Spherical/Parabolic mirror

[Tycho Brahe]

Okay, I get now what the difference is theoretically, that the parabolic mirror brings the light to a truer focus, but whats the difference practically looking down the tube? Are spherical mirrors more blurred or harder to focus?

[barkis]

Yop can't measure the difference between a paraboloidal mirror, and a spherical one of the same size and focal length on the surface with spherometer, or any other mechanical device.

If you place a mirror in a vertical position on a rest, and place a light source at it's radius of curvature. (That is twice it's focal length), if you pick up the reflected light at that point, the point of light will flood the mirror with light. If you place a knife edged blade into the reflected cone of light exactly at the point of focus, and gently move the knife into the beam, the result would be that the light would extinguish almost immediately.Which is the characteristic of the Spherical mirror, as all the zones on it come to the same point of focus, which is not good for parallel rays coming in from infinity. If it is a Paraboloid, the knife will reveal shadow patterns, first at the centre zone of the mirror, as you gently move the kife edge back, and re introduce it into the beam, the a different shadow pattern will be seen, the mirror will look deformed, but of course it is, as different zones on it's surface have a different focal point. It is getting these shadows in the correct place that is the essence of the parabola. Figuring the mirror to achieve this, allows the parallel rays from infinity, to be brought to a good focus.

There is a longitudenal axis along which the knife edge moves, to intercept the zones between the mirrors central zone, and the edge zones. The curve between the two has to be a very smooth one, and in relationship to the required theoretical figure on the mirrors surface. That is why the parabola is more expensive.

Although, a perfect sphere is not an easily achieved figure either.

I hope that goes some way to explain the difference.

The differences are measured in millionths of an inch.

Ron.

[Tycho Brahe]

Thanks barkis, I didnt know the difference couldnt be measured with standard tools!!! Thats an interesting way to tell the difference, I'll try that when I get my mirror. What I meant was;

1. If me as a beginner looked through a telescope with a parabolic mirror and a similar sized one with a spherical mirror would I notice a big difference?

2. I take it the normal mirrors people grind at home are spherical? Apparently my little infinity has a parabolic mirror in it...

[John]

.....1. If me as a beginner looked through a telescope with a parabolic mirror and a similar sized one with a spherical mirror would I notice a big difference?

2. I take it the normal mirrors people grind at home are spherical? Apparently my little infinity has a parabolic mirror in it...

It depends on the focal ratio of the mirror I think. A spherical mirror will work OK at slow focal ratios (eg: F/10) but not in faster focal ratios.

While I'm sure that some DIY mirrors turn out spherical I believe it is possible to grind and polish your own mirror to a decent parabaloid if you are prepared to put the effort in (not that I've ever done it )

[barkis]

John is perfectly correct Tycho.

A long focus Newtonian of 150mm diameter, and a focal ratio of f9, will perform very well if the mirror is spherical.

On the other hand, if it has a ratio of f5, it would only deliver at lower powers. High power views would have some spherical aberration, and not be as good as a paraboloid.

Of course doing a comparison between the two, would need to be done under exactly the same conditions in order for the difference to be seen.

The larger objectives, 200mm, 250mm, and 300mm plus, with fast focal lengths would have a paraboloid mirror. A spherical one would be undesirable in such instruments.

EDIT: To answer your question about amateur mirror making. A lot depends on the guy doing the work.

Some ATM's can turn out exquisite mirrors, and can easily equal, and in some cases, better commercially made ones. Some are very dedicated to the work.

I don't think there are as many UK ATM's nowadays, but there are some. It is huge in the States of course, but it is a huge Nation.

Most dedicated mirror making amateurs, will very accurately figure their mirrors, except in the cases where it is unnecessary to do so, for example a very long focus planetary Newtonian, custom made, with a diagonal small enough to do the job, and no more. Thin support for the secondary. The scope can perform as good as an Apo.

and definitely no Chromatic aberration.

Ron.

Ron.

[KaStern_Former_Member]

Hello Folks,

A long focus Newtonian of 150mm diameter, and a focal ratio of f9, will perform very well if the mirror is spherical.

a 6" f/9 spherical mirror will not be diffraction limited. The bigger the aperture

the longer the f/ratio has to be so that the blurr fits into the airy disc size.

A 114/900mm mirror will not be diffraction limited, but since it is used with a secondary

wich masks a part of the primary the reat of the mirror will be diffraction limited

(if no other aberration is present besides spherical aberration).

A 200mm mirror will be diffraction limited when it is f/12 of longer, especially with

a typically sized 50mm secondary in place.

Greetings, Karsten

[FraserClarke]

As the others say; depends on the size and f/ratio of the mirror. 150mm f/9 is about on the limit (Karsten is right, a sphere is not diffraction limited -- but it is very close).

Anything above 150mm and for any practical use has to be parabolized. Almost all amateur made mirrors are parabolic. It's not a 'big' job to go from a sphere to a parabola (a bigger job the faster the mirror). It only takes about 10-20 minutes of polishing to parabolize a spherical mirror. However, with all the testing, and going wrong, and fixing it, and going wrong again, etc etc... it can be quite a drawn out process.

To show the differences between a sphere and a parabola, I've attached some spot diagrams comparing a f/9 150mm sphere with a f/9 150mm parabola. They probably need a bit of explaining...

The first set show the spot diagrams from the optics, and ignore the effects of diffraction. I've plotted four field points, corresponding to on-axis (top-left), 0.2 (top-right), 0.3 (bottom-left) and 0.5 (bottom-right) degrees off-axis (equivalent to the edge of 1 degree field of view). The little black circle in the middle is the size of the airy ring -- the diffraction limit of the telescope (~1 arcsecond in this case). If the spot is mostly inside this, the instrument is diffraction limited. You can see that a sphere never produces a 'perfect image' - but is pretty close to the diffraction limit in the middle. The parabola on the other hand produces a perfect image (single point) on-axis (top-left box). As you go off axis, you start to see coma appearing.

The second set show the on-axis star image ("PSF") including diffraction for the sphere and the parabola. I made them with a log scale so that you can see the diffraction rings more easily -- they wouldn't be so obvious at the eyepiece of course. You can see that the sphere is not quite as sharp as the parabola -- but it's not too bad.

The sphere will get rapidly worse as you go faster than f/9, or larger than 150mm. You'd certainly notice the difference at the eyepiece for most amateur telescopes...

150mmf9sphere.pdf

150mmf9parabola.pdf

150mmf9parabola_psf.pdf

150mmf9sphere_psf.pdf

[barkis]

Well thanks guys, I appreciate your Input.

I think I should have said f9.1 for the 150mm to make it as near as possible, however, we live and learn.

I just hope Tycho got something out of this.

Ron.

[Tycho Brahe]

Thanks guys, its really helping! Teabag, I'll have a look at your post in a bit, just off out to look at some stars!!! Its a 6" F8... so what do you think for a planetary scope?

[Tzitzis]

Well if I use a 130mm reflector with a f/6.9 with spherical mirror will I be able to get a normal view?

Sorry'm so new, I do not even own a scope but I intend to buy one and I was looking at a reflector with the above focal ratio and apperture.