Noise levels as a function of pixel size

Discussion in 'Digital Photography' started by Alfred Molon, Dec 13, 2005.

  1. Alfred Molon

    Alfred Molon Guest

    Is there some formula or scientific basis to estimate noise levels as a
    function of pixel size? At the moment I'm assuming that noise levels
    decrease with the square root of the size increase, i.e. doubling the
    pixel area should lower noise levels by the square root of 2. Is this
    correct? I'm only referring to "pixel" noise, i.e. not read noise, A/D
    conversion noise and other external noise sources.
     
    Alfred Molon, Dec 13, 2005
    #1
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  2. The photon-limited noise is proportional to the square root of the number
    of photons collected. So, if everything else is equal, a pixel which is
    double the linear size will connect four times the number of photons, and
    the noise will be twice as much. Therefore the signal to noise ratio will
    be doubled.

    Doubling the area will increase the signal-to-noise ratio by a factor of
    square root (2), with the signal being doubled and the noise being root 2
    higher.

    David
     
    David J Taylor, Dec 13, 2005
    #2
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  3. Photon counting is a Poisson statistics problem, so the noise goes like
    the square root of the signal. The signal/noise ratio thus goes like
    1/sqrt(signal). Doubling the linear size of a pixel increases the area
    (and hence the signal) by a factor of four. The noise only doubles, so
    s/n doubles.

    More generally, the s/n ratio scales with the linear size of the pixel.

    -dms
     
    Daniel Silevitch, Dec 13, 2005
    #3
  4. Alfred Molon

    Lourens Smak Guest

    No. Try a Kodak 14n and a Canon 5D both at iso 1600, and you'll see.

    Lourens
     
    Lourens Smak, Dec 15, 2005
    #4
  5. Alfred Molon

    Scott W Guest

    There are limits to noise performance base on pixel size. Not every
    camera comes close to these limits, but no camera passes them.

    Scott
     
    Scott W, Dec 15, 2005
    #5
  6. Alfred Molon

    miso Guest

    I don't see why this would be any different than low noise amplifier
    design, so double the area and the SNR improves by 3db (linear square
    root of two).

    I don't know if cameras do this, but you could sample the sensor with
    the shutter closed, then sample with the shutter opened. A certain
    amount of noise will be cancelled. [Double correlated sampling.]
     
    miso, Dec 15, 2005
    #6


  7. Yes, there is scientific basis to estimate noise levels as a function of
    pixel size.

    The intrinsic noise from the CCD or CMOS pixel is mainly a function of
    thermal energy, and independent of pixel size. The signal is a result of
    light hitting the pixel surface, which is a function of pixel size because a
    larger pixel collects more light. Therefore a larger pixel will have a
    higher signal to noise level. So if you get the same signal output, a larger
    pixel will have less noise than a smaller pixel.


    Wannabe
    =======
     
    WannabeSomeone, Dec 15, 2005
    #7
  8. Alfred Molon

    Tony Polson Guest


    And the 'full frame' 6 MP Contax N Digital has noise levels that are
    even worse than the Kodak!

    Far worse, in fact, even at low ISO.

    ;-)
     
    Tony Polson, Dec 15, 2005
    #8
  9. Alfred Molon

    SMS Guest

    See "http://clarkvision.com/imagedetail/does.pixel.size.matter/"
     
    SMS, Dec 16, 2005
    #9
  10. Alfred Molon

    prep Guest

    You have an upper limit on the well capacity, and that sets the best
    possible SN. Increasing size increases well capacity if the doping
    profiles are not changed, so that is a plus in high light conditions.
    But the larger area pixel will collect more photons in low light as
    well increasing SN there.
    Nope. You now have 1/sqrt2 noise and 1/2 signal. You have removed any
    dark current bias if you do it right though.

    --
    Paul Repacholi 1 Crescent Rd.,
    +61 (08) 9257-1001 Kalamunda.
    West Australia 6076
    comp.os.vms,- The Older, Grumpier Slashdot
    Raw, Cooked or Well-done, it's all half baked.
    EPIC, The Architecture of the future, always has been, always will be.
     
    prep, Dec 16, 2005
    #10
  11. Not quite. When you subtract the dark frame you have virtually no
    effect on the signal, since all that is being removed is the dark
    current, not half of the signal. However, you have an *additional*
    noise source of equal value (2 uncorrelated frames) to the original
    frame and thus increase the total noise to sqrt(2) of the original.
    An estimate of SNT from your figures would give the correct effect, but
    your reasoning wasn't quite right.
     
    Kennedy McEwen, Dec 16, 2005
    #11
  12. Not quite. When you subtract the dark frame you have virtually no
    effect on the signal, since all that is being removed is the dark
    current, not half of the signal. However, you have an *additional*
    noise source of equal value (2 uncorrelated frames) to the original
    frame and thus increase the total noise to sqrt(2) of the original.
    An estimate of SNR from your figures would give the correct effect, but
    your reasoning wasn't quite right.
     
    Kennedy McEwen, Dec 17, 2005
    #12
  13. An aside: one way to reduce this extra noise is to take several dark
    frames and average them. That reduces the noise *in the average dark
    frame* by a factor of sqrt(N). With even a modest value of N, the
    additional noise due to dark frame subtraction is reduced well below the
    noise in the image itself.

    I think this is common in astronomical imaging, but digital cameras only
    use a single dark frame.

    Dave
     
    Dave Martindale, Dec 17, 2005
    #13
  14. Alfred Molon

    John Francis Guest

    Still not useful.

    That technique works in astronomical imaging because what's being
    averaged is a complete image, with both (deterministic) signal
    and (random) noise.

    If you take several (random) noisy dark frames, and average them
    together, you'll end up with an average noise close to zero. But
    that doesn't help you if you've only got a single frame with signal;
    although you know the average noise is zero, that doesn't give you
    a better estimate of the noise in your single image frame.
     
    John Francis, Dec 17, 2005
    #14
  15. Exactly, and this is one reason why I was apparently a little pedantic
    about Prep's reasoning - this would not be apparent from his reasoning,
    however it is clear from the correct reasoning that if you reduce the
    noise on the dark frame *before* subtracting it you can avoid degrading
    the overall noise in the final result.
     
    Kennedy McEwen, Dec 17, 2005
    #15
  16. True, it doesn't improve the noise in the single frame - nothing you do
    subsequently can reduce that. However, using the technique Dave
    suggested, you can correct for the dark current sourced noise without
    introducing additional noise.

    We need to distinguish between different noise types to discuss this
    sensibly. Misho used the term "noise" generically, however the approach
    he suggested would improve the spatial noise (fixed pattern dark level
    noise) at the expense of increased temporal noise (random noise changing
    from frame to frame). The method Dave suggested avoids increasing the
    random noise, thus permitting the spatial noise to be eliminated,
    leaving only the temporal noise of the single image frame. This usually
    results in a significant improvement in CCD/CMOS sensor sourced images.
     
    Kennedy McEwen, Dec 17, 2005
    #16
  17. Alfred Molon

    JPS Guest

    In message <dnvskj$eop$>,
     
    JPS, Dec 17, 2005
    #17
  18. Yeah, "noise" is too general a term. Fixed pattern noise is noise
    because it interferes with the desired signal, but it's not noise
    because it isn't really random (either spatially or temporally). Photon
    and electron noise is random, and is noise without any argument.

    Dave
     
    Dave Martindale, Dec 18, 2005
    #18
  19. Alfred Molon

    JPS Guest

    In message <do2do4$nve$>,
    .... and will always be there, even if all other forms of noise can be
    eradicated.
    --
     
    JPS, Dec 18, 2005
    #19
  20. And photon noise is the dominant noise source in any good
    modern digital camera. At the lowest end, read noise
    contributes.

    But what we can hope to see is improvements in quantum efficiency.
    A 2 to 3x improvement in quantum efficiency would help
    the small size P&S sensors perform more like current
    large pixel DSLR sensors. And the DSLR sensors would
    be proportionally better too!

    Roger
     
    Roger N. Clark (change username to rnclark), Dec 18, 2005
    #20
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