11-08-2011, 09:28 PM
[quote name='ssh33' timestamp='1320783595' post='12774']
Thanks Wim! That is a lot of numbers. I like pictures better. Kidding, but they say that there is a part of a joke in every joke, you know.
With all seriosness:
1. I don't understand how a starting constant of 1600 describes every lens. Shouldn't the resulting diffraction limit in line pairs per millimiter be different for different lenses? [/quote]
This is just the general lens diffraction limit, which is influenced only by the relative size of the aperture. When light hits an edge, it will diffuse, it will bend a little around that edge, making a straight line slightly blurred at the edge, or a circle slightly blurred at the perimeter.
In simple terms, you can visualize this as standard size blur, which obviously gets bigger relatively speaking the smaller the diameter of the aperture gets. 2 mm of 50 mm is only 4 %, 2 mm of 6 mm is 33 %. IOW, the smaller the aperture the less detail will be clear in an image. This is what this is about.
Now, if a lens is world class, optimally corrected, etc. on average it may be able to resolve more than 400 lp/mm. However, due to diffraction limits, it will not be able to go beyond that 400 lp/mm, because of diffraction. We call that lens diffraction limited at F/4 (which automatically implies it is diffraction limited at all smaller apertures too). Genrally speaking very few photographic lenses get better than this, because the increasing effect of optical aberrations at larger apertures tend to keep resolution generally below 450 lp/mm, even with the best lenses
Lenses that are not world class, but just merely excellent or very good, may not resolve 400 lp/mm, but maybe 300 lp/mm. If you do a quick calculation, you will find that that lens is diffraction limited at around F/5.6.
Less good lenses may only be diffraction limited by F/11 or F/16. Beyond that, and you can shot just as well through frosted glass <img src='http://forum.photozone.de/public/style_emoticons/<#EMO_DIR#>/biggrin.gif' class='bbc_emoticon' alt='
' />.
The number 1600 is distilled from some complex mathematical formulas, and is a very good approximation.
Apologies, my bad. I'll correct my reply above.
My formula actually is the way to calculate the aperture at which the sensor is diffraction limited.
The resolution of the sensor in lp/mm obviously is pixels/mm divided by 2, or in your case, D700, 59 lp/mm. Decimal points in lp/mm do not make a lot of sense, you can't really resolve less than a line pair. In order to resolve a line, you need a pair of lines with contrast (1 black, 1 white). <img src='http://forum.photozone.de/public/style_emoticons/<#EMO_DIR#>/biggrin.gif' class='bbc_emoticon' alt='' />
Anyway, based on the Rayleigh criterion, you get to 42 lp/mm at the diffraction limit of F/11 (145 lp/mm diffraction limit), and to 22 lp/mm at F/45. However, I suggest you don't go beyond F/18 or F/19, because by then the image tends to get mushy overall - OOF areas and DoF areas tend to cross into each other by that aperture.
HTH, and apologies, kind regards, Wim
Thanks Wim! That is a lot of numbers. I like pictures better. Kidding, but they say that there is a part of a joke in every joke, you know.
With all seriosness:
1. I don't understand how a starting constant of 1600 describes every lens. Shouldn't the resulting diffraction limit in line pairs per millimiter be different for different lenses? [/quote]
This is just the general lens diffraction limit, which is influenced only by the relative size of the aperture. When light hits an edge, it will diffuse, it will bend a little around that edge, making a straight line slightly blurred at the edge, or a circle slightly blurred at the perimeter.
In simple terms, you can visualize this as standard size blur, which obviously gets bigger relatively speaking the smaller the diameter of the aperture gets. 2 mm of 50 mm is only 4 %, 2 mm of 6 mm is 33 %. IOW, the smaller the aperture the less detail will be clear in an image. This is what this is about.
Now, if a lens is world class, optimally corrected, etc. on average it may be able to resolve more than 400 lp/mm. However, due to diffraction limits, it will not be able to go beyond that 400 lp/mm, because of diffraction. We call that lens diffraction limited at F/4 (which automatically implies it is diffraction limited at all smaller apertures too). Genrally speaking very few photographic lenses get better than this, because the increasing effect of optical aberrations at larger apertures tend to keep resolution generally below 450 lp/mm, even with the best lenses
Lenses that are not world class, but just merely excellent or very good, may not resolve 400 lp/mm, but maybe 300 lp/mm. If you do a quick calculation, you will find that that lens is diffraction limited at around F/5.6.
Less good lenses may only be diffraction limited by F/11 or F/16. Beyond that, and you can shot just as well through frosted glass <img src='http://forum.photozone.de/public/style_emoticons/<#EMO_DIR#>/biggrin.gif' class='bbc_emoticon' alt='
' />.The number 1600 is distilled from some complex mathematical formulas, and is a very good approximation.
Quote:2. My math is way off.
Lens diffraction limit (1600/22)*2=145.45
Nikon D700 pixel spacing is 8.45 µm, so sensor diffraction limit is 3.2x8.45=27.04
Now if you put this together: 1/145.45 + 1/27.04 = 0.043857 - thats nowhere near 20.
What am I doing wrong?
Apologies, my bad. I'll correct my reply above.
My formula actually is the way to calculate the aperture at which the sensor is diffraction limited.
The resolution of the sensor in lp/mm obviously is pixels/mm divided by 2, or in your case, D700, 59 lp/mm. Decimal points in lp/mm do not make a lot of sense, you can't really resolve less than a line pair. In order to resolve a line, you need a pair of lines with contrast (1 black, 1 white). <img src='http://forum.photozone.de/public/style_emoticons/<#EMO_DIR#>/biggrin.gif' class='bbc_emoticon' alt='
' />Anyway, based on the Rayleigh criterion, you get to 42 lp/mm at the diffraction limit of F/11 (145 lp/mm diffraction limit), and to 22 lp/mm at F/45. However, I suggest you don't go beyond F/18 or F/19, because by then the image tends to get mushy overall - OOF areas and DoF areas tend to cross into each other by that aperture.
HTH, and apologies, 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 ....