Re: [ATM] How far from the telescope should an artifical star beplaced

["vladimir" <svla@isp.com>]

I started it late last night (and mailed to Nils
by mistake), and now it's got a conclusion.
An appropriate distance for any chosen (over)
correction error induced to a paraboloid can be
also found using the conic relations.

For any given object distance "s" in units of mirror's
f.l. an ideal conic K with zero 3rd order spherical aberration is:

K= -[(2/s)-1]^2

Max surface deviation "z" of this conic vs. parabola is
z=(K+1)(d^4)/8R^3, which after substituting for K
becomes

z=[(1/s)-(1/s^2)](d^4)/2R^3

"d" being the mirror semi-diameter and R the r.o.c.

With the wavefront error at best focus (w) being half the
surface error, the object distance in terms of the induced
wavefront error is

(1/s)-(1/s^2)=w(R^3)/d^4

Approximating (1/s)-(1/s^2) ~ 1/(s+1), which errs 1%
for s=10f.l. and less for greater object distance, the
appropriate distance "s" in units of mirror's f.l. for any
chosen induced wavefront error "w" is given by

s~[(d^4)/wR^3]-1

For most practical purposes "-1" can be dropped.
After replacing "d" by D/2 and R by 2f, it reduces to:

s~D/128wF^3

which is same as relation given by Suiter (Star testing
astronomical telescopes, p84).

For large/fast mirrors it may be inconvenient to place
artificial star far enough to sufficiently minimize induced
over-correction, so it needs to be taken into account.
If the induced error is "W" and tested error "Wt", the
effective mirror correction error "Wm" is Wm=Wt-W.
If mirror tests near-perfect (Wt~0) at 0.25 wave overcorrection
distance (W=0.25), that makes it 0.25 wave under-corrected
(Wm=-0.25). If it tests 0.5 wave over-corrected(Wt=0.5),
that makes it 0.25 wave over-corrected (Wm=0.25),
and so on.

Vlad





----- Original Message ----- 
From: "Bruce MacDonald" <brumac@gmail.com>
To: "ATM List" <atm@atmlist.net>
Sent: Wednesday, October 05, 2005 2:41 PM
Subject: [ATM] How far from the telescope should an artifical star be placed


> G'Day all...
> "As far as necessary such that the rays of light from the pinpoint
> source are effectively parallel to each other when they encounter the
> objective mirror"
>
> OK, how far is that?
>
> Thanks,
> BM
> _______________________________________________
> ATM mailing list http://www.atmlist.net/
> 

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