Re: [APML] stacking & adding film images

[Wei-Hao Wang <wang@IfA.Hawaii.Edu>]

Hi Steve,

On Mon, 29 Mar 2004, Steve Walters wrote:

> Wei-Hao,
> 
> Then perhaps you can explain to me why I have found this to be true. I
> routinely image at Cherry Springs PA which is the darkest site around the
> east coast (I sure envy your sites in Hawaii). I have photographed for up to
> 3 hours there on E200 and recorded practically no sky fog at least at the
> zenith. But in comparing images taken at 1 hour, 2 hours and 3 hours, I do
> not find fainter objects recorded on the longer exposures. It is true that
> objects that did record were more dense on the longer exposures. But fainter
> objects did not appear.

Mauna Kea has excellent transparency and atmospheric stability but 
may not be the darkest site.  Indeed, the sky brightness measured by 
observaories suggested that the sky over Mauna Kea may be brighter 
than Kitt Peak by >0.5 mag.  

Exposure of 3 hours on E200 with no sky fog is very hard to imagine.
What's your focal ratio?  With F/5 and E100S on Mauna Kea, I start to 
get nonzero density when exp time is >20 minutes.  

On the other hand, no sky fog and a limiting magnitude, both as you
stated, contradict with each other.  Photographic limiting magnitude
exists only when there is sky fog.  With sky fog, one cannot record stars
with surface brightness fainter than the sky.  If as you stated, there is
no sky fog, there should not be a limiting magnitude and longer exposure
should give you fainter objects.  

The situation you stated sounds really strange to me.  If you don't mind
spending some time on this, could you scan the images?  I'm very
interested to learn about this.

> 
> Also, it is curious to me why you consider sky fog to be noise. There is
> nothing random about it. It is uniformly distributed across the image and
> has steady magnitude. In order for stacking to help, there must be some
> randomness about the noise in order for the steady signal to gain SNR
> through stacking. That's because the noise, being random, won't always be
> present in an image while the signal will be. So stacking an image with sky
> fog will not improve the SNR of a dim star because both the sky fog and the
> star will accumulate at the same rate (stacking). If the SNR is  zero
> because the star and the sky fog are at the same leve, it will still be zero
> after dozens of images are stacked.
> 
> Steve...
> 

Sky itself is not a noise.  However, it produces noise.
It's certainly not true that the sky fog is uniform.  The sky is,
but the sky fog recorded on film is not.  

On CCD images, photon noise dominates.  There is always a nosie in each
pixel whose rms value is square root of the number of photon recorded in
that pixel.  No matter how we calibrate the CCD image, we never get
uniform sky.  There is always a pixel to pixel brightness fluctuation
due to the photon noise.  This is the nature of electromagnetic wave.  
It always exists.

This photon noise of course exists on film images as well.  Furthermore,
film grains produce even nasty effects.  The well known rms grainuity 
is to measure the small scale density fluctuation (the noise) in a reagion
which is supposed to be uniform.  Because of the photon noise and film
grains, the sky recorded is never uniform.  There is always a random noise
on the sky fog.  This noise will reduce, relative to the mean value of
the sky, if we increase the exposure or stack images.  We can detect a
faint object only after this noise reduces and becomes a few times
weaker than the signal from the object.

The ratio between the object and the sky will never change.  This is not
S/N.  S/N is the ratio between the object and the noise on the sky.  This
will increase as we increase exposure time or stack images.

Hope this clarifies.

I'm going to shutdown the telescope and leave Mauna Kea soon.  Let me
rejoin the discussion after I go back to Honolulu tonight.

Cheers,

Wei-Hao

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