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# Percentage or magnitude?

12 replies to this topic

### #1 Thphy

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Posted 12 May 2019 - 10:52 PM

I’ve got a question:

Those of you that are better at math than me, is my calculation correct? I’m wanting to calculate the percentage gain of my 20x110 ultras over my 25x100mm. I’m getting 75% or maybe .75 / 3/4 gain in magnitude. Kevin at Oberwerk calculated a 34% gain. He said:

The formula is radius squared times pi. So the radius of the 25x100 (operating at 95mm) is 47.5. Squared and times pi, surface area is 7084mm's. The radius of the 20x110 (operating at 110mm) is 55. Squared and times pi, it's 9499mm. That's a 34% increase over 7084mm.

To get my number or percentage, I’m dividing the large number into the smaller (percentage calculation) and I get 0.745. So is this 75% light grasp or 3/4 magnitude? It’s been a while since I’ve calculated light grasp percentage.

Todd

### #2 DeanD

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Posted 13 May 2019 - 12:38 AM

Hi Todd. Good question.

It is a lot easier if you ignore pi and the radius (because pi cancels out), and simply square the diameter of the lens. I am not sure why the 25x100's are only 95mm diameter and the 20x110's are 110mm diameter, but I assume you have measured them. So (110 squared)/(95 squared) = (12100/9025) = 1.34, or a 34% increase in area (or light grasp) for the 110's vs the 95's, as Kevin said. If the 25x100's were really 100mm, then it would be 12100/10000 = 1.21, or 21% increase in area.

However, stellar magnitude is a logarithmic function. The easiest (approximate) formula for calculating limiting stellar magnitude is (7.5 + 5 log aperture (in cm)) - although some may argue about 7.5 as a starting point. (Ask our sponsor for the formula: https://www.astronom...ting-magnitude/ - and note the qualifiers for conditions, age etc.)

So, for 100mm lenses the limiting magnitude is 7.5 + 5(log 10 = 1) = 12.5

For 110mm lenses, it is 7.5 + 5(log 11=1.04) = 12.7

and for 95mm lenses it is 7.5 + 5(log 9.5=0.98) = 12.4

Hope that helps,

All the best,

Dean

### #3 Thphy

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Posted 13 May 2019 - 12:47 AM

Thank you Dean...

The 25x100’s operate at 95mm according to Kevin because the prisms in the 25x100’s are smaller and don’t utilize all 100mm of aperture. The Celestron 25x100’s are about 93mm of 100mm. That is where that came from. The 25x100’s don’t have the larger stepped prisms like the 20x110’s do.

As for the pi, your equation is what I’m used to, I used that in the past, just forgot about it. Thank you very much for your reply.

Todd

Hi Todd. Good question.

It is a lot easier if you ignore pi and the radius (because pi cancels out), and simply square the diameter of the lens. I am not sure why the 25x100's are only 95mm diameter and the 20x110's are 110mm diameter, but I assume you have measured them. So (110 squared)/(95 squared) = (12100/9025) = 1.34, or a 34% increase in area (or light grasp) for the 110's vs the 95's, as Kevin said. If the 25x100's were really 100mm, then it would be 12100/10000 = 1.21, or 21% increase in area.

However, stellar magnitude is a logarithmic function. The easiest (approximate) formula for calculating limiting stellar magnitude is (7.5 + 5 log aperture (in cm)) - although some may argue about 7.5 as a starting point. (Ask our sponsor for the formula: https://www.astronom...ting-magnitude/ - and note the qualifiers for conditions, age etc.)

So, for 100mm lenses the limiting magnitude is 7.5 + 5(log 10 = 1) = 12.5
For 110mm lenses, it is 7.5 + 5(log 11=1.04) = 12.7
and for 95mm lenses it is 7.5 + 5(log 9.5=0.98) = 12.4

Hope that helps,

All the best,

Dean

Edited by Thphy, 13 May 2019 - 12:49 AM.

### #4 Tony Flanders

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Posted 13 May 2019 - 05:46 AM

It's worth pointing out that although your 20x110 binoculars gather 34% more light than your 25x95's, which corresponds to 0.3 magnitude, that does not mean that they will show stars or deep-sky objects that are 0.3 magnitude fainter.

That's because magnification is at least as important as aperture in determining what you can see -- especially where stars are concerned, slightly less so for DSOs. Given identical optical quality, 25x95 binoculars should show stars considerably fainter than those that are visible in 20x110s, due to the increased magnification. And in the great majority of cases, they should also show fainter DSOs.

The main benefits of the 20x110s would be the greatly increased true field of view due to the lower magnification, plus the subjective sensation of a brighter image.

Personally, I would probably prefer 25x95s -- again assuming identical optical quality. In the real world, differences in optical quality might well outweigh considerations of magnification and aperture, however.

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### #5 Thphy

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Posted 13 May 2019 - 07:53 AM

I agree with all that you said.. thanks. My 25x100’s operate at 95mm because of the smaller prisms that do not catch the full cone of light from the objective. This is according to Kevin at Oberwerk. I did compare the two last night and 5x didn’t make much difference in the view of the objects other than being much dimmer. I actually saw less detail in M81 & 82 because of the dimmer view, 35% dimmer. Now I’m sure the 28x110mm might be pretty good, but I wanted a brighter & wider view. I had them out this morning at 4:15am because the sky was very clear and I could finally see the Milky Way (barely though) because of lots of humility and light pollution. The binoculars framed M8 & M20 nicely. So I am happy with these 20x110’s. Since the 25x100’s show objects much dimmer, They’ll get less use until I sell them. Thank you for your input...

Todd

It's worth pointing out that although your 20x110 binoculars gather 34% more light than your 25x95's, which corresponds to 0.3 magnitude, that does not mean that they will show stars or deep-sky objects that are 0.3 magnitude fainter.

That's because magnification is at least as important as aperture in determining what you can see -- especially where stars are concerned, slightly less so for DSOs. Given identical optical quality, 25x95 binoculars should show stars considerably fainter than those that are visible in 20x110s, due to the increased magnification. And in the great majority of cases, they should also show fainter DSOs.

The main benefits of the 20x110s would be the greatly increased true field of view due to the lower magnification, plus the subjective sensation of a brighter image.

Personally, I would probably prefer 25x95s -- again assuming identical optical quality. In the real world, differences in optical quality might well outweigh considerations of magnification and aperture, however.

### #6 DeanD

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Posted 13 May 2019 - 08:03 AM

It's worth pointing out that although your 20x110 binoculars gather 34% more light than your 25x95's, which corresponds to 0.3 magnitude, that does not mean that they will show stars or deep-sky objects that are 0.3 magnitude fainter.

That's because magnification is at least as important as aperture in determining what you can see -- especially where stars are concerned, slightly less so for DSOs. Given identical optical quality, 25x95 binoculars should show stars considerably fainter than those that are visible in 20x110s, due to the increased magnification. And in the great majority of cases, they should also show fainter DSOs.

The main benefits of the 20x110s would be the greatly increased true field of view due to the lower magnification, plus the subjective sensation of a brighter image.

Personally, I would probably prefer 25x95s -- again assuming identical optical quality. In the real world, differences in optical quality might well outweigh considerations of magnification and aperture, however.

Thanks Tony. There was a Sky&Telescope article a number of years ago that picked up this point, and suggested the best way to compare binoculars for astronomy viewing (assuming the same optical quality) was to use a figure equal to the magnification times the aperture. In  this case, 25x95=2375, which is better than 20x110=2200...

However, quality plays a big part too: my Tak 22x60's give my 25x100's a real run for their money due to much better contrast and sharper images. In fact I would say they beat the 25x100's for all-round astro viewing. I wont be selling them any time soon...

All the best,

Dean

Edited by DeanD, 13 May 2019 - 08:03 AM.

### #7 Rich V.

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Posted 13 May 2019 - 10:35 AM

Todd, here's an article that may be useful to you regarding your subject; it's one of many subjects covered in the "Best Of" section pinned to the top of this forum.  Many newcomers are not aware of this trove of archived information.  There's lots of good reading that may help your understanding of some of the principles involved with your optics.

https://www.cloudyni...performance.pdf

Rich

### #8 Thphy

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Posted 13 May 2019 - 11:57 AM

Thank you..

Todd, here's an article that may be useful to you regarding your subject; it's one of many subjects covered in the "Best Of" section pinned to the top of this forum. Many newcomers are not aware of this trove of archived information. There's lots of good reading that may help your understanding of some of the principles involved with your optics.

https://www.cloudyni...performance.pdf

Rich

### #9 Rich V.

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Posted 13 May 2019 - 04:26 PM

An example from out under the stars-- on a rich star field like the Pleiades, comparing faint stars seen directly between my 16x72 APMs and my 22x70 WOs, even though the APMs have nearly twice the exit pupil area so would be considered twice as bright on diffuse objects, the WOs clearly show more stars.  Despite the smaller exit pupils, the higher mag binos go deeper.

Rich

### #10 Thphy

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Posted 13 May 2019 - 06:43 PM

I understand the point of magnification and seeing the objects closer, but I guess if I want to get closer, I’ll buy a telescope. Binoculars for me are for nice rich field views. My 20x110’s frame the Pleiades and the coat hanger nicely. Also M8 & M20 frame nicely as well. M31 is going to look awesome as well. If I could afford the 25x150 Fujinon binoculars, those are what I’d love to have. 25x is a great magnification for binoculars. 20x is less but still great. I prefer to have a brighter view and when I compared my Oberwerk 25x100 (working at 95mm) with my Oberwerk 20x110’s (working at 110mm) of the galaxy pair M81 & M82, the view with my 20x110’s were visually two times brighter and the sky wasn’t as black, the view through the 25x100’s was much darker and less pleasing. The galaxies were too dim to see any detail. My views with the 20x110’s reminded me of the brightness I saw through the 25x150 Fujinon binoculars. 5x more isn’t much more, it’s noticeable but not dramatic. I don’t think I’ll see more stars with 25x vs 20x. Every little bit helps with splitting double stars, but I’m not really into that. I just like the wide vast views of the galaxies and nebulae and star clusters. I would like to look through a pair of 28x110’s, but the exit pupil is much less.

Does anyone here have both the 20x110’s and 28x110’s? If so, please describe the difference and brightness of the objects.

Todd

Edited by Thphy, 13 May 2019 - 07:04 PM.

### #11 Tony Flanders

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Posted 14 May 2019 - 06:02 AM

An example from out under the stars-- on a rich star field like the Pleiades, comparing faint stars seen directly between my 16x72 APMs and my 22x70 WOs, even though the APMs have nearly twice the exit pupil area so would be considered twice as bright on diffuse objects, the WOs clearly show more stars.  Despite the smaller exit pupils, the higher mag binos go deeper.

Rich

I would say that because of the smaller exit pupils, the higher mag binos go deeper. Another way of saying the same thing, of course, is that they go deeper because of the higher magnification. If you hold aperture constant, those two statements are identical.

For any given aperture, the optimal exit pupil for seeing faint stars is certainly no bigger than 1 mm, and maybe even smaller than that. It's impossible to generalize about deep-sky objects; there are even a few that are best visible at exit pupils as big as 5 or 7 mm. But in at least 90% of all cases, the optimal exit pupil for seeing DSOs is 2 mm or smaller. For me, anyway.

It may sound paradoxical, but in the great majority of cases, making the apparent surface brightness of extended objects lower by stretching them over a bigger area makes them easier to detect, and also allows you to see more detail within them. This presupposes the use of averted vision, of course. But trying to view faint objects with direct vision is like trying to win a Marathon while wearing ankle weights.

Edited by Tony Flanders, 14 May 2019 - 06:10 AM.

### #12 GlennLeDrew

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Posted 15 May 2019 - 02:28 PM

I got one of the first run of Celestron 25X100s. It was *great*. It used a stepped first prism, the wider entrant aperture permitting full 100mm aperture performance. The optics were beautifully aligned in each barrel, with excellent concentricity from objective to eyepiece. Image sharpness was what one would expect from a decent, airspaced achro doublet of f/3.9.

Today's specimens are a travesty by comparison. Not full aperture performance, awful non-concentricity in *both* barrels being the norm. And notably poorer imagery.

I upgraded mine by adapting a pair of 15mm f.l. 85 degree AFoV eyepieces taken from a Bushnell Xtra-Wide 10X50. This boosted the TFoV from 2.4 degrees to 3.5, while slightly increasing the magnification to 26X. This notably improved the observation of larger dark clouds and nebulae. For instance, with this instrument (unfiltered) I first saw the huge Witch Head reflection nebula, near Rigel.

In my Gallery (link in sig, below) are some pics related to this bino, including an opened-up shot of the prism assembly clearly showing the stepped prism.

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### #13 Thphy

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Posted 15 May 2019 - 03:00 PM

Glenn..

That is really cool and I did not know that the first round of Celestron binocular’s were that good. Kevin at Oberwerk said that the current Celestron 25x100 binoculars now have approximately 93 mm of aperture because of the smaller baffled prisms. I’m surprise that they have gone down in quality like that. I had a pair of those two years ago and I sold them to a friend of mine but now I have the 20 x110mm Ultras by Oberwerk, I absolutely love the view that I get out of these. I now wear glasses because I am 49 years old and my right eye has an astigmatism and the right side of the binoculars doesn’t really come to perfect focus because of that without my glasses, but when I wear my glasses, I get nice star points, pinpoint images. These are by far the best pair of binoculars I have ever owned. It’s a different sensation whenever you look through someone else’s binoculars versus owning a pair of your own and you see the difference more clearly when you actually own them. I almost went for the 28X model but I wanted my binoculars to show me a wider field of view and brighter images.I can actually see color in the Eskimo nebula with my 20X binoculars, the nebula itself isn’t real large but it is easily visible. I’ll have to go check out your photos that you have on your binoculars, I am curious to see that.

I got one of the first run of Celestron 25X100s. It was *great*. It used a stepped first prism, the wider entrant aperture permitting full 100mm aperture performance. The optics were beautifully aligned in each barrel, with excellent concentricity from objective to eyepiece. Image sharpness was what one would expect from a decent, airspaced achro doublet of f/3.9.

Today's specimens are a travesty by comparison. Not full aperture performance, awful non-concentricity in *both* barrels being the norm. And notably poorer imagery.

I upgraded mine by adapting a pair of 15mm f.l. 85 degree AFoV eyepieces taken from a Bushnell Xtra-Wide 10X50. This boosted the TFoV from 2.4 degrees to 3.5, while slightly increasing the magnification to 26X. This notably improved the observation of larger dark clouds and nebulae. For instance, with this instrument (unfiltered) I first saw the huge Witch Head reflection nebula, near Rigel.

In my Gallery (link in sig, below) are some pics related to this bino, including an opened-up shot of the prism assembly clearly showing the stepped prism.

Edited by Thphy, 15 May 2019 - 03:01 PM.

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