See the Attachment Above for the BPI Table of Data
The Binocular Performance Index, BPI as referred to here, was developed in summer/fall 2003. This article expands on the original and adds further information. The concept remains primarily the same, however, the application is a little changed based on more experience and data. Although the end result BPI (index) is rather simple, some of the basis for approach is not. I’ve attempted to provide explanation here for the basis of approach. This article and the original article should provide the explanation needed to understand the basis behind the development of the index.
There are a number of methods used to predict binocular performance, some simple like this, magnification x aperture. Here you would have a performance index that gives a factor of 7x (or 10x or 15x) to magnification and then a whopping factor of 35 (or 50 or 70) to aperture. Obviously, this index assigns far more weight to aperture. In another article I discussed this method and showed what I feel to be its shortcomings. You might refer to Bartel’s paper on Visual Optimum Detection Magnification and Clark’s paper on Optimum Magnified Visual Angle (both available in the CN binocular forum web links). Both give excellent support to the need for magnification to see. Except maybe for faint extended broad nebula or very low light terrestrial viewing, I can’t think of an application where that kind of weighting on aperture would give a good indication of binocular performance for most astronomical viewing.
Allan Adler has given us what I consider a better representation of actual binocular performance. The Adler Index rates binocular optics by magnification times the square root of aperture. This approach reduces the weight of aperture and more closely equalizes the factors for magnification and aperture. In almost every case, this formula puts greater emphasis on magnification than aperture.
These are not scientific formulae, but a simplified method to indexing performance. Based on the aperture masking tests I’ve done on binoculars in the past, results seemed to indicate that magnification holds greater weight. Just how much weight was always the question? I've adopted Adler Index for reasons stated previously, but in addition I've adjusted Adler Index with a factor for attributes of binocular quality. Arbitrarily, I applied a plus or minus 10% adjustment to Adler’s Index to account for binocular qualities, including light transmission (coatings), resolution and contrast. You can find that explanation in my CN Reports - Binocular Performance Article.
There are other qualities that enhance or diminish performance, such as off-axis alignment, illumination of exit pupil, percentage of image sharpness and chromatic aberration. All have an impact on rating the performance of a binocular. Not all will be addressed here, since some will never be measured by the average user. For most astronomy observing the adjusted Adler Index, which I refer to as the Binocular Performance Index, or BPI, seems to more closely represent field results.
What impact can be seen by some of the qualities mentioned?
The ability to discriminate close stars in dense clusters allows you to see the cluster better resolved. M36 and M67 are good examples. A binocular that has optimized the craftsmanship of the lens, producing a fine pinpoint star image, such as the Fujinon FMT-SX 16x70 or the Nikon 12x50 SE, can see more stars in these clusters than equally sized binoculars that have not achieved the same level of quality. In a lower quality binocular, the star images formed by the lens are larger and more of the densely packed stars blend together.
Is there any way to put a value on an incremental increase in performance due to better resolution? Yes, I think so. Set a standard for the upper and lower limit of resolution and then compare a premium to a standard binocular in the same size.
First a standard must be set for upper and lower limit of resolution. I will show this for two binocular sizes a 12x50 and a 25x100.
To determine the maximum clean resolution of a lens, calculate the Rayleigh Limit for the objective diameter. For the 12x50 it is 138/50 = 2.8 arcseconds and for the 25x100mm it is 138/100 = 1.4 arcseconds. Of course these resolution limits could only possibly be achieved at high magnifications, much higher than normally used in binoculars.
To determine the low limit of resolution, calculate what the lens could show at the lowest magnification. For that we will assume a magnification that gives a 7mm exit pupil. A few binoculars will fall outside these criteria but that will not significantly affect the outcome. For the 50mm lens low magnification would be 50/7 = 7.1x, and for the 100mm lens it would be 100/7 = 14.2x. Now that we have the lowest magnification, we must determine how wide a pair must be for our eyes to see it when only magnified by such low magnification. For this we must also assume a range of visual acuity. For most people, stars can be seen as separate when they are magnified to an apparent size (or separation) of about 150 to 180 arcseconds. Using 180 arcseconds, for the 50mm lens we get a separation of 180/7.1 = 25 arcseconds. For the 100mm lens we get 180/14.2 = 12.7 arcseconds. For me personally, I would use a visual acuity of 160 arcseconds and I would get 22.5 and 11.2 arcseconds, but this will not produce a significant effect, as you will see.
We now have the upper and lower limits of resolution for our binocular lenses. For the 50mm lens it is 2.8 to 25 arcseconds. For the 100mm lens it is 1.4 to 12.7 arcseconds. Obviously, each of these binoculars can resolve wider stars, but those would be well outside the resolution limit range and become an easy target.
Compare two binoculars of the same size lens. In the 50mm binoculars, the range is 25-3 = 22 arcseconds, therefore any 50mm binocular that can see resolution 22/10 = 2.2 arcseconds closer than another can be said to see 10% better resolution. Likewise any 100mm lens that can see (12.7-1.2 = 11.5)/10 = 1.15 arcseconds closer can be said to see 10% better resolution.
Without being to critical of any binoculars, and without observing thru each one to determine its ability to resolve, in general it is found that higher quality binoculars do indeed provide better resolution. However, most all binoculars with an equal power magnification generally vary by no more than 1 or 2 arcseconds. That would indicate most are in a range of about 10% better or lesser resolution when compared to each other.
It is relatively easy to verify whether or not a binocular can provide a fine enough resolution to reach your visual acuity. Acuity can be established with any scope that can use fairly low powers on fairly easy doubles or it will have been established with the best binoculars. All others will be attempting to match it. For instance, I have measured mine many times at about 160 arcseconds. In any 10x binocular I should be able to see 160/10 = 16 arcsecond doubles. In any 12x binocular, I should be able to see double stars that are 160/12 = 13.3 arcseconds wide. In any 20x binocular, I should see stars 160/20 = 8 arcseconds wide and in all 25x binoculars I should see stars separated by 160/25 = 6.4 arcseconds.
A comparison can now be made at almost any magnification, regardless of aperture. A Nikon SE 12x50 compared to any standard 12x50 and a BT100 binocular telescope at 25x compared to a standard 25x100 and a Fujinon 16x70 will help illustrate. I have reached my limit of visual acuity with the Nikon 12x50 SE, Fujinon FMT-SX 16x70 and the BT100 at several magnifications. With each these three, I have split doubles that result in apparent separations between 150 and 160 arcseconds. Not unexpectedly, binoculars such as these reach some of the best resolution in dense clusters. I was not able to reach the same level with Orion Ultraview 10x50, Orion Giant 16x80, Celestron Skymaster 25x100, Oberwerk 22x100 or an assortment of others.
Several things have an affect on the limiting magnitude of a binocular. Coatings will have an affect on the total light transmission. Lack of coatings on internal glass surfaces will contribute to internal reflections, reducing contrast. Proper baffles and blackening of surfaces will help control stray reflections, improving contrast. Any reduction in contrast will prevent you from seeing the faintest stars at the limits of the binocular, as these require optimum conditions and performance to see. The best coatings and contrast will result in significantly deeper limiting magnitude.
Limiting magnitude will determine just how deep you can see. Deeper LM will increase the number of stars you can see in a given field. Lower LM will reduce the number of stars seen and may reduce the size of or completely eliminate from your view all types of objects, including faint open and globular clusters, galaxies and planetary nebulae.
Comparisons of some binoculars within equal size clearly begin to show the affect of these various qualities on the limits of magnitude that can be achieved. In these few cases a difference in coatings can be seen. Nikon 12x50 SE can see 0.3-0.4mag deeper than Nikon 12x50 AE or Pentax PCF III 12x50. Pentax PCF WP 10x50 can see several tenths deeper than Nikon AE 10x50 or Orion Ultraview 10x50. The Oberwerk 15x70/’03 FMC can see several tenths deeper than the Oberwerk 15x70/’02 MC.
In addition to all mentioned above, limiting magnitude will be significantly affected by magnification and this leads to an understanding of why magnification must be given substantially more weight than aperture in a performance index.
How is BLM Different than LM in a Scope?
There are several published well-read articles and graphs providing the amateur with an attempt to theorize what limit a binocular should see. Some of these develop predictions based on the rules of aperture. Some of these fail to take into account the full impact of magnification or the inability of aperture to perform to its full potential if anything less than optimum magnification is used. This is the case of the employment of aperture in binoculars. For everything other than maximum light gathering, binocular aperture is not used to its full potential. Another entirely different discussion would need to take place if we were to address the use of that same binocular aperture to observe faint diffuse extended objects.
You’ve heard time after time, in a scope “Aperture Rules”. It is the primary factor in light gathering and controls the LM. But, what if you only use your scope (just as the case in binoculars) with low magnification? Are you reaching LM? NO! You will not reach LM with a scope unless you use optimum magnification. The best explanation I have found for this comes from “Amateur Astronomer’s Handbook”, by Sidgwick.
That’s the biggest difference between LM in a scope and BLM in binoculars. The scope allows you to vary the magnification. In the binoculars, magnification is fixed. Sidgwick explains clearly how we arrive at the optimum magnification and it usually falls between 24D and 30D, where D is aperture in inches. Some large scope users believe they find optimum magnification at 18D to 25D, and some even say 10D. These are not magnifications that will allow you to reach the limiting magnitude of your scope, especially small scopes 8” and less.
Binoculars are a lot closer to minimum magnification than optimum magnification. Minimum is generally accepted as that which produces a 7mm exit pupil, an exit pupil that would provide maximum brightness for an observer with a 7mm eye pupil. A binocular with a 4mm exit pupil is operating at 6.3D; with a 5mm exit pupil at 5.1D and with a 7mm exit pupil is operating at 3.6D.
Based on this, it becomes apparent that normal LM formulae with calculations rooted in optimum performance cannot always be used for binoculars. With the single exception of brightness, binoculars do not operate at optimum or utilize the full potential of the aperture. Limiting Magnitude has an impact on numbers of stars seen in loose or dense open clusters and observation of objects such as open clusters, galaxies, globular clusters and planetary nebulae all benefit to varying degree from increased magnification. This leads to the consideration that for most all astronomy objects observed with binoculars, performance will not be weighted by aperture, but will be most influenced by magnification.
Incremental increases in magnification have far more influence on Binocular Limiting Magnitude (BLM) gain than incremental increases in aperture. Changes to magnification or aperture (area of the lens) show each 10% increase in magnification will increase BLM by ~0.12 to 0.15 mag and each 10% increase in area of aperture will increase BLM by ~0.03 to 0.05mag. This shows magnification was measured to have approximately three to four times the affect on the gain in BLM. When it comes to the question ”How deep can you see?” in binoculars, magnification has greater influence on performance than aperture.
Increases in magnification have far more influence on BLM than increases in aperture.
Having developed the Binocular Performance Index, (BPI), and comparing it to a array of results from studying Binocular Limiting Magnitude, (BLM), it was discovered that the unadjusted Adler Index did not accurately rank the binoculars in line with the recorded BLM, but that the adjusted Adler Index (BPI) did closely match the BLM. So, while this formula may not give a good indication of performance on faint diffuse nebulae, it does more accurately reflect Limiting Magnitude, numbers of stars seen in open clusters, resolvability of dense open clusters and observation of objects such as galaxies, globular clusters and planetary nebulae. In other words, for most astronomical objects, the BPI may give a more accurate indication of performance.
How to Determine BPI
For any binocular you can determine the Binocular Performance Index (BPI) by starting with magnification and aperture. Multiply magnification times the square root of the diameter of the aperture in mm. A 10x50 would be 10x 7.1 = 71. 25x100 would be 25x10 = 250. Then consider the adjustments attributes and qualities of the binocular. Somewhat subjective, but not nearly as much as you might think.
For light transmission and contrast consider the coatings and baffles. The best coatings reflect the least amount of light.
An FMC binocular is the standard, no adjustment.
Any binocular with premium coatings and excellent baffles and blackening, add 10%.
Any binocular with any shiny interior surfaces or without complete FMC, deduct 10%.
For resolution, generally premium binoculars will show an improvement, add 10%.
This attribute, not generally known unless tested, cannot be assumed. Without the opportunity to test binoculars being considered, no deductions should be taken.
The benefit of long term testing may eventually result in a table of rankings. But the user without significant test data may not have sufficient information to rank two closely paired binoculars. However, the difference between high quality and low or average quality may be determined by adding the 10% factor to the high quality binocular.