The f/ratio myth and camera size

Discussion in 'Digital Photography' started by Roger N. Clark (change username to rnclark), Feb 5, 2006.

  1. There are often questions about smaller versus larger pixels
    and the corresponding camera size. Many of us would like smaller
    cameras that did just as good a job as larger ones. Is that
    possible? No, at least in terms of signal-to-noise that can
    be recorded. Here is why.

    There is a common idea in photography that exposure doesn't
    change between different size cameras when at the same f/ratio.
    For example, the sunny f/16 rule says a good exposure for a daylight
    scene is 1/ISO at f/16. Thus for ISO 100 film, you use a 1/100
    second exposure on an 8x10 camera at f/16, a 4x5 camera at f/16,
    a 35mm camera at f/16, an APS-C digital camera at f/16, down to the
    smallest point and shoot camera at f/16 (assuming the small camera
    goes to f/16). This leads people to think cameras scale
    easily and still give the same image. But there is a fallacy
    in this idea, and that is spatial resolution on the subject.
    The smaller camera, even at the same f/ratio, has a smaller lens
    which collects a smaller number of photons per unit time.
    The smaller camera gets the same exposure time because the UNIT
    AREA in the focal plane represents a larger angular size on the
    subject.

    The rate of arrival of photons in the focal plane of a lens
    per unit area per unit time is proportional to the square of
    the f-ratio. Corollary: if you keep f/ratio constant, and change
    focal length then the photons per unit area in the focal plane is
    constant but spatial resolution changes.

    So how does this apply to making smaller cameras?

    The problem is that if you scale a camera down, say 2x, the
    aperture drops by 2x, the focal length drops by 2x (to give the
    same field of view), the sensor size drops by 2x, and the pixel
    size drops by 2x (to give the same spatial resolution
    on the subject). It should be obvious by this point
    that per unit time the aperture has collected only
    1/4 the number of photons. Also, the smaller pixels each
    collect 1/4 less photons since their area is
    divided by 4 to keep spatial resolution constant.

    Another way to look at the problem is aperture collects light, the
    focal length spreads out the light, and the pixels are buckets that
    collect the light in the focal plane. BUT THE TOTAL NUMBER OF PHOTONS
    DELIVERED TO THE FOCAL PLANE IS ONLY DEPENDENT ON APERTURE
    (ignoring transmission losses of the optics).

    Back to the camera example: scale a camera down by 2x keeping
    f/ratio and spatial resolution constant. You lose 4x the
    photons entering the lens with the smaller camera, and since you
    you must use 2x smaller pixels, the area is 4x less, so you LOSE
    ANOTHER 4x photons/pixel. Thus, photons delivered to a pixel for a
    given resolution on the subject goes as the 4th power of the
    aperture (and camera size)! Decreasing your camera by 2x
    means 16x less photons per pixel if you want to maintain field of
    view and megapixel count!

    This is just what we observe with small cameras: their
    smaller sensors have smaller full well capacities, that get filled
    for a given exposure time with a smaller number of photons.
    That in turn means higher noise because there are fewer
    photons.

    Check out this web page for more info on this subject:
    http://home.earthlink.net/~stanleymm/f_ratio_myth.htm

    Roger Clark
    Photos, other digital info at: http://www.clarkvision.com
     
    Roger N. Clark (change username to rnclark), Feb 5, 2006
    #1
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  2. Roger N. Clark (change username to rnclark)

    Rich Guest

    Higher noise under what conditions? If the shot has a sufficient
    illumination level
    and the ISO setting on the camera is low enough, you should see no more
    noise
    from most small pixel cameras than from a large pixel camera. However,
    this only
    applies to scenes with relatively small illumination "spreads." If
    there are
    deep shadows (essentially, underexposed areas) then they will
    demonstrate
    noise to some extent. The question is, what pixel size is needed to
    keep noise
    relatively unnoticeable in shots with wide illumination ranges?
    My guess is that no current camera can produce a completely noise free
    image when all
    areas are taken into account, because none of them have the pixel well
    capacity and
    dynamic range to handle scenes with wide-ranging illumination levels.
    This is especially true when people insist on underexposing areas in
    order to "control" highlights in other areas. When they manipulate the
    curves of the image to bring out
    detail in the underexposed areas, those areas display noise, lack of
    contrast, depressed colour values and restricted tonal ranges.
    -Rich
     
    Rich, Feb 5, 2006
    #2
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  3. Rich wrote:
    > Higher noise under what conditions?


    All conditions comparable between large and small cameras.
    If you have X photons with big camera A for a given f/stop
    and exposure time (e.g. 1/400 second at f/8), then on a
    small camera B for the same exposure and f/stop, you get
    less photons per pixel. Signal to noise ratio is the square
    root of the number of photons collected. The smaller camera
    collects less photons so has worse signal to noise.
    You might expose longer but smaller pixels have less capacity to
    store electrons (converted photons) so the smaller camera simply
    can never make up the difference.

    > If the shot has a sufficient
    > illumination level
    > and the ISO setting on the camera is low enough, you should see no more
    > noise
    > from most small pixel cameras than from a large pixel camera.


    No. See above.

    > However, this only
    > applies to scenes with relatively small illumination "spreads." If
    > there are
    > deep shadows (essentially, underexposed areas) then they will
    > demonstrate
    > noise to some extent.


    It has nothing to do with illumination spread. Because less
    photons are collected by the small camera, the dynamic range
    is less too.

    > The question is, what pixel size is needed to
    > keep noise
    > relatively unnoticeable in shots with wide illumination ranges?


    That is a subjective question with a variable answer, depending
    on the scene dynamic range and what is acceptable to the user.
    The fact is that we have many many wonderful photographs from
    film which has lower signal to noise than many point and shoot
    digital cameras, and on slide film with very narrow dynamic range.
    So P&S can still take great photos and in the hands of good
    photographers, many great images can be obtained. But a larger
    camera can generally do better, just like 35mm versus 4x5 film.

    > My guess is that no current camera can produce a completely noise free
    > image when all
    > areas are taken into account, because none of them have the pixel well
    > capacity and
    > dynamic range to handle scenes with wide-ranging illumination levels.


    To get noise free, you need infinite photons, which is not possible.
    But tens of thousands of photons per pixel makes very high
    signal to noise images. The sweet spot in my opinion, are
    cameras with 6 to 9 micron pixels. There is no reason a small P&S
    camera could not have 8 micron size pixels with a pixel count
    over 8 million.

    Roger
     
    Roger N. Clark (change username to rnclark), Feb 6, 2006
    #3
  4. Roger N. Clark (change username to rnclark)

    Scott W Guest

    Roger N. Clark (change username to rnclark) wrote:
    > There are often questions about smaller versus larger pixels
    > and the corresponding camera size. Many of us would like smaller
    > cameras that did just as good a job as larger ones. Is that
    > possible? No, at least in terms of signal-to-noise that can
    > be recorded. Here is why.
    >
    > There is a common idea in photography that exposure doesn't
    > change between different size cameras when at the same f/ratio.
    > For example, the sunny f/16 rule says a good exposure for a daylight
    > scene is 1/ISO at f/16. Thus for ISO 100 film, you use a 1/100
    > second exposure on an 8x10 camera at f/16, a 4x5 camera at f/16,
    > a 35mm camera at f/16, an APS-C digital camera at f/16, down to the
    > smallest point and shoot camera at f/16 (assuming the small camera
    > goes to f/16). This leads people to think cameras scale
    > easily and still give the same image. But there is a fallacy
    > in this idea, and that is spatial resolution on the subject.
    > The smaller camera, even at the same f/ratio, has a smaller lens
    > which collects a smaller number of photons per unit time.
    > The smaller camera gets the same exposure time because the UNIT
    > AREA in the focal plane represents a larger angular size on the
    > subject.
    >
    > The rate of arrival of photons in the focal plane of a lens
    > per unit area per unit time is proportional to the square of
    > the f-ratio. Corollary: if you keep f/ratio constant, and change
    > focal length then the photons per unit area in the focal plane is
    > constant but spatial resolution changes.
    >
    > So how does this apply to making smaller cameras?
    >
    > The problem is that if you scale a camera down, say 2x, the
    > aperture drops by 2x, the focal length drops by 2x (to give the
    > same field of view), the sensor size drops by 2x, and the pixel
    > size drops by 2x (to give the same spatial resolution
    > on the subject). It should be obvious by this point
    > that per unit time the aperture has collected only
    > 1/4 the number of photons. Also, the smaller pixels each
    > collect 1/4 less photons since their area is
    > divided by 4 to keep spatial resolution constant.
    >
    > Another way to look at the problem is aperture collects light, the
    > focal length spreads out the light, and the pixels are buckets that
    > collect the light in the focal plane. BUT THE TOTAL NUMBER OF PHOTONS
    > DELIVERED TO THE FOCAL PLANE IS ONLY DEPENDENT ON APERTURE
    > (ignoring transmission losses of the optics).
    >
    > Back to the camera example: scale a camera down by 2x keeping
    > f/ratio and spatial resolution constant. You lose 4x the
    > photons entering the lens with the smaller camera, and since you
    > you must use 2x smaller pixels, the area is 4x less, so you LOSE
    > ANOTHER 4x photons/pixel. Thus, photons delivered to a pixel for a
    > given resolution on the subject goes as the 4th power of the
    > aperture (and camera size)! Decreasing your camera by 2x
    > means 16x less photons per pixel if you want to maintain field of
    > view and megapixel count!

    I believe you are off on this one. For the same f/number the photon
    flux at the sensor is the same. Take your case of scaling down a
    camera by a factor of two, the lens collects 1/4 the photons but it
    also spreads these photons out over 1/4the area that the larger camera
    does. The number of photons per sensor is therefor scales as the area
    of the sensor. So I believe you are looking at a 2nd power decrease
    not 4th.

    Scott
     
    Scott W, Feb 6, 2006
    #4
  5. Scott W wrote:
    > Roger N. Clark (change username to rnclark) wrote:
    >
    >>There are often questions about smaller versus larger pixels
    >>and the corresponding camera size. Many of us would like smaller
    >>cameras that did just as good a job as larger ones. Is that
    >>possible? No, at least in terms of signal-to-noise that can
    >>be recorded. Here is why.
    >>
    >>There is a common idea in photography that exposure doesn't
    >>change between different size cameras when at the same f/ratio.
    >>For example, the sunny f/16 rule says a good exposure for a daylight
    >>scene is 1/ISO at f/16. Thus for ISO 100 film, you use a 1/100
    >>second exposure on an 8x10 camera at f/16, a 4x5 camera at f/16,
    >>a 35mm camera at f/16, an APS-C digital camera at f/16, down to the
    >>smallest point and shoot camera at f/16 (assuming the small camera
    >>goes to f/16). This leads people to think cameras scale
    >>easily and still give the same image. But there is a fallacy
    >>in this idea, and that is spatial resolution on the subject.
    >>The smaller camera, even at the same f/ratio, has a smaller lens
    >>which collects a smaller number of photons per unit time.
    >>The smaller camera gets the same exposure time because the UNIT
    >>AREA in the focal plane represents a larger angular size on the
    >>subject.
    >>
    >>The rate of arrival of photons in the focal plane of a lens
    >>per unit area per unit time is proportional to the square of
    >>the f-ratio. Corollary: if you keep f/ratio constant, and change
    >>focal length then the photons per unit area in the focal plane is
    >>constant but spatial resolution changes.
    >>
    >>So how does this apply to making smaller cameras?
    >>
    >>The problem is that if you scale a camera down, say 2x, the
    >>aperture drops by 2x, the focal length drops by 2x (to give the
    >>same field of view), the sensor size drops by 2x, and the pixel
    >>size drops by 2x (to give the same spatial resolution
    >>on the subject). It should be obvious by this point
    >>that per unit time the aperture has collected only
    >>1/4 the number of photons. Also, the smaller pixels each
    >>collect 1/4 less photons since their area is
    >>divided by 4 to keep spatial resolution constant.
    >>
    >>Another way to look at the problem is aperture collects light, the
    >>focal length spreads out the light, and the pixels are buckets that
    >>collect the light in the focal plane. BUT THE TOTAL NUMBER OF PHOTONS
    >>DELIVERED TO THE FOCAL PLANE IS ONLY DEPENDENT ON APERTURE
    >>(ignoring transmission losses of the optics).
    >>
    >>Back to the camera example: scale a camera down by 2x keeping
    >>f/ratio and spatial resolution constant. You lose 4x the
    >>photons entering the lens with the smaller camera, and since you
    >>you must use 2x smaller pixels, the area is 4x less, so you LOSE
    >>ANOTHER 4x photons/pixel. Thus, photons delivered to a pixel for a
    >>given resolution on the subject goes as the 4th power of the
    >>aperture (and camera size)! Decreasing your camera by 2x
    >>means 16x less photons per pixel if you want to maintain field of
    >>view and megapixel count!

    >
    > I believe you are off on this one. For the same f/number the photon
    > flux at the sensor is the same. Take your case of scaling down a
    > camera by a factor of two, the lens collects 1/4 the photons but it
    > also spreads these photons out over 1/4the area that the larger camera
    > does. The number of photons per sensor is therefor scales as the area
    > of the sensor. So I believe you are looking at a 2nd power decrease
    > not 4th.
    >
    > Scott
    >

    Scott,
    You are correct. I forgot to include that for the smaller lens
    at half the focal length, the area on the subject doubles, canceling
    one of the squared terms. So, yes, I agree that the relation
    scales as the square not as the 4th power.

    So halving the camera size means pixels get 1/4 the photons.
    A good example is the Canon 20D with 6.4 micron pixels and a
    maximum signal at ISO 100 of 50,000 electrons, compared to
    the Canon S60 with 2.8 micron pixels with a maximum signal
    of about 11,000 electrons at ISO 100. The pixel size is
    6.4^2 / 2.8^2 = 5.2x scaling, similar to the 50000/11000
    = 4.5 scaling of maximum recorded signal.

    Then, for photon noise limited systems, signal-to-noise ratio
    scales as the square root of the camera size.

    Roger
     
    Roger N. Clark (change username to rnclark), Feb 6, 2006
    #5
  6. Roger N. Clark (change username to rnclark)

    Hunt Guest

    In article <>, says...


    [SNIP]
    >
    >Roger Clark
    >Photos, other digital info at: http://www.clarkvision.com


    Without getting into photons/nanosecond striking the recording medium, I'll
    give you a very rough set of observations in doing studio shooting over 30
    years for the advertising industry.

    Shot is set up for 4x5 and all is dialed in to, say f/16 on E-100 4x5.
    Polaroids look good, and the E-6 confirms that all is excellent. Client
    decides that 8x10 is needed, instead. Same lights, same power settings, same
    film, but in 8x10. Whoa, it now looks like f/11 is the aperture that is
    required, and the E-6 processing confirms it. Bellows factors? No, this is not
    a macro shot. Finally, the client wants some 35mm, and with the same lighting
    -dang, we're now shooting at f/22! Again, the E-6 line shows that this is
    correct. I've seen it too many times. The exposures are approximate, and
    sometimes the differences were in 2/3 /f, and not full /f-stops, but it was
    closer to 1 per camera size difference. Six x six CM was always between 4x5
    and 35mm.

    Hunt
     
    Hunt, Feb 6, 2006
    #6
  7. Roger N. Clark (change username to rnclark)

    Scott W Guest

    Roger N. Clark (change username to rnclark) wrote:
    > Scott W wrote:
    > > Roger N. Clark (change username to rnclark) wrote:
    > >
    > >>There are often questions about smaller versus larger pixels
    > >>and the corresponding camera size. Many of us would like smaller
    > >>cameras that did just as good a job as larger ones. Is that
    > >>possible? No, at least in terms of signal-to-noise that can
    > >>be recorded. Here is why.
    > >>
    > >>There is a common idea in photography that exposure doesn't
    > >>change between different size cameras when at the same f/ratio.
    > >>For example, the sunny f/16 rule says a good exposure for a daylight
    > >>scene is 1/ISO at f/16. Thus for ISO 100 film, you use a 1/100
    > >>second exposure on an 8x10 camera at f/16, a 4x5 camera at f/16,
    > >>a 35mm camera at f/16, an APS-C digital camera at f/16, down to the
    > >>smallest point and shoot camera at f/16 (assuming the small camera
    > >>goes to f/16). This leads people to think cameras scale
    > >>easily and still give the same image. But there is a fallacy
    > >>in this idea, and that is spatial resolution on the subject.
    > >>The smaller camera, even at the same f/ratio, has a smaller lens
    > >>which collects a smaller number of photons per unit time.
    > >>The smaller camera gets the same exposure time because the UNIT
    > >>AREA in the focal plane represents a larger angular size on the
    > >>subject.
    > >>
    > >>The rate of arrival of photons in the focal plane of a lens
    > >>per unit area per unit time is proportional to the square of
    > >>the f-ratio. Corollary: if you keep f/ratio constant, and change
    > >>focal length then the photons per unit area in the focal plane is
    > >>constant but spatial resolution changes.
    > >>
    > >>So how does this apply to making smaller cameras?
    > >>
    > >>The problem is that if you scale a camera down, say 2x, the
    > >>aperture drops by 2x, the focal length drops by 2x (to give the
    > >>same field of view), the sensor size drops by 2x, and the pixel
    > >>size drops by 2x (to give the same spatial resolution
    > >>on the subject). It should be obvious by this point
    > >>that per unit time the aperture has collected only
    > >>1/4 the number of photons. Also, the smaller pixels each
    > >>collect 1/4 less photons since their area is
    > >>divided by 4 to keep spatial resolution constant.
    > >>
    > >>Another way to look at the problem is aperture collects light, the
    > >>focal length spreads out the light, and the pixels are buckets that
    > >>collect the light in the focal plane. BUT THE TOTAL NUMBER OF PHOTONS
    > >>DELIVERED TO THE FOCAL PLANE IS ONLY DEPENDENT ON APERTURE
    > >>(ignoring transmission losses of the optics).
    > >>
    > >>Back to the camera example: scale a camera down by 2x keeping
    > >>f/ratio and spatial resolution constant. You lose 4x the
    > >>photons entering the lens with the smaller camera, and since you
    > >>you must use 2x smaller pixels, the area is 4x less, so you LOSE
    > >>ANOTHER 4x photons/pixel. Thus, photons delivered to a pixel for a
    > >>given resolution on the subject goes as the 4th power of the
    > >>aperture (and camera size)! Decreasing your camera by 2x
    > >>means 16x less photons per pixel if you want to maintain field of
    > >>view and megapixel count!

    > >
    > > I believe you are off on this one. For the same f/number the photon
    > > flux at the sensor is the same. Take your case of scaling down a
    > > camera by a factor of two, the lens collects 1/4 the photons but it
    > > also spreads these photons out over 1/4the area that the larger camera
    > > does. The number of photons per sensor is therefor scales as the area
    > > of the sensor. So I believe you are looking at a 2nd power decrease
    > > not 4th.
    > >
    > > Scott
    > >

    > Scott,
    > You are correct. I forgot to include that for the smaller lens
    > at half the focal length, the area on the subject doubles, canceling
    > one of the squared terms. So, yes, I agree that the relation
    > scales as the square not as the 4th power.
    >
    > So halving the camera size means pixels get 1/4 the photons.
    > A good example is the Canon 20D with 6.4 micron pixels and a
    > maximum signal at ISO 100 of 50,000 electrons, compared to
    > the Canon S60 with 2.8 micron pixels with a maximum signal
    > of about 11,000 electrons at ISO 100. The pixel size is
    > 6.4^2 / 2.8^2 = 5.2x scaling, similar to the 50000/11000
    > = 4.5 scaling of maximum recorded signal.
    >
    > Then, for photon noise limited systems, signal-to-noise ratio
    > scales as the square root of the camera size.

    Would not the S/N ratio scale with the size of the camera. If I make
    pixels with twice the linear dimensions I get 4 time the photons but
    only 2 times the noise for a gain of 2 in S/N.

    Scott
     
    Scott W, Feb 6, 2006
    #7
  8. Roger N. Clark (change username to rnclark)

    Scott W Guest

    Roger N. Clark (change username to rnclark) wrote:
    > Scott W wrote:
    > > Roger N. Clark (change username to rnclark) wrote:
    > >
    > >>There are often questions about smaller versus larger pixels
    > >>and the corresponding camera size. Many of us would like smaller
    > >>cameras that did just as good a job as larger ones. Is that
    > >>possible? No, at least in terms of signal-to-noise that can
    > >>be recorded. Here is why.
    > >>
    > >>There is a common idea in photography that exposure doesn't
    > >>change between different size cameras when at the same f/ratio.
    > >>For example, the sunny f/16 rule says a good exposure for a daylight
    > >>scene is 1/ISO at f/16. Thus for ISO 100 film, you use a 1/100
    > >>second exposure on an 8x10 camera at f/16, a 4x5 camera at f/16,
    > >>a 35mm camera at f/16, an APS-C digital camera at f/16, down to the
    > >>smallest point and shoot camera at f/16 (assuming the small camera
    > >>goes to f/16). This leads people to think cameras scale
    > >>easily and still give the same image. But there is a fallacy
    > >>in this idea, and that is spatial resolution on the subject.
    > >>The smaller camera, even at the same f/ratio, has a smaller lens
    > >>which collects a smaller number of photons per unit time.
    > >>The smaller camera gets the same exposure time because the UNIT
    > >>AREA in the focal plane represents a larger angular size on the
    > >>subject.
    > >>
    > >>The rate of arrival of photons in the focal plane of a lens
    > >>per unit area per unit time is proportional to the square of
    > >>the f-ratio. Corollary: if you keep f/ratio constant, and change
    > >>focal length then the photons per unit area in the focal plane is
    > >>constant but spatial resolution changes.
    > >>
    > >>So how does this apply to making smaller cameras?
    > >>
    > >>The problem is that if you scale a camera down, say 2x, the
    > >>aperture drops by 2x, the focal length drops by 2x (to give the
    > >>same field of view), the sensor size drops by 2x, and the pixel
    > >>size drops by 2x (to give the same spatial resolution
    > >>on the subject). It should be obvious by this point
    > >>that per unit time the aperture has collected only
    > >>1/4 the number of photons. Also, the smaller pixels each
    > >>collect 1/4 less photons since their area is
    > >>divided by 4 to keep spatial resolution constant.
    > >>
    > >>Another way to look at the problem is aperture collects light, the
    > >>focal length spreads out the light, and the pixels are buckets that
    > >>collect the light in the focal plane. BUT THE TOTAL NUMBER OF PHOTONS
    > >>DELIVERED TO THE FOCAL PLANE IS ONLY DEPENDENT ON APERTURE
    > >>(ignoring transmission losses of the optics).
    > >>
    > >>Back to the camera example: scale a camera down by 2x keeping
    > >>f/ratio and spatial resolution constant. You lose 4x the
    > >>photons entering the lens with the smaller camera, and since you
    > >>you must use 2x smaller pixels, the area is 4x less, so you LOSE
    > >>ANOTHER 4x photons/pixel. Thus, photons delivered to a pixel for a
    > >>given resolution on the subject goes as the 4th power of the
    > >>aperture (and camera size)! Decreasing your camera by 2x
    > >>means 16x less photons per pixel if you want to maintain field of
    > >>view and megapixel count!

    > >
    > > I believe you are off on this one. For the same f/number the photon
    > > flux at the sensor is the same. Take your case of scaling down a
    > > camera by a factor of two, the lens collects 1/4 the photons but it
    > > also spreads these photons out over 1/4the area that the larger camera
    > > does. The number of photons per sensor is therefor scales as the area
    > > of the sensor. So I believe you are looking at a 2nd power decrease
    > > not 4th.
    > >
    > > Scott
    > >

    > Scott,
    > You are correct. I forgot to include that for the smaller lens
    > at half the focal length, the area on the subject doubles, canceling
    > one of the squared terms. So, yes, I agree that the relation
    > scales as the square not as the 4th power.
    >
    > So halving the camera size means pixels get 1/4 the photons.
    > A good example is the Canon 20D with 6.4 micron pixels and a
    > maximum signal at ISO 100 of 50,000 electrons, compared to
    > the Canon S60 with 2.8 micron pixels with a maximum signal
    > of about 11,000 electrons at ISO 100. The pixel size is
    > 6.4^2 / 2.8^2 = 5.2x scaling, similar to the 50000/11000
    > = 4.5 scaling of maximum recorded signal.
    >
    > Then, for photon noise limited systems, signal-to-noise ratio
    > scales as the square root of the camera size.

    Would not the S/N ratio scale with the size of the camera. If I make
    pixels with twice the linear dimensions I get 4 time the photons but
    only 2 times the noise for a gain of 2 in S/N.

    Scott
     
    Scott W, Feb 6, 2006
    #8
  9. Roger N. Clark (change username to rnclark)

    Ian Anderson Guest

    Hello Scott.

    I have an issue with the following statement.
    > also spreads these photons out over 1/4the area that the larger camera
    > does.

    Now I am not overly well versed in the compromises made in the design
    photographic optics, but I can tell you that in difraction limited
    astronomical optics the angular resolution increases ( diffraction disk
    diameter decreases) in proportion to the diameter of the objective. This
    means that if you double the objective (lens/mirror) diameter and maintain
    the f-ratio, the diffraction disk remains a constant size. I recognise
    that this is counter-intuitive but it is determined by wave diffraction
    theory.
    Do a Google on "f +ratio +diffraction +disk +size" and you will find that
    this subject is well covered, particulary in photographic terms. I only
    looked at this one and it seems to be quite useful.
    http://www.cambridgeincolour.com/tutorials/diffraction-photography.htm

    Regards
    Ian



    On Sun, 05 Feb 2006 18:49:15 -0800, Scott W wrote:

    > Roger N. Clark (change username to rnclark) wrote:
    >> There are often questions about smaller versus larger pixels
    >> and the corresponding camera size. Many of us would like smaller
    >> cameras that did just as good a job as larger ones. Is that
    >> possible? No, at least in terms of signal-to-noise that can
    >> be recorded. Here is why.
    >>
    >> There is a common idea in photography that exposure doesn't
    >> change between different size cameras when at the same f/ratio.
    >> For example, the sunny f/16 rule says a good exposure for a daylight
    >> scene is 1/ISO at f/16. Thus for ISO 100 film, you use a 1/100
    >> second exposure on an 8x10 camera at f/16, a 4x5 camera at f/16,
    >> a 35mm camera at f/16, an APS-C digital camera at f/16, down to the
    >> smallest point and shoot camera at f/16 (assuming the small camera
    >> goes to f/16). This leads people to think cameras scale
    >> easily and still give the same image. But there is a fallacy
    >> in this idea, and that is spatial resolution on the subject.
    >> The smaller camera, even at the same f/ratio, has a smaller lens
    >> which collects a smaller number of photons per unit time.
    >> The smaller camera gets the same exposure time because the UNIT
    >> AREA in the focal plane represents a larger angular size on the
    >> subject.
    >>
    >> The rate of arrival of photons in the focal plane of a lens
    >> per unit area per unit time is proportional to the square of
    >> the f-ratio. Corollary: if you keep f/ratio constant, and change
    >> focal length then the photons per unit area in the focal plane is
    >> constant but spatial resolution changes.
    >>
    >> So how does this apply to making smaller cameras?
    >>
    >> The problem is that if you scale a camera down, say 2x, the
    >> aperture drops by 2x, the focal length drops by 2x (to give the
    >> same field of view), the sensor size drops by 2x, and the pixel
    >> size drops by 2x (to give the same spatial resolution
    >> on the subject). It should be obvious by this point
    >> that per unit time the aperture has collected only
    >> 1/4 the number of photons. Also, the smaller pixels each
    >> collect 1/4 less photons since their area is
    >> divided by 4 to keep spatial resolution constant.
    >>
    >> Another way to look at the problem is aperture collects light, the
    >> focal length spreads out the light, and the pixels are buckets that
    >> collect the light in the focal plane. BUT THE TOTAL NUMBER OF PHOTONS
    >> DELIVERED TO THE FOCAL PLANE IS ONLY DEPENDENT ON APERTURE
    >> (ignoring transmission losses of the optics).
    >>
    >> Back to the camera example: scale a camera down by 2x keeping
    >> f/ratio and spatial resolution constant. You lose 4x the
    >> photons entering the lens with the smaller camera, and since you
    >> you must use 2x smaller pixels, the area is 4x less, so you LOSE
    >> ANOTHER 4x photons/pixel. Thus, photons delivered to a pixel for a
    >> given resolution on the subject goes as the 4th power of the
    >> aperture (and camera size)! Decreasing your camera by 2x
    >> means 16x less photons per pixel if you want to maintain field of
    >> view and megapixel count!

    > I believe you are off on this one. For the same f/number the photon
    > flux at the sensor is the same. Take your case of scaling down a
    > camera by a factor of two, the lens collects 1/4 the photons but it
    > also spreads these photons out over 1/4the area that the larger camera
    > does. The number of photons per sensor is therefor scales as the area
    > of the sensor. So I believe you are looking at a 2nd power decrease
    > not 4th.
    >
    > Scott
     
    Ian Anderson, Feb 6, 2006
    #9
  10. Scott W wrote:

    > Roger N. Clark (change username to rnclark) wrote:
    >
    >>Scott W wrote:
    >>
    >>>Roger N. Clark (change username to rnclark) wrote:
    >>>
    >>>
    >>>>There are often questions about smaller versus larger pixels
    >>>>and the corresponding camera size. Many of us would like smaller
    >>>>cameras that did just as good a job as larger ones. Is that
    >>>>possible? No, at least in terms of signal-to-noise that can
    >>>>be recorded. Here is why.
    >>>>
    >>>>There is a common idea in photography that exposure doesn't
    >>>>change between different size cameras when at the same f/ratio.
    >>>>For example, the sunny f/16 rule says a good exposure for a daylight
    >>>>scene is 1/ISO at f/16. Thus for ISO 100 film, you use a 1/100
    >>>>second exposure on an 8x10 camera at f/16, a 4x5 camera at f/16,
    >>>>a 35mm camera at f/16, an APS-C digital camera at f/16, down to the
    >>>>smallest point and shoot camera at f/16 (assuming the small camera
    >>>>goes to f/16). This leads people to think cameras scale
    >>>>easily and still give the same image. But there is a fallacy
    >>>>in this idea, and that is spatial resolution on the subject.
    >>>>The smaller camera, even at the same f/ratio, has a smaller lens
    >>>>which collects a smaller number of photons per unit time.
    >>>>The smaller camera gets the same exposure time because the UNIT
    >>>>AREA in the focal plane represents a larger angular size on the
    >>>>subject.
    >>>>
    >>>>The rate of arrival of photons in the focal plane of a lens
    >>>>per unit area per unit time is proportional to the square of
    >>>>the f-ratio. Corollary: if you keep f/ratio constant, and change
    >>>>focal length then the photons per unit area in the focal plane is
    >>>>constant but spatial resolution changes.
    >>>>
    >>>>So how does this apply to making smaller cameras?
    >>>>
    >>>>The problem is that if you scale a camera down, say 2x, the
    >>>>aperture drops by 2x, the focal length drops by 2x (to give the
    >>>>same field of view), the sensor size drops by 2x, and the pixel
    >>>>size drops by 2x (to give the same spatial resolution
    >>>>on the subject). It should be obvious by this point
    >>>>that per unit time the aperture has collected only
    >>>>1/4 the number of photons. Also, the smaller pixels each
    >>>>collect 1/4 less photons since their area is
    >>>>divided by 4 to keep spatial resolution constant.
    >>>>
    >>>>Another way to look at the problem is aperture collects light, the
    >>>>focal length spreads out the light, and the pixels are buckets that
    >>>>collect the light in the focal plane. BUT THE TOTAL NUMBER OF PHOTONS
    >>>>DELIVERED TO THE FOCAL PLANE IS ONLY DEPENDENT ON APERTURE
    >>>>(ignoring transmission losses of the optics).
    >>>>
    >>>>Back to the camera example: scale a camera down by 2x keeping
    >>>>f/ratio and spatial resolution constant. You lose 4x the
    >>>>photons entering the lens with the smaller camera, and since you
    >>>>you must use 2x smaller pixels, the area is 4x less, so you LOSE
    >>>>ANOTHER 4x photons/pixel. Thus, photons delivered to a pixel for a
    >>>>given resolution on the subject goes as the 4th power of the
    >>>>aperture (and camera size)! Decreasing your camera by 2x
    >>>>means 16x less photons per pixel if you want to maintain field of
    >>>>view and megapixel count!
    >>>
    >>>I believe you are off on this one. For the same f/number the photon
    >>>flux at the sensor is the same. Take your case of scaling down a
    >>>camera by a factor of two, the lens collects 1/4 the photons but it
    >>>also spreads these photons out over 1/4the area that the larger camera
    >>>does. The number of photons per sensor is therefor scales as the area
    >>>of the sensor. So I believe you are looking at a 2nd power decrease
    >>>not 4th.
    >>>
    >>>Scott
    >>>

    >>
    >>Scott,
    >>You are correct. I forgot to include that for the smaller lens
    >>at half the focal length, the area on the subject doubles, canceling
    >>one of the squared terms. So, yes, I agree that the relation
    >>scales as the square not as the 4th power.
    >>
    >>So halving the camera size means pixels get 1/4 the photons.
    >>A good example is the Canon 20D with 6.4 micron pixels and a
    >>maximum signal at ISO 100 of 50,000 electrons, compared to
    >>the Canon S60 with 2.8 micron pixels with a maximum signal
    >>of about 11,000 electrons at ISO 100. The pixel size is
    >>6.4^2 / 2.8^2 = 5.2x scaling, similar to the 50000/11000
    >>= 4.5 scaling of maximum recorded signal.
    >>
    >>Then, for photon noise limited systems, signal-to-noise ratio
    >>scales as the square root of the camera size.

    >
    > Would not the S/N ratio scale with the size of the camera. If I make
    > pixels with twice the linear dimensions I get 4 time the photons but
    > only 2 times the noise for a gain of 2 in S/N.
    >
    > Scott
    >

    Scott,
    I think you have clearly demonstrated that I should not do
    math and watch the superbowl at the same time ;-).
    Yes, you are correct.

    Roger
     
    Roger N. Clark (change username to rnclark), Feb 6, 2006
    #10
  11. "Ian Anderson" <> wrote:
    > Now I am not overly well versed in the compromises made in the design
    > photographic optics, but I can tell you that in difraction limited
    > astronomical optics the angular resolution increases ( diffraction disk
    > diameter decreases) in proportion to the diameter of the objective.


    Yes. But that's irreleveant here. The 50% MTF diffraction term is roughly
    800/(f number) in pictorial imaging, and the resolution of the sensors in
    dSLRs runs from 40 (60) (5D) to 60 (90) (D2x). (Numbers in parens are the
    Nyquist frequency, regular numbers are the practical limit of these sensors.

    So if you plug in some numbers here, you find that the sensors are the main
    limitation at f/16 or f/11 and wider. (Consumer dcams usually need to be
    shot at exactly f/5.6 for optimal resolution.)

    David J. Littleboy
    Tokyo, Japan
     
    David J. Littleboy, Feb 6, 2006
    #11
  12. Roger N. Clark (change username to rnclark)

    bmoag Guest

    Dear Dinosaurs:
    Once upon a time film speeds of 10 were considered impossible, let alone
    color reproduction.
    A little knowledge is a dangerous thing, particularly if you think you know
    what cannot be done.
     
    bmoag, Feb 6, 2006
    #12
  13. Roger N. Clark (change username to rnclark)

    Bruce Murphy Guest

    "bmoag" <> writes:

    > Dear Dinosaurs:
    > Once upon a time film speeds of 10 were considered impossible, let alone
    > color reproduction.
    > A little knowledge is a dangerous thing, particularly if you think you know
    > what cannot be done.


    I realise that you probably don't believe in photons, or quantum
    mechanics, or probably even dinosaurs, but you really should learn a
    little physics before spouting off.

    B>
     
    Bruce Murphy, Feb 6, 2006
    #13
  14. Roger N. Clark (change username to rnclark)

    Stacey Guest

    Roger N. Clark (change username to rnclark) wrote:

    >>

    > Scott,
    > You are correct. I forgot to include that for the smaller lens
    > at half the focal length,


    And you're still sure there is nothing else you forgot or left out of your
    "theory" ?

    --

    Stacey
     
    Stacey, Feb 6, 2006
    #14
  15. Roger N. Clark (change username to rnclark)

    Stacey Guest

    bmoag wrote:

    > Dear Dinosaurs:
    > Once upon a time film speeds of 10 were considered impossible, let alone
    > color reproduction.


    Exactly

    > A little knowledge is a dangerous thing, particularly if you think you
    > know what cannot be done.


    Very dangerous when they create a website like it's the last word yet are
    still making errors in the math years into their "theory"..

    --

    Stacey
     
    Stacey, Feb 6, 2006
    #15
  16. Stacey wrote:

    > Very dangerous when they create a website like it's the last word yet are
    > still making errors in the math years into their "theory"..


    At least most of us acknowledge our mistakes, learn from
    them and move on.
     
    Roger N. Clark (change username to rnclark), Feb 6, 2006
    #16
  17. Roger N. Clark (change username to rnclark)

    Skip M Guest

    Skip M, Feb 6, 2006
    #17
  18. Roger N. Clark (change username to rnclark)

    Mark² Guest

    Stacey wrote:
    > bmoag wrote:
    >
    >> Dear Dinosaurs:
    >> Once upon a time film speeds of 10 were considered impossible, let
    >> alone color reproduction.

    >
    > Exactly
    >
    >> A little knowledge is a dangerous thing, particularly if you think
    >> you know what cannot be done.

    >
    > Very dangerous when they create a website like it's the last word yet
    > are still making errors in the math years into their "theory"..


    No.
    It's only dangerous when they refuse to acknowledge mistakes and correct
    them.
    Roger has done both.
     
    Mark², Feb 6, 2006
    #18
  19. Roger N. Clark (change username to rnclark)

    Mark² Guest

    Skip M wrote:
    > I think I have a headache...


    Me too.
    -So glad you don't have to master the above to shoot a nice photo...
    :)
    OTOH...Those nice cameras and other gismos are possible because of those who
    can.


    -Double :) :)
     
    Mark², Feb 6, 2006
    #19
  20. Roger N. Clark (change username to rnclark)

    Neil Ellwood Guest

    On Sun, 05 Feb 2006 22:28:50 -0800, Skip M wrote:

    > I think I have a headache...

    That is from reading pseudo-scientific babble. He has misread a lot of
    literature. When you scale down you have to scale everything down.

    --
    Neil
    Delete l to reply
     
    Neil Ellwood, Feb 6, 2006
    #20
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