A guide for choosing a sensible eyepiece collection using the exit pupil

[Piero]

This text considers the previous thread http://stargazerslounge.com/topic/43171-eyepieces-the-very-least-you-need/ but aims to show how to build the collection using the exit pupil explicitly. I tried to report the information in a more systematic and clear way, adding explanations and details which were under the lines. To me this thread should be considered as a complement of the previous document (which is an evaluable one), not a replacement.

Introduction

The reason for building up a collection using the exit pupil is that this is independent of the telescope (therefore different from the magnification which is specific). The exit pupil is the size of the image exiting from the eyepiece and coming to our eye. Because of our eye pupil can shrink up to about 0.5mm and enlarge up to about 7mm, we are interested in eyepieces within the range 0.5mm-7mm. Alternatively, the exit pupil can be interpreted as a measure of brightness.

Why are we focusing on image brightness, instead of object magnification?

First of all, there is an important relationship: the larger the exit pupil, the brighter the image, the lower the magnification. We focus on image brightness because targets in the sky can be somehow divided by groups according to their brightness.

• To observe very dim objects one should consider eyepieces showing a bright image (therefore we use an eyepiece which has a large exit pupil or alternatively has low power). If the exit pupil is too small, the object might not even be visible. The useful exit pupil range for this class is 3mm-7mm. Examples of targets belonging to this class are extended nebulae and faint galaxies.

• When observing moderately dim objects, one could push the magnification a bit more. This magnification comes to the cost that the overall image becomes dimmer. In this case the observer is using a medium size exit pupil or medium power eyepiece. The useful exit pupil range for this class is 1.2mm-3mm. Examples of these targets are bright galaxies, open and globular clusters and planetary nebulae.

• When observing bright objects, the observer can magnifying even more. Although the overall image becomes dimmer, the object will still be bright enough to show some detail. In this case, the observer is using a high power eyepiece or using a small exit pupil. The useful exit pupils for this class are <1.2mm. Examples of this targets are planets, moon, double stars and certain planetary nebulae.

This is the general reason why it is said that one would need only three eyepieces to observe a lot of targets.

Choosing an eyepiece set

The next point is to use the previous information and select a set of eyepieces. This will require some basic mathematics, but nothing more than multiplication or division.

Let’s start by defining the telescope focal ratio. This is the telescope focal length divided by telescope aperture (e.g. telescope aperture: 200mm, telescope focal length: 1000mm, telescope focal ratio: 1000/200=5 or simply F5).

NB this has been corrected from f6

Now, an easy way to calculate the exit pupil is dividing the eyepiece focal length by the telescope focal ratio. For instance, an eyepiece with focal length of 25mm, will have an exit pupil of 25mm/5=5mm when used with the telescope proposed in the previous example.

Now it is the time to add some constraints.

• As mentioned above, the human eye pupil (whose diameter controls the amount of light we can detect) can shrink / enlarge in the range 0.5mm-7mm. Of note, some reports show that the exit pupil decreases with age, and that the maximum exit pupil in old people is about 5.5mm. I will not consider this latter point in this discussion though.
• Most of us live under moderately light polluted skies. A large exit pupil could increase the sky background brightness so much that it appears light grey. Distinguishing between a light grey object and a grey sky is a difficult task for our eye. Our eye would work out contrast differences a bit better when the sky is darker. In obstructed telescopes, a large exit pupil under a light polluted sky could also reveal the shadow of the secondary mirror which is better to avoid. Therefore, under moderately light polluted sky, it would be better not to have eyepieces with more than 4mm-4.5mm exit pupil.
• Astronomy is an outdoor hobby and obviously affected by atmospheric conditions (seeing). Unfortunately, not everyone lives under pristine dry skies which are not affected by wind and other kind of atmospheric turbulences. Seeing can limit the maximum useful magnification. In the UK, most observers rarely go beyond 200x-220x. For a Dobson 8” F6, this means that an eyepiece with exit pupil <1.0mm (200x) might not be used very much.

The above constraints show that we are interested in a range of eyepieces giving exit pupils between 0.5mm and 4mm-4.5mm, with a maximum power of about 200x.

To build this eyepiece selection, we start from an exit pupil of 1mm and use a factor of 1.4x.

This factor is the minimum to see appreciable differences in terms of image brightness (or magnification). Therefore we obtain the following range: 0.5mm - 0.7mm - 1mm - 1.4mm - 2.0mm - 2.7mm - 3.9mm

For a Dobson 200mm F6, these exit pupils will give the following eyepieces focal lengths (up to 200x): 6mm - 8.6mm - 12mm - 16.8mm - 23.5mm. Of course one does not need to get all these eyepiece focal lengths, but could simply select the lower power 24mm, the medium power 12mm and the high power 6mm (3 eyepieces). Alternatively, s/he could get a barlow 2x in combination with the 24mm and 17mm to get an additional medium power 12mm and medium-high power 8.5mm (2 eyepieces + barlow 2x).

For a Maksutov Cassegrain 127mm F11.8, the above exit pupils will result in the following eyepiece focal lengths: 8.6mm - 12.1mm - 16.9mm - 23.6mm - 33.1mm - 46.3mm . Again, not all these eyepieces are needed, but one can play a similar game as for the dobson 200mm case.

Other considerations:

• Consider eyepieces with similar apparent field of view (afov, as indicated on the eyepiece). E.g. a Tele Vue Nagler 13mm (afov: 82 degrees) and will show about the same real field of view of a Plossl 20mm (afov: 50 degrees). These two eyepiece will not work nicely together.
• Eye relief. This is the distance between the eye and the eyepiece lens. This was not really an option in the past, but thankfully nowadays many eyepiece companies are becoming quite sensitive to people wearing spectacles. Eyepieces with focal lengths above 20mm are generally comfortable in terms of eye-relief. Below that, the eyepiece eye relief could be tight or really uncomfortable (e.g. plossls) if one needs to wear spectacles to observe (e.g. people suffering from astigmatism). For these people, eyepieces with 20mm eye relief should be considered.
• If an observer lives under dark skies and is interested in very faint targets, the investment in a very low power eyepiece could be worth being considered (e.g. 6.0-6.5mm exit pupil).
• If an observer is predominantly interested in planetary or double star observation, it could be worth considering closing between eyepieces gaps at high power or evaluating the option of a zoom eyepiece.

[Stu]

Great stuff Piero, really useful guide and an excellent approach to building a logical set of eyepieces.

The only thing I disagree with is that it does not give me any form of justification for owning all the eyepieces I have

[Stu]

Great stuff Piero, really useful guide and an excellent approach to building a logical set of eyepieces.

The only thing I disagree with is that it does not give me any form of justification for owning all the eyepieces I have

Actually, that's not true I was joking. I have scopes ranging from f5.9 to f14.3 so this does require a wide range from 3 ish mm up to 31 or more.

[Piero]

Thanks Stu 

I also have more than three eyepieces and use them all quite a lot! 

This is not required though and that is, I think, the message a beginner should receive. Nowadays we have a lot of options available in the market. This is great, but is also a big problem for a beginner who wants to get a useful set of eyepiece without spending a fortune. With this guide I hope there is a message on how to choose this set, why choosing in this way and which targets these eyepieces can be used for.

Along with learning the constellations and star hopping, this should be the minimum required as far as eyepiece equipment concerns. 

You said an interesting comment about the large number of eyepieces one could have.

I should have mentioned that, because we measure the eyepiece exit pupil from the telescope focal ratio, if telescopes have same or similar focal ratio, the collection of eyepieces is transferable between telescopes (apart from magnification). In contrast, if one has telescopes with different focal ratios, other eyepieces might be required. This last case could lead to more eyepiece sets. 

(p.s. We commented on this at the same time!   ) 

[PHIL53]

Let’s start by defining the telescope focal ratio. This is the telescope aperture divided by telescope focal length (e.g. telescope aperture: 200mm, telescope focal length:1200, telescope focal ratio: 1200/200=5 or simply F5).

Very interesting but you may wish to correct a typing error to avoid confusing readers: 1200/200 = 6 or simply F6

[Piero]

Let’s start by defining the telescope focal ratio. This is the telescope aperture divided by telescope focal length (e.g. telescope aperture: 200mm, telescope focal length:1200, telescope focal ratio: 1200/200=5 or simply F5).

Very interesting but you may wish to correct a typing error to avoid confusing readers: 1200/200 = 6 or simply F6

Thanks for your correction.    

Could a moderator correct this for me, please? Thanks!

[Stu]

Thanks for your correction.

Could a moderator correct this for me, please? Thanks!

Done

[Paul73]

Good post Piero.

Interestingly, for my f4.7 10", the "most used eyepieces" box contains: 6, 8, 12, 17, 24 (&30)mm offerings.

This was built on exit pupil size / contrast at the long end and UK atmospheric constraints at the short end. The above is almost exactly as you set out.

Paul

[Moonshane]

I think that building an eyepiece collection based on exit pupil if fine until you change scopes to, or use a different scope which has, a much different focal ratio. It's an excellent write up though.

I try and cover all eventualities and have a main set of 40, 26, 17, 12, 9, 7 and 6-3mm eyepieces which by good luck or judgement broadly follow the 1.4x rule. I also have a supporting cast of plossls at 32, 25, 20, 15 and 11mm ( I plan to buy the 8mm too), same story!

[laudropb]

Very interesting report. I started out by getting a quality zoom eyepiece which more or less gives the same exit pupil sizes that you recommend. I also found that not having to change eyepieces, especially when lunar observing was a great boon. Thanks for taking the time and effort to compile this data. It will be of great help to all beginners.

[John]

Very interesting stuff Piero

I have to confess that it's only in the long focal length eyepieces where I consider exit pupil, sticking to 5.8mm as the largest exit pupil I get. I often find that my next eyepiece down, which gives a 4mm exit pupil, is a better choice for seeing faint deep sky objects even though I give up a little in true field of view to achieve this.

At the other end of the range I find that eyepieces with a focal length of less than 3mm show up the floaters in my observing eye too much, regardless of the scope thay are used in so I don't go there.

While perhaps theoretically 3 eyepieces is enough, I've found that, especially at the shorter focal lengths, having more choice gives more options and more chance to find a focal length that is the "goldilocks" one for the target and observing conditions on a particular night. Thats my lame excuse for owning 10 eyepieces anyway

I do agree that 3 or 4 well chosen focal lengths will keep an observer going for some time though.

[YKSE]

Thanks for taking the time for writing  this excellent guide, should be very helpful for beginners to have some insight about how the eyepieces work in the whole system.

Multiple scopes do complicated things up, and that why I think good zooms are sound starting point for many.

[Piero]

Good post Piero.

Interestingly, for my f4.7 10", the "most used eyepieces" box contains: 6, 8, 12, 17, 24 (&30)mm offerings.

This was built on exit pupil size / contrast at the long end and UK atmospheric constraints at the short end. The above is almost exactly as you set out.

Paul

I think that is the point: to get a set of eyepieces which have reasonable distances between them. Whether this exactly hits the exit pupils of 0.7mm, 1.0mm, 1.4mm, 2.0mm, 2.7mm, 4.0mm doesn't really matter as long as there is a proportion between eyepiece focal lengths which is similar to this scale, in order to cover the observation of multiple targets.

Of course, experience, interest and owning multiple telescopes can lead to the need of additional eyepieces to the minimum 3-4 that a single telescope would require to be used exhaustively.

However, for a beginner who has just bought his/her first telescope (and therefore faced a modest investment) I think it is important to get the minimum number of eyepieces to be able to enjoy this hobby using the whole equipment. 

[Charic]

Let’s start by defining the telescope focal ratio. This is the telescope aperture divided by telescope focal length (e.g. telescope aperture: 200mm, telescope focal length:1200, telescope focal ratio: 1200/200=5 or simply F5).

Very interesting but you may wish to correct a typing error to avoid confusing readers: 1200/200 = 6 or simply F6

 Piero,  there is another correction that needs MOD intervention, I'll PM you.

Still a good read for newcomers to the hobby.

I've  based my EP collection on two  parameters,  highest power &  lowest  power for my needs? This is where the focal ratio assists my calculations. The focal ratio alone  equals my shortest focal length EP, and by  multiplying the focal ratio by my pupil size equates to the longest focal length eyepiece I require. Anything else in-between is a bonus, and simply helps me to better 'frame' my subject. Yes you need two, maybe three EP's but I still prefer the greater choice offered by having several EPs.

[Piero]

 Piero,  there is another correction that needs MOD intervention, I'll PM you.

Still a good read for newcomers to the hobby.

I've  based my EP collection on two  parameters,  highest power &  lowest  power for my needs? This is where the focal ratio assists my calculations. The focal ratio alone  equals my shortest focal length EP, and by  multiplying the focal ratio by my pupil size equates to the longest focal length eyepiece I require. Anything else in-between is a bonus, and simply helps me to better 'frame' my subject. Yes you need two, maybe three EP's but I still prefer the greater choice offered by having several EPs.

Thanks very much for spotting this, Charic!

Interestingly, we all didn't! 

I also enjoy having more options than just three. With my TV-60, my current set has 8 exit pupils:

4.0mm - 2.2mm - 1.6mm - 1.2mm - 0.9mm - 0.6mm - 0.5mm - 0.2mm

I do not use the 1.6mm very much because the corresponding magnification is quite similar to the 2.2mm and 1.2mm. However this will change in the future when I will buy a Dobson (I am leaning towards the OOVX10). Being this an F5, my eyepiece set will give exit pupils of: 

5.0mm - 2.7mm - 2.0mm - 1.5mm - 1.1mm - 0.7mm - 0.6mm - 0.3mm 

Apart from the very short exit pupils (0.6mm, 0.3mm) which result in too high magnification, the full set is transferable and reasonably optimised without having to make new purchases, which was my aim! 

All this with 4 eyepieces + 1 focal extender 

[phil125]

Very interesting. Food for thought.

[Piero]

For those who feel the need to better understand their current equipment, the following spreadsheet may be helpful: 

https://docs.google.com/spreadsheets/d/1KtV9Hl0XRQ-IGLiCjxIGSzss-b9TJ_j8ssk0lhh5UpI/edit?usp=sharing       

 

It was created some time ago for computing the parameters for my equipment. Of course, it can be downloaded and updated with your data. 

Download:  File => Download as => Microsoft Excel (.xlsx) OR OpenDocument Format (.ods).

The only thing one needs to do is to edit the light blue fields.

 

 

A quick overview

Below, you can see a sheet called Eyepieces, and one sheet for each telescope. You can simply duplicate a telescope sheet to add another telescope. Here is a screenshot of the Eyepieces sheet.

 

 

After filling in the eyepiece data, you can see a screenshot showing how these eyepieces work on the Tak 100mm f7.4 (2nd sheet). The telescope data can be changed by editing the light blue cells. This spreadsheet computes the exit pupil and many other parameters for you. Data up to two barlows (or tele-extenders or focal reducers) can also be added (see second panel). The other important parameter is the FOV which is computed using the eyepiece field stop if this is specified in Eyepieces (True Field (°) = 57.3° x eyepiece field stop / telescope focal length) or the AFOV otherwise (TFoV = AFoV / Magnification).

 

 

 

In addition, a table computing the optimal selection of eyepieces by exit pupil for the selected telescope is provided at the bottom of the page. Essentially, this gives an indication for deciding the eyepiece focal lengths one could consider for most visual work given a certain telescope.