Re: ATM Spheres, Parabolas etc.

["James W. Burrows" <burrjaw@halcyon.com>]

 At 21:57 1999-07-19 -0700, Michael Perata @ p-solutions wrote: 
>>>>
> I am mostly math disadvantaged so it is easier for me to visualize outcomes rather than "see" it in a formula.
>   
> Given a ROC of 100" how can I plot a parabola and a hyperbola, against a sphere so I see the differences as if looking through a cross section of the curves/mirror. I know when dealing with optics, the differences a minisule, but I do have the ability to plot the curves (Autocad) and zoom in to see the differences.
>   
> Having owned a large R-C in the past, I would like my first ATM project to be another R-C in the range of 18-20". I understand, and appreciate, that this is not trivial task.
<<<<

A conic section through the origin (x-axis along the optical axis; W.J.Smith, Modern Optical Engineering, p. 392):

y² - 2Rx + (b+1)x² = 0

(b = deformation constant, R = ROC).  Solving for the height of section x vs. zone radius y,

x = y²/(R + sqrt(R² - (b+1)y²))

You'd plot 3 curves of x vs. y for b=0 (sphere), b=-1 (parabola), b<-1 (hyperbola).

Don't even think of doing an 18-20" RC for your first ATM project!  You're talking about a 30-40 k$ instrument if you purchased it.  Take a look at Texereau, p. 148.  A prerequisite would be to get rid of some your math disadvantage.