09-25-2011, 11:47 AM
Hi BC,
[quote name='Brightcolours' timestamp='1316943888' post='11831']
The best SLR lenses rarely achieve over 100lp/mm. [/quote]
That is always only true in combination with a medium, or at contrast levels of 50% (MTF-50). I deliberately mentioned air images here, and furthermore, this is at the Rayleigh criterion, which essentially is the measure at which these values are taken, and which is the industry standard for these measurements (other than MTF-50, which was a later development).
No, not really. The generally accepted wavelength used for this is 0.000512 mm, or approximately 0.0005 mm, close to green light (0.00055 mm), and on average close to the average of the daylight spectrum. This is a value generally used for photographic lenses and resolution and diffraction calculations.
Actually, diffraction occurs at all apertures. The diffraction limit is purely defined as the highest resolution possible at a specific aperture due to diffraction, and although there is a complex mathematical equation to derive this, in practical terms the Rayleigh limit can be approached by 1600/N, in lp/mm, where N is the f-stop (IOW, for F/4 the diffraction limit is 1600/4 = 400 lp/mm). At the Rayleigh limit, MTF = 9 %, and lenses have little response at higher frequencies, hence the definition of this limit at this point.
The reason I chose F/4 here, is simply that at larger apertures, the optical aberrations cause havoc, and generally substantially lower resolution as a result. In theory at F/1.6 one could achieve 1000 lp/mm, but that type of resolution is only achieved by very expensive single frequency corrected lenses with accompanying single frequency light sources.
In air images at the Rayleigh limit, the best lenses achieve 400 lp/mm at F/4, some slightly more at slightly larger apertures (450 lp/mm), but better than that it doesn't really get for general photographic lenses.
And a lens is called diffraction limited, if it achieves those values, because although it could possibly resolve more, this isn't possible due to diffraction.
All of this also means that if a lens is diffraction limited at relatively large apertures, it has a better lens based resolution characteristic than those lenses which are diffraction limited at smaller apertures.
Furthermore, we are still talking lens based diffraction resolution here. System resolution depends both on medium (sensor or film) resolution, and lens resolution at the aperture used. This formula is as follows: 1/system_resolution = 1/lens_resolution_at_f-stop + 1/medium_resolution. IOW, system resolution is always less than its lowest common denominator. If there is a big difference between lens and medium resolution, system resolution will be close to the medium resolution, but still a little below it. BTW, a sensor "outresolves" a lens when the lens resolution at a specific aperture is lower than the Nyquist frequency of the sensor, divided by 3.2 and by sensor height in mm, which is the relative distance required to determine the difference between two adjacent Airy disks. This figure also has lp/mm as dimensions.
With sensors the situation is slightly more complex, however, especially when it comes to tests. The sensor resolution essentially is the Nyquist frequency divided by 2, but the AA-filter cuts off higher frequencies from a certain level up. Furthermore, if you look at the test on Photozone, apparently ImaTest reads beyond the Nyquist frequency (which I personally do not believe, unless under the hood a different contrast level is used, but Klaus has strong arguments in its favour), which is why with very good lenses the lw/ih numbers in the MTFs here end up very high on the resolution scale.
This also explains why with older cameras and lower resolutions, the lense curves are rather flat topped, instead of showing a concavoconvex curve (rounded top, hollow bottom) if plotted on the same graph for centre and corner resolutions.
So far my ramblings <img src='http://forum.photozone.de/public/style_emoticons/<#EMO_DIR#>/biggrin.gif' class='bbc_emoticon' alt='
' />.
Kind regards, Wim
[quote name='Brightcolours' timestamp='1316943888' post='11831']
The best SLR lenses rarely achieve over 100lp/mm. [/quote]
That is always only true in combination with a medium, or at contrast levels of 50% (MTF-50). I deliberately mentioned air images here, and furthermore, this is at the Rayleigh criterion, which essentially is the measure at which these values are taken, and which is the industry standard for these measurements (other than MTF-50, which was a later development).
Quote:The diffraction limits you talk about seem to be based in a very specific wavelength of monochromatic light. With a normal light spectrum, diffraction limited resolution sets it way sooner. Your 400 lp/mm at f4 sits very close to g-line wavelength, which is in the ultra violet part of the spectrum (wavelength 435.8mm, 470 lp/mm). So I think the poster above putting it in the blue part of the spectrum is possibly right.
No, not really. The generally accepted wavelength used for this is 0.000512 mm, or approximately 0.0005 mm, close to green light (0.00055 mm), and on average close to the average of the daylight spectrum. This is a value generally used for photographic lenses and resolution and diffraction calculations.
Quote:You will see diffraction limiting resolution from about f4 and up, with the Nikon 1 system. That is on pixel level of course, and I agree with you that, like in the film era, we should not put too much importance in diffraction softening of the projected image.
Actually, diffraction occurs at all apertures. The diffraction limit is purely defined as the highest resolution possible at a specific aperture due to diffraction, and although there is a complex mathematical equation to derive this, in practical terms the Rayleigh limit can be approached by 1600/N, in lp/mm, where N is the f-stop (IOW, for F/4 the diffraction limit is 1600/4 = 400 lp/mm). At the Rayleigh limit, MTF = 9 %, and lenses have little response at higher frequencies, hence the definition of this limit at this point.
The reason I chose F/4 here, is simply that at larger apertures, the optical aberrations cause havoc, and generally substantially lower resolution as a result. In theory at F/1.6 one could achieve 1000 lp/mm, but that type of resolution is only achieved by very expensive single frequency corrected lenses with accompanying single frequency light sources.
In air images at the Rayleigh limit, the best lenses achieve 400 lp/mm at F/4, some slightly more at slightly larger apertures (450 lp/mm), but better than that it doesn't really get for general photographic lenses.
And a lens is called diffraction limited, if it achieves those values, because although it could possibly resolve more, this isn't possible due to diffraction.
All of this also means that if a lens is diffraction limited at relatively large apertures, it has a better lens based resolution characteristic than those lenses which are diffraction limited at smaller apertures.
Furthermore, we are still talking lens based diffraction resolution here. System resolution depends both on medium (sensor or film) resolution, and lens resolution at the aperture used. This formula is as follows: 1/system_resolution = 1/lens_resolution_at_f-stop + 1/medium_resolution. IOW, system resolution is always less than its lowest common denominator. If there is a big difference between lens and medium resolution, system resolution will be close to the medium resolution, but still a little below it. BTW, a sensor "outresolves" a lens when the lens resolution at a specific aperture is lower than the Nyquist frequency of the sensor, divided by 3.2 and by sensor height in mm, which is the relative distance required to determine the difference between two adjacent Airy disks. This figure also has lp/mm as dimensions.
With sensors the situation is slightly more complex, however, especially when it comes to tests. The sensor resolution essentially is the Nyquist frequency divided by 2, but the AA-filter cuts off higher frequencies from a certain level up. Furthermore, if you look at the test on Photozone, apparently ImaTest reads beyond the Nyquist frequency (which I personally do not believe, unless under the hood a different contrast level is used, but Klaus has strong arguments in its favour), which is why with very good lenses the lw/ih numbers in the MTFs here end up very high on the resolution scale.
This also explains why with older cameras and lower resolutions, the lense curves are rather flat topped, instead of showing a concavoconvex curve (rounded top, hollow bottom) if plotted on the same graph for centre and corner resolutions.
So far my ramblings <img src='http://forum.photozone.de/public/style_emoticons/<#EMO_DIR#>/biggrin.gif' class='bbc_emoticon' alt='
' />.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 ....