[LONG] Theoretical estimates for film-equivalent digital sens

Discussion in 'Digital Photography' started by Ilya Zakharevich, Mar 6, 2005.

  1. This or similar topics appear quite often, but most treatments avoid
    starting "from first principles". In particular, the issues of
    photon Poisson noise are often mixed up with electron Poisson noise,
    thus erring close to an order of magnitude. Additionally, most people
    assume RGB sensors; I expect that non-RGB can give "better" color
    noise parameters than (high photon loss) RGB. [While I can easily
    detect such errors in calculations of others, I'm in no way a
    specialist, my estimates may be flawed as well... Comments welcome.]

    Initial versions of this document were discussed with Roger N Clark;
    thanks for a lot of comments which lead to major rework of
    calculations; however, in order of magnitude the conclusions are the
    same as in the beginning of the exchange... [I do not claim his
    endorsement of what I write here - though I will be honored if he does
    ;-]

    I start with conclusions, follow with assumptions (and references
    supporting them), then conclude by calculations, and consideration of
    possible lenses.

    CONCLUSIONS:
    ~~~~~~~~~~~

    Theoretical minimal size of a color sensor of sensitivity 1600ISO,
    (which is equivalent to Velvia 50 36x24mm in resolution and noise)
    is 13mm x 8.7mm. Similar B&W sensor can be 12x8mm. Likewise,
    theoretical maximum sensitivity of 3/4'' 8MP color sensor is
    1227 ISO.

    [All intermediate numbers are given with quite high precision; of
    course, due to approximations in assumptions, very few significant
    digits are trustworthy.]

    These numbers assume QE=1, and non-RGB sensor (to trade non-critical
    chrominance noise vs. critical luminance noise). For example, in a
    2x2 matrix one can have 2 cells with "white" (visible-transparent)
    filter, 1 cell with yellow (passes R+G) filter, another with cyan
    (passes G+B) filter.

    ASSUMPTIONS:
    ~~~~~~~~~~~

    a) Photopic curve can be well approximated by Gaussian curve
    V(lambda) = 1.019 * exp( -285.4*(lambda-0.559)^2 )
    see
    http://home.tiscali.se/pausch/comp/radfaq.html

    b) Solar irradiation spectrum on the sea level can be well approximated
    by const/lambda in the visible spectrum (at least for the purpose
    of integration of photopic curve). See

    http://www.jgsee.kmutt.ac.th/exell/Solar/Intensity.html
    http://www.clas.ufl.edu/users/emartin/GLY3074S03/images/solarirradiance.htm

    In the second one lower horizontal axis is obviously in nm, and the
    upper one complete junk. Sigh...)

    c) Sensitivity of the sensor is noise-bound. Thus sensitivity of
    a cell of a sensor should be measured via certain noise level
    at image of 18% gray at normal exposure for this sensitivity.

    d) The values of noise given by Velvia 50 film and Canon 1D Mark II
    at 800ISO setting at image of 18% gray are "acceptable". These
    two are comparable, see
    http://clarkvision.com/imagedetail/digital.signal.to.noise/
    Averaging 15 and 28 correspondingly, one gets 21.5 as the "acceptable"
    value of S/N in the image of 18% gray.

    e) Noise of the sensor is limited by the electron noise (Poisson noise
    due to discrete values of charge); other sources of noise are
    negligeable (with exposition well below 40sec). See
    http://www.astrosurf.com/buil/d70v10d/eval.htm

    f) The AE software in digital cameras is normalizing the signal so
    that the image of 100% reflective gray saturates the sensor.
    [from private communication of Roger Clark; used in "d"]

    g) Normal exposure for 100ISO film exposes 18% gray at 0.08 lux-sec.
    See
    http://www.photo.net/bboard/q-and-a-fetch-msg?msg_id=004kMM

    h) The color "equivalent resolution" numbers in
    http://clarkvision.com/imagedetail/film.vs.digital.1.html
    may be decrease by 25% to take into account recent (as of
    2005) improvements in demosaicing algorithms. E.g., see
    http://www.dpreview.com/reviews/konicaminoltaa200/page12.asp
    Taking largest numbers (Velvia 50 again, and Tech Pan), this gives
    16MP B&W sensor, and 12MP color sensor.

    i) Eye is much less sensitive to the chrominance noise than to
    luminance noise. Thus it makes sense to trade chrominance
    noise if this improves luminance noise (up to some limits).

    In particular, sensors with higher-transparency filter mask give
    much lower luminance noise; the increased chrominance noise (due
    to "large" elements in the to-RGB-translation matrix) does not
    "spoil" the picture too much.

    j) To estimate Poisson noise is very simple: to get S/N ratio K, one
    needs to receive K^2 particles (electrons, or, assuming QE=1,
    photons).

    METAASSUMPTION
    ~~~~~~~~~~~~~~

    In any decent photographic system the most important component
    of performance/price ratio is the lenses. Since the price of the
    lens scales as 4th or 5th power of its linear size, decreasing
    the size of the sensor (while keeping S/N ratio) may lead to
    very significant improvements of performance/price.

    Details in the last section...

    [This ignores completely the issue of the price of accumulated
    "legacy" lenses, so is not fully applicable to professionals.]

    Since sensor is purely electronic, so (more or less) subject to
    Moore law, the theoretical numbers (which are currently an order
    of magnitude off) have a chance to be actually relevant in not
    so distant time. ;-)

    PHOTON FLOW OF NORMAL EXPOSURE
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    First, we need to recalculate 0.08 lux-sec exposure into the the
    photon flow.

    Assume const/lambda energy spectral density (assumption b),
    integration of photonic curve gives const*0.192344740294
    filtered flow. With constant spectral density at
    1 photon/(sec*mkm*m^2), const = h * c, so the eye-corrected energy
    flow is 3.82082403851941e-20 W/m^2 = 2.60962281830876e-17 lux.

    Thus 0.08 lux-sec corresponds to (constant) spectral density
    3065.57711860622 photon/(mkm*mkm^2). This is the total photon flow
    of the image of 18% gray normally exposed for 100ISO film.

    B&W SENSOR
    ~~~~~~~~~~
    One can imagine (among others) 3 different theoretical types of B&W
    sensor: one giving "physiologically correct" response of the
    photopic curve, one accepting all photons in the "extended visible"
    range of the spectrum 380 to 780nm, and an intermediate one, one
    accepting all photons in the "normal visible" range of the spectrum
    400 to 700nm. See
    http://en.wikipedia.org/wiki/Visible_light

    To cover the first case, one needs to multiply the value obtained in
    the previous section by the integral of the photopic curve,
    0.106910937 mkm; for the other, one needs to multiply by the width
    of the window, 0.4 mkm, and 0.3 mkm. Resulting values are
    327.7437, 1226.23, and 919.673 photon/mkm^2 as the flow of 18% gray
    normally exposed for 100ISO film.

    However, since photopic curve should not produce any particularly
    spectacular artistic effect, it makes sense to have the sensor
    of maximal possible sensitivity, and achieve the photopic response
    (if needed) by application of a suitable on-the-lens filter. So we
    ignore the first value, and use the other two. For example, the
    smaller value gives photon Poisson noise S/N ratio of 21.5 with a
    square cell of 0.70896 mkm. The larger value of the window,
    0.4 mkm, results in a square cell of 0.613977 mkm. These are
    smallest possible sizes of the cell which can provide the required
    S/N ratio at exposure suitable for 100ISO film.

    To have 1600ISO sensor, these numbers should be quartupled; 16MP
    3:2 ratio sensor based on the 0.4mkm spectral window results in
    12x8mm sensor.

    OPTIMIZING THE COLOR MASK
    ~~~~~~~~~~~~~~~~~~~~~~~~~

    For color sensor, theoretical estimates are complicated by the
    following issue: different collections of spectral curves for the
    filter mask can result in identical sensor signal after suitable
    post-processing. (This ignores noise, and de-mosaicing artefacts.)
    Indeed, taking a linear combination of the R,G,B cells is equivalent
    to substituting the transparency curves for mask filters by the
    corresponding linear combination. (This assumes the linear
    combination curve fits between 0 and 1.)

    As we saw in B&W SENSOR section, a more transparent filter results
    in higher S/N at the cell; if the filter is close to transparent,
    cell's signal is close to luminance, thus higher transparency
    results in improvement of luminance noise.

    To estimate color reproduction, take spectral sensitivity curves
    of the different types of sensors cells. Ideally, 3 linear
    combinations of these curves should match the spectral sensitivity
    curves of cones in human eyes. Assuming 3 different types of sensor
    cells, this shows that spectral curves of cells should be linear
    combinations of spectral sensitivity curves of cones. In
    principle, any 3 independent linear combinations can be used for
    sensors curves; recalculation to RGB requires just application of
    a suitable matrix. However, large matrix coefficients will result
    in higher chrominance noise. (Recall that we assume that [due to
    high transparency] the luminance is quite close to signals
    of the sensors, thus matrix coefficents corresponding to luminance
    can't be large; thus all that large matrix coefficients can do is
    to give contribution to CHROMINANCE noise.)

    Without knowing exactly how eye reacts to chrominance and luminance
    noise it is impossible to optimize the sensor structure; however,
    one particular sensor structure is "logical" enough to be close to
    optimal: take 2 filters in a 2x2 filter matrix to be as transparent
    as possible while remaining a linear combination of cone curves.
    This particular spectral curve is natural to call the W=R+G+B curve.
    Take two other filters to be as far as possible from W (and
    from each other) while keeping high transparency; in particular,
    keep the most powerful (in terms of photon count) G channel, and
    remove one of R and B channels; this may result, for example, in
    the following filter matrix

    W Y W Y W Y W Y
    C W C W C W C W
    W Y W Y W Y W Y
    C W C W C W C W

    here C=G+B, Y=R+G. Since the post-processing matrix R=W-C, B=W-G,
    G=C+Y-W does not have large matrix coefficients, the increase in
    chrominance noise is not significant.

    Above, W means the combination of the cone sensitivity curves with
    maximal integral among (physically possible) combinations with
    "maximal transparency" being 1. While we cannot conclude that this
    results in the optimal mask, recall the following elementary fact:
    to estimate the maximal *value* f(x) one can make quite large errors
    in the *argument* x, and still get good approximation for f(xMAX).
    Thus choosing the matrix above gives a pessimistic estimate, AND one
    should expect that it is not very far of the correct one.

    TRANSPARENCY OF THE COLOR MASK
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    Actually, what is R, G, B in colorimetry are in turn linear
    combinations of responses of cones. Use cones sensitivity curves
    from
    http://www.rwc.uc.edu/koehler/biophys/6d.html

    Now use RR, GG, and BB to denote *these* curves, not "usual" R, G, B
    of colorimetry. Since I could not find these data in table form,
    the values below are not maximal possible, but just first
    opportunities which come to mind.

    Using 0.9RR+0.35GG, one gets a quite flat curve; one may assume that
    in range 0.42--0.65nm the sensitivity is above 0.9. with one at
    700nm going down to 0.6, and 400nm going down to 0.8. So the
    filter "compatible" with cone sensitivity curves can easily achive
    0.9 transparency in the range 400--700nm, which would give photon
    count 827.705822 photon/mkm^2 in the W (R+G+B) type cell. Taking
    GG and 0.9RR+0.35BB curves as other types of sensors, one gets
    average transparency about 0.8 and 0.85. Taking average
    transparency of the filter over a 2x2 WCWY matrix cell 0.85, one
    gets photon count averaged over different kinds of color-sensitive
    cells as 781.722165 photon/mkm^2.

    As above, we assume that this average photon count is the count
    giving contribution into luminance noise.

    FINAL ESTIMATES
    ~~~~~~~~~~~~~~~

    With above average photon count at a cell, to get S/N ratio 21.5
    one needs a square cell of 0.768975 mkm. Recall that this is the
    the smallest possible cell which can provide the required S/N ratio
    at exposure suitable for 100ISO film.

    Quadrupling to get sensitivity 1600ISO, and taking 12MP equivalent
    of 36x24mm Velvia 50, one gets the 13 x 8.7 mm sensor.

    HOW GOOD CAN 36x34mm SENSOR GO?
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    In other direction, 36x24 mm color sensor at sensitivity 1600ISO can
    (theoretically) be equivalent (or better) than 10 x 6.6 cm Velvia 50
    film; that is 1/2 frame of 4x5 in film. In yet other words, take
    36x24mm sensor with resolution and noise better than 4x5 Velvia 50
    film; it has theoretical maximum of sensibility at 800ISO.
    Likewise, to achieve resolution and noise of 8x10in Velvia 50 film,
    the maximal sensibility of 36x24mm sensor is 200ISO.

    THE QUESTION OF LENSES
    ~~~~~~~~~~~~~~~~~~~~~~

    Of course, preceeding section completely ignores the issue of
    lenses; on the other hand, a cheap prosumer zoom lens with
    28--200mm equivalent paired with a digital sensor easily gives
    resolution of 3.3mkm per single line (with usable image diameter
    about 11mm, see
    http://www.dpreview.com/reviews/konicaminoltaa200/page12.asp
    ); so we know it is practically possible to create a lens which
    saturates the theoretical resolution of 1600ISO sensor (but probably
    not 800ISO and 200ISO sensor!). It is natural to expect that a
    non-zoom lens could saturate resolution of 800ISO sensor.

    This gives theoretical resolution limit of a "practical" lens +
    800ISO digital 36x24mm sensor: it is equivalent to best 4x5in 50ISO
    film (with non-zoom lens). With zoom lense, one can achieve quality
    of 2.5x4in 50ISO film; sensor is at 1600ISO, lense is 28-200mm zoom.

    Some more estimates of how practical is "practical": the zoom
    mentioned above is bundled with $600 street price camera which
    weights about 580g. Assume the lens takes 1/2 of the price, and
    1/4 of the weight. Rescaling from 11mm diagonal image size to the
    36x24mm image size will increase price to $70K--$280K (assuming that
    price is proportional to 4th-5th power of the size [these numbers
    were applicable 20 years ago, I do not know what holds today]), and
    will increase the weight to 9kg.

    On the other hand, the 4:3 aspect ratio sensor of the same area as
    the mentioned above 13 x 8.6 mm sensor (1600ISO sensor equivalent
    in quality to Velvia 50 at 36x24mm) is 12.2 x 9.17mm, diagonal is
    15.26mm. It is 0.9'' sensor (in the current - silly - notation).

    Rescaling the mentioned above lens to this size gives lens price
    $1100--$1500, and weight about 750g; both quite "reasonable".
    Recall that this 28--200 equivalent zoom lens will saturates resolution
    of an equivalent of Velvia 50 36x24mm film.
    Ilya Zakharevich, Mar 6, 2005
    #1
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  2. Ilya Zakharevich

    Scott W Guest

    Re: Theoretical estimates for film-equivalent digital sens

    A very nice write up, I will admit I have not gone through all of it
    yet in detail. One thing to consider is that CCD have a read out noise
    of around 10 electrons, whereas this noise level will not greatly
    effect the signal to noise when looking at 400 detected photons with an
    noise level of 20 electrons it will start to dominate in darker parts
    of the scene. For instance by the time you are down 5 stops from full
    white the readout noise will be larger then the photon noise, by a
    small amount.

    The idea of using non-RGB filters is sound and a number of CCD sensors
    have used filters more like C, Y and M. Why RGB is used on digital
    cameras I am not sure.

    Scott
    Scott W, Mar 6, 2005
    #2
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  3. Re: Theoretical estimates for film-equivalent digital sens

    [A complimentary Cc of this posting was sent to
    Scott W
    <>], who wrote in article <>:
    > A very nice write up, I will admit I have not gone through all of it
    > yet in detail. One thing to consider is that CCD have a read out noise
    > of around 10 electrons, whereas this noise level will not greatly
    > effect the signal to noise when looking at 400 detected photons with an
    > noise level of 20 electrons it will start to dominate in darker parts
    > of the scene. For instance by the time you are down 5 stops from full
    > white the readout noise will be larger then the photon noise, by a
    > small amount.


    This is a very valid remark. However, note that these were
    *theoretical* estimates; after translation into this language your
    remark becomes:

    Readout noise should be decreased too; otherwise shadows noise is
    going to be well above Poisson noise.

    Thanks,
    Ilya
    Ilya Zakharevich, Mar 9, 2005
    #3
  4. Ilya Zakharevich

    Guest

    Re: Theoretical estimates for film-equivalent digital sens

    Scott W <> wrote:
    > The idea of using non-RGB filters is sound and a number of CCD sensors
    > have used filters more like C, Y and M. Why RGB is used on digital
    > cameras I am not sure.


    My guess is that to do otherwise would increase the chroma noise too
    much. Chroma noise in digital cameras at high ISO is already
    intrusive, and anything that increases it may be unwelcome, even if
    sensitivity improved. Without direct experimental data it's hard to
    say.

    The other issue is how well non-RGB filters could be made to
    approximate the colour matching functions of typical display systems.
    Red and green are quite well matched by sensors of a typical camera,
    but the blue is quite a way off because its spectral sensitivity is
    too broad.[1] It would be a matter of measuring some physically
    realizable filters and seeing what colour matching functions resulted.

    Andrew.

    [1] The Reproduction of Colour, 6th Edition, Robert Hunt, p556.
    , Mar 9, 2005
    #4
  5. Ilya Zakharevich

    HvdV Guest

    Ilya Zakharevich wrote:

    > PHOTON FLOW OF NORMAL EXPOSURE
    > ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    >
    > First, we need to recalculate 0.08 lux-sec exposure into the the
    > photon flow.
    >
    > Assume const/lambda energy spectral density (assumption b),
    > integration of photonic curve gives const*0.192344740294
    > filtered flow. With constant spectral density at
    > 1 photon/(sec*mkm*m^2), const = h * c, so the eye-corrected energy
    > flow is 3.82082403851941e-20 W/m^2 = 2.60962281830876e-17 lux.

    What unit is 'mkm', wavenumber?
    -- Hans
    HvdV, Mar 9, 2005
    #5
  6. Re: Theoretical estimates for film-equivalent digital sens

    [A complimentary Cc of this posting was sent to

    <>], who wrote in article <>:
    > My guess is that to do otherwise would increase the chroma noise too
    > much. Chroma noise in digital cameras at high ISO is already
    > intrusive, and anything that increases it may be unwelcome, even if
    > sensitivity improved. Without direct experimental data it's hard to
    > say.


    When I look on the digital images of a gray surface (those of "compare
    two cameras" kind), it looks like my perception of noise is not
    related to chrominance noise at all. At least a camera with higher
    measured individual-channel R/G/B noise can produce much lower visible
    noise if its noise reduction algorithm favors luminance noise (as
    confirmed by luminance noise graph). Of course, it is in no way
    scientific conclusion, but I may have seen about ten such
    comparisons...

    > The other issue is how well non-RGB filters could be made to
    > approximate the colour matching functions of typical display
    > systems.


    AFAIU, this has nothing to do with display (output) system, but only
    with input system (cones). As far as the filters match cones, you can
    postprocess colors into *any* display system (if the initial color is
    in the gamut of the display system).

    And if you do not match the cone sensitivity, colors which look the
    same will get different when stored. After this no amount of
    post-processing will be able to fix this.

    Hope this helps,
    Ilya
    Ilya Zakharevich, Mar 10, 2005
    #6
  7. [A complimentary Cc of this posting was sent to
    HvdV
    <>], who wrote in article <3059$422f4a27$3e3aaa83$>:
    > > filtered flow. With constant spectral density at
    > > 1 photon/(sec*mkm*m^2), const = h * c, so the eye-corrected energy
    > > flow is 3.82082403851941e-20 W/m^2 = 2.60962281830876e-17 lux.

    > What unit is 'mkm', wavenumber?


    Yes (?); Wavelength. IIRC, wavenumber is 1/wavelength (or some such;
    2pi comes to mind...).

    [BTW, because of non-linearity of wavelength vs wavenumber, spectral
    density which constant per wavelength becomes very non-constant when
    measured per wavenumber.]

    Yours,
    Ilya
    Ilya Zakharevich, Mar 10, 2005
    #7
  8. Re: Theoretical estimates for film-equivalent digital sens

    lid writes:

    >[1] The Reproduction of Colour, 6th Edition, Robert Hunt, p556.


    I didn't realize that the 6th edition was out. Does it say how it
    differs from the previous edition (e.g. in a preface?).

    I do have the 3rd, 4th, and 5th editions already, but they don't cover
    digital imaging much.

    Dave
    Dave Martindale, Mar 11, 2005
    #8
  9. Ilya Zakharevich

    HvdV Guest

    Hi Ilya,
    >
    >
    > Yes (?); Wavelength. IIRC, wavenumber is 1/wavelength (or some such;
    > 2pi comes to mind...).

    Yes, wavenumber is 2 * pi / lambda, units m^-1
    >
    > [BTW, because of non-linearity of wavelength vs wavenumber, spectral
    > density which constant per wavelength becomes very non-constant when
    > measured per wavenumber.]

    Yes, but the choice is arbitrary. Since wavenumber which is proportional to
    photon energy, an interesting quantity for many applications, spectroscopy
    people tend towards wavenumber whereas optical people like wavelength since
    resolving power scales with that.

    BTW, can you substantiate your interesting assumption:
    ----
    In any decent photographic system the most important component
    of performance/price ratio is the lenses. Since the price of the
    lens scales as 4th or 5th power of its linear size, decreasing
    the size of the sensor (while keeping S/N ratio) may lead to
    very significant improvements of performance/price.
    ---
    with some examples?
    The tradeoff of lens aperture and expense vs sensor size determines
    ultimately the size and shape of the digital camera. After the 'fashion
    factor' of course.

    -- hans
    HvdV, Mar 11, 2005
    #9
  10. Re: Chrominance noise vs luminance one

    [A complimentary Cc of this posting was sent to

    <>], who wrote in article <>:
    > Scott W <> wrote:
    > > The idea of using non-RGB filters is sound and a number of CCD sensors
    > > have used filters more like C, Y and M. Why RGB is used on digital
    > > cameras I am not sure.

    >
    > My guess is that to do otherwise would increase the chroma noise too
    > much. Chroma noise in digital cameras at high ISO is already
    > intrusive, and anything that increases it may be unwelcome, even if
    > sensitivity improved. Without direct experimental data it's hard to
    > say.


    Judge for yourself: visit

    http://ilyaz.org/photo/random-noise

    Yours,
    Ilya
    Ilya Zakharevich, Mar 12, 2005
    #10
  11. Re: Rescaling the lense

    [A complimentary Cc of this posting was sent to
    HvdV
    <>], who wrote in article <7ac8b$4232019c$3e3aaa83$>:
    > In any decent photographic system the most important component
    > of performance/price ratio is the lenses. Since the price of the
    > lens scales as 4th or 5th power of its linear size, decreasing
    > the size of the sensor (while keeping S/N ratio) may lead to
    > very significant improvements of performance/price.
    > ---
    > with some examples?
    > The tradeoff of lens aperture and expense vs sensor size determines
    > ultimately the size and shape of the digital camera. After the 'fashion
    > factor' of course.


    a) First of all, my assumption on how rescaling the lense affects
    image quality was "incomplete" (read: wrong ;-). Part of fuzziness
    due to difraction does not change; but part of fuzziness due to
    optical imperfection scales up with the lense linear size (since
    all the light rays passing through the system scale up, the spot in
    the focal plane which is the diffraction-less image of a
    point-source will scale up as well).

    This has two effects: sweet spot (in F-stops) scales up (i.e., to
    the worse) as sqrt(size); and best resolution scales down as
    1/sqrt(size). So my estimates for "perfect lense" for an ideal
    36x24mm sensor were wrong, since I erroneously assumed that the
    sweet spot does not change.

    b) One corollary is that when you scale sensor size AND LENSE up n
    times, it makes sense to scale up the size of the pixel sqrt(n)
    times. In other words, you should increase the sensitivity of the
    sensor and number of pixels both the same amount - n times.
    Interesting...

    c) The estimages on price vs. size: IIRC, this was from a review in a
    technical magazine on optical production ("Scientific publications
    of LOMO" or some such) in end of 80s. Since technology could have
    changed meanwhile (digitally-controlled machinery?), the numbers
    could have changed...

    Hope this helps,
    Ilya
    Ilya Zakharevich, Mar 12, 2005
    #11
  12. Re: Chrominance noise vs luminance one

    Ilya Zakharevich wrote:
    []
    > Judge for yourself: visit
    >
    > http://ilyaz.org/photo/random-noise
    >
    > Yours,
    > Ilya


    Grey is one colour to test this on - what about a more sensitive colour
    like skin-tones?

    Cheers,
    David
    David J Taylor, Mar 12, 2005
    #12
  13. Re: Chrominance noise vs luminance one

    [A complimentary Cc of this posting was sent to
    David J Taylor
    <-this-bit.nor-this-part.uk>], who wrote in article <poHYd.3079$>:
    > > Judge for yourself: visit
    > >
    > > http://ilyaz.org/photo/random-noise


    > Grey is one colour to test this on - what about a more sensitive colour
    > like skin-tones?


    The script is there. Feel free to edit it to change the base value.
    Or just modify the .png by adding a constant bias...

    Yours,
    Ilya
    Ilya Zakharevich, Mar 12, 2005
    #13
  14. Re: Theoretical estimates for film-equivalent digital sens

    [A complimentary Cc of this posting was sent to
    Scott W
    <>], who wrote in article <>:
    > A very nice write up, I will admit I have not gone through all of it
    > yet in detail. One thing to consider is that CCD have a read out noise
    > of around 10 electrons, whereas this noise level will not greatly
    > effect the signal to noise when looking at 400 detected photons with an
    > noise level of 20 electrons it will start to dominate in darker parts
    > of the scene. For instance by the time you are down 5 stops from full
    > white the readout noise will be larger then the photon noise, by a
    > small amount.


    On the second thought, maybe this issue is not as crucial as it may
    sound. Remember that 12 electrons noise is present on Mark II, and
    its 800ISO setting is "considered nice". It has S/N=28 at Zone V; so
    the electron noise at Zone III should be about 13 electrons; while 12
    electrons readout noise will increase this to total about 17
    electrons, we must conclude that such a noise (S/N=9) at Zone III is
    not very bad. Likewise for Zones II and I.

    So: either Mark II produces noticable noise in zones I--III, or
    readout noise 12 electrons is already small enough to be "not
    important".

    Yours,
    Ilya
    Ilya Zakharevich, Mar 13, 2005
    #14
  15. Re: Chrominance noise vs luminance one

    [A complimentary Cc of this posting was NOT [per weedlist] sent to
    Ilya Zakharevich
    <>], who wrote in article <d0vkf9$1io5$>:
    > > > Judge for yourself: visit


    > > > http://ilyaz.org/photo/random-noise


    > > Grey is one colour to test this on - what about a more sensitive colour
    > > like skin-tones?


    > The script is there. Feel free to edit it to change the base value.
    > Or just modify the .png by adding a constant bias...


    Actually, it may be a little bit more than just changing the base
    value. Luminance is calculatable from Luma only very close to neutral
    gray; thus having a skin-tone with luma-less noise may have
    significant luminance noise.

    One needs to experiment with both constant-luma noise and
    constant-luminance noise, and see which one is less perceivable by
    eye. Summary: one may need also to modify the vector 0.2126 0.7152
    0.0722 to take into account gamma (via derivatives of x^2.2 at R'G'B'
    values of skin tone).

    Yours,
    Ilya
    Ilya Zakharevich, Mar 13, 2005
    #15
  16. Ilya Zakharevich

    paul Guest

    Re: Chrominance noise vs luminance one

    Ilya Zakharevich wrote:
    >
    >>>>Judge for yourself: visit

    >
    >
    >>>> http://ilyaz.org/photo/random-noise

    >
    >
    > ...Luminance is calculatable from Luma only very close to neutral
    > gray; thus having a skin-tone with luma-less noise may have
    > significant luminance noise.
    >
    > One needs to experiment with both constant-luma noise and
    > constant-luminance noise, and see which one is less perceivable by
    > eye. Summary: one may need also to modify the vector 0.2126 0.7152
    > 0.0722 to take into account gamma (via derivatives of x^2.2 at R'G'B'
    > values of skin tone).




    Any chance of an executive summary of this study. I just cannot see what
    the exercise is all about.

    The photoshop RAW converter has color (chrominance) & regular
    (luminance) noise reduction & I noticed the color noise reduction does
    almost nothing. It seems you are saying color noise is indeed
    insubstantial in comparison but maybe I'm missing the boat on that?

    thanks!
    paul, Mar 13, 2005
    #16
  17. Re: Chrominance noise vs luminance one

    Ilya Zakharevich wrote:
    > [A complimentary Cc of this posting was NOT [per weedlist] sent to
    > Ilya Zakharevich
    > <>], who wrote in article
    > <d0vkf9$1io5$>:
    >>>> Judge for yourself: visit

    >
    >>>> http://ilyaz.org/photo/random-noise

    >
    >>> Grey is one colour to test this on - what about a more sensitive
    >>> colour like skin-tones?

    >
    >> The script is there. Feel free to edit it to change the base value.
    >> Or just modify the .png by adding a constant bias...

    >
    > Actually, it may be a little bit more than just changing the base
    > value. Luminance is calculatable from Luma only very close to neutral
    > gray; thus having a skin-tone with luma-less noise may have
    > significant luminance noise.
    >
    > One needs to experiment with both constant-luma noise and
    > constant-luminance noise, and see which one is less perceivable by
    > eye. Summary: one may need also to modify the vector 0.2126 0.7152
    > 0.0722 to take into account gamma (via derivatives of x^2.2 at R'G'B'
    > values of skin tone).
    >
    > Yours,
    > Ilya


    Thanks, Ilya. I don't have the time to do detailed work on this right
    now, but at least I hope it triggers /someone/ to check this out. Your
    comments about the gamma remind me of the "constant luminance failure"
    errors in colour TV - takes me back a long time.

    http://www.poynton.com/notes/video/Constant_luminance.html

    Cheers,
    David
    David J Taylor, Mar 13, 2005
    #17
  18. Re: Chrominance noise vs luminance one

    [A complimentary Cc of this posting was sent to
    paul
    <>], who wrote in article <>:
    > >>>>Judge for yourself: visit


    > >>>> http://ilyaz.org/photo/random-noise


    > Any chance of an executive summary of this study. I just cannot see what
    > the exercise is all about.


    Did you see the pictures on the URL above?

    > The photoshop RAW converter has color (chrominance) & regular
    > (luminance) noise reduction & I noticed the color noise reduction does
    > almost nothing. It seems you are saying color noise is indeed
    > insubstantial in comparison but maybe I'm missing the boat on that?


    How I see the pictures, the eye sensitivity for chrominance noise is
    not much higher than 10% of sensitivity for luminance one. [But my
    eyes are kinda special, so I would appreciate if somebody else - with
    normal vision - confirms this.]

    Yours,
    Ilya
    Ilya Zakharevich, Mar 13, 2005
    #18
  19. Ilya Zakharevich

    paul Guest

    Re: Chrominance noise vs luminance one

    Ilya Zakharevich wrote:
    > [A complimentary Cc of this posting was sent to
    > paul
    > <>], who wrote in article <>:
    >
    >>>>>>Judge for yourself: visit

    >
    >
    >>>>>>http://ilyaz.org/photo/random-noise

    >
    >
    >>Any chance of an executive summary of this study. I just cannot see what
    >>the exercise is all about.

    >
    >
    > Did you see the pictures on the URL above?
    >
    >
    >>The photoshop RAW converter has color (chrominance) & regular
    >>(luminance) noise reduction & I noticed the color noise reduction does
    >>almost nothing. It seems you are saying color noise is indeed
    >>insubstantial in comparison but maybe I'm missing the boat on that?

    >
    >
    > How I see the pictures, the eye sensitivity for chrominance noise is
    > not much higher than 10% of sensitivity for luminance one. [But my
    > eyes are kinda special, so I would appreciate if somebody else - with
    > normal vision - confirms this.]



    So that's equal noise on left & right? No doubt the left looks 90% more
    noisy. I suppose if I zoomed way in, I could see the color noise.
    paul, Mar 13, 2005
    #19
  20. Ilya Zakharevich

    HvdV Guest

    Re: Rescaling the lense

    Hi Ilya,
    > [A complimentary Cc of this posting was sent to
    > HvdV
    > <>], who wrote in article <7ac8b$4232019c$3e3aaa83$>:

    Substitute 'hans' for 'nohanz', sorry for the paranoia.

    >>In any decent photographic system the most important component
    >>of performance/price ratio is the lenses. Since the price of the
    >>lens scales as 4th or 5th power of its linear size, decreasing
    >>the size of the sensor (while keeping S/N ratio) may lead to
    >>very significant improvements of performance/price.
    >>---
    >>with some examples?
    >>The tradeoff of lens aperture and expense vs sensor size determines
    >>ultimately the size and shape of the digital camera. After the 'fashion
    >>factor' of course.

    >
    >
    > a) First of all, my assumption on how rescaling the lense affects
    > image quality was "incomplete" (read: wrong ;-). Part of fuzziness
    > due to difraction does not change; but part of fuzziness due to
    > optical imperfection scales up with the lense linear size (since
    > all the light rays passing through the system scale up, the spot in
    > the focal plane which is the diffraction-less image of a
    > point-source will scale up as well).
    >
    > This has two effects: sweet spot (in F-stops) scales up (i.e., to
    > the worse) as sqrt(size); and best resolution scales down as
    > 1/sqrt(size). So my estimates for "perfect lense" for an ideal
    > 36x24mm sensor were wrong, since I erroneously assumed that the
    > sweet spot does not change.

    Hm, not so sure you were very wrong. I don't know much about lens design, but
    I do know errors like spherical aberration scale up in a non-linear fashion
    if you increase aperture. And that's only one of the many errors.
    Then there are amplifying econimical factors like a much smaller lens copy
    number.
    BTW, if you keep aperture constant the diffraction spot stays the same. It
    scales with the wavelength, the sine of the half-aperture angle, and for
    completeness, also the refractive index of the medium.
    >
    > b) One corollary is that when you scale sensor size AND LENSE up n
    > times, it makes sense to scale up the size of the pixel sqrt(n)
    > times. In other words, you should increase the sensitivity of the
    > sensor and number of pixels both the same amount - n times.
    > Interesting...

    Sizing up the lens and sensor gets you more information about the object,
    with the square of the scale. You can average that information with bigger
    pixels to get a better SNR, but you could do that also in postprocessing.
    >
    > c) The estimages on price vs. size: IIRC, this was from a review in a
    > technical magazine on optical production ("Scientific publications
    > of LOMO" or some such) in end of 80s. Since technology could have
    > changed meanwhile (digitally-controlled machinery?), the numbers
    > could have changed...

    It's clear that it is cheaper now to make aspherical lenses, and there are
    also new glasses available.
    I was hoping for a plot with a lenses with similar view angles in it with on
    the horizontal axis the formats and vertically the price. I guess it should
    be possible to dig this out of ebay..

    -- Hans
    HvdV, Mar 13, 2005
    #20
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