is the perception of magnification linear?

[smoothound54]

hi folks

another newbie Question I am afraid......

I am trying to plan a spread of EPs to cover a wide spectrum with minimum outlay - and a question arises

for a 1000mm FL the delta in Mag between an 18mm and 19mm EP is only X3 (ie x52 compared to x55) this represents a notional 6% increase - and it could be argued its pointless owning both

whereas the delta between a 5mm and a 6mm is X34 (166 compared to 200) this represents a 20% increase

question:- is the noticable change as perceived by the eye comparably greater as the figures suggest? I ask because in other human senses (such as hearing) perceived change is not always linear.

I guess this is quite important when planning a stable of EPs - IF the perception of view is according to the Magnification numbers - you would tend to cluster you focal lengths towards the short end of the spectrum to give a uniform spread of Mag

so the question boils down to this - setting aside issues like usable magnification, exit pupil limits and eye relief etc - assuming you wanted to cover all options - should a stable of EPs be based on a uniform spread of mag? or focal length? or some other rule of thumb?

I am sure that there are numerous wrinkles in the answer - but its a general principle question only so its only a broad strategy I am looking for

cheers

alan

[E621Keith]

Magnification itself grows exponentially. 100x is twice as big as 50x (delta = 50x), but you need 200x to get twice as big as 100x (delta 100x).

Your percentage change measurement is a much indication of actual magnification change than the absolute difference in magnification.

Whether you can perceive these changes depends on you experience. You can train your eyes/brain to 'see' things other people may not be able to see.

Take a look at this thread. There are some good advice on eyepieces selection

[acey]

By "perception of magnification" what you really mean is "perception of angular area". If you double the magnification then the angular area increases by a factor of four (and more generally by a factor of n^2 where n is the magnification). Try standing a fixed distance away from a target (e.g. four metres away from a picture on a wall). Then walk closer until you're two metres away. This is equivalent to doubling the power of an eyepiece.

For an eyepiece set you want three powers: low, medium and high. These are fixed by two factors: your eye and the atmosphere. An eyepiece creates a disc of light (the exit pupil) which generally should be no larger than your own eye pupil (since you would otherwise have wasted light not reaching your retina) and should be bigger than about 0.5mm (since diffraction in the eye will limit any further visibility of detail below that size).

Exit pupil = (eyepiece focal length)/(telescope focal ratio), so

Eyepiece focal length = (exit pupil) x (telescope focal ratio), where

Focal ratio = (focal length)/(aperture)

Let's say that your eye pupil is 7mm (a typical figure for people below middle age). You say your telescope focal length is 1000mm but don't state the aperture. Let's say it's 150mm so the focal ratio is 1000/150 = 6.7.

The lowest useable power is then an eyepiece with focal length 7 x 6.7 = 46.9mm (magnification 1000/46.9 = 21.3)

The highest useable power is an eyepiece with focal length 0.5 x 6.7 = 3.35mm (magnification 1000/3.35 = 298.5)

Both figures are approximations based on assumptions about the eye - eyerybody's eye is different so you've just got to find out what works for you.

The atmosphere places a limit on magnification: on many nights you might not get any benefit from more than x300, so for larger apertures this has to be taken into account as well as exit pupil. Another obvious factor is commerical availability: you buy the nearest focal length to what you want.

In practice if you were using lowest and highest available powers then you'd probably want 2 rather than one magnification to fill in the middle. Here is where the logarithmic effect you alluded to comes in: you could proceed by multiplying the focal length (or magnification) by a constant factor. In this case I would suggest 0.415 ( = (3.35/46.9)^(1/3) ). Then you would have the following focal lengths:

46.9mm (x21.3)

19.5mm (x51.3)

8.1mm (x123.5)

3.4mm (x294)

This is assuming that the telescope is "diffraction limited", i.e. of highest quality. On a budget 6" f6.7 you may well find that a 3.4mm eyepiece is useless, regardless of the quality of the sky or eye.

But there is another factor we haven't taken into account, which is that visual acuity at low light levels is best for an exit pupil in the approximate range 2-3mm. This would correspond to focal length 13.4 - 20.1mm This suggests that if you had eyepieces of those focal lengths then you'd probably end up using them more than the others - you would tend to find they gave the best view. So you could start by getting something in that range (e.g. a 20mm eyepiece) and work out from there towards lowest and highest powers.

You probably got a 20mm eyepiece free with your scope. So my advice is that you stick with that for a while, get to know your scope, your eye and the sky, then think about expanding your collection, one eyepiece at a time. Go for something towards the higher end (e.g. 8mm), then the lower (e.g. 32mm), then fill in any gaps you feel to be remaining.

Don't go for "minimal outlay", go for quality. And don't go for a whole set all at once, go for eyepieces one at a time. It takes a while to find what's right for you, and you'll find that you want to replace eyepieces as your experience increases. Buying a whole set just means you'll be trying to sell a whole set somewhere down the line - or (like me) you'll wind up with a lot of old low- or mid-price eyepieces that you never use, plus three expensive ones that you use all the time.

[smoothound54]

Magnification itself grows exponentially. 100x is twice as big as 50x (delta = 50x), but you need 200x to get twice as big as 100x (delta 100x).

Your percentage change measurement is a much indication of actual magnification change than the absolute difference in magnification.

Whether you can perceive these changes depends on you experience. You can train your eyes/brain to 'see' things other people may not be able to see.

Take a look at this thread. There are some good advice on eyepieces selection

http://stargazerslou...least-you-need/

thanks keith for further clarification of the maths - which helps. the point about experience and training etc I wish to set aside as I am trying to keep all things equal - lets assume we are talking about the perception of an individual

i guess your version of the maths supports a view that the same % change in mag at the upper end and lower end of the range would tend to be percieved to be the same differnce by the same person (with any given level of training/experience)

to clarify I think you are saying that a 20% increase over 20mag (ie to 24mag) would be perceived the same relative chanage as a 20% increase over 100mag (to 120mag) - by the same person? or do I misunderstand?

cheers

alan

[smoothound54]

By "perception of magnification" what you really mean is "perception of angular area". If you double the magnification then the angular area increases by a factor of four (and more generally by a factor of n^2 where n is the magnification). Try standing a fixed distance away from a target (e.g. four metres away from a picture on a wall). Then walk closer until you're two metres away. This is equivalent to doubling the power of an eyepiece.

For an eyepiece set you want three powers: low, medium and high. These are fixed by two factors: your eye and the atmosphere. An eyepiece creates a disc of light (the exit pupil) which generally should be no larger than your own eye pupil (since you would otherwise have wasted light not reaching your retina) and should be bigger than about 0.5mm (since diffraction in the eye will limit any further visibility of detail below that size).

Exit pupil = (eyepiece focal length)/(telescope focal ratio), so

Eyepiece focal length = (exit pupil) x (telescope focal ratio), where

Focal ratio = (focal length)/(aperture)

Let's say that your eye pupil is 7mm (a typical figure for people below middle age). You say your telescope focal length is 1000mm but don't state the aperture. Let's say it's 150mm so the focal ratio is 1000/150 = 6.7.

The lowest useable power is then an eyepiece with focal length 7 x 6.7 = 46.9mm (magnification 1000/46.9 = 21.3)

The highest useable power is an eyepiece with focal length 0.5 x 6.7 = 3.35mm (magnification 1000/3.35 = 298.5)

Both figures are approximations based on assumptions about the eye - eyerybody's eye is different so you've just got to find out what works for you.

The atmosphere places a limit on magnification: on many nights you might not get any benefit from more than x300, so for larger apertures this has to be taken into account as well as exit pupil. Another obvious factor is commerical availability: you buy the nearest focal length to what you want.

In practice if you were using lowest and highest available powers then you'd probably want 2 rather than one magnification to fill in the middle. Here is where the logarithmic effect you alluded to comes in: you could proceed by multiplying the focal length (or magnification) by a constant factor. In this case I would suggest 0.415 ( = (3.35/46.9)^(1/3) ). Then you would have the following focal lengths:

46.9mm (x21.3)

19.5mm (x51.3)

8.1mm (x123.5)

3.4mm (x294)

But there is another factor we haven't taken into account, which is that visual acuity at low light levels is best for an exit pupil in the approximate range 2-3mm. This would correspond to focal length 13.4 - 20.1mm This suggests that if you had eyepieces of those focal lengths then you'd probably end up using them more than the others - you would tend to find they gave the best view. So you could start by getting something in that range (e.g. a 20mm eyepiece) and work out from there towards lowest and highest powers.

You probably got a 20mm eyepiece free with your scope. So my advice is that you stick with that for a while, get to know your scope, your eye and the sky, then think about expanding your collection, one eyepiece at a time. Go for something towards the higher end (e.g. 8mm), then the lower (e.g. 32mm), then fill in any gaps you feel to be remaining.

Don't go for "minimal outlay", go for quality. And don't go for a whole set all at once, go for eyepieces one at a time. It takes a while to find what's right for you, and you'll find that you want to replace eyepieces as your experience increases. Buying a whole set just means you'll be trying to sell a whole set somewhere down the line - or (like me) you'll wind up with a lot of old low- or mid-price eyepieces that you never use, plus three expensive ones that you use all the time.

thanks for the time and trouble Acey - this is exactly what I was looking for! - and FYI I always planned to go for quality - for an F5 its essential - but I will start by buying say 2 EPs and a decent extender - and I want to buy ones that will compliment the eventual stable - rather than buying ad-hoc .... this for me represents minimum outlay - not going for cheapo gear - so your explanation on perception helps a lot - many thanks

al

[smoothound54]

for completeness i found this calculator useful

http://www.davidpaulgreen.com/tec.html

and I had my pupil dia. estimated a few nights ago - about 6mm (age!)

[AndyEllis]

Magnification itself grows exponentially. 100x is twice as big as 50x (delta = 50x), but you need 200x to get twice as big as 100x (delta 100x).

I think this is the main point here.... so basically, doubling the magnification is simply a function of halving the focal length of the EP, so a set along the lones of 50mm, 25mm, 15mm, 10mm, 6mm, 4mm.... always being aware of the limits of your scope would do it...

Sorry to simplify - it's worth knowing the equations so you can work out things like your fov (and whether or not an object will fit in it), but most planetarium softwares will put a nice neat circle in if you tell it the scope you use and the EP size...

[acey]

Geometric progression of focal length is a convenient rule of thumb, not a law of perception, but it has been widely advocated and the general principle is easily stated. Let:

min = minimum desired exit pupil

max = maximum desired exit pupil

n = number of desired eyepieces

p = ratio of successive focal lengths

Then p^(n-1) = max/min, i.e. p = (max/min)^(1/(n-1))

Example: let min = 1mm, max = 6mm, n = 4. Then p = 6^(1/3) = 1.82 and the desired exit pupils (in mm) are 1, 1.82, 3.30, 6.

The eyepiece focal length is (exit pupil) x (telescope focal ratio), so if the scope is f5 then the focal lengths (in mm) are 5, 9.1, 16.5, 30.

The magnification is (telescope focal length/eyepiece focal length) so if the scope has focal length 1000mm then the magnifications are 200, 110, 60.6, 33.3.

[John]

This is not very scientific but I've found it very useful to have closely spaced eyepieces, in focal length terms, for high magnification viewing so that you can find the optimum one for the scope / conditions. For my scopes which range from 663mm to 1590mm in focal length, my high power eyepieces are 8mm, 6mm, 5mm, 4mm and 3.5mm. The last two won't get much use in the longer focal length scope though, due to the limitations of the seeing conditions.

Exit pupil size is also something that needs to be understood and taken into account in eyepiece selection. Some exit pupil sizes get the optimum performance from narrowband filters for example, too large an exit pupil and some of the light gathered by the scope wont make it though your iris, to narrow an exit pupil and floaters in your eye start to make themselves apparent.

Personally, I've found the advice notes on the Tele Vue website very useful in understanding the issues and making choices, even if Tele Vue is not the brand eventually selected:

http://www.televue.com/engine/TV3_page.asp?id=108#Eyepieces

[AndyEllis]

I think I'm with John on this - for hi-mag, I have a 4mm, 5mm, 6mm, 7mm, 9mm.... they tend to only be used for planets and lunar features... maybe the odd PN, but I guess it depends (as John says) on the scope you are using

[E621Keith]

Another thing to consider is seeing limit. When you get into magnification in excess of 200x, atmospheric turbulence will have a major effect on your view, so it's a good idea to have more choices at the higher magnification end. You can select the eyepiece that will give you optimum high magnification. Enough to magnify the planets, but not excessive such that the view is blured by turbulence.

When you are working near the seeing limit, a good zoom can be better than a good fixed eyepiece.

[smoothound54]

I think this is the main point here.... so basically, doubling the magnification is simply a function of halving the focal length of the EP, so a set along the lones of 50mm, 25mm, 15mm, 10mm, 6mm, 4mm.... always being aware of the limits of your scope would do it...

Sorry to simplify - it's worth knowing the equations so you can work out things like your fov (and whether or not an object will fit in it), but most planetarium softwares will put a nice neat circle in if you tell it the scope you use and the EP size...

thanks andy - yes I did the maths as well - its pretty straight forward - the formulas are pretty basic - and as you indicate I had worked out that according to pure maths/optics there should be a natural weighting towards the shorter focal length to get an even spread of magnification coverage (asymptotic)

I just wanted to check in case there was some weird non-linear rule about the brain's perception of magnification to factor in - and some of the information from acey helps here (acuity)

but basically aside from exit pupil (which is again simple maths) - it would seem there is no significant non-mathmatical perception factor to take into account

this makes planning straightforward

thanks to all

alan

[John]

Each element, ie: focal length, exit pupil, eye relief and apparent v's true field of view is straightforward enough however finding what suits you (and your wallet !) best can be somewhat less precise - one thing you will see posted a lot here is that eyepiece selection is a personal thing, ie: what works for one person will not be at all right for someone else. That can't be worked out with maths, unfortunately

[smoothound54]

This is not very scientific but I've found it very useful to have closely spaced eyepieces, in focal length terms, for high magnification viewing so that you can find the optimum one for the scope / conditions. For my scopes which range from 663mm to 1590mm in focal length, my high power eyepieces are 8mm, 6mm, 5mm, 4mm and 3.5mm. The last two won't get much use in the longer focal length scope though, due to the limitations of the seeing conditions.

Exit pupil size is also something that needs to be understood and taken into account in eyepiece selection. Some exit pupil sizes get the optimum performance from narrowband filters for example, too large an exit pupil and some of the light gathered by the scope wont make it though your iris, to narrow an exit pupil and floaters in your eye start to make themselves apparent.

Personally, I've found the advice notes on the Tele Vue website very useful in understanding the issues and making choices, even if Tele Vue is not the brand eventually selected:

http://www.televue.c...d=108#Eyepieces

great link thanks John

[smoothound54]

Geometric progression of focal length is a convenient rule of thumb, not a law of perception, but it has been widely advocated and the general principle is easily stated. Let:

min = minimum desired exit pupil

max = maximum desired exit pupil

n = number of desired eyepieces

p = ratio of successive focal lengths

Then p^(n-1) = max/min, i.e. p = (max/min)^(1/(n-1))

Example: let min = 1mm, max = 6mm, n = 4. Then p = 6^(1/3) = 1.82 and the desired exit pupils (in mm) are 1, 1.82, 3.30, 6.

The eyepiece focal length is (exit pupil) x (telescope focal ratio), so if the scope is f5 then the focal lengths (in mm) are 5, 9.1, 16.5, 30.

The magnification is (telescope focal length/eyepiece focal length) so if the scope has focal length 1000mm then the magnifications are 200, 110, 60.6, 33.3.

great minds! that was more or less my orginal plan (not quite that low since my pupil at a shade under 6mm) - once I had writtewn it down this prompted my question to check for wrinkles - of which there are a few - thanks guys

I will start with a couple of EP and an extender and that will probably by the limit of my bravery vis-avis the good lady for 12 months or so! I need to plan nowish as a west-ward business trip is on the cards in the next month or three

again thanks guys for all the help - this has been really educational

Al