ATM 16x intensity

[Greg Granville <greg@laser.arl.psu.edu>]

>Just to clarify things here, this 16X `rule' only applies, I think, when
>you consider two telescope _of equal focal length_. If you simply scale
>the telescope up say by doubling both the aperture and focal length then
>the intensity increase by doubling aperture is only a factor of four. The
>physical dimension of the airy pattern at the focal plane of an F5
>telescope is the same whether it be a 10" or 100". If you double the
>aperture but keep the FL the same then you halve the focal ratio and the
>airy pattern will be halve the size. 

Even if the FL stays constant, the 16x increase in intensity only works on
point sources which (ideally) put all their photons into the smaller airy
disk. On extended objects, which are the kind where we are normally want
more brightness, the total brightness of the object increases just 4x for a
doubling of aperture (until the exit pupil limit is reached). 
Yes, the airy disks are 4x brighter, but light from the object is spread
over 4 times as many of them at any given magnification.

In reality, I don't think you'd quite see a 16x increase on stars either. It
becomes increasingly difficult to see a true airy disk as aperture
increases. The minimum size of the airy disk is limited by local seeing
conditions. Once this limit is reached, you shouldn't notice much more than
a 4x intensity increase on stars if you continue to double the aperture.

This all based on some very quick reasoning, so I could have easily
overlooked something :-(

~~~
Greg Granville  Applied Research Lab - PSU 
greg@laser.arl.psu.edu      greg@penn.com  
      http://users.penn.com/~greg