Adler's Mag/Aperture Formula for Binoculars
Tony Flanders
the September issue of Sky and Telescope. On the whole, I liked
it a lot, although perhaps not as much as the on-line version of
the same that has been posted for some time on Tod Gross's web
site at http://www.weatherman.com/binadler.htm.
I do have doubts about one thing, though: Adler's new formula
for computing the "performance" of binoculars given the aperture
and magnification. He claims that not only is the old formula
wrong that gives overwhelming priority to aperture, but so is
the familiar revision, presented by Roy Bishop among others as:
performance = magnification * aperture
He claims that this still gives too much weight to aperture,
or equivalently, too little to magnification, and proposes:
perf = mag * sqrt(aperture)
and suggests that even this may overstate the importance of
aperture. Somehow, this seems wrong to me.
A few comments as a preamble. First, nobody is claiming that
this function provides an *absolute* measure of performance,
just that the higher the number, the better the performance.
So in fact, Adler's formula could equally well be stated as:
perf = mag^2 * aperture, or
perf = 10 * mag * sqrt(aperture) + 5, or even
perf = mag^4 * aperture^2
all of which would yield identical rankings.
Second, the range of magnifications and apertures for "normal"
binoculars is quite small -- something like 7x35 to 20x80.
Compare that to magnification ranges of 15X to 400X and aperture
ranges of 60mm to 500mm for common amateur telescopes. With such
a small range of magnifications and apertures, the divergence
between a least-squares fit of Adler's formula and
c1 * magnification * aperture + c2, for optimally chosen
c1 and c2, is going to be pretty small -- especially considering
that the value being measured is inherently subjective.
Third, as Adler hints in his article, there is no single measure
of binocular "performance" that is valid across all objects. If
you are trying to separate close bright double stars -- a real
issue when viewing many open clusters with binoculars -- then
magnification is the only thing that counts, and aperture is
totally irrelevant, within the range found in common binoculars.
For viewing faint fuzzies, aperture is much more important.
Finally, for some reason, Adler glosses over the single biggest
ill effect of higher magnification, once you have resigned yourself
to using a mount to cure the shakes. If magnification is so all-
important, why not boost the magnification as high as the aperture
will allow; why not 25x50 binoculars, or even 50x50?
The answer, of course, is field of view. Adler mentions that
increasing aperture can lose field of view, and indeed, there
are fewer wide-field 10x70 binoculars than 10x50 binoculars.
But this is, to my mind, a third-order effect as compared to
the loss in FOV that comes with increased magnification.
Adler makes clear that even for close-up detailed views, FOV
is *still* one of the things that he likes most about binoculars --
seeing the object in context, as he says. But the higher the
power, the smaller the context. For me, and I think most people,
the wide FOV is the single biggest asset of binoculars.
Having said all that, I think that Adler's formula understates
the importance of aperture. His argument seems to be based
largely on the fact that he finds relatively little difference
between binoculars with identical magnification and exit pupils
varying from 5mm to 7mm -- say, 10x50 vs. 10x70.
Now, I agree wholeheartedly with that assessment of 10x70
binoculars, but I do not find it at all surprising, in view of
the fact that I have measured my eye's pupils at 5.5mm. That
implies that 10x70 binoculars are actually working as 10x55
for me, so I expect little difference. Adler, on the other
hand, has measured his pupils at 6.5mm, and so attributes
the small improvement to a very shallow performance vs.
aperture curve.
Three counter-arguments. First, measurements of eye's pupils
are not terribly reliable; I give an error bar of +- 0.5mm
to my own. Add the same error bar to Adler's, and our pupils
might not be different at all.
Second, there is some reason to believe that the outermost
part of the eye's lens is not very useful for astronomy.
People with 7mm pupils do *not* seem to be able to see
fainter stars or DSOs than people with 5mm pupils, contrary
to what theory would suggest.
Third, I am quite sure that the curve of performance vs.
exit pupil (holding aperture constant) is *not* linear at
any point. For viewing faint fuzzies, my impression is that
the performance actually increases up to an exit pupil of
around 1.2mm to 2.5mm, depending on the object, then decreases
slowly to around 3mm, then decreases quite rapidly between 3mm
and 4.5mm, and then starts to level off, becoming constant at
5.5mm, the size of my own eye's pupil.
In short, by basing his formula on the difference between
10x50 and 10x70 binoculars, which I agree is small, I think
that Adler underestimates the difference between 10x30 and
10x50 binoculars, which I think is quite large. I haven't
actually used 10x30 binoculars, but I have spent a fair
amount of time doing astronomy with 8x25 binoculars, and
I find their small aperture to be a very significant handicap.
I find them *far* inferior to my 7x35 binoculars, whereas
Adler's formula predicts that they should be nearly identical.
- Tony Flanders
zgse...@netway.com
Interesting points regarding Adler's piece, however, I'm concerned
that someone reading your remarks without having read the article in
question, might misunderstand. (The article is on page 94 of the
September Sky & Telescope.)
tony_f...@yahoo.com (Tony Flanders) wrote:
>
>Finally, for some reason, Adler glosses over the single biggest
>ill effect of higher magnification, once you have resigned yourself
>to using a mount to cure the shakes. If magnification is so all-
>important, why not boost the magnification as high as the aperture
>will allow; why not 25x50 binoculars, or even 50x50?
I'm not sure what you mean by "glossing over" since he does describe
the trade off between magnification and field quite thoroughly, in my
opinion. In fact, he spends two columns of the article talking about
it. Your next paragraph seems to me at least to support this:
>
>The answer, of course, is field of view. Adler mentions that
>increasing aperture can lose field of view, and indeed, there
>are fewer wide-field 10x70 binoculars than 10x50 binoculars.
>But this is, to my mind, a third-order effect as compared to
>the loss in FOV that comes with increased magnification.
>Adler makes clear that even for close-up detailed views, FOV
>is *still* one of the things that he likes most about binoculars --
>seeing the object in context, as he says. But the higher the
>power, the smaller the context. For me, and I think most people,
>the wide FOV is the single biggest asset of binoculars.
>
>
>In short, by basing his formula on the difference between
>10x50 and 10x70 binoculars,
I am certain that you did not intend to do so here Tony, but this
statement might lead someone to conclude Adler's formula is based on
this single example. This isn't the case, and he says so. If you read
page 96 you'll see that the formula is based on a considerable amount
of experimentation.
>that Adler underestimates the difference between 10x30 and
>10x50 binoculars, which I think is quite large. I haven't
>actually used 10x30 binoculars,
I own by 10x30 and 10x50s (which rate 55 and 71 respectively on
Adler's scale) and find this difference to be about right. (I think
too that on the Adler scale, a difference of 16 IS quite large, so I'm
not sure how this disagrees with your experiences.
>but I have spent a fair
>amount of time doing astronomy with 8x25 binoculars, and
>I find their small aperture to be a very significant handicap.
>I find them *far* inferior to my 7x35 binoculars, whereas
>Adler's formula predicts that they should be nearly identical.
It's possible that you're seeing a difference in optical quality here
too -- which is why Adler's scale is described simply as an indicator
and not an absolute measure.
For what it's worth, at present I own 7 binoculars and find Adler's
scale a better predictor of relative performance than either Bishop's
(which is good too) or the Zeiss method.
It'll be interesting to read more observations like yours.
Regards,
Gary Seronik
(Remove the "z" for my actual e-mail address.)
Harald Lang
Hi there, you wrote in
<news:958c21.020730...@posting.google.com>:
<<
I do have doubts about one thing, though: Adler's new formula
for computing the "performance" of binoculars given the aperture
and magnification. He claims that not only is the old formula
wrong that gives overwhelming priority to aperture, but so is
the familiar revision, presented by Roy Bishop among others as:
performance = magnification * aperture
He claims that this still gives too much weight to aperture,
or equivalently, too little to magnification, and proposes:
perf = mag * sqrt(aperture)
and suggests that even this may overstate the importance of
aperture. Somehow, this seems wrong to me.
>>
I use the following formula to estimate how much dimmer
stars I can see in a binocular compared to naked eye:
+mag = 3 Log D + 2*Log X + 0.6
(D=lens diam. in cm, X=magnification)
so for instance, with my 10x42, I see
3*Log 4.2 + 2*Log 10 + 0.6 = 4.5 magnitudes dimmer, whereas with my
20x60 3*Log 6 + 2*Log 20 + 0.6 = 5.5 magnitudes dimmer than naked
eye, etc.
The background is this: some time during WWII (I don't have
the litterature available here, so this is from memory) a fellow
called Blackwell made a very thorough study of what can be
detected by the eye under very dim light (for military purposes,
I suppose). These data were used by Roger N. Clark in his book
"Visual Astronomy of the Deep Sky". (There were some discussion
between him, me , Mel Bartels and Nils Olof Carlin about some
details in that book, some of which appeared in this ng.)
Anyway, one thing that comes out from Blackwell's data is
that for small objects, like a star, if the background darkens by
one magnitude (per unit angular area) then one can see about 0.4
magitudes dimmer stars (small objects), at least in the range
relevant for the current issue.
From this it is rather strightforward to derive the formula
+mag = 3*Log D + 2*Log M - 3*Log y
where y=diameter of the eye pupil; I have set this to 0.63cm just
to get the round number 0.6. Indeed, the star is brighter by
5*Log(D/y) magnitudes, and the background is dimmer by 5*Log(y/e)
magnitudes (per unit angular area), where e=D/X = exit pupil. You
get it from there.
Anyway (as if anybody is still reading..) this means that
aperture has a *higher* weight than magnification --the weight is
3 for aperture and 2 for magnification --, contrary to Adler's
experience. However -- I must hasten to add -- "my" formula
concerns how dim stars (point sources) can be detected;
Adler talks about extended fussy blobs which is something
different. From Blackwell's data, in this case also the size of
that blob matters, and things get really messy.
I haven't made any serious attempt to verify "my" formula
empirically, but it seems at least to give the ballpark.
Maybe somebody can ask Rush Limbaugh (sp?) what he thinks
about this formula? What does the Constitution say?
Cheers -- Harald
Rich N.
Hi Harald,
Please let us know when you do make a serious attempt
to verify "your" formuls empirically.
At Rush lets everyone know what point of view he is coming
from, unlike the "balanced" network news.
Clear skies,
Rich
----
Harald Lang wrote in message ...
Rich N.
Hi Tony,
I'll see if I can add a little to Gary's fine reply.
One night at a local star party I tried observing M27 with my
then new Orion 15x63 MGs. Once I got to the right spot in the
sky, M27 was quite easy to see. I tried it with my 10x50 Leica and
10x70 Fujinon FMT-SX but because of the relatively small size
of M27 I had to really search the field to see it. With my 12x50
Nikon SE and 12x50 Leica BA it was easier to spot than with the
10x binoculars but still not as easy to see as with the 15x binocular.
Try finding M57 with a 10x binocular, even a 10x100. You need
enough magnification to let your eye notice it. A 70mmTV Pronto
will show M57 with relative ease if you use enough magnification.
Jay Freeman has done a lot of deep sky observing with his little
55mm f/8 Refractor Red APO. One of his "tricks" is to pick an
eyepiece that will give an exit pupil with the best balance of
magnification and contrast.
Binoculars are a passion with Alan. He takes great care with
his observations. It isn't something he does just so he can write an
article in a magazine. IHMO, he writes to share his finds and passion
with others.
Clear skies,
Rich
Sketcher
quality but different apertures and magnifications, so I can't provide
details that support one formula or another. Nevertheless I'll add a
few things:
IMO mathematical, equation-based binocular performance ratings are
primarily useful to less experienced observers. From experience I
know what works well for me.
I've conducted some binocular experiments. I can state as an
experimental fact that the magnification of any pair of binoculars is
dependant upon the object distance. A pair of binoculars focused at
infinity will be functioning at a lower magnification than the same
pair of binoculars focused on a nearer object.
A related result: The same pair of binoculars used by a far-sighted
person, a person with "normal" vision and a near-sighted person (at
any given object distance) will be functioning at different
magnifications when used without eyeglasses. The near-sighted person
will be stuck with the lowest magnification. The far-sighted person
will end up with the highest magnification.
Some binoculars don't utilize the full diameters of their objectives.
I've experimentally verified this.
How accurate are the magnifications engraved on the various
binoculars? For what object distance is that magnification
determined? For who's eyes?
Then there's the observer's pupil diameter, the type of object being
observed, the observing conditions (dark sky, polluted sky, bright
sky, etc).
All of the above considered leads me to prefer Bishop's very simple
and easy to use magnification times aperture formula. That formula is
accurate enough to get the newbies started on the right foot and
simple enough for most anyone to remember and use. That rating is
coincidentally (and very conveniently) marked right on the outside of
the binoculars themselves!
Splitting hairs with more refined (than Bishop's) equations is
pointless in light of all the variables that can swing the results
form one refined formula to another once real binoculars are used
under real conditions by real people. IOW, even a *perfect* equation
is no better than an approximation in an imperfect world.
Sketcher
Bill Meyers
Agreed.
To me the value of Alan's Adler's article is that he argues that for
astronomy, magnification deserves more importance in relation to aperture
than traditional formulas give it, and Alan modifies the formula to reflect
that.
It is the case that in comparing binoculars of the same magnification,
say 12 x 50, 12 x 60 and 12 x 70, the two formulas rank these binoculars
the same way.
But where binoculars of different magnifications and different
apertures are compared, the two formulas sometimes rank them differently.
Under Roy Bishop's formula, 10 x 70's rank higher (better) than 15 x 45's,
but under Alan's formula, 15 x 45's rank higher than 10 x 70's.
The result obtained by Alan comports much better with my experience.
Ciao,
Bill Meyers
Tony Flanders
> Hi Tony:
>
> Interesting points regarding Adler's piece, however, I'm concerned
> that someone reading your remarks without having read the article in
> question, might misunderstand. (The article is on page 94 of the
> September Sky & Telescope.)
Agreed. My posting was not meant to be intelligible without reading
the article. I suppose that I should also say something that seems
obvious to me, but might not be to somebody else, namely that I
agree whole-heartedly with almost everything that Adler says in
his article, in particular:
* The two different "styles" of viewing, widefield vs. closeup.
Very useful way distinction, IMHO.
* The immense importance of sitting down while observing.
* The immense value of magnification, and the fact that it has
been historically under-valued as compared to aperture.
My disagreement is merely on one formula, and amounts in practice
only to a small refinement.
I said:
> In short, by basing his formula on the difference between
> 10x50 and 10x70 binoculars,
Gary responded:
> I am certain that you did not intend to do so here Tony, but this
> statement might lead someone to conclude Adler's formula is based on
> this single example. This isn't the case, and he says so. If you read
> page 96 you'll see that the formula is based on a considerable amount
> of experimentation.
Actually, for what it is worth, Adler says that his formula is based
on heavy experimentation with 10x50 vs. 10x70, and also on 15x45
and 15x63 models. Four data points is *not* sufficient to fit
a curve like this, especially considering possible variation in
optical quality among different units and the inherently subjective
nature of what is being measured.
Now, in fact, it is clear that he has taken many more binoculars
into account; he also mentions the Canon IS 18x50 in the article,
and the article posted at Todd Gross's site lists many more.
- Tony Flanders
Tony Flanders
> Try finding M57 with a 10x binocular, even a 10x100. You need
> enough magnification to let your eye notice it.
I have, using my 10x50. Given the fact that my pupils only open
to 5.5mm, a 10x100 would presumably have little extra benefit.
Somewhat to my surprise, I had a strong hunch about which of the
numerous field stars was M57, even though I could not really pin
it down as non-stellar. And when I checked my charts, it turned
out that my hunch was right.
But I could not agree more that M57 is an example of an object
where magnification is all-important. I find the benefit on M27
to be a bit smaller; the view through my 10x50 binoculars is
quite satisfying.
I can say without the slightest hesitation that I prefer the
view of every object I have ever looked at in my Canon IS 15x45
binoculars to the view in my Celestron Ultima 10x50 -- in most
cases, by a very wide margin. But that should be no surprise;
just about any formula that takes magnification into account
at all is going to rate a 50% increase in magnification higher
than a 10% drop in aperture.
> Binoculars are a passion with Alan. He takes great care with
> his observations. It isn't something he does just so he can write an
> article in a magazine. IHMO, he writes to share his finds and passion
> with others.
Oh, I have no doubt about that.
Perhaps the wisest conclusion is that no single formula can really
sum up the "performance" of any given combination of aperture and
magnification -- there are just too many variables concerned.
Consider a concrete case. Let's avoid exit pupils over 5mm, where
different people's eye pupils are going to affect the results a lot.
The Canon IS 15x45 are a popular and well-known example of binoculars
with a small exit pupil, namely 3mm. Let's compare them to a pair of
12x55 binoculars, which we can make by masking down one of the popular
pairs of 12x60 or 12x70 on the market.
Bishop's formula predicts that the 15x45 and the 12x55 should be
nearly equivalent. Adler predicts that the 15x45 should be quite
a bit better, while Lang predicts that they should be worse.
Which one is right?
Well, there's no reason in the world why they shouldn't all be
right. First of all, given the question of which one of those
they would rather own, Bishop, Adler, and Lang would probably
all agree that the difference is likely to be small enough so
that they would pick the pair with the best optical quality
and the best "feel". Second, it seems almost certain that the
15x45 will be best (say) for observing M57, while the 12x55
may well be superior for viewing Orion's sword-and-belt region
due to their larger field of view. And as for M31, the
preference might well depend on the observer. And on how
dark the sky is.
- Tony Flanders
zgse...@netway.com
>> In short, by basing his formula on the difference between
>> 10x50 and 10x70 binoculars,
>
>Gary responded:
>
>> I am certain that you did not intend to do so here Tony, but this
>> statement might lead someone to conclude Adler's formula is based on
>> this single example. This isn't the case, and he says so. If you read
>> page 96 you'll see that the formula is based on a considerable amount
>> of experimentation.
>
>Actually, for what it is worth, Adler says that his formula is based
>on heavy experimentation with 10x50 vs. 10x70, and also on 15x45
>and 15x63 models. Four data points is *not* sufficient to fit
>a curve like this, especially considering possible variation in
>optical quality among different units and the inherently subjective
>nature of what is being measured.
That part is only an example. I think you might have overlooked a
passage a little further along (next column, same page as the part you
seem to have noticed) where he makes it clear that he's not basing it
on so limited a sample: "After years of comparing binoculars of
differing magnification and objective size while viewing deep-sky
objects, I've found a more accurate astro index..."
I feel certain that Alan would agree wholeheartedly with you that four
data points is not sufficient.
Jon Isaacs
>But I could not agree more that M57 is an example of an object
>where magnification is all-important.
I agree, it looks quite nice at powers greater than 40X or so and of course at
200X is quite remarkable.
Viewing such a small target with binoculars seems to me to be more of a
challenge than a quest for detail. It is just not a binocular target IMHO.
In my view, binoculars ought to be used as a companion to a telescope. In that
way, the strength of binoculars are the wide field views and I question
sacrificing wide views for the ability to glimpse small targets that are best
with a scope anyway.
Just some simple minded thinking.
Jon Isaacs
Rich N.
Jon Isaacs wrote in message <20020801091751...@mb-cq.aol.com>...
Jon, we are in agreement. I was just making a point using an
extreme example.
I usually am looking at much larger objects (star fields) when using
binoculars. I often find 7x doesn't magnify as much as I would like.
I prefer 8x or 8.5x for wide views, while 12x is fine for most of my high
power needs. This is for hand held binocular viewing.
Rich
Tony Flanders
> Under Roy Bishop's formula, 10 x 70's rank higher (better) than 15 x 45's,
> but under Alan's formula, 15 x 45's rank higher than 10 x 70's.
> The result obtained by Alan comports much better with my experience.
Agreed. It occurs to me how small the difference is between Adler's
formula and my own.
If you hold magnification constant, I claim that performance rises
rapidly between an exit pupil of 3mm and 5mm, and then increasingly
slowly from 5mm to 7mm. Adler's formula, by contrast, posits a
constant rate of increase all the way from 3mm to 7mm. Our curves
meet at the ends but diverge (a little) in the middle.
Binoculars with exit pupils smaller than 3mm or larger than 7mm
are sufficiently rare that they don't really enter the picture.
- Tony Flanders