Field of view vs magnification (1 Viewer)

tenex · Aug 2, 2019

Obviously there's an inverse relationship between FOV and magnification, but why isn't it exactly inverse? Top quality 10x binos offer FOV from 330 (typically) to 360 ft, from which one would predict 412 to 450 ft at 8x, 470 to 514 ft at 7x. But in fact few 8x binos exceed 400, and 450 is exceptional at 7x. If you want to sacrifice magnification for FOV, why do you get cheated?

Steve C · Aug 3, 2019

FOV is a function of the eyepiece. As the demands of a wider angular field increase, so do other factors, like eye relief, and various other aberrations that need correction. It seems that most eye piece designs that function well fall in approximately in the 6-8* range, give or take. A 6* 10x and an 8* 8x will have approximately equal afov. To get there with a 7x, a 9* or so eyepiece is needed. The only more or less modern 7x with a 9.3* eyepiece was the defunct Zen Ray 7x36. That width has some edge distortion issues, and the ZR was criticized for it. I think it comes down th what eye piece design works in a particular binocular design

typo · Aug 3, 2019

Just to add a bit more to Steve's explaination there are a couple of other design considerations.

I'll stick to roof models for nor now. Generally the 8x42 and 10x42 are housed in the same body which would normally indicate the objectives have the same focal length and they share the same prisms. It means the eyepieces will need to have different designs in order to provide the different focal lengths. In many cases this also results in a change in eye relief, with the10x often being a little shorter. That makes the angle of view through the eye lens of the eyepiece wider, and therefore potentially a wider apparent field of view. I say potentially, as not every binocular uses the full width of the eyepiece in both the 8x and 10x, but the large majority of the binoculars I've checked do.

The f-ratio of the objective is another potential FoV consideration I suspect but I've not not spotted any candidates where it appeared to be the controlling difference. The choice of prism size does it seems. Larger heavier prisms unsurprisingly can accommodate wider light paths than smaller lighter ones, and can result in the 8x models having a narrower FoV/AFoV than the 10x.

Obviously it's the designer's job to juggle these different parameters and they will make different choices for different customer categories and bugets. From what I've see there are usually fewer compromises at the heavy/expensive end of the market.

David

jring · Aug 3, 2019

Hi,

Steve C was close, but not quite. There is actually two things called field of view, the apparent one (or afov) and the true one (called tfov).
The latter what is given in f at 1000y or m at 1000m but it can also be expressed in degrees (tfov in deg = tfov in m at 1000m / 17.45 - too lazy to look up the conversion for imperial).
The former is also expressed in degrees and is a measure for how much black you see around the image when looking through the instrument - from none at all for astro EPs with more than 85 deg afov to tunnel vision for 50 deg or less.

And afov is indeed a property of the eyepiece construction. There is this little joke among astro people: wide afov, good eye relief, light & compact eyepiece - choose any two!
It actually contains a lot of truth as for simple geometry reasons, you need a big eye lens for a wide afov and good eye relief plus in general wide field eyepieces need more complex designs with lots of elements to work well. That is the reason why most binocular eyepieces top out at around 65 deg afov.

Also there is a rough formula that afov = magnification * tfov - this is not quite right for several reasons but will be close in most but very pathologic cases.
So if you have a given 65 deg eyepiece and prism assembly and put different objectives in front of it to start your new binocular line the old style, you get 8 deg tfov for the 8x version, 6.5 deg tfov for the 10x version and 5.4 deg tfov for the 12x version. With the 7x version you should get 9.2 deg but that often means your light cone is too big for the existing prism assembly and thus a simpler eyepiece with less afov is chosen to make things fit.

Joachim

wllmspd · Aug 3, 2019

There are a few (generally old, Porro, low eye relief) binoculars that get past 70degree AfOv. The recent Nikon WX got to 80, but that was just a proof of concept. You can get wider apparent angle using Astro eyepieces in binomscopes, but then lower power views means huge prisms and you also run up into the spacing of the human eyes (if the eyepieces are too big then your eye spacing isn’t enough to use two at the same time).
There’s not a lot of clever (economical) design options if we want light, compact and glasses friendly.

Peter

tenex · Aug 4, 2019

I asked about real FOV, not apparent. I stated it in feet rather than degrees to avoid any possible confusion. I'm familiar with the effects of eyepiece design on apparent field, and the compromises involved.

I think a principal reason I dislike 7-8x binoculars is that they don't provide as much additional real field as they give up in magnification. If my 10x32 gives 360 ft, why would I step down to 7x to get only 50-60 ft more? That's not enough of a practical advantage for difficult-to-track subjects.

typo · Aug 4, 2019

tenex said:
..... If you want to sacrifice magnification for FOV, why do you get cheated?

Sorry, I thought that was the question?

David

jring · Aug 4, 2019

tenex said:
I think a principal reason I dislike 7-8x binoculars is that they don't provide as much additional real field as they give up in magnification. If my 10x32 gives 360 ft, why would I step down to 7x to get only 50-60 ft more? That's not enough of a practical advantage for difficult-to-track subjects.

If you compare a wide angle pair of 10x32 with a not so wide angle pair of 7x bins (see my post you were not interested in for reasons), that's what you get. Take a wide angle pair of 8x32 or wait for the new Kowa 6.5x...

Joachim

tenex · Aug 5, 2019

jring said:
If you compare a wide angle pair of 10x32 with a not so wide angle pair of 7x bins (see my post you were not interested in for reasons), that's what you get. Take a wide angle pair of 8x32 or wait for the new Kowa 6.5x...

You made a good point: a 7x bino isn't designed in isolation, but as part of a series with common components. That may be the best answer so far. Yes, I'd be interested to see the 6.5x BD II. If it delivers the claimed FOV, it may have been better customized for its purpose? (Even the 8x sounds very promising.)
.

Troubador · Aug 5, 2019

Tenex

You don’t always get cheated!

Take a look at Zeiss’s FL range of binos.

The 10x42 has a linear fov of 330’.

Reduce the magnification by 20% to 8x and one might hope for a 20% increase in fov to 396’ but actually the FL 8x42 has 405’. Nice bonus!

Moving down a step to 7x this is a 30% reduction from 10x so one might hope for a 30% increase in fov to 429’ but again, the FL 7x42 does better this and has 450’.

OK, the FL 42mm binos are discontinued now and SF only has 10x and 8x, but let’s take a look at these two anyway.

SF 10x42 has a fov of 360’ so calculating in the same way as above, a 20% reduction in magnification should yield a fov 20% greater, i.e. 432’, but actually SF 8x42 has 444’.

So sometimes Tenex you do get to have your cake and eat it too.

Lee

Tringa45 · Aug 5, 2019

Troubador said:
Tenex

You don’t always get cheated!

Take a look at Zeiss’s FL range of binos.

The 10x42 has a linear fov of 330’.

Reduce the magnification by 20% to 8x and one might hope for a 20% increase in fov to 396’ but actually the FL 8x42 has 405’. Nice bonus!

Moving down a step to 7x this is a 30% reduction from 10x so one might hope for a 30% increase in fov to 429’ but again, the FL 7x42 does better this and has 450’.

OK, the FL 42mm binos are discontinued now and SF only has 10x and 8x, but let’s take a look at these two anyway.

SF 10x42 has a fov of 360’ so calculating in the same way as above, a 20% reduction in magnification should yield a fov 20% greater, i.e. 432’, but actually SF 8x42 has 444’.

So sometimes Tenex you do get to have your cake and eat it too.

Lee

Lee,

What did Disraeli say about statistics?

Percentages can distort things, as 8x is 20% less than 10x, but 10x is 25% more than 8x!

If you simply multiply the FOV in ft. by the magnification in the examples you gave, we end up with 3150 for the 7x42, 3240 for the 8x42 and 3300 for the 10x42. The calculated ISO AFOVs would be 55,4°, 56,7° and 57,6° for the 7x, 8x and 10x respectively.

Regards,
John

Troubador · Aug 5, 2019

John

LOL.
Its true you can 'prove' many different things with the same statistics, but I am staying with the calculations I posted above, because as far as I understand it, this is how Tenex was framing the question, and he definitely did not include AFOV* (see post 6).

Lee

Tringa45 · Aug 5, 2019

Lee,

Tenex may deny an interest in AFOV, but what he's really saying is that in general, and in binocular families in particular, there is a decrease in subjective field of view (AFOV) with decreasing magnification, and he's right.

I don't think anyone is specifically interested in how many metres of fence they can see at 1000 m, but that figure has a direct trigonometrical relationship to the angular FOV and in combination with magnification can give us an approximation of the subjective FOV. If one is really interested in measuring it, here's how: https://www.birdforum.net/showpost.php?p=3696705&postcount=1.

Someone once suggested that if you multiply the FOV in metres by the magnification and get a result over 1000 (or 3000 for ft.), then the subjective FOV would be acceptable to most. That is the case for the 42 mm Zeiss FL models in my post #11 and the diiferences, though rather marginal, underline Tenex' assertion.

John

tenex · Aug 5, 2019

Tringa45 said:
What did Disraeli say about statistics?
Percentages can distort things, as 8x is 20% less than 10x, but 10x is 25% more than 8x!

John is right here: Lee's percentages make the situation look better than more straightforward math. (Inveterate optimism?) I was simply multiplying FOV by the ratio of magnification, as John illustrated, which is the sense of the question as I asked it, how one parameter varies (quite inversely or not) as a function of the other.

I wonder why someone hasn't marketed a truly optimized 7x bino with a 500+ ft FOV. Is it not worthwhile because 7x isn't popular, or is this the reason 7x isn't popular?

P.S. Regarding FOV vs AFOV, yes, of course they're related, I was just trying not to go off on tangents about how field curvature affects AFOV and so on.

Steve C · Aug 6, 2019

tenex said:
I wonder why someone hasn't marketed a truly optimized 7x bino with a 500+ ft FOV. Is it not worthwhile because 7x isn't popular, or is this the reason 7x isn't popular?

The reason is likely due to the non existence of satisfactory eye pieces that will deliver similar across the field image sharpness compared to the 6-8* eye pieces used in 8x and 10x binoculars. That and eye relief adequate for eye glass users. A really good 7x with 500'+ fov might make 7x popular, but as as it stands, 7x is probably not popular enough to tempt anybody to develop the required eye piece designs.

Tringa45 · Aug 6, 2019

tenex said:
I wonder why someone hasn't marketed a truly optimized 7x bino with a 500+ ft FOV. Is it not worthwhile because 7x isn't popular, or is this the reason 7x isn't popular?

Well, Tenex, there is a 7x50 with a 563 ft FOV - the Nikon WX.
Apart from the disadvantage of individual focus, it is also likely to induce intolerable stress in your arms and on your bank account.

John

Chosun Juan · Aug 6, 2019

Troubador said:
Tenex

You don’t always get cheated!

Take a look at Zeiss’s FL range of binos.

The 10x42 has a linear fov of 330’.

Reduce the magnification by 20% to 8x and one might hope for a 20% increase in fov to 396’ but actually the FL 8x42 has 405’. Nice bonus!

Moving down a step to 7x this is a 30% reduction from 10x so one might hope for a 30% increase in fov to 429’ but again, the FL 7x42 does better this and has 450’.

OK, the FL 42mm binos are discontinued now and SF only has 10x and 8x, but let’s take a look at these two anyway.

SF 10x42 has a fov of 360’ so calculating in the same way as above, a 20% reduction in magnification should yield a fov 20% greater, i.e. 432’, but actually SF 8x42 has 444’.

So sometimes Tenex you do get to have your cake and eat it too.

Lee

Tringa45 said:
Lee,

What did Disraeli say about statistics?
Percentages can distort things, as 8x is 20% less than 10x, but 10x is 25% more than 8x! ....

LOL ! :-O John is correct :t:

330÷8×10 = 412.5 ...... no bonus with only 405 !
330÷7×10 = 471 .......... soz 450 just ain't up to scratch !

360÷8×10 = 450 .......... ripped off at a mere 444 !

So when you crunch the numbers correctly (themselves approximations but at least consistent for comparison purposes) you don't get to have all of your low powered cake because you've been cheated out of part of it ! :eat: :cat:

The reasons are as have been mentioned - eyepiece design and FOV and ER requirements and corresponding prism size required (not always available when modularity and economies of scale are factors taken into account for the business case).

Despite the OP's protestations to the contrary this is precisely the point of the entire thread !

Chosun :gh:

marcsantacurz · Aug 6, 2019

My understanding is the TFOV = field stop diameter / f_obj x 57.3*. In a 2 lens binocular (ignoring any limitations from the prisms), the FS point is like the objective focal point, but for the largest off-axis ray that is within the eye piece aperture, and the FS diameter is twice the distance of that point to the axis.

The magnification is the ratio of focal lengths f_obj / f_eye. I do not think there is any strict relationship between f_eye, f_obj, and the two lens FS diameter. If one could make a larger aperture eyepiece with the same focal length, you would have the same magnification and a larger TFOV. It would probably tweek the eye relief or cause more distortion or aberrations. Also, the AFOV is going to be based on the divergence of those rays out the eyepiece. I assume that the limiting factor is the chromatic aberration of the eyepiece as it becomes larger and needs to bend the light more to keep the same f_eye.

For example (I'm just making up a few numbers here), if you have a 152mm (6") tube and 42mm objective, you could have a 135.2mm f_obj and 16.8mm f_eye for a magnification of 8. If you have a 20mm field stop, then you would have an 8.5* TFOV. The objective f# = 135.2/42 =3.2 and the ocular f# = 24 / 16.8 = 1.4 (I'm just estimating the ocular aperture at 24mm > 20mm field stop).

Marc

typo · Aug 6, 2019

This might help.
https://sites.google.com/site/rchamon/home/field-of-view-of-telescopes

David

Binastro · Aug 6, 2019

My 7x35 Minolta Standard MK has a field of 578ft at 1000 yds measured using accurate star separations (11.05 degrees).

It works well although with short eye relief, which is O.K. for me as I don't use glasses with binoculars.

I think Gijs also liked the one he tested and the measured transmission was higher than I thought it would be.

I don't know what all the fuss is about as 7x binoculars were available with 13 degree fields also, years ago.

Generally I think that modern binoculars have pathetically small fields of view.

Regards,
B.

P.S.
Both the Amplivid 6x24 and Soviet 6x24 Porro have fields of about 636ft at 1000 yds.

The Visionking 5x25 has a field or 800ft at 1000 yds, about 15.4 degrees measured. It is a pity my one is of such poor optical quality.
If it was well made and more expensive I would use it a lot.

Field of view vs magnification (1 Viewer)

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