RE: [APML] stacking & adding film images

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

Hi everyone,

I have some thoughts about stacking film images.  Please correct
me if I write something nonsense.  (I'm at 14000 feet and there is
a lack of oxygen.)  It's a little long and is for those who really
care about the details of image processing.  Skip it as you wish.

# There is no difference between improving S/N and going deeper.
  They are exactly the same thing.  By improving S/N, we can 
  better tell if a faint signal on the sky fog is a real faint 
  celestial object or is just noise produced by film grains 
  (or whatever else), i.e., we get a deeper image.  

  In other words, stacking images to improve S/N is similar to
  increasing exposure time.  Both give us deeper images.

# In CCD imaging, stacking many short exposures is equivalent to
  taking a long exposure.  The only thing matters is the number of
  photons we collect.  More photons = higher S/N = deeper images.
  It doesn't matter whether we collect these photons at once
  (a long exposure) or in pieces (many short exposures).

  The same should apply to film images.  The only difference 
  between CCD and film is that CCD is linear but film is nonlinear.
  For CCD, adding two 10min exposures is precisely equivalent to
  taking a 20min exposure (assuming that readout noise and bias of 
  CCD is not important).  This is not the case for film.  

  Nevertheless, it is still true that stacking short film exposures 
  will deepen the image.

# Stacking CCD images is straightforward -- just add them.  
  (There is no difference between adding and averaging in terms of
  S/N.  They only differ by a constant and this constant has no
  effect on S/N or depth.)
  Adding is statistically correct for CCD images.  But again, this
  may not be the case for film images because film is nonlinear.

  How to stack film images to achieve the greatest depth?  I haven't 
  seen any detailed, statistical analysis that really convinces me 
  on this issue.  

  Personally, I would still use adding (or averaging).  As long as 
  each image has the same exposure time, adding is fine and should 
  produce the best S/N and the greatest depth.  If the exposure times 
  of the images are very different, straight adding is certainly wrong.  
  I imagine that the images must be weighted in a very nonlinear way 
  before they can be added.  Perhaps the statistically correct
  weighting (if exists) would even change within each single image
  as a function of image density in different areas.  

  Before I average images of different exposure times, I calibrate
  them (in Registar) and then weight them with their exposure times. 
  I know this is wrong.  I just simply don't know a better way to 
  handle this.
  
# Adding (=averaging, again) film images will not enhance the 
  vignetting.  On the other hand, multiplication will.  For example, 
  in a vignetted image the brightness ratio between the field center 
  and the corner is 3:1.  After averaging two similar images, the 
  brightness ratio is still 3:1, not changed.  But after multiplying
  them, the brightness ratio becomes 9:1, enhanced.

  The primary effect of multiplication is doubling the contrast,
  as shown above.  This effect is valuable in "classical darkrooms."  
  It also improves the S/N, of course, but the improvement is not 
  statistically optimized.  Now, we have "digital darkrooms."
  We don't need multiplication as much as we did in classical 
  darkrooms.  We can first average the images to optimize the 
  S/N enhancement and then use curves to change the contrast.

# Finally, what is the best strategy to take deep film images?
  Single long exposure?  Or many short exposures stacked?
  I would say, long exposure is still the best way to go.
  
  When a film starts to get exposed, photons are not used to
  create Ag condensation.  It has to reach a critical exposure
  before a latent image can form.  After the critical exposure, the
  latent image starts to grow very slowly.  This is the "toe" 
  in the HD curve of film.  Only after a certain exposure time, 
  the latent image grows rapidly ("straight line" in the HD curve).  
  I had measured the S/N of three films (E200, Provia 400F, and
  Centuria 400).  All of them show that the S/N increases very
  slowly during the critical exposure phase and the toe phase.
  Only after the exposure reaches the straight line, S/N increases
  rapidly with exposure time.

  In other words, every time we take a short exposure, we waste 
  time on the critical exposure and the toe without gaining much S/N.  
  (Pre-flash may be able to help on this but the background fog that 
  it produces has negative effect on S/N, too.)
  If we take a single long exposure, we only waste this time once.  
  For this reason, the S/N on each short exposures is not optimized.  
  Stacking 10 5min exposures will not give us an S/N as high as a 
  single 50min exposure.  

  This is pretty much supported by my S/N test results.  Later after
  I come back to sea level, I can scan some real astro images of
  long and short exposure times to see if I can reach the same 
  conclusion.  

Cheers,

Wei-Hao

______________________________________________________________________
Wei-Hao Wang  :)

Institute for Astronomy at University of Hawaii

Address:                       Phone: 808-956-9867                  
2680 Woodlawn Drive            Personal Website:
Honolulu, HI 96822             http://www.ifa.hawaii.edu/~wang
______________________________________________________________________



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