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Thread: Do digital sensors have an MTF?

  1. #1
    xpatUSA's Avatar
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    Do digital sensors have an MTF?

    Talking only about the sensor itself and how it would respond to perfect light patterns right there at the sensor face. Talking about spatial pattern frequencies of less than the limit du jour, e.g. Nyquist et al. Not talking about lenses, apertures, Airy discs, CoC's, etc, etc.

    Consider a pattern with black/white line pairs at 2 pixels per pair, perfectly aligned with the pixels of course. Is the resulting contrast 100% e.g. a MTF of 1? Or is it less and, if so, why?

    Ted

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    Re: Do digital sensors have an MTF?

    If no lens system is involved then the MTF should be 1. Can see no reason why it should be otherwise. It's all rather academic though and a little bit meaningless in everyday photography!

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    xpatUSA's Avatar
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    Re: Do digital sensors have an MTF?

    Quote Originally Posted by Marty View Post
    If no lens system is involved then the MTF should be 1. Can see no reason why it should be otherwise. It's all rather academic though and a little bit meaningless in everyday photography!
    Thanks Marty but, sadly, I do mainly table-top macro work and am suffering a current compulsion to know everything about image resolution .

    To answer my own post, it turns out that even a "hard" final image does not actually have an MTF of 1 or 100% according to this gentleman at LumoLabs, see http://www.falklumo.com/lumolabs/articles/sharpness/ and scroll down to Section 1.2.1. He reckons an MTF of about 0.64 at the Nyquist limit of 0.5 cycles/pixel.

    His following Sections (1.2.2 etc), although well-written and interesting, introduce post-processing and the use of lenses and so are not relevant to this post.

    So, a digital sensor does have an MTF by virtue of fact that it is a discrete sampling device.

    best regards,

    Ted
    Last edited by xpatUSA; 29th February 2012 at 02:36 PM. Reason: getting old . . .

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    Marty's Avatar
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    Re: Do digital sensors have an MTF?

    Hi Ted,
    You know, after I posted my initial reply, I spent the whole afternoon pondering your question... After one of those awful brain-teasing sessions in which one goes through all kinds of mathematical hoops, to prove something ridiculous such as 1=1.... I finally decided that it was perhaps a bit fanciful to expect an MTF of the full 100%.

    I'm rather shocked though to read that the true figure is as low as 64% !!! I'm very surprised at that. I will take time to read the article at the link you've provided here and no doubt that will finish my poor brain off for the day!

    Thanks for the info.

    marty

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    xpatUSA's Avatar
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    Re: Do digital sensors have an MTF?

    Quote Originally Posted by Marty View Post
    Hi Ted,

    I'm rather shocked though to read that the true figure is as low as 64% !!! I'm very surprised at that.
    I guess it's all relative, though, because the quoted 64% is at the Nyquist limit of the sensor so, from the point of view of lenses for example, it's a pretty good value. On my camera (Foveon sensor, 9um pixel pitch) that would be a contrast of 64% at 55 line pairs/mm (at the sensor) but, in practice, less than 10% would be more likely when taking a real shot through a lens.

    best regards,

    Ted
    Last edited by xpatUSA; 29th February 2012 at 04:06 PM. Reason: corrected lines/mm to pairs

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    Steaphany's Avatar
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    Re: Do digital sensors have an MTF?

    Reading this thread, the 64% looked familiar, so I opened up an Open Office spread sheet and did a couple quick calculations. First was a Monte Carlo model of the area under a half cycle, 0 to Pi, of a Sine curve and with 2500 samples, I calculated 64%. Then I simply did a numerical integration of a half cycle, 0 to Pi, of a Sine curve and, with 2000 samples, plain as day I also got 64%.

    What you both need to remember is that optical MTF values and performance measurements are made with a continuously swept sine wave which by definition limits the maximum possible contrast to 64%, actually 63.66%. The only way you can achieve greater would be by employing a step or square wave function, where the transitions between white and black go immediately from 1.000 to 0.000, of course Normalized.

    As another Foveon shooter, with a Sigma SD14, I did plenty of number crunching to understand the sensor's performance.
    Last edited by Steaphany; 29th February 2012 at 07:03 PM. Reason: Typo

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    Re: Do digital sensors have an MTF?

    My circle of confusion just exploded

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    Re: Do digital sensors have an MTF?

    To get an contrast of 100%, one pixel should be black (0%), and its neighbour white (100%).
    That means you need a square wave signal perfectly in phase with the sensor.

    If you use a sine wave, the extremes will be at 0 and at 100, so the centre of each pixel gets
    either 0 or 100 % signal. It's when you near the edges, that things get interesting, as a sine
    wave has a smooth transition between min and max value. So, taking the black pixels: centre
    will get 0 intensity, the border will get 50% intensity => average over the pixel will be greater
    than 0% signal. Same reasoning for white pixels: centre at 100%, borders at 50% => average
    below 100%.

    So, black pixels are above 0%, white pixels below 100 % => contrast gets lowered (and see
    above for the precise math)

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    Steaphany's Avatar
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    Re: Do digital sensors have an MTF?

    Quote Originally Posted by revi View Post
    perfectly in phase with the sensor.
    This reminded me of a caveat to be mindful of when the MTF sine periodicity matches the photosite to photosite pitch.

    If the MTF "cycle length" matches the photosite to photosite pitch and the n * Pi / 2 position of the cycle match the photosite boundaries, as described by Remco, where the Peak White and Peak Black is centered in the middle of each adjacent photosite, the maximal contrast measurements will be 64% for the White and 36% for the Black. ( This presumes that the active area of the photosite is 100% of it's width, in reality the active photo sensing area is often less than 50% of the photosite pitch )

    But, If the MTF "cycle length" matches the photosite to photosite pitch and the n * Pi / 2 position of the cycle match the photosite centers where the Peak White and Peak Black fall on the photosite boundaries, adjacent photosites will be equally illuminated and no detection of the MTF will be possible. The measured photosite output will be 50%.

    This implies that phase alignment error as small as half of a single photosite width can throw off MTF measurements.

    The same phenomenon can throw off resolution measurements, which are performed with a Square wave or Step function, as the phase alignment error of half a single photosite width can make the difference between resolving the line pairs or detecting nothing.

    In this age of digital imagers, MTF and Resolution tests need to have the sensor swept through a laterial distance of one photosite width to ensure an accurate measurement and to bypass potential test errors.
    Last edited by Steaphany; 1st March 2012 at 01:37 PM.

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    xpatUSA's Avatar
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    Re: Do digital sensors have an MTF?

    Thanks All for your responses, which will take me some time to digest since my math knowledge stops shortly before messrs Newton, Fourier, et al. Remember that the OP referred to a perfect image perfectly aligned with the [imperfect] sensor pixels thereby trying to avoid discussion of practical matters like alignment, test errors although I do appreciate the relevance of such matters, of course.

    Having struggled for a few months reading all the right literature I'm trying to start at just one element, i.e. the sensor and then go one step at a time from there.

    So now I need some help with the aforementioned functions. Firstly, the MTF that I was referring to is the kind measured by the slant-edge technique albeit defined in terms of a luminance ratio. Here's the proof in the link I gave previously:

    Do digital sensors have an MTF?

    Do digital sensors have an MTF?


    Do digital sensors have an MTF?
    He says:

    Above is the MTF(f) curve where f is given in cy/px. [He] already discussed this unit and 0.5 cy/px corresponds to 1 LW/px and is the Nyquist limit. MTF(f) is the Fourier transform of the LSF and can be solved in closed form (for f given in cy/px):
    MTF(f) = sinc(π f) where sinc(x) := sin(x)/x is the sinus cardinalis
    therefore MTF(0.5 cy/px) = 2/π or 0.6366 [my emphasis]
    The edge-spread assumption does bother me, how does he deduce that?

    Secondly, stemming from my analog audio amp days, is not a square wave comprised of all the odd harmonics of the fundamental frequency and, if so, how does that relate to the presentation of a square function to a digital sensor? Specifically, if the fundamental is at Nyquist, are not all it's harmonics in aliasing territory? I imagine not, I am obviously missing something, duh.

    best regards,

    Ted
    Last edited by xpatUSA; 1st March 2012 at 05:37 PM. Reason: getting old . . .

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    Re: Do digital sensors have an MTF?

    Many people are concerned about the MTF values of their lenses, and as a result choose their lenses carefully.

    The MTF of the sensor will surely have some effect on the outcome of the image too, and it is interesting. Is there anything that one can do to improve or change it?

    Glenn

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    2 penny for the guess..

    Re: Do digital sensors have an MTF?

    Glenn,

    Were rumours that removing the Bayer filter from sensor will increase performance, from contrast point of view. (but I don't recomend to anyone)

    Leo

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    Re: Do digital sensors have an MTF?

    Quote Originally Posted by LeoLeo View Post
    Glenn,

    Were rumours that removing the Bayer filter from sensor will increase performance, from contrast point of view. (but I don't recomend to anyone)

    Leo
    Leo:

    Isn't that what the Nikon D800E is all about - no Bayer filter? Or am I mixing it up with something else.

    Glenn

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    Re: Do digital sensors have an MTF?

    Quote Originally Posted by xpatUSA View Post
    <...>

    Secondly, stemming from my analog audio amp days, is not a square wave comprised of all the odd harmonics of the fundamental frequency and, if so, how does that relate to the presentation of a square function to a digital sensor? Specifically, if the fundamental is at Nyquist, are not all it's harmonics in aliasing territory? I imagine not, I am obviously missing something, duh.

    best regards,

    Ted
    Well, if you sample a square wave at twice its fundamental frequency f, can you see any difference with a sine wave of frequency f?
    (As a reminder, 2f would be the sampling frequency required to reconstruct a sine wave of frequency f according to the Nyquist theorem)

    Another complication with a sensor is that the photosites integrate the signal over a certain area, where sample theory usually considers discrete samples of negligable size. So we cannot differentiate between a square wave and a sine wave, anyway, due to the nature of the measuring device. (That the photosites only capture photons over part of their surface means that the real situation is somewhere in between, complicating things a bit more.)

    Remco

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    Re: Do digital sensors have an MTF?

    Quote Originally Posted by Glenn NK View Post
    Leo:

    Isn't that what the Nikon D800E is all about - no Bayer filter? Or am I mixing it up with something else.

    Glenn
    Remove the Bayer filter and you will have a black and white camera. But since you are not filtering red, green or blue then maybe more light will get through. This would improve light gathering ability. I am not sure about contrast.

    The D800E has no anti-aliasing filter. This is a filter that spreads out frequency patterns at less than the width of your pixels. This frequency is so small that your sensor cannot measure them. However if left unchecked they can produce secondary patterns on the sensor when multiples of the frequency intersect with the spatial frequency of the sensor. This is Moire.

    Moire will be present when you have a very consistent high frequency pattern. This is because it is the multiples of the frequency that cause the intersection with the sensor spatial frequency. So you need a very ordered fine grain pattern. For example a fine cloth fabric or the windows on a skyscraper in the distance.

    If the anti-alias filter was perfect then it would only affect the frequencies that your sensor cannot measure. So removing it would make no difference. However it is not perfect. It also filters small spatial frequencies that your sensor can measure and contributes a 'smudging' of light at the pixel level. So removing it can make the pixel signal cleaner.

    I am interested in reviews of the two new Nikon D800 cameras. Removing the filter cannot make that much difference. In my head it is just splitting the light that may fall on a single pixel to perhaps 80% one pixel and 20% the other. A good sharpening method such as deconvolution should be able to eliminate this smudge. Deconvolution relies on knowing the spread function of a perfect light source, I.e. the power of the anti-aliasing filter. This could possibly be measured and used to correct the pixel level sharpness. The crude approximation of unsharp mask at 300% at 0.3 pixels radius seems to do a good job anyway.

    My impression is that the D800E is a marketing ploy. A version of the D7000 (same pixel size) with no anti-alias filter was not necessary. Why so for full frame where lens corner performance will degrade images more than the anti-alias filter?

    Alex

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    Re: Do digital sensors have an MTF?

    Yah, the other filter.

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    Re: Do digital sensors have an MTF?

    Quote Originally Posted by revi View Post
    Well, if you sample a square wave at twice its fundamental frequency f, can you see any difference [compared?] with a sine wave of frequency f?
    (As a reminder, 2f would be the sampling frequency required to reconstruct a sine wave of frequency f according to the Nyquist theorem)
    Remco
    Ummm, Would that depend on the phasing with respect to the pixel frequency?

    Looks like I was combining theory and the real world in the original post. I mentioned a "perfect pattern", without saying square or sine, sitting in front of a real sensor. From what you've said, I now realize that "MTF" in the title was implying a sinusoidal pattern, so perhaps that MTF value of 0.64 (2/pi) still holds and discussion about square waves becomes a side-track.

    In the LumoLab link, transcribed in an earlier post above, the gentleman derives an MTF from a perfect, but pixelated, slant edge by using QuickMTF on a computer-generated image. So, if I had perhaps postulated a perfect slant edge image in glorious B&W at the sensor face, then could it be said that 0.64 is the best MTF you can get with that test method?

    This thread is still about sensors and do they have an MTF? Can frequency-limited, imperfect optical sampling systems be said to have an MTF? Does the anti-alias filter contribute such that even if everything was perfect downstream from the filter?

    (I wonder about posters who ask questions but provide no answers, and here I am doing it myself! Sorry.)

    Ted

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    Re: Do digital sensors have an MTF?

    Quote Originally Posted by Glenn NK View Post
    Many people are concerned about the MTF values of their lenses, and as a result choose their lenses carefully.
    If I knew what MTF meant, I might be concerned as well!!

    The scientific/mathematical knowledge on display here is quite overwhelming and way, way beyond my understanding.

    But the exchanges just remind me what a broad and wonderful church CiC is.

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    Re: Do digital sensors have an MTF?

    Quote Originally Posted by LeoLeo View Post
    Glenn,

    Were rumours that removing the Bayer filter from sensor will increase performance, from contrast point of view. (but I don't recomend to anyone)

    Leo
    For astronomical imaging, the highest quality cameras employ imagers lacking any Bayer masking and the color of an astronomical image is "created" by a succession of exposures through a number of filters. The post processing includes colorizing and combining the channels into what is presented as a color image.
    Last edited by Steaphany; 3rd March 2012 at 01:22 PM.

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    Re: Do digital sensors have an MTF?

    Quote Originally Posted by Glenn NK View Post
    Many people are concerned about the MTF values of their lenses, and as a result choose their lenses carefully.

    The MTF of the sensor will surely have some effect on the outcome of the image too, and it is interesting. Is there anything that one can do to improve or change it?
    Glenn
    Yes, improve one's composition/style to the point no one notices that the image is not in focus...

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