 then, to your eyes, is no different than a 7X28. Therefore the TW factor would be 14 vs. 20 for the 10X40.<BR> Before I'm sure of this, I'd like to test this theory. I'm not infallible. E

I appreciate the effort, E. I've never heard or read an explanation of this, though I haven't done a lot of research on it, either. [img]images/icons/smile.gif" border="0[/img] Haven't read that Barsness book on optics yet, hmmmmm ........

Now I gotta ask: What does the twilight factor test/demonstrate?? Why do we bother even calculating that number?<P>Wade

<BLOCKQUOTE><font size="1" face="Verdana, Helvetica, sans-serif">quote:</font><HR>Originally posted by Waders:<BR><STRONG>Now I gotta ask: What does the twilight factor test/demonstrate?? Why do we bother even calculating that number?</STRONG><HR></BLOCKQUOTE><BR>"The twilight factor is a mathematical calculation that allows a comparison of visual performance in low light among different size binoculars. However, it is important to understand that only in combination with an accurately adjusted high-contrast optical system and a LARGE EXIT PUPIL that a high twilight factor allows you to better distinguish details in poor lighting conditions. Therefore, when selecting binoculars, the twilight factor should play a secondary role to the size of the exit pupil. The LEICA 7x42, for example, is an excellent binocular for low-light use due to it's large exit pupil of 6mm even though it's twilight factor is smaller than in the LEICA 8x42 or 10x42 binocular."<P>Just found that at <A HREF="http://www.birdware.com/leicrit.htm" TARGET=_blank>www.birdware.com/leicrit.htm</A> . Verrrrrry interesting! But deceptive! [img]images/icons/laugh.gif" border="0[/img]<P>Be sure to read the paragraph dealing with the Exit Pupil on that site, too .... its an eye opener! Cheers. Dan