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making a hyperbolic mirror for the MPCC MKIII?

Mirror Making
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#26 davidc135

davidc135

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Posted 13 December 2021 - 04:43 AM

In a single concave mirror coma, the sagittal coma  blur (b) varies with the square of the aperture ratio (f-number), or N², and the the distance off-axis, h:

b = h/16N² 

 

In other words, coma of a concave mirror is independent of the conic constant (and waves of correction).

 

The coma contribution for an 8“ f/4 paraboloid is the same as that of an 8” f/4 sphere or 8" f/4 hyperboloid. The reason MPCC MK111 doesn't work so well with an 8" f/4 paraboloid is because it was probably designed for a paraboloid of a specific f-ratio other than f/4. Clearly, a single set of corrector optics cannot be optimal for a whole spectrum of focal ratios. But it will work partially for a certain limited spectrum, within reason. 

Thanks for the info on coma.

I was referring to spherical aberration. Afaik, a two element coma corrector such as the MPCC MK111 can't correct both the S.A and coma in any paraboloid, regardless of the F ratio. Hence the need to hyperbolise the primary or add an extra (or more) corrector element.

 

It would be interesting to compare coma correction in MK111 / optimised hyperboloids in various focal ratios. My feeling is that coma is well suppressed or removed over a range. The Paracorr solves sufficiently for both SA and coma over a spectrum of F ratios.

 

If a coma corrector induces coma at the same rate as the primary but of opposite sign and the primary conic influences SA but not coma then it's easy to see there is a solution. Possible false colour and I assume field curvature need addressing too. Astigmatism?

 

David


Edited by davidc135, 13 December 2021 - 04:54 AM.


#27 MKV

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Posted 13 December 2021 - 11:31 AM

I was referring to spherical aberration. Afaik, a two element coma corrector such as the MPCC MK111 can't correct both the S.A and coma in any paraboloid, regardless of the F ratio. Hence the need to hyperbolise the primary or add an extra (or more) corrector element.

 

It would be interesting to compare coma correction in MK111 / optimised hyperboloids in various focal ratios. My feeling is that coma is well suppressed or removed over a range. The Paracorr solves sufficiently for both SA and coma over a spectrum of F ratios.

 

If a coma corrector induces coma at the same rate as the primary but of opposite sign and the primary conic influences SA but not coma then it's easy to see there is a solution. Possible false colour and I assume field curvature need addressing too. Astigmatism?

Yes, the presence of SA (over- or under-correction) alters the appearance of coma but not the contribution  of coma (as an offense against the sine condition, or OSC) by the surface. If you look at the Seidel coma coefficient values you'll see that they are independent of the SA or the conic constant.

 

coma independent.jpg

 

The surface contribution to the optical path difference (OPD), and consequently SA, is (1±ε²)/(8f³), where ε² is the mirror's eccentricity (ε) squared, and f is the mirror's focal length. On the other hand, the surface contribution to coma is simply 1/(4f²). 

 

So, cleaver designers like Paul Lind back in 1996, or Ed Jones in 2016 used both contributions to control coma contribution and maintain a suitable appearance of the image blur due to SA. As you noted, to eliminate coma and spherical aberration one needs at least another (3rd) element, or more. Some choices of glasses available today can also help.

 

There's very little astigmatism in these Ross-type corrector systems. Any astigmatism is overwhelmed by coma and SA. For paraboloids, astigmatism drops to zero when the aperture stop is at the mirror's focus. The contribution of weak hyperboloids (such as -1.2875 or -1.36, etc.) to astigmatism is insignificant in Newtonian configurations with the aperture stop at f. If the aperture stop is at the mirror, he sagittal astigmatism will be zero and the surface of best definition will be curved with a radius of curvature equal to f , and overcorrected, i.e. convex to the sky.


Edited by MKV, 13 December 2021 - 11:32 AM.



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