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Spectroscopy: SNR vs Aperture

  1. Aug 4, 2011 #1
    Anyone know a source for a mathematical analysis relating the slit-size/throughput for a spectrometer vs SNR?

    I find that I always get better SNR (but not necessarily resolution) with a wider slit or higher throughput monochromator when doing emissions work.
    Fritz
     
  2. jcsd
  3. Aug 4, 2011 #2

    Drakkith

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    Staff: Mentor

    This seems similar to having a larger aperture for my telescope. More light gathering for the object. I'm not familiar with spectrometers so I don't know for sure if the effect is the same for slit width. I THINK that if you double the light gathering area, you double the light from the object but only get the square root of the new noise. I know that's how it works for S/N ratio from exposure times, but I'm not sure about aperture. So, if correct, then increasing the signal from 100 to 200 increases the noise from 10 to about 14, and the S/N Ratio from 10 to 14 as well. (All numbers acquired from thin air)

    If someone knows for sure please tell us!
     
  4. Aug 10, 2011 #3
    Thanks for the reply. There is indeed a correlation between a telescope and a spectrometer-not a lot of difference in fact. The slitwidth servers as a frequency domain integrating device, resulting mathematically in something similar to pixel binning on the CCD. I was interested in finding a rigorous anaylsis including effects on resovling power etc. Spectrochemical Analysis (Ingle) grazes the issue but is inconcise.

    Thanks again,
    Fritz
     
  5. Aug 12, 2011 #4

    Claude Bile

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    Science Advisor

    Higher signal is equivalent to taking more samples in time. Basic statistics says that the SNR is proportional to the square root of the sample size.

    Claude.
     
  6. Aug 12, 2011 #5
    You are correct on the basic statistics of the sample size. I think that for photon driven CCD's things become a bit more complex due to the Shot noise that increases with photon flux.

    Basically we have 4 variables in this type of spectroscopy:
    1) Exposure time per sample
    2) number of samples taken before refreshing the CCD (call it S)
    3) number of collective samples compounding (2) above (call it N)
    4) number of pixels aggregated together to define one "point" on the sample (e.g. binning)

    The first 3 are time domain clustering, the later is frequency domain. All of these variables can be jockeyed around to get the best SNR.

    Increasing S in lieu of N has advantages since the CCD read noise is the same while the number of samples increases, overwhelming the read noise. The think shot noise increases linearly with all 4. According to my calculations (4) decreases the SNR as the square root of the number of binned pixels.

    It is my conjecture that increasing slit size at the expense of resolving power, is comparable mathematically to increasing the binning factor in (4).

    Thanks,
    Fritz
     
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