Re: [ATM] The zonal Foucault test is free of inherent correction bias

["vladimir sacek" <vlad@copper.net>]

Ken Lowther wrote:

>> It results from the familiar relation for longitudinal aberration, 
>> LA=h^2/R. If  "h" is replaced by D/2 and R by 2FD, it becomes LA=D/8F. In 
>> other words, longitudinal spherical of a paraboloid at r.o.c. is double 
>> its sagitta (depth).
>
>
> I haven't played the equations for a while.  What are h, R and D?

"h" is the zonal hight, R the r.o.c. and D the diameter of a mirror (F is 
the F# of the mirror at infinity focus). Putting D/2 for "h" gives the total 
longitudinal aberration at the r.o.c.

>> The easier way is simply to scale the focal zone geometry.
>> Doubling the mirror diameter will result in doubling of all linear 
>> aberrations, including the transverse spherical. But the Airy disc 
>> diameter (2.44LambdaF) won't change, resulting in doubling of the 
>> relative blur size - and the wavefront aberration.
>>
> I though Airy disc size went down as per:
>
> r = 127.1/D    (for yellow light in which Lambda = 0.00055mm)
>
> Where D is diameter, so the larger D the smaller the disc?

This is an angular value, in arc seconds. I'm not sure where it comes from, 
being somewhere between the angular Airy disc radius (1.22Lambda/D in 
radians,  multiplied by 206,265 for arc seconds)  and the full width at 
half-maximum (FWHM=Lambda/D in radians).

In any case, angular size of the Airy disc diminishes with the increase in 
aperture due to the increase in f.l. and, consequently, image scale. In 
fact, given F#, physical dimensions of focal diffraction are just the same 
in a 10cm and 10m aperture. It is only due to the change in the image scale 
that its angular size diminishes, resulting in improved angular resolution.

Vlad 


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