Cames
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Reged: 08/04/08
Posts: 49
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I understand that some of the 4.5 inch Newtonian primary mirrors have a spherical figure and are not parabolized.
For such small mirrors with a nearly perfect spherical shape, would one expect the observed intrafocal/extrafocal star test images to be identical? Or, would the star test images show the characteristics of spherical aberration?
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ϕ
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Mike I. Jones
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Reged: 07/02/06
Posts: 1572
Loc: Fort Worth TX
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The edge difference "d" between a sphere and paraboloid is pretty close to
d = Aperture^4 / [1024 x (Focal Length)^3]
if d=0.00000271", or 1/8 wavelength of mid-range visible light at 0.555um at the mirror surface, the resulting wavefront error would be double that or 1/4 wave, the Rayleigh limit. Setting the mirror aperture to 4.25" and solving the above for the focal length gives a value of about 49.0", and a minimum focal ratio of f/11.5. This would be at the hairy edge of acceptability for a spherical 4.25" mirror. At focal ratios below f/11.5, you would begin to see the differences in intra and extrafocal imagery you mention above.
If the edge difference drops to 1/16 wave (1/8 wave on the wavefront), the focal length increases to about 61.75" or about f/14.5. A well-made spherical 4.25" f/14.5 mirror would give exquisite definition over a wide field, better than most any achromat or apochromat of equivalent focal ratio (except for central obstruction and spider vane diffraction), and of course with no color error at all, zero. The spherical figure would, however, have to be corrected well below the 1/16 wavelength edge difference for the mirror to give the imagery it is capable of.
Mike
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DAVIDG
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Posts: 1985
Loc: Hockessin, De
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A number of years ago I was refiguring a 6" f/8 and had to a perfect sphere before I start to parabolize it. At a sphere, a 6" f/8 is just alittle over a 1/4 wave. I installed the mirror in the telescope to see how well a spherical mirror would perform and what the star test would look like. One could not miss the spherical abberation in the star. On the inside of focus the shadow of the secondary was immediately visible and many rings were visible. On the outside of the focus, the disk was evenly illuminated and no rings were visible and I had to rack the eyepiece out a larger distance to have the shadow of the secondary become visible.
So for a 4.5" f8 to f/10 spherical mirror the spherical abberation will be easy to see in the star test.
- Dave
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Homemade 'scopes 8"f/7,6" f/5", 6"f/4, 4.25" Schief. 60mm Coronagraph,60mm H-alpha system, 4.25" White-light Solar Newtonian,solar spectroscope, 4.5" f/16 Schupmann Medial refractor, 14 Stellafane awards 7 in optics
Engineering = Taking what you have and making what you need.
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Mike I. Jones
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Reged: 07/02/06
Posts: 1572
Loc: Fort Worth TX
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Yep, 6^4 / (1024 x 48^3) = 0.0000114", or a little over 1/2 wave on the mirror, or about 1.06 wave on the wavefront.
For 1/4 wave max wavefront error (1/8 wave on the mirror) you can twiddle the above formula to give
Minimum focal ratio = [ D/(128 x wavelength) ]^(1/3)
Aperture D and wavelength units have to match.
If the mirror and wavelength units are inches, the formula simplifies to
Minimum focal ratio = 7.119 x (Aperture)^(1/3)
In real words, take the cube root of the mirror aperture in inches, multiply by 7.119, and that gives the minimum focal ratio that a mirror can be left spherical and meet the Rayleigh 1/4 wave limit.
Running this out for common mirror sizes gives:
_3.00 .... f/10.27
_4.25 .... f/11.53
_6.00 .... f/12.94
_8.00 .... f/14.24
10.00 .... f/15.33
12.25 .... f/16.52
and of course assumes that the spherical surfaces are at least 1/10 wave P-V, which is a challenge in itself. A 3" scope is pretty small but OK for the moon, brighter planets and brighter double stars, while beyond 6" the tube length is getting impractical. So mirrors in the 3-4.25" range are the only ones to really consider leaving spherical as practical.
Mike
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Mark Harry
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Reged: 09/05/05
Posts: 3124
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And everyone was saying that a 6" F/10 made a fine mirror year before last.  I said no. Your formula comes to about F/12.9 for a 6 for 1/4 wave Rayleigh limit, which is of significant error to be noticeable.
Not good enough for a long mirror, which is likely planetary, don't you agree?
Mark
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So many projects, so little time!
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gregj888
sage
Reged: 03/26/06
Posts: 301
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Cames,
Many of the new breed of 4.25" scopes have a spherical mirror and field corrector of sorts built into the focuser. If the tube is about 24" long and the FL on the scope says 1000mm or so, it's probably of this style.
Greg
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Mark Harry
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Reged: 09/05/05
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Loc: Northeast
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Mike wrote:" If the mirror and wavelength units are inches, the formula simplifies to
Minimum focal ratio = 7.119 x (Aperture)^(1/3)
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What would your formula look like for 1/8th wave smooth undercorrected error?
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So many projects, so little time!
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Mark Harry
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Reged: 09/05/05
Posts: 3124
Loc: Northeast
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I made a 6" F/13.63, with the central 4.5" as dead-nuts sphere, and an edge that was rolled out .015" on fixed source tester. My spreadsheet says it's a smidge over 1/40th PVW. (I think, about 1/37th) I think that a perfect sphere would have just about reached 1/7th PVW. Do you think that checks out, Mike? Fun mirror to make- validated my sensitivity parameters with my tester nicely.
M.
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So many projects, so little time!
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wh48gs
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Reged: 03/02/07
Posts: 458
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Quote:
The edge difference "d" between a sphere and paraboloid is pretty close to
d = Aperture^4 / [1024 x (Focal Length)^3]
That defines surface deviation vs. reference parabola focusing at paraxial focus. But vs. so called "best fit parabola", which focuses at the point midway between paraxial and marginal focus (i.e. "best" or "diffraction focus"), the surface deviation is four times smaller, and so is the resulting wavefront error.
The wavefront error of spherical mirror at best focus is given by:
W=D/2048F^3
Quarter wave p-v on the wavefront of s.a. should be quite obvious in defocused pattern, but it is still conventionally "diffraction limited".
Vla
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Dick Parker
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Reged: 08/17/07
Posts: 247
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Mike Jones –
I am familiar with the formula you used, and when I run the numbers, I get similar results. But that does not square with OSLO, so, I am curious.
I modeled a 6 inch diameter spherical mirror, trying various focal lengths, in OSLO and got the following results:
At f/8.3334, ROC = 100 inches, PkVal OPD = .398 (or 1/2.51 wave), Strehl = .619
At f/9.74, ROC =117 inch, PkValOPD = .248 (or 1/4 wave), Strehl = .827
At f/10, ROC = 120 inch, PkValOPD = .23 (or just better than 1/4 wave), Strehl = .848 (All rays traced inside Airy Disk)
At f/12, ROC = 144 inch, PkValOPD = .133 (or 1/7.5 wave), Strehl = .947 (I made one of these. Stunning performer)
At f/13.6 ROC = 163 inch, PkValOPD = .0918 (or 1/10.9 wave), Strehl = .97 (Mark describes slight roll out at edge of his which would be an improvement over spherical as he says)
The formula says it takes f/12.94 to be 1/4 wave, not f/9.74. What does ZMAX say??
Dick Parker
Edited by Dick Parker (11/09/09 11:35 PM)
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wh48gs
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Reged: 03/02/07
Posts: 458
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Quote:
I modeled a 6 inch diameter spherical mirror, trying various focal lengths, in OSLO and got the following results:
At f/8.3334, ROC = 100 inches, PkVal OPD = .398 (or 1/2.51 wave), Strehl = .619
At f/9.74, ROC =117 inch, PkValOPD = .248 (or 1/4 wave), Strehl = .827
You are doing something wrong. For the first mirror, OSLO gives 0.2452 wave PV and 0.07122 wave RMS in e-line, when set on the minimized RMS blur, and 0.2371 PV and 0.071 when set on best focus, only slightly off the theoretical value for best focus of 0.2355 wave PV and 0.0702 wave RMS.
The RMS for lower-order spherical is smaller than the PV by a constant ratio of sq.rt. 11.25. According to the Strehl for 0.248 wave PV, the RMS is 0.0689, with the PV/RMS ratio of 3.6. That is not spherical aberration at best focus.
Vla
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sixela
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Reged: 12/23/04
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Loc: Boechout, Belgium
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Post deleted by sixela
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400mm f/4.46 self made Dobsonian on Tom Osypowski equatorial platform
Orion Starblast (114mm f/4 reflector, Alt/Az)
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Mike I. Jones
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Vla's point is well taken - that the simple formula I first showed takes you to paraxial focus rather than minimum RMS focus. It was the best answer I could provide to "Cames" in the short window of time I had. This implies that the minimum spherical mirror focal ratios could come down some, but not a lot. I'll do the same simulations in Z and get back to the thread on this.
Mike
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sixela
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Reged: 12/23/04
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Here's 2007's thread.
As far as 6" f/10 is concerned, here's what Bratislav had to say (after Mark Harry posted some simulations using paraxial focus) about best focus
Quote:
More along the lines of 1/7 p-v (front, not surface!), 1/25 WRMS, 0.94 Strehl.
Whether 0.94 Strehl (or even the point spread function, which does contain more qualitative information) is good enough was beaten to death in 2007.
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400mm f/4.46 self made Dobsonian on Tom Osypowski equatorial platform
Orion Starblast (114mm f/4 reflector, Alt/Az)
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Mark Harry
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Reged: 09/05/05
Posts: 3124
Loc: Northeast
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"Not good enough for a long mirror, which is likely planetary, don't you agree?"
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With all said before, noone except me (that I know of) made any direct comparisons. But I suppose it's useless to argue with those convinced of their calculations. The end use should govern what is deemed 'good enough'.
M.
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So many projects, so little time!
Edited by Mark Harry (11/10/09 08:51 AM)
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sixela
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Reged: 12/23/04
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Quote:
With all said before, noone except me (that I know of) made any direct comparisons.
A quote (addressed directly to you) from Chriske in 2007's thread:
Quote:
Mark, 6" f/10 has been our course scope until now, most people wont see the difference between that 6" f/10 sperical or parabola. We've tested it years ago on several occasions side by side. During testing almost nobody could detect the 'bad' scope.
Of course, he then went on to say that for perfect optics the mirror should be parabolised - nobody is disputing that. But in less perfect hands than yours, it might be penny wise and pound foolish (at least according to several people).
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400mm f/4.46 self made Dobsonian on Tom Osypowski equatorial platform
Orion Starblast (114mm f/4 reflector, Alt/Az)
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Mike I. Jones
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Reged: 07/02/06
Posts: 1572
Loc: Fort Worth TX
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As I just PM'd Alexis, I think this is another good example of quantitative versus qualitative, inexperienced versus experienced. Optical design codes like ZEMAX, OSLO, CODE-V, etc. can calculate what a star image will look like to high precision, but when that prediction is viewed on an computer monitor it doesn't really represent or explain the visual appearance. And of course the visual appearance and perception of a star image is in itself very subjective, based on the years of experience the viewer has and the quality of her/his vision. An observer new to a telescope might think an image to be very sharp, while a seasoned observer might find the same image lacking. Yet they look the same to both on a computer monitor.
I think this thread has run its course, don't you? Dick and Vlad have brought up some good optical theory and optical modeling questions - I suggest we start a new thread to continue the discussion.
Mike
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deSitter
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Reged: 12/09/04
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Vla's statement squares with Sam Brown and my own experience. A 4.25" f/10 smooth sphere could hardly be improved on.
-drl
Quote:
Quote:
The edge difference "d" between a sphere and paraboloid is pretty close to
d = Aperture^4 / [1024 x (Focal Length)^3]
That defines surface deviation vs. reference parabola focusing at paraxial focus. But vs. so called "best fit parabola", which focuses at the point midway between paraxial and marginal focus (i.e. "best" or "diffraction focus"), the surface deviation is four times smaller, and so is the resulting wavefront error.
The wavefront error of spherical mirror at best focus is given by:
W=D/2048F^3
Quarter wave p-v on the wavefront of s.a. should be quite obvious in defocused pattern, but it is still conventionally "diffraction limited".
Vla
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sixela
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Reged: 12/23/04
Posts: 10853
Loc: Boechout, Belgium
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It'd still be interesting to see post #3432614 but for best (lowest RMS error on the wavefront) focus, lest we leave the reader with only formulas for paraxial focus (which are arguably not as relevant). But yes, I agree that for the rest we might just as well start a new thread.
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400mm f/4.46 self made Dobsonian on Tom Osypowski equatorial platform
Orion Starblast (114mm f/4 reflector, Alt/Az)
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Dick Parker
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Reged: 08/17/07
Posts: 247
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Vlad -
I forgot to set the wave 1 to 555 per Mike's original premise, and did not focus on min RMS. When I do, I get your numbers.
Thank you
I await Mike's ZMAX on a new thread
Dick Parker
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