Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Diffraction numbers
#1
I use photozone.de religiously, have been a big fan since you started.

It would be interesting to see how lenses perform beyond f11.



I shoot long exposures with 9-10 stop ND filters and often use lenses at their minimum aperture. The desired effect is motion blur (water, clouds, branches in the wind, etc) contrasting with the sharpness of the still subjects in the frame.



MTF numbers up to the lens' minimum aperture would be very helpful. Small crops showing the diffraction quality would be awesome too but I think I'm pushing it.



[Image: 4010258544_5a93be5ab7_z.jpg]
#2
MFT numbers at small apertures are irrelevant in most cases, as by F/11 virtually all modern lenses are diffraction limited anyway. You can find the diffraction limit of a lens at a certain aperture, for the Rayleigh criterion (9% contrast, the point at which a good lens can still distinguish two adjacent lines easily), by dividing the number 1600 (lp/mm) by the aperture number, e.g., for F/16 that would be 1600 lp/mm / 16 = 100 lp/mm. Multiply by 2 for the number of pixels required per mm to resolve this.



For the sensor you can use the simplified formula of 3.2 X pixel spacing in micrometer for sensor diffraction limits expressed as an aperture. If the aperture becomes smaller than the sensor diffraction limit, you will not resolve anymore detail anyway, although it may still be worthwhile to stop down further for more depth of field, provided resolution doesn't get too low.



Sensor resolution may be calculated by dividing the pixel height by the number of mm the image is high, resulting in pixels/mm, divided by two again to get resolution in lp/mm. F.e., if the sensor has 3600 pixels on the side where it is 24 mm high, it will have a pixel density of 150 pixels/mm and a resolution potential of 75 lp/mm.



You also need to take into account that overall system resolution is equal to the inverse of (1/lens resolution at f-stop used + 1/sensor resolution), all in lp/mm. If you do get below 20 lp/mm on FF, I would certainly stop closing down the aperture any further, because 20 lp/mm is the resolution average amateurs can get from their 35 mm colour negatives (good amateurs may get 40 lp/mm). Of course on APS-C, this becomes 30-35 lp/mm (and 60-70 lp/mm).



HTH, 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 ....
#3
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 millimeter be different for different lenses?



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?
#4
[quote name='ssh33' timestamp='1320783595' post='12774']

Now if you put this together: 1/145.45 + 1/27.04 = 0.043857 - thats nowhere near 20.

[/quote]



You overlook one word in Wims post ... in this case an important one ... "inverse" ...



1/x + 1/y = 1/z



you calculated 1/x + 1/y = z



so .. take the inverse of 0.0438 ... and you are there!



Rainer
#5
[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='Big Grin' />.



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='Big Grin' />



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 ....
#6
[quote name='Rainer' timestamp='1320787482' post='12775']

You overlook one word in Wims post ... in this case an important one ... "inverse" ...



1/x + 1/y = 1/z



you calculated 1/x + 1/y = z



so .. take the inverse of 0.0438 ... and you are there!



Rainer

[/quote]

Yes, the inverse needs to be taken, but we are not there yet <img src='http://forum.photozone.de/public/style_emoticons/<#EMO_DIR#>/biggrin.gif' class='bbc_emoticon' alt='Big Grin' />.



The 3.2 X pixel spacing formula serves to calculate the aperture at which a sensor is diffraction limited, not the resolution <img src='http://forum.photozone.de/public/style_emoticons/<#EMO_DIR#>/biggrin.gif' class='bbc_emoticon' alt='Big Grin' />. I made that more clear in my post. The resolution obviously is the sensor height in pixels divided by the sensor height in mm, divided by two to get to lp/mm (Nyquist fequency expressed a different way). I added that to my original reply.



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 ....
#7
Most lenses perform more or less the same with smaller f-values. So it is not all that exciting to do MTF measurements for f-values smaller than f11.



Light gets "bent" (diffracted) around edges, and the smaller the hole the light has to pass through, the bigger precentage of the light will diffracted and end up in neighbouring pixels.



Of course, longer focal lengths have bigger apertures with the same f-value, so less light gets to be diffracted. But the apertures with longer lenses are further away too, so the diffracted light will hit further away pixels too.



You will find that with lenses of similar focal length diffraction will more or less always take a similar toll on the resolving power of the system, and even lenses with different focal lengths will show similar behavior.

There are some slight differences (due to factors I do not understand), but they are quite insignificant if sharpness id paramount to you (because then you have to shoot at f5.6-f8 or something).
  


Forum Jump:


Users browsing this thread:
1 Guest(s)