Re: [ATM] A more or less new optical test

["Everett Cairns" <ecairns@mcmaster.ca>]

----- Original Message ----- 
From: "Michael Peck" <mpeck1@ix.netcom.com>
To: <atm@atmlist.net>
Sent: Monday, October 31, 2005 10:44 AM
Subject: [ATM] A more or less new optical test


> For anyone interested in non-interferometric optical tests that might
> be amateur friendly a preprint just showed up on the arxiv discussing
>
>
Perhaps this is a good time to mention the tilted wire version of the 
Foucault test.
Start with a line source as commonly used in the Foucault test. Test with a 
straight edge (a fine wire or"phase knife, almost everyone has one of these 
hiding in a video cassette,  are better than the usual knife edge). The only 
difference from the Foucault test is that the test edge is DELIBERATELY 
TILTED relative to the source by a very small amount, and only a narrow 
strip across a mirror diameter is illuminated. The latter condition is 
easily realised if you use a laser pointer illuminating a slit for the 
source. On a projection screen where your eye would have been you will see a 
curved line.If you stretch the screen till approximately square,by whatever 
means you find convenient( cylinder lens,prism, tilting the screen, 
photoshop stretch) you soon realise that this is a plot of ray deviation 
from the axis for all zones along the illuminated DIAMETER of the mirror. 
Equivalently this is a plot of mirror slope relative to a test sphere 
centered on the knife edge. At the paraxial focus this should be a parabola 
from axial to rim point on the curve. If you draw this parabola on the 
screen, and start at the axial point, moving out adding up the signed area 
between the ideal and the observed curves (you can do this roughly in your 
head if you are testing during mirror figuring), you get the mirror 
profile.If you move the test edge away from the mirror, the curve changes as 
expected, and watching the area between the two curves, you can find the 
"best" focus.
    This is a good quick and dirty test. I have used it and it works.Once 
you have set up the correct slope of the knife, it is a quantitative test 
where you can record by sketch or photo, the primary data which is the 
figure on the projection screen. HOWEVER. Like all Foucault similar tests 
that are best explained by gemetric optics, it really requires a physical 
optics simulation to find the limits of application.
P.S. The geometric explanation is to consider each horizontal slice of the 
tester as an independent foucault tester set up to find the ray with the 
deviation appropriate to its knife position. This independence is only a ray 
optic figment of our imagination! But it works for an 8inch f6. When doesn't 
it work so well? 

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