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Parabolic or Spherical Mirror?

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#1 penguinx64

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Posted 07 January 2014 - 10:32 AM

What's the difference between a parabolic or spherical mirror in a reflector telescope? Which one is better?

#2 Paco_Grande

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Posted 07 January 2014 - 11:27 AM

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#3 stevecourtright

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Posted 07 January 2014 - 11:27 AM

A: A Parabolic mirror is the ideal shape. See applet below.

http://www.geogebrat.../student/m11884

#4 Joe Aguiar

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Posted 07 January 2014 - 01:08 PM

Post deleted by Joe Aguiar

#5 SpooPoker

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Posted 07 January 2014 - 01:16 PM

Manufacturers typically supply parabolic mirrors for all Newtonians >= 6" unless the focal ratio of the smaller scope was below 8 (i.e. 114mm f/5).

Spherical mirrors usually pop up on smaller aperture Newtonians sold on the cheap - i.e. the many 4.5" f/8 incarnations out there.

The Spherical mirror does not have a true optical axis, but if we drew a line from the center of the mirror, we would notice that light rays are not all focussed to one point, rather the light will focus at different points. This is called spherical aberration and its effect may be significant for smaller focal ratio's (< f/7), distracting for medium focal ratio's (f/8 - f/9) and negligible for longer focal ratios. A Parabolic mirror does not have this particular problem although off axis aberrations will be its bugbear (albeit these are correctable with specially designed lenses that slip into the focusser).

A spherical mirror, in principle, should work within the diffraction limit of a 4.5" f/8 scope and thus be acceptable. However, in my experience, once one throws in other manufacturing errors / optical imprecision's, I have rarely found a spherical mirror primary Newtonian to work as well as its parabolic counterpart. Case in point, a C4.5 f/7.9 Vixen with parabolic mirror usually outperforms the typical 4.5" f/8 Newtonian with spherical mirror. I noticed this most on Venus during a thin crescent phase (5% illumination). The spherical mirror made Venus look 30% lit while the parabolic, Venus looked as it should have.

#6 BigC

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Posted 07 January 2014 - 01:28 PM

Very little at high focal ratios;note Herschell's 6" was about an f14 so the view is still diffraction limited.

Spherical surfaces are easier to make.

Using parabolic mirrors allows scopes to be more managable in physical length.

Probably the only Newtonian reflectors you should consider buying are ones with parabolic mirrors ,with the exceptions of the small 76mmF9 and 114F8.

#7 MeridianStarGazer

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Posted 07 January 2014 - 01:29 PM

A spherical mirror is very inexpensive to make, and can be done by machine. A parabolic mirror is polished from a similar sized sphere and is done by hand. Asymmetrical errors to its form can happen if not done right, and getting it right costs more money. I like my spherical mirror because I know that even if the manufacturer was incompetent, it is pretty hard to mess up a spherical mirror.

If the f# is at least 8, and the aperture 4.5" or less, you can probably get away with a spherical mirror and save money.

Like SpooPoker said, most large mirrors come parabolic standard. If they did not, you would see a fuzzy image at all but the lowest powers.


Binoculars have spherical surfaces. So do most eyepieces. Stars do get a little fuzzy towards the edge of the view, but this is not noticeable in my peripheral vision.

If you want larger aperture to see fainter stuff, you need to pay $$$ for a parabolic mirror. By $$$, I mean at least $300. Or you can get a small table top for $200. Low f# scopes require more accurate collimation, though. A parabola has an axis, whereas a sphere does not.

If you are happy with 4.5" and f8, you can get a good OTA on a cheap AZ mount for $70 shipped. It is called the Celestron Powerseeker.

#8 Jon Isaacs

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Posted 07 January 2014 - 02:01 PM

What's the difference between a parabolic or spherical mirror in a reflector telescope? Which one is better?


Paul:

As has been said, for a Newtonian, a parabolic mirror is the right shape and on axis, all the light is focused to a point. Your 4.5 inch F/4 Starblast definitely has a parabolic mirror.

Mirrors are ground to a sphere and then corrected to a parabola, it's a very small correction and with small, slower mirrors, the difference is small enough it can be ignored without out major consequences. With larger and faster scopes, a parabola is definitely a necessity. One hears of a scope being "over corrected" or "under corrected", that simply means that too much or too little correction from a sphere.

Most other common designs, refractors, SCTs and MAKs, are based on spherical optics. The SCTs and MAKs correct the spherical aberration/errors with corrector plates..

Jon

#9 BigC

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Posted 07 January 2014 - 02:01 PM

You CAN get just a bit larger acceptable spherical if you find one of the older Meade 130mm F7.8 Newtons with actual focal length of 1020mm,NOT the newer Jones-type short-tube.That is the largest widely sold spherical mirror Newtonian scope that I know.I believe all the 130mm f5 OTA are parabolic.

#10 Geo31

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Posted 07 January 2014 - 02:47 PM

A: A Parabolic mirror is the ideal shape.


Not for an SCT. :grin:

#11 jrcrilly

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Posted 07 January 2014 - 02:52 PM

A: A Parabolic mirror is the ideal shape.


Not for an SCT. :grin:


Nor for anything else other than a Newtonian or a Classical Cassegrain. ;)

#12 Geo31

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Posted 07 January 2014 - 02:55 PM

A: A Parabolic mirror is the ideal shape.


Not for an SCT. :grin:


Nor for anything else other than a Newtonian or a Classical Cassegrain. ;)


Or a Gregorian :grin:

#13 MeridianStarGazer

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Posted 07 January 2014 - 03:14 PM

...

Most other common designs, refractors, SCTs and MAKs, are based on spherical optics. The SCTs and MAKs correct the spherical aberration/errors with corrector plates..

Jon


And the aspherical corrector plate makes the SCT cost a lot. But something has to be aspherical if you want a large aperture.

#14 David Knisely

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Posted 07 January 2014 - 03:52 PM

SpooPoker wrote:

Manufacturers typically supply parabolic mirrors for all Newtonians >= 6" unless the focal ratio of the smaller scope was below 8 (i.e. 114mm f/5).

Spherical mirrors usually pop up on smaller aperture Newtonians sold on the cheap - i.e. the many 4.5" f/8 incarnations out there.

The Spherical mirror does not have a true optical axis, but if we drew a line from the center of the mirror, we would notice that light rays are not all focused to one point, rather the light will focus at different points. This is called spherical aberration and its effect may be significant for smaller focal ratio's (< f/7), distracting for medium focal ratio's (f/8 - f/9) and negligible for longer focal ratios. A Parabolic mirror does not have this particular problem although off axis aberrations will be its bugbear (albeit these are correctable with specially designed lenses that slip into the focuser).

A spherical mirror, in principle, should work within the diffraction limit of a 4.5" f/8 scope and thus be acceptable. However, in my experience, once one throws in other manufacturing errors / optical imprecision's, I have rarely found a spherical mirror primary Newtonian to work as well as its parabolic counterpart. Case in point, a C4.5 f/7.9 Vixen with parabolic mirror usually outperforms the typical 4.5" f/8 Newtonian with spherical mirror. I noticed this most on Venus during a thin crescent phase (5% illumination). The spherical mirror made Venus look 30% lit while the parabolic, Venus looked as it should have.


Actually, a spherical telescope mirror does have an optic axis. It runs along the radius of curvature of the mirror and intersects the mirror's center. Unfortunately, for light from infinity, the spherical mirror does not have a mathematically precise focal point. However, there is a point where for relatively small mirrors with a long enough f/ratio, a spherical mirror can be used instead of a paraboloidal one.

One way to rate telescope mirrors is by seeing how much their surfaces deviate from a perfect parabolic shape. One common rule of thumb states that the telescope's optics must not produce a wavefront error of more than 1/4 wave in order to prevent optical degradation. This requirement is sometimes extended somewhat to require that the mirror's surface must not deviate from a "perfect" paraboloidal surface by more than an eighth wave (approximately 2.71 millionths of an inch) in order for the mirror to be considered for astronomical use. By comparing the sagital depths of a sphere and a parabola of equal focal length, it can be seen that the difference between the two often exceeds the rule of thumb by quite a margin for short and moderate f/ratios. A spherical surface can be "fudged" into deviating less strongly from a parbolic shape by extending the focal length very slightly, such that its surface would "touch" a similar parabolic mirror's surface at its center and at its outside edges. This minimizes the surface difference between the two. Such spherical mirrors must have a minimum f/ratio in order to achieve this. According to Texereau (HOW TO MAKE A TELESCOPE, p.19) the formula is 88.6D**4 = f**3 (** means to the power of: ie: 2**3 = "two cubed" = 8), where f is the focal length and D is the aperture (in inches). Substituting F=f/D to get the f/ratio, we get: F = cube-root (88.6*D). The following minimums can just achieve the 1/8th wave surface rule of thumb:

APERTURE . . TEXEREAU MINIMUM F/RATIO
3 inch . . . . . . f/6.4
4 inch . . . . . . f/7.1
6 inch . . . . . . f/8.1
8 inch . . . . . . f/8.9
10 inch. . . . . . f/9.6
12 inch. . . . . . f/10.2

The above f/ratios might be fairly usable for an astronomical telescope's spherical primary mirror, as they do just barely satisfy the 1/4 wave "Rayleigh Limit" for wavefront error. However, amateurs looking for the best in high-power contrast and detail in telescopic images (especially those doing planetary observations) might be a little disappointed in the performance of spherical mirrors with the above f/ratios. Practical experience has shown that at high power, the images produced by spherical mirrors of the above f/ratios or less tend to lack a little of the image quality present in telescopes equipped with parabolic mirrors of the same f/ratios.

In reality, it is more important to consider what happens at the focus of telescope, rather than just how close the surface is to a parabolic shape. In general, spherical mirrors do not focus light from a star to a point. Their curves and slopes are not similar enough to a paraboloid to focus the light properly at short and moderate f/ratios. This effect is known as "Spherical Aberration" and causes the light to only roughly converge into what is known as "the Circle of Least Confusion", (see: ASTRONOMICAL OPTICS, by Daniel J. Schroeder, c. 1987, Academic Press, p.48-49). This "circle" is a blur the size of about (D**3)/(32R**3), where D is the diameter of the mirror and R is its radius of curvature. The larger the radius of curvature is, the smaller the circle of least confusion is. If the circle of least confusion is a good deal larger than the diffraction disk of a perfect imaging system of that aperture, the image may tend to look a little woolly, with slightly reduced high power contrast and detail. For example, for the Texereau use of a 6 inch f/8.1 spherical mirror, the circle of least confusion is nearly *1.7 times* the size of the diffraction disk produced by a perfect 6 inch aperture optical system.

For most spherical mirrors focusing light from infinity, the focal length is about half the mirror's radius of curvature. Thus, to improve the image, we can use f/ratios longer than Texereau's limits to reduce the size of the circle of least confusion to a point where it is equal to the size of a parabolic mirror's diffraction disk (one definition of "Diffraction-limited" optics). NOTE: the term "Diffraction-limited" has a variety of interpretations, such as the Marechal 1/14 wave RMS wavefront deviation, as well as the more commonly referred to 1/4 wave P-V "Rayleigh Limit". If we set the angle the confusion circle subtends at a point at the center of the mirror's surface equal to the resolution limit of the aperture of a "perfect" paraboloidal mirror (which is 1.22(Lambda)/D, where Lambda is the wavelength of light), we can come to a formula for the minimum f/ratio needed for a sphere to produce a more "diffraction-pattern limited" image. That relation is:

D = .00854(F**3) (for D in centimeters and F is the f/ratio), and for English units: D = .00336(F**3).

Thus, the minimum f/ratio goes as the cube root of the mirror diameter, or the "Diffraction Pattern-Limited" F/RATIO: F = 6.675(D**(1/3)).

For example, the typical "department store" 3 inch Newtonian frequently uses a spherical f/10 mirror, and should give reasonably good images as long as the figure is smooth and the secondary mirror isn't terribly big. For common apertures, the following approximate minimum f/ratios for Diffraction-pattern limited Newtonians using spherical primary mirrors can be found below:

APERTURE . . . F/RATIO FOR DIFF. PATTERN-LIMITED SPHERICAL MIRRORS
-----------------------------------------------------------------------------
3 inches . . . . . . f/9.6 (28.8 inch focal length)
4 inches . . . . . . f/10.6 (42.4 inch focal length)
6 inches . . . . . . f/12.1 (72.6 inch focal length)
8 inches . . . . . . f/13.4 (107.2 inch focal length)
10 inches. . . . . . f/14.4 (144 inch focal length)
12 inches. . . . . . f/15.3 (183.6 inch focal length)

Using f/ratios fairly close to those above for spherical mirrors in Newtonian telescopes should yield very good low and high power images. However, spherical mirrors with f/ratios significantly smaller than those listed above or given by our second formula can yield high power views which may be a bit lacking in sharpness, contrast, and detail. Indeed, a few commercial telescope manufacturers routinely use spherical mirrors at f/ratios even shorter than those given by Texereau, and these products should be avoided. An eight inch Newtonian using an f/13.4 spherical mirror could produce good images, but would also have a tube length of nearly 9 feet, making it harder to mount, use, store, and keep collimated. Thus, using spherical mirrors for diffraction pattern-limited Newtonians with the above f/ratios for apertures above 6 inches is probably somewhat impractical. The old argument about eyepieces performing better with long-focal length telescopes has been all but negated by the recent improvements in eyepiece design. Those who are grinding their own mirrors might wish to make spherical mirrors with f/ratios between the Texereau values and the fully diffraction pattern-limited numbers, as these could still yield fairly good performance without the need for parabolizing. In the long run, it is probably better to use a well-figured (1/8th wave wavefront error or less) parabolic primary mirror for moderate focal ratios and a small secondary mirror (obstructing 20 percent or less of the primary mirror diameter) rather than using a spherical mirror in moderate to large-sized Newtonians designed for planetary viewing.

Clear skies to you.

#15 MeridianStarGazer

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Posted 07 January 2014 - 04:18 PM

If someone has a spherical mirror, say, 6" f8, and it was very smooth, how easy would it be to lessen the image quality by not doing a good job of parabolizing it? Are most parabolic mirrors near this area going to be better than their spherical counter parts, regardless of what company made it?

#16 sg6

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Posted 07 January 2014 - 04:45 PM

A parabolic mirror is better then a spherical mirror, the light comes to a better focus.

Parabolics are not the ideal, for that you need a hyperbolic profile. Go find out the profile of Hubble, it is not parabolic for the reason it isn't good enough.

If you want a hyperbolic mirror then expect to pay.

#17 Seldom

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Posted 07 January 2014 - 05:38 PM

Showing my ignorance here. Isn't a hyperbolic mirror an over corrected parabola? If not, what's the difference?

#18 *skyguy*

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Posted 07 January 2014 - 05:50 PM

I have a homemade 6" f/10 reflector with an Edmund Scientific premium spherical mirror. It also has a curved vane spider and 25mm secondary mirror. When compared directly to my 6" F/8 Criterion RV-6 scope with a parabolic mirror ... the 6" f/10 spherical mirror beats it hands-down in every category! You need to try a quality long f-ratio spherical mirror to see how really good they can be compared to a parabolic mirror.

#19 Achernar

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Posted 07 January 2014 - 05:55 PM

Spherical mirrors by themselves cannot focus light sharply into a single focal point unless they are small and have a very long focal ratio. In that event, the difference in curvature between a spherical and a parabolic mirror is small enough to be ignored. That is why you could build a 4.25-inch F/10 or 6-inch F/12 and get excellent image quality. But the tube of course will be very long. It's much easier to make a good spherical mirror than a parabolic one, whose center is deeper and the outer regions shallower than a spherical mirror. A parabolic mirror will focus light sharply to a single focal point on it's own, and forms a sharp image on it's own where a spherical mirror requires the assistance of lenses and or another mirror to achieve the same end result.

Taras

#20 Achernar

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Posted 07 January 2014 - 06:02 PM

Yes, it is a parabolic mirror that is over-corrected. However, some telescopes, most notably Ritchey-Cheretin Cassegrains use both a hyperbolic primary and secondary mirror to eliminate the coma that occurs in parabolic mirrors. Most space telescopes are R-C's and many professional ground based telescopes are R-C's too. Takahasi makes photo-visual telescopes that also have a hyperbolic primary mirror.

Taras

#21 David Knisely

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Posted 07 January 2014 - 06:18 PM

A parabolic mirror is better then a spherical mirror, the light comes to a better focus.

Parabolics are not the ideal, for that you need a hyperbolic profile. Go find out the profile of Hubble, it is not parabolic for the reason it isn't good enough.

If you want a hyperbolic mirror then expect to pay.


Actually, a hyperboloidal mirror by itself is not ideal, as it too does not focus light from infinity to a point (in mirror-grinding circles, it might be considered basically a somewhat over-corrected paraboloid). To get one to do that requires an additional curved mirror, as is the case with the Ritchey-Chretian Cassegrain telescope. The Ritchey-Chretien is designed to minimize off-axis coma (the reason it was supposed to be used on the Hubble Space Telescope). It uses a hyperboloidal concave primary and a hyperboloidal convex secondary mirror (along with possibly a field flattener for wider field imaging). For a Newtonian telescopes designed for amateur use, a Paraboloid is still the best overall figure for the primary mirror. Coma in Newtonians designed for amateur use can be better attacked by using a near-focus coma corrector like the Paracorr. Clear skies to you.

#22 brianb11213

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Posted 07 January 2014 - 06:55 PM

I have a homemade 6" f/10 reflector with an Edmund Scientific premium spherical mirror. It also has a curved vane spider and 25mm secondary mirror. When compared directly to my 6" F/8 Criterion RV-6 scope with a parabolic mirror ... the 6" f/10 spherical mirror beats it hands-down in every category! You need to try a quality long f-ratio spherical mirror to see how really good they can be compared to a parabolic mirror.

Well, the optical quality of the allegedly parabolic mirror may well be worse than the spherical mirror even when considered as a parabola.

There is another effect here which affects mirrors made from normal glass (but not Zerodur or special ceramics with low coefficient of thermal expansion). When a sherical mirror is cooling, the curve deepens towards a parabola. It used to be common amongst amateur telescope makers to take this into account and deliberately leave the mirror undercorrected so that the correct figure occurred during normal operation when the mirror is slowly cooling.

BTW the 1/4 wave mentioned in several posts above is a poor measure of optical excellence - a really good mirror will have no deviations exceeding 1/10 wave.

#23 David Knisely

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Posted 07 January 2014 - 07:10 PM

Brianb11213 wrote:

BTW the 1/4 wave mentioned in several posts above is a poor measure of optical excellence - a really good mirror will have no deviations exceeding 1/10 wave.


The Rayleigh 1/4 wave p-v wavefront error was never intended as a designator for "optical excellence". It is merely a "bare minimum" of acceptable mirror quality, and mirrors that significantly exceed that level of wavefront error should be sent back (or re-figured). Clear skies to you.

#24 jrcrilly

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Posted 07 January 2014 - 07:23 PM

Showing my ignorance here. Isn't a hyperbolic mirror an over corrected parabola? If not, what's the difference?


Semantics, I guess. A parabola is a specific profile. A hyperboloid is anything beyond a parabola so there's no specific profile for that.

#25 planet earth

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Posted 07 January 2014 - 07:23 PM

I have a homemade 6" f/10 reflector with an Edmund Scientific premium spherical mirror. It also has a curved vane spider and 25mm secondary mirror. When compared directly to my 6" F/8 Criterion RV-6 scope with a parabolic mirror ... the 6" f/10 spherical mirror beats it hands-down in every category! You need to try a quality long f-ratio spherical mirror to see how really good they can be compared to a parabolic mirror.


I wish that was true, but in fact this only tells only tells you the Criterion mirror wasn't figured to the standard of the 6 f10 spherical mirror, but in the right opticians hands could be figured to the same or better standard then the 6 f10 although not really necessary.
Sam


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