[Aavso-photometry] Time series for GK Persei

[Jim Roe]

Michael Koppelman wrote:
> Except that a faster focal ratio will focus the light on a smaller 
> number of pixels so that it may indeed saturate faster, if I'm not 
> mistaken.
> 
> M.
> 
> 
> On Mar 23, 2008, at 3:19 PM, Jim Roe wrote:
>> I'm afraid this is a common misconception.  F/# does not improve the
>> exposure of point sources (like stars) - aperture rules!  F/# impacts
>> exposure of extended objects like nebulae.
> 

Well, yes and no.  One needs to compare apples to apples, oranges to 
oranges.  I believe the original comparison was to an 8-in f/4 (f=800 
mm) and a 12-in f/10 (f=3000 mm).  We're talking CCDs here so we need to 
consider the properties of the chip.

Consider a chip with 7.4 u square pixels (there are chips in this range, 
I believe).  The 8-in will put 2 arcsec of sky across each pixel and the 
12-in will put only 0.51 arcsec of sky across each pixel.  Now we know 
that "point sources" are, at best, imaged as Airy disks and the 
approximate diameter of such disks would be 0.56 arcsec for the 8-in and 
  0.375 arcsec for the 12-in.  Clearly both of these Airy disks would 
fit within one pixel on the chip and the 12-in, which is pouring photons 
onto the chip at 2.25 X the rate of the 8-in, will saturate first. 
(Unless you have very bright skies - don't we all?  The 2 arcsec pixel 
covers 16 X as much sky as the 0.51 arcsec pixel so the total signal 
threatening to saturate would have 16X as much sky background to add to 
the star signal.)

Of course, we never see diffraction limited seeing for long exposures. 
Suppose we actually observe 4 arcsec "seeing disks."  The star image in 
the 8-in would be spread out over 4 pixels, but it would be 64 pixels 
for the 12-in.  But this is the apples to oranges comparison.  Can you 
call an image spread out over 64 pixels a "point?"  You can get the same 
result by de-focusing (which is sometimes recommended for bright stars).

On the other hand, is it apples to apples to compare 2 arcsec resolution 
to 0.51 arcsec resolution?  It is commonly recommended to match your 
chip to your focal length and 2 arcsec per pixel is often cited as near 
optimum for long exposure use.  To get the 12-in example up to 2 arcsec 
per pixel requires a chip with 24 u pixels (available in the STL-1001 
for one example).  In that case, whatever the seeing disk is, both 
scopes would cover the same number of pixels on the chip and the 12-in 
exposes 2.25X faster than the 8-in.  Of course, the 24 u pixels are 
(quite) likely to have a greater well depth which changes the saturation 
  level, so is that a fair comparison? :-(

Bottom line - do what you can with what you've got! But if you are 
starting new or planning an upgrade (new camera, more aperture), do a 
little math and get as close to optimum as you can. :-)

Jim Roe [ROE]
Wentzville, Missouri