Parabolic v Spherical primary mirror and focal ratio.

[Alfian]

Hi all, this must have been covered somewhere before so apologies if its a bit of a chestnut.I appreciate that faster scopes work better with parabolic primary mirrors but wondered if there was a point, focal ratio wise, that it ceases to be an appreciable issue whether the primary is parabolic or sperical?

I'm almost certain that the primary in my f7.3 Tal1 is spherical but seems to work well enough, yet a scope like the F8 Skywatcher 150 Dob has a parabolic mirror.

Is parabolic simply optically a better "solution" no matter what?

[John]

My (limited) understanding of this is that, in the newtonian design, a spherical mirror can produce differaction limited performance when it is F/8 or slower. Some other scope designs such as SCT's and Mak-Newtonians do use faster spherical primaries but use the corrector or meniscus lens and / or the secondary mirror or a sub-aperture corrector to correct the abberations and deliver a good quality image.

[Laurie61]

It is, I think, also related to aperture. Light coming to the focal point becomes less accurate as it is generated further off axis, so a bigger spherical mirror of the same f produces more spherical aberration ? I think amateur mirror makers used to consider 6" as the point at which you should use parabolic even at longer f. 

[DaveS]

I think the limit will be when the difference between the spherical and parabolic surfaces is less than 1/4 wave. I'm not sure but I seem to recall somewhere around 4" at f/8 or longer. In other words, for all practical purposes parabolic is the only viable option.

[HD-AP]

Hi

A mirror to be left spherical and satisfy rayleigh's criterion  

must have a miniumum f/d ratio.

some examples below

6"  f/d  8.2

8"  f/d  9.0

10" f/d 9.6

12" f/d 10.4

[Peter Drew]

Provided that the F ratio is 8 or longer I would prefer a good spherical mirror to a poor paraboloid of the same F. 

[Astrobits]

Hi

 

A mirror to be left spherical and satisfy rayleigh's criterion  

must have a miniumum f/d ratio.

some examples below

 

6"  f/d  8.2

8"  f/d  9.0

10" f/d 9.6

12" f/d 10.4

Not sure where you got those numbers from.

According to the book by James Muirden a 6" spherical mirror at f/10 needs 3/10ths of wavelength of glass removed from the centre to make it parabolic. That error would give 6/10th of wavefront error, i.e. over twice Rayleigh's limit. To get a 6" spherical mirror to keep within the 1/4 wave limit it's f ratio needs to be about 12.

An 8" needs to be f/15 and a 12" f/17.

These are all assuming that ne correction elements are used, i.e a normal Newtonian set up.

Nigel

[Alfian]

Hi again, and thanks for the comments. Did not mean to stir up a debate, but must confess its interesting. My knowledge of the technical aspects/physics of this is almost zilch but I must read up. A quick appropriately worded search incorporating "rayleigh's criterion" came up with a page from P.S Harrington's Star Ware which gives a table showing the minimum focal length to satisfy the criterion as (abbreviated) 

3" - f6.3; 4.5" - f7.3; 6" - f8.2;  8" - f9; 10"- f9.6. Must read up further and discover  how  this all this works!

[Astrobits]

It would appear that our reference sources disagree.

However if a 6" f/8 mirror met rayleigh's criterion then surely all the books written on making your own 6" f/8 mirror would not guide you through the parabolisation process!!!

Perhaps more investigation on this is needed. I am not averse to making a 200-250mm spherical mirror at f/10 to see how it actually performs.

Nigel

[HD-AP]

Not sure where you got those numbers from.

According to the book by James Muirden a 6" spherical mirror at f/10 needs 3/10ths of wavelength of glass removed from the centre to make it parabolic. That error would give 6/10th of wavefront error, i.e. over twice Rayleigh's limit. To get a 6" spherical mirror to keep within the 1/4 wave limit it's f ratio needs to be about 12.

An 8" needs to be f/15 and a 12" f/17.

These are all assuming that ne correction elements are used, i.e a normal Newtonian set up.

Nigel

Hi nigel

The source of the figures i gave were  from andre couder's formula

                                             f 3 = 34.9D 4     f and D are in cm 

     Or in inches   it's              f 3 = 88.6 D 4     f and D are in inches

This formula and reference are in jean Texerau's book  How to make a telescope

[Astrobits]

Hi HD-AP

I can confirm that those figures in your post are as in Texereau's book.

However, Both James Muirden's book and Mel Bartel's website state that about half a wavelength ( the formula actually gives 0.6 lambda ) of glass needs to be removed from a 6" f/8 spherical mirror for it to become a parabola. This error would be doubled at the wavefront giving a 1.2 wave error, or almost 5 times Rayleighs limit.

As I said in my previous post these sources are in apparent disagreement and will need further investigation to resolve. Suffice it to say that in my 40 years of dabbling in mirror making it has never been suggested that a 6' f/8 mirror does not need parabolising!

Nigel

[John]

I thought that the TAL2, their 6" F/8 newtonian, had a spherical mirror ?

Maybe I've got that wrong though

[Alfian]

Well guys, I think I got my answer in terms of "general" principles even if the practical execution of them is disputable. The Tal 1 at 110/805 works just fine but is clearly built to the useful limit for a spherical mirror at that apertue. It seems that to build larger reflectors 8"+ with spherical mirrors, though possible, starts to make matters impractical unless you can build an observatory around it. 

Thanks for the time and information.

[AndyH]

I thought that the TAL2, their 6" F/8 newtonian, had a spherical mirror ?

Maybe I've got that wrong though

 No, you're right John. Nowt wrong with the views through my 2M, but it has been many years since it's had a run out.

There was, in the mid 2000's a Tal 150P8 made, for a short while, which was as like the Tal-2, but with a Parabolic f8 mirror and a different sized secondary. Don't know if any saw these shores, but they were sold by TalScopes of Canada, when they were the N. American importer. They also offered mirror sets, so folks may have uprated their Tal-2's then, butI've heard little  to no talk regarding it.

The only regular parabolic newt that Tal made was the fast 150P @ F5.

[Sporadic Dobstronomer]

The difference between a sphere and a paraboloid is (near enough) given by
r^4 / 8R^3
where r is the radius of the mirror and R is the radius of curvature.

(For mathematical types: if I remember rightly this is the first term of the binomial expansion of the difference in depth between a circle and a parabola)
For a 6" f/10, r= 3" and R= 120" and the difference between a sphere and a parabloloid works out as 5.9E-6 inch or 0.15 microns or 0.27 wave (wavelength= 0.555micron)

This agrees near enough with Muirden's figure of 3/10 wave

[HD-AP]

Hi

 N.B.  my previous replies were to the op's question not my personal opinion

 fyi i would never contemplate using a spherical mirror in a newtonian above 4 inches apeture .

The link below provides a good discussion on this subject .  

http://www.cloudynights.com/topic/447807-parabolic-or-spherical-mirror/

[Alfian]

Hi

 N.B.  my previous replies were to the op's question not my personal opinion

 fyi i would never contemplate using a spherical mirror in a newtonian above 4 inches apeture .

The link below provides a good discussion on this subject .  

http://www.cloudynights.com/topic/447807-parabolic-or-spherical-mirror/

Thanks for the ongoing interest in this. The discussion in the link is very interesting. I quite like the term "circle of least confusion" - I feel if I can aim to stay inside that I might be OK! In real terms, the Tal came along and as a long standing itch that needed a scratch I bought it and certainly do not regret doing so. For its 4.3" of aperture it gives surprisingly good views. If I was to buy another  reflector it would almost certainly be a 6"/F8 which will have a parabolic primary - so its a bit of an academic issue. Interesting though and I've learned quite a lot too - thanks to all.