02-08-2012, 11:26 AM
Hi Frank,
[quote name='Frank' timestamp='1328677175' post='15658']
Thank you for your clarification and explanation, Wim. I took a look at the pz test result of the Nikon 14-24mm lens on DX3, the central resolution power (MTF50) of the lens before diffraction coming in is very close to the resolution power of D3x, which is 84 lp/mm. Seems not a problem for D800, whose resolution power is 103 lp/mm as pointed out by you. The border resolution may be a different story, but seems not bad for the 14-24mm lens. (I know that this kind of comparison between cameras may not be inaccurate, but perhaps not totally wrong.) [/quote]
You can't really take the Photozone measurements as values you will obtain when shooting normal pictures. These are calculated values based on MTF-50 measurements of purely black and white test subjects. Furthermore, I found that when comparing test sites which do indicate where measurements are made, that what is considered here a border measurement, is considered an corner or extreme corner measurement on many other sites.
Do note that based on lens optics rules, it will never be (physically, optically) possible to get lw/ih as obtained in these tests. These are theoretical values only, for comparison purposes, nothing else, based on measurement but twiddled, optimized, calculated. If you take the resolution rule, for a given MTF-contrast setting, you will find that 1/system-resolution = 1/lens-resolution-at-fstop + 1/medium-resolution, where medium-resolution is equal to sensor resolution or film resolution, whatever has been used as a recording medium.
I use the Rayleigh criterion for lens resolution (and diffraction calculation), as this is a very good indicator for real life shooting, which is MTF-9 rather than MTF-50, and an industry standard used in the film era, and for this criterion an average wavelength is used of 0.000512 mm, i.e., in the green band of the spectrum, where the human eye is most sensitive, and which is considered representative for a typical daylight spectrum. Obviosuly, the resolution will be a little higher or lower depending on the wavelength, but this makes for a very good average, and has been in use since the 1930s if I am not entirely mistaken.
The Rayleigh limit (line pairs per mm) = 1/(1.22 Nω) = 0.82/(Nω), with N the numerical aperture and ω the wave lenght in mm. The figure one then gets for the diffraction limit of a lens is 1600/N lp/mm, being the maximum a lens can resolve due to diffraction, based on this criterion.
A sensor has a Nyquist resolution, which can be expressed in lp/mm as well. Essentially, that is the number of pixels per mm, divived by 2, and rounded to the nearest whole number - a line requires two pixels minimum after all for resolution.
The lens aperture at which a sensor will resolve more than the lens can when stopped down, or the sensor diffraction limit, is equal to the point where the lens due to diffraction limits starts resolving less than the sensor is capable of. In the case of the D800, this limit is 103 lp/mm, and that is reached at approximately f/16: 1600/103 = ~16 after all.
Another way to calculate this is by multipying the sensel size in microns by a factor of 3.2 for the Raleigh criterion, which amounts to exactly the same number. 3.2 is essentially the 3.2 X the radius of the Airy disk, which is required in order to be able to distinguish two adjacent Airy disks. Note that this factor is 2.8 for MTF-50, IOW, there is more leeway in the MTF-9 number on that basis (although less from a contrast POV of course <img src='http://forum.photozone.de/public/style_emoticons/<#EMO_DIR#>/biggrin.gif' class='bbc_emoticon' alt='
' />).
BTW, the MTF-50 lens diffraction limit for photographic purposes is approximately 760 lp/mm divided by numerical aperture. Based on that you actually get the numbers you calculated <img src='http://forum.photozone.de/public/style_emoticons/<#EMO_DIR#>/biggrin.gif' class='bbc_emoticon' alt='' />.
No need to worry. There were/are, supposedly, films which can resolve 1000 lp/mm, although in practical use they only reach 200-400 lp/mm. A top quality, world class photographic lens, manages 400 lp/mm or slightly more (Rayleigh criterion), i.e., is diffraction limited from F/4 or F/3.5 already, i.e, is so well corrected, that optical aberrations are non-consequential at those and smaller apertures. IOW, there are films out there which can record more, in lp/mm, than some of the current sensors can, but thoe are specialist films. It is quite amazing though to see where we are now, with iso speeds as we have now - not possible with film. For more detail one needs to go to much larger film size, 4X5 inch and 8X10 inch these days - MF backs are already outdoing film as well in MF sizes.
And yes, a lens will have resolution fall-off towards the edges, but that is a given in optics.
As to the lens and system resolution formulas: because of the inverse nature of resolution addition in a system, resolution can never be more than its lowest common denominator (1/sys-res = 1/lens-res + 1/sensor-res), and the higher lens resolution and sensor resolution are, the higher the resulting system resolution will be, whether one uses the Rayleigh criterion or MTF-50 criteria. IOW, there si no need to worry about this diffraction limit - where this really becomes important where DoF starts to play a role: at a certain diffraction limit, the details become so mushy that further stopping down doesn't help, because sharpness decreases more than the increase in DoF. On average for FF this is around the F/18 mark, and around F/13-F/14 for APS-C sensors, but it does depend a lot on the lenses used: the more contrasty a lens is, the further one can stop down. Also, with digital, there is more leeway than there is with film, as there always is a second, intermediate, optical path with film which digital doesn't have. And this second optical path, be it scanning or printing, also obeys to the optical laws, and hence loses further resolutuion, whereas with digital that resolution entirely depends on size printed or displayed, not much else. Plus, it is easy to increase contrast with digital in a useful way, which is much more dificult with film.
Films don't really show more details then sensors, they are bound by the same physical rules as sensors regarding size of pixels or film grain when it comes to recording of details. And generally speaking, developing a film for MTF-50 is rather different than for MTF-9, and makes for quite a different view of the details. High contrast, vs usable contrast in phorographs. Furthermore, after development, 35 mm film will have a resolution of 20-40 lp/mm when done by a hobbyist (which equates to about 6 MP only, sensor wise!), and possibly up to 60 lp/mm when done by a pro lab (about 12 MP sensor wise) - this for colour negatives. B&W gets a little higher, iso 25-50 B&W film may get to about 100-120 lp/mm, while keeping the contrast differences on a reasonably good level for printing, i.e., a nice tone scale. Films with more resolution have to be developed to much higher contrast levels in order to get all the details, but then, the tone curve becomes very steep.
The main difference between film and sensors is that blacks are black in film, where we still get usable image data but more noise at the lowest levels of recording with sensors, and that film often still has some leeway at the high end of the dynamic range, whereas sensors just lose data when overexposed (hence ETTR). Film works more like the human eye this way. However, film isn't really analog either, even if processing film is <img src='http://forum.photozone.de/public/style_emoticons/<#EMO_DIR#>/biggrin.gif' class='bbc_emoticon' alt='' />.
In short, until we reach the same resolution with sensors as with films, and I mean high resolution films here, there is no need to worry, and even then, we are only in a similar situation as with the finest grained films out there anyway, be it at much, much higher iso speeds <img src='http://forum.photozone.de/public/style_emoticons/<#EMO_DIR#>/biggrin.gif' class='bbc_emoticon' alt='' />.
Is film better? No, it isn't, it is different, that's all.
Kind regards, Wim
[quote name='Frank' timestamp='1328677175' post='15658']
Thank you for your clarification and explanation, Wim. I took a look at the pz test result of the Nikon 14-24mm lens on DX3, the central resolution power (MTF50) of the lens before diffraction coming in is very close to the resolution power of D3x, which is 84 lp/mm. Seems not a problem for D800, whose resolution power is 103 lp/mm as pointed out by you. The border resolution may be a different story, but seems not bad for the 14-24mm lens. (I know that this kind of comparison between cameras may not be inaccurate, but perhaps not totally wrong.) [/quote]
You can't really take the Photozone measurements as values you will obtain when shooting normal pictures. These are calculated values based on MTF-50 measurements of purely black and white test subjects. Furthermore, I found that when comparing test sites which do indicate where measurements are made, that what is considered here a border measurement, is considered an corner or extreme corner measurement on many other sites.
Do note that based on lens optics rules, it will never be (physically, optically) possible to get lw/ih as obtained in these tests. These are theoretical values only, for comparison purposes, nothing else, based on measurement but twiddled, optimized, calculated. If you take the resolution rule, for a given MTF-contrast setting, you will find that 1/system-resolution = 1/lens-resolution-at-fstop + 1/medium-resolution, where medium-resolution is equal to sensor resolution or film resolution, whatever has been used as a recording medium.
Quote:While for diffraction, you stated that "sensor diffraction limit for the sensor is F/16", while my estimation is around f/7 for green light of wavelength 555nm. I would like to tell you how I did the calculation and check with you if I have made some mistake.
The angular diameter of the Airy disk of light diffraction is a=1.22L/D, where L is the wavelength of the light, D is the diameter of the lens' aperture. Since D=f/N, f is the focal length and N is the aperture, the linear diameter of the Airy disk on the image sensor is then (when focused at infinity) p=af=1.22LN. The pixel square of D800 has a side of length p0=0.0049mm=4900nm. Then, the aperture when p=p0 is N=p0/1.22L. For red light of 750nm, I get N=5.4. For blue light of 390nm, I get N=10. For green light of 555nm (which human eye is most sensitive to), I get N=7.2. Could you tell me how did you get the f/16? Had we used different criteria?
I use the Rayleigh criterion for lens resolution (and diffraction calculation), as this is a very good indicator for real life shooting, which is MTF-9 rather than MTF-50, and an industry standard used in the film era, and for this criterion an average wavelength is used of 0.000512 mm, i.e., in the green band of the spectrum, where the human eye is most sensitive, and which is considered representative for a typical daylight spectrum. Obviosuly, the resolution will be a little higher or lower depending on the wavelength, but this makes for a very good average, and has been in use since the 1930s if I am not entirely mistaken.
The Rayleigh limit (line pairs per mm) = 1/(1.22 Nω) = 0.82/(Nω), with N the numerical aperture and ω the wave lenght in mm. The figure one then gets for the diffraction limit of a lens is 1600/N lp/mm, being the maximum a lens can resolve due to diffraction, based on this criterion.
A sensor has a Nyquist resolution, which can be expressed in lp/mm as well. Essentially, that is the number of pixels per mm, divived by 2, and rounded to the nearest whole number - a line requires two pixels minimum after all for resolution.
The lens aperture at which a sensor will resolve more than the lens can when stopped down, or the sensor diffraction limit, is equal to the point where the lens due to diffraction limits starts resolving less than the sensor is capable of. In the case of the D800, this limit is 103 lp/mm, and that is reached at approximately f/16: 1600/103 = ~16 after all.
Another way to calculate this is by multipying the sensel size in microns by a factor of 3.2 for the Raleigh criterion, which amounts to exactly the same number. 3.2 is essentially the 3.2 X the radius of the Airy disk, which is required in order to be able to distinguish two adjacent Airy disks. Note that this factor is 2.8 for MTF-50, IOW, there is more leeway in the MTF-9 number on that basis (although less from a contrast POV of course <img src='http://forum.photozone.de/public/style_emoticons/<#EMO_DIR#>/biggrin.gif' class='bbc_emoticon' alt='
' />). BTW, the MTF-50 lens diffraction limit for photographic purposes is approximately 760 lp/mm divided by numerical aperture. Based on that you actually get the numbers you calculated <img src='http://forum.photozone.de/public/style_emoticons/<#EMO_DIR#>/biggrin.gif' class='bbc_emoticon' alt='
' />.Quote:Any way, my worrisome is that when the resolution of the sensor is much larger than the resolution of the lens, if the extra resolution of the sensor still useful. I have no experience with films. But I know that the 35mm black and white film usually has a resolution much larger than the lens. But I also heard that finer films can diplay more details in the image, although I don't understand why.
Best regards,
Frank
No need to worry. There were/are, supposedly, films which can resolve 1000 lp/mm, although in practical use they only reach 200-400 lp/mm. A top quality, world class photographic lens, manages 400 lp/mm or slightly more (Rayleigh criterion), i.e., is diffraction limited from F/4 or F/3.5 already, i.e, is so well corrected, that optical aberrations are non-consequential at those and smaller apertures. IOW, there are films out there which can record more, in lp/mm, than some of the current sensors can, but thoe are specialist films. It is quite amazing though to see where we are now, with iso speeds as we have now - not possible with film. For more detail one needs to go to much larger film size, 4X5 inch and 8X10 inch these days - MF backs are already outdoing film as well in MF sizes.
And yes, a lens will have resolution fall-off towards the edges, but that is a given in optics.
As to the lens and system resolution formulas: because of the inverse nature of resolution addition in a system, resolution can never be more than its lowest common denominator (1/sys-res = 1/lens-res + 1/sensor-res), and the higher lens resolution and sensor resolution are, the higher the resulting system resolution will be, whether one uses the Rayleigh criterion or MTF-50 criteria. IOW, there si no need to worry about this diffraction limit - where this really becomes important where DoF starts to play a role: at a certain diffraction limit, the details become so mushy that further stopping down doesn't help, because sharpness decreases more than the increase in DoF. On average for FF this is around the F/18 mark, and around F/13-F/14 for APS-C sensors, but it does depend a lot on the lenses used: the more contrasty a lens is, the further one can stop down. Also, with digital, there is more leeway than there is with film, as there always is a second, intermediate, optical path with film which digital doesn't have. And this second optical path, be it scanning or printing, also obeys to the optical laws, and hence loses further resolutuion, whereas with digital that resolution entirely depends on size printed or displayed, not much else. Plus, it is easy to increase contrast with digital in a useful way, which is much more dificult with film.
Films don't really show more details then sensors, they are bound by the same physical rules as sensors regarding size of pixels or film grain when it comes to recording of details. And generally speaking, developing a film for MTF-50 is rather different than for MTF-9, and makes for quite a different view of the details. High contrast, vs usable contrast in phorographs. Furthermore, after development, 35 mm film will have a resolution of 20-40 lp/mm when done by a hobbyist (which equates to about 6 MP only, sensor wise!), and possibly up to 60 lp/mm when done by a pro lab (about 12 MP sensor wise) - this for colour negatives. B&W gets a little higher, iso 25-50 B&W film may get to about 100-120 lp/mm, while keeping the contrast differences on a reasonably good level for printing, i.e., a nice tone scale. Films with more resolution have to be developed to much higher contrast levels in order to get all the details, but then, the tone curve becomes very steep.
The main difference between film and sensors is that blacks are black in film, where we still get usable image data but more noise at the lowest levels of recording with sensors, and that film often still has some leeway at the high end of the dynamic range, whereas sensors just lose data when overexposed (hence ETTR). Film works more like the human eye this way. However, film isn't really analog either, even if processing film is <img src='http://forum.photozone.de/public/style_emoticons/<#EMO_DIR#>/biggrin.gif' class='bbc_emoticon' alt='
' />.In short, until we reach the same resolution with sensors as with films, and I mean high resolution films here, there is no need to worry, and even then, we are only in a similar situation as with the finest grained films out there anyway, be it at much, much higher iso speeds <img src='http://forum.photozone.de/public/style_emoticons/<#EMO_DIR#>/biggrin.gif' class='bbc_emoticon' alt='
' />.Is film better? No, it isn't, it is different, that's all.
Kind regards, Wim
Gear: Canon EOS R with 3 primes and 2 zooms, 4 EF-R adapters, Canon EOS 5 (analog), 9 Canon EF primes, a lone Canon EF zoom, 2 extenders, 2 converters, tubes; Olympus OM-D 1 Mk II & Pen F with 12 primes, 6 zooms, and 3 Metabones EF-MFT adapters ....