From Edward Arnold GRAFTON
® . . . . . . . Date: Thu, 25 Dec 2003 20:14:13 -0600 (CST)
Subject: Re: [Saturn-ALPO] Re: Saturn on December 16th.
At 10:22 AM 12/25/03 +0100, Paolo R. Lazzarotti
wrote:
>I
attach you a formula by astronomer Paolo Tanga (who's
reading us in
>CC)
measuring the Tmax for a correct planetary imaging:
>
>Tmax [sec] = 1150xPxM/D
>
>Where:
P is the rotation's period of a planet [hours]; M is the max
>rotation
allowed at the CENTER of the disc [arcsec] and D its apparent
>diameter [arcsec].
>Assumed
a resolution power of 0.43 arcsec for your C11, Nyquist says you
>have
to put this separation in 2 pixels; so you would have a 0.21 image
>scale
with you.
>But
you also well know this is an high value for a fine imaging, so I
>agree
with you to use smaller values as you are doing.
>
>Assumed
you didn't resample your final image, you managed a 0.09
>arcsec/pixel, so this is M parameter of the above formula.
>
>Tmax = 1150x10.5x0.09/20.5 = 53 secs.
>
Hi Guys
For this discussion lets assume that the 2x sampling for max resolution is
correct, although I am no longer as convinced of this as I once was. Let me
also state that I have not see a rigorous mathematical proof to refute the 2x
rule as applied to our application.
The application of this
rule DOES NOT extend to the time window of gathering
images for later averaging or "stacking". The 2x rule is satisfied by
the image scale (sampling) and the TIME
WINDOW OF A SINGLE FRAME. All the SAMPLING CRITERIA is completed on the INDIVIDUAL FRAMES.
Stacking or averaging the individual frames is a REGISTRATION issue not a
sampling issue. During the registration and "stacking" ones hopes to
maintain the resolution already captured on the individual
frames and improve the S/N. The resolution captured on each frame would
be at best .43 arc seconds. If the planet rotated less than .43 it was not
resolved by the scope. The window calculated from the formula given by Paolo's
formula would then be 253 seconds.
In practice it would take
10/10 seeing for several minutes to achieve the .43 arc seconds resolution,
which I have never seen. In fact the seeing might have to be .43 arc seconds/2
to achieve the .43 arc seconds resolution since that is the sampling being
performed by the required Nyquest 2x rule!
>Damian Peach wrote:
>I would agree with you that this isnt an appropriate timing to reaching the theoretical
limit of the
>telescope, but the fact remains
that you are NEVER going to resolve low contrast spot-like features
>better than ~0.5", so the
window works (as proved time and time again by Grafton/Myself.)
>You are not taking into account
noise is a major limiting factor in resolution of low contrast detail >to
this level. Halving the window would not improve resolution, as the image would
be so much more
>noisy, resulting in
this detail being lost in the noise. Why shorten the window when the one being >used already
works regardless of the seeing!?.
This S/N point is a good
one. None of the low contrast spots that I have imaged have shown on any one
frame. The resolution is there but it is lost in the noise and can only be
recovered by improving the S/N by "stacking" many images. The latest
dark spot that Damian imaged is a good example. The low contrast .7 arc second
spot imaged by Damian would have gone undiscovered if the S/N would have been
lower than he achieved, due to a less a less productive imaging strategy having
been employed, ie a shorter window.
® . . . . . . .Date:
Fri, 26 Dec 2003 09:26:59 -0600 (CST)
Subject:
Re: [Saturn-ALPO] Re: Saturn on December 16th.
Paolo R. Lazzarotti wrote:
>Hi Ed,
>
>What you say is
correct; the M parameter of my formula is referred to
>the max blur accepted.
>If you don't want any
blur in your final image, that means the first
>frame and the last one
have to be captured before the planet would spin
>1 pixel at least at the
center of its disk.
>If your image is
sampled at 0.4 arcsec/pixel, that
means you can accept
>a max blur of 0.4 secs; if you sample at 0.2 arcsec/pixel,
you can
>accept a max blur of
0.2 secs and so on.
>
>I assumed Damian's
image scale as 0.09 arcsec/pixel, so my consideration
>is right.
>But if he was 2x
resizing the final image, than the appropriate value to
>consider is 0.18. This
is clear!
>
>>In practice it
would take 10/10 seeing for several minutes to achieve the
>>.43
arcseconds resolution, which I have never seen. In fact the seeing might
>>have to be .43 arc
seconds/2 to achieve the .43 arcseconds resolution
since
>>that is the
sampling being performed by the required Nyquest 2x
rule!
>>
>Yes, the discussion
we're feeding is based on the math.
Hi Paolo
I would love to see a mathematical
solution to this issue but my feeble mind does not corporate! We all know of Rayleigh's criteria for resolution which states that the sin(a)=1.22L/D
where L is the wavelength of light
and D is aperture. For small angles sin(a)= a (units in radians ).
For Damian's .28 meter
scope (11 inch) scope: a=1.22x500x10^-6nm/.28m radians =2.18x10^-3 radians.
Given that there are 57.295 degrees/radian and 3600 arc seconds per degree,
this works out to .45 arc seconds. The wavelength used above was 500nm. A CCDs sensitivity runs from about
400nm to about 1000nm so according to this criteria the resolution would vary
between .36 arc seconds at 400nm to .9 arc seconds at 1000 nm. This is all well
and good but as we know the Enke's division is
sometimes resolved on Damian's Saturn images and is smaller than the .36 arc
second threshold.
This ambiguity calls into
question as to the actual resolution obtainable with a given aperture for
extended objects. From my experience red or IR images almost always have better
resolution that blue light images, no dought to the kindness of the atmosphere at the longer
wavelengths. But this further complicates this simple look at the theory as the
scope should have better resolution at the blue wavelengths. If one were to
only consider the above math it would lead one to a shorter imaging window (due
to the .36 arc second resolution) and using blue light. I seriously doubt that
anyone would recommend this approach for better resolution especially given the
low QE od CCDs at this end
of the spectrum which would degrade the S/N (and therefore the resolution) of
the image.
Given my uncertainty about
the credibility of the 2x sampling rule and the apparent ambiguity of Rayleigh's criteria, I think that the math can only be used
a starting point. I would love to see these issues resolved from a mathematical
point of view for our application but until then there will remain an element
of "Black Magic" in obtaining high resolution images guided by the
success of employed techniques.
® . . . . . . .Date:
Tue, 30 Dec 2003 10:47:20 -0600 (CST)
Subject:
Jupiter Observation December 30th 2003 at 10:42 UT
Hi Jupiter Observers
Here is an observation from
December 30th 2003 at 10:42 UT. The transparency was excellent, 9/10 and the
seeing was very good, 7/10 with moderate dew. The weather was very cool with
the temperatures in the upper
30s F.
Image at http://www.ghg.net/egrafton/12-30-03.jpg
Ed Grafton,
Barlow Projection
to f/27 aprox .21 arc seconds per pixel.
Image data:
BLUE + IR rejection,
.6 seconds, Edmunds filter
GREEN + IR
rejection, .4 seconds, Edmunds filter
RED + IR rejection, .2
seconds, Edmunds filter
Clear
filter, No IR .13 seconds,
Edmunds filter
Ed GRAFTON (
