E-mail from the Kielder Forest observatory team.

[CumbrianGadgey]

Hi.

some of you may know that I am trying to produce a spreadsheet for people to use that recommends an eyepiece set for a given scope.

It's a bit of fun really but if it works and is useful to people then great. Where I really got bogged down was the age old question of what magnification can be used. Even after making allowances for things such as secondary obstructions, light transmission, mirror efficiency etc, it was inevitably going to suggest higher than x200 with a big, good quality telescope.

So far, I have handled this by having a traffic light colour scheme on the offered eyepieces. Green for below x220, amber for x220 to x300 and red for anything beyond, the latter two with cautionary notes.

Still being curious about just what is really possible in different areas I wrote to the Kielder Forest observatory team and got a detailed and very helpful reply. Here it is.

On this basis, I will check my spreadsheet and may make a couple of slight revisions, but what I had is not far off. Of course, x500 as the upper limit of the 16" unit is from a designated dark sky area with no streetlights and stupidly warm houses around to mess with the image. I'm thinking of a plan to help with my own observations. I will insert a big switch in the town's electricity supply and sneak a valve into the gas main. A few days in advance of a good weather forecast, I'll turn them both off so that everybody's house cools down. It also eliminates the light pollution. Maybe I shouldn't have mentioned my cunning plan on a public website...oops.

Dear Mark,

many thanks for your enquiry about telescope magnification at Info Visit Kielder. I have been forwarded your message below. I am volunteer at Kielder Observtory and keen amateur myself, using and making telescopes. I also work in the field of astronomical instrumentation at the CfAI section of Durham Universitie's Department of Physics.

The main rule of thumb I give about the maximum magnification is that it should not be more than 1.5x to 2x the diameter of a given telescope aperture in millimeters. Saying that, small telescopes may get a bit higher (so, a 60mm refractor could do more than 120x at the moon or a bright planet) and larger telescopes run easier into limitations by the atmospheric conditions. I observed with 457x at my home built 257mm Newtonian when the seeing was steady, which is about the maximum I could do with such an instrument.

Even if the atmospheric seeing conditions are excellent, the instrument of a given aperture produces a diffraction image in the focal plane. From a given magnification onwards, only this diffraction pattern gets bigger without any gain of information. The only way to gain more spatial information is increasing the diameter of the mirror - all this assuming the optics is diffraction limited and there is no atmospheric turbulence.

In practice it is this turbulence that in most cases gets into the way of the highest magnifications. While smaller telescopes show a planet image that still looks rather sharp but wobbles back and forth, larger apertures show multiple images superimposed and blurring out each other. The reason is the scale of the air parcels that act like weak lenses, introducing the blur. For all the model with "air parcels" is just a model, the experience with speckle interferometry or adaptive optics at large observatories shows that there are spatial variations of a certain size called the "Fried parameter". If the Fried parameter is large (cell size e.g. 25cm), the seeing is very good while otherwise too many small perturbations will cause too many multiple images blurring each other.

Another aspect of magnification is optical aberrations of a given telescope. Our 0.5m telescope at Kielder was initially only good for relatively low magnifications as the mirror was overcorrected (about 20% towards the hyperbolic). However, thanks to a coma corrector that has the additional degree of freedom of correcting the spherical term, we now get useful images up to about 300x. Maybe at good seeing even higher, but as the scope must be pushed constantly (it is an equatorial Dobsonian,

undriven) visitors will struggle when the magnification is too high.

At the driven 16" we can magnify up to about 400x-500x when the seeing permits. However, when we have larger groups in the domes we get additional "dome seeing" as the warm air created escapes through the dome slit. Hence, here again a slightly lower magnification will provide better views.

200x on your 130mm Newtonian still fits the bill of 1.5 - 2x the diameter in mm. I had a couple of new starters in my garden yesterday who brought their 130/900mm Skywatcher telescope. With 180x (10mm eyepiece and 2x

Barlow) the view on Jupiter was stunning once the scope cooled down. Only the Barlow lens let the image down a bit, while another Barlow lens from my observatory showed tack-sharp results. So I truly believe you can go up to 200x or even to 250x before the image collapses and blurs.

By the way, the main factor for magnification is the local seeing.

Observing from a paved area or even through an opened window will see lots of heat rising in front of the telescope. If you are on a grassed area and you do not look over houses which are either warm from the daytime sun or because they are heated in the winter, you should enjoy calmer images with more detail.

I hope I could help you with my lines. If you have any more questions, please feel free to drop me an email.

[Laurie61]

Quote "Even if the atmospheric seeing conditions are excellent, the instrument of a given aperture produces a diffraction image in the focal plane. From a given magnification onwards, only this diffraction pattern gets bigger without any gain of information. The only way to gain more spatial information is increasing the diameter of the mirror - all this assuming the optics is diffraction limited and there is no atmospheric turbulence."

This is a graph showing the points raised above   

This shows the magnification needed to show all the detail various size scopes generate, in theory there is no need to go beyond this magnification. As scopes increase in aperture they need better seeing to exploit their potential.    

[CumbrianGadgey]

Quote "Even if the atmospheric seeing conditions are excellent, the instrument of a given aperture produces a diffraction image in the focal plane. From a given magnification onwards, only this diffraction pattern gets bigger without any gain of information. The only way to gain more spatial information is increasing the diameter of the mirror - all this assuming the optics is diffraction limited and there is no atmospheric turbulence."

This shows the magnification needed to show all the detail various size scopes generate, in theory there is no need to go beyond this magnification. As scopes increase in aperture they need better seeing to exploit their potential.    

If I have this right, I'm not sure that the graph above shows what magnification people will find useful or that the scope can achieve.

This is how my logic goes: What the chart does is to take 180 seconds of arc and divide that by the resolution of a telescope in arcseconds, using yellow light. The yellow light is just to allow a margin for error and ensure that red light is also distinguishable. Essentially, it is looking at the ability of the human eye to comfortably differentiate between two points of light. This will be the magnification that allows us to see, for example, a pair of binary stars as two distinctly separate items. It does not say that the magnification cannot be incresed from this. If it is, our EP simply shows us the two stars further apart. It uses 180 arcseconds as a figure because the resolving power of human vision varies from 30 to 120 arc seconds for 20/10 to 20/40. 20/20 vision is not the best, as is a common misconception. It is the average or nominal resolving power able to resolve 60 arcseconds. The 180 figure means that even someone with 20/40 eyesight (bad) can resolve even the red part of the spectrum at the suggested magnification. My eyes are about 20/30.

There's another thing about that chart I'm not sure about and that's planetary observation. My current telescope can resolve yellow light at about 1 second of arc, which maxes Jupiter at solar conjunction about fifty 'pixels' in diameter, or made up of 1960 bits the scope can resolve. Theoretically, going anything over x90 is a waste of time based on resolution and my eyesight. That does not mean I don't want to see the image at x180 or x220, even if it is no clearer!

There may be a very important reason for this. Our eyes have two sets of completely different receptor cells, with the colour ones centred more on the retina and greyscale ones further out. When the pupil dilates at night, it exposes all the greyscale cells as it tries to gather as much light as possible, which is why our vision goes black and white at night. With Jupiter on x60, it is very small and not covering all of the colour receptors in the eye and almost none of the rods. I'm just guessing here but maybe we prefer the larger image because it stimulates what the brain accepts as a better balance of photo-receptors. This would be a psychological reason to prefer a larger image to a smaller one, even if it is no more detailed. All I know is that I prefer x180 to x60! We may also prefer larger magnification than is strictly necessary for binary stars, simply because our brain likes looking at bigger pictures!

[Laurie61]

"If I have this right, I'm not sure that the graph above shows what magnification people will find useful or that the scope can achieve."

​Yes you are right, the graph is a guide to the level of magnification needed to allow the average human eye extract all the information present in an image, generated by different size scopes. It assumes the scope is working nominally so cooled, collimated ect.  In reality conditions on the night and the target being observed will dictate magnification.   

"There's another thing about that chart I'm not sure about and that's planetary observation. My current telescope can resolve yellow light at about 1 second of arc, which maxes Jupiter at solar conjunction about fifty 'pixels' in diameter, or made up of 1960 bits the scope can resolve. Theoretically, going anything over x90 is a waste of time based on resolution and my eyesight"

If you have a scope of 5-6" with 1 arc sec resolution the graph suggests a magnification between 160-190 x before the typical eye can see all the detail present which is in line with your own experiences with Jupiter. If you can see this detail at about 90 x your eyes have roughly twice the resolution of the theoretical eye used to generate the graph ? As magnification increases contrast reduces which is also a factor for picking out detail, so working out how much magnification is needed, in theory, allows you to achieve the optimal image size. This is assuming that the object is bright enough to allow this in the first place.   

Another factor to take into consideration is the exit pupil generated by various scope/ eyepiece combinations, I tend to stay within 1-7 mm. As this number reduces, below 1 mm, it can exacerbate floaters which can be a problem and at the other end of the range it can be too big for the eye's pupil to accommodate, which dims the image. Again different individuals, eye's, will have their own acceptable working range.   

[Pig]

All quite simple then