Re: ATM "Diffraction Limited" a definition

["Alan Levin" <ailevin@ix.netcom.com>]

> Date:          Tue, 18 Feb 1997 16:24:41 -0800
> From:          PFAFF2@delphi.com (Robert  C. Pfaff)
> Subject:       Re: ATM "Diffraction Limited" a definition
> To:            atm@shore.net
> Reply-to:      PFAFF2@delphi.com (Robert  C. Pfaff)


> I am not sure if I understood what you are saying but my understanding
> is the the diameter of the diffraction spot decreases with decreasing
> f ratio. That means a 2" f4 mirror and a 100" f4 mirror will
> have the same size diffraction spot. The 100" mirror will have much
> greater resolving power because of greater focal length.
> More focal lenght gives more magnification at the same f ratio
> enabling you to separate the spots. 
> 
> Bob Pfaff

Bob,

I think there are a number of things to sort out here.  The spot
size I was speaking of was angular.  If you look at Andy's formula
you will find that it is a ratio of the wavelength of light to the
diameter of the mirror and is thus unitless (length divided by
length).  It is the extent of the Airy disk in radians.  As the
focal length of the mirror gets longer, the image scale at focus gets
larger, but the angle that the Airy disk covers is the same and
depends only on the aperture.  


I agree that in your example the Airy disk of the 100 inch F4 mirror
and the Airy disk of the 2 inch F4 mirror will measure the same
number of microns at their respective prime focus..  The difference
is that for the 2 inch telescope that prime focus spot represents 3
arcseconds of the sky while the 100 inch telescope prime focus spot
represents a .06 arcsecond resolution look at the sky  (atmosphere
willing).  You can make the image scale of the 2 inch larger and
larger by increasing the focal length, but you will never be able to
resolve sub arcsecond features of anything at prime focus.

The image scale, that is how many microns at prime focus correspond
to how many arcseconds in the sky, depends on focal length.  But the
resolution, that is the smallest feature in the sky, in arcseconds,
that the telescope can resolve, depends on the aperture size.

Good Observing,
Alan