iangreenhalgh1
Joined: 18 Mar 2011
Posts: 15685
Expire: 2014-01-07
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 Posted: Mon May 14, 2012 5:20 pm Post subject: |
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iangreenhalgh1 wrote:
Codswallop is an ancient word, Elizabethan at least, maybe older, it literally means the vomit of a cod.
On this diffraction thing, I always thought that it was to do with the size of the sensor/film, an APS-C sensor being diffraction limited around f11, 35mm film/sensor around f16, larger formats at smaller apertures.
Some info on diffraction and the maths needed to work it out for a given imaging system:
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Lenses are sharpest between about two stops down from maximum aperture and the aperture where diffraction, an unavoidable consequence of physics, starts to dominate. For 35mm lenses, this is typically between f/5.6 (f/8 for slow zooms) and f/11. At large apertures, resolution is limited by aberrations (astigmatism, coma, etc.), which lens designers work valiantly to overcome. MTF wide open is almost always poorer than MTF at f/8.
Diffraction worsens as the lens is stopped down (the f-stop is increased). The equation for the Rayleigh diffraction limit, adapted from R. N. Clark's scanner detail page, is,
Rayleigh limit (line pairs per mm) = 1/(1.22 Nω)
N is the f-stop setting and ω = the wavelength of light in mm = 0.0005 mm for a typical daylight spectrum. (0.00055 mm is the wavelength of green light, where the eye is most sensitive, but 0.0005 mm may be more representative of daylight situations.) I've seen a simple rule of thumb, Rayleigh limit = 1600/N, which corresponds to ω = 0.000512 mm. The light circle formed by diffraction, known as the Airy disk, has a radius equal to1/(Rayleigh limit).
The MTF at the Rayleigh limit is about 9%. Significant Rayleigh limits are 149 lp/mm @ f/11, 102 lp/mm @ f/16, 74 lp/mm @ f/22, and 51 lp/mm @ f/32. Larry, an experienced lens designer, finds these numbers to be somewhat conservative because the Rayleigh limit is based on a spot, which has lower resolution than a band. His numbers of 125 lp/mm @ f/16 and 64 lp/mm @ f/32 are derived from a Kodak chart he contributed to Robert Monaghan's Lens Resolution Testing page. Most lenses are aberration-limited (relatively unaffected by diffraction) at f/8 and below. The OTF (optical transfer function) curve in David Jacobson's Lens Tutorial shows how MTF (the magnitude of OTF) varies with spatial frequency for a purely diffraction-limited lens at f/22.
We can derive some interesting relationships from David Jacobson's graph. At the Rayleigh diffraction limit of 68 lp/mm (for f/22, ω = 555 nm = 0.000555 mm), MTF is approximately 9%. It is 10% at about 64 lp/mm and 50% at 32 lp/mm. The following relationships therefore hold for diffraction-limited lenses:
f10 = 0.77/(Nω) ; N = F-stop; ω = the wavelength of light in mm = 0.0005mm
f50 = 0.38/(Nω) = 0.46*Rayleigh limit
The diffraction curve is somewhat difficult to express mathematically, but it can be approximated-- matched at the 10% and 50% MTF points-- by the equation used in the MTFcurve program ( f50 is the same as flens; f50 and lord are the third and fourth input arguments to MTFcurve),
MTFdiffraction-ltd(f) ~= 1/(1+| f/f50|lord) ( f50 = 0.38/(Nω); lord = 3.17)
The question remains, at what f-stop does a lens become diffraction limited? The best estimate is the f-stop where the diffraction-limited f50 (0.38/(N ω)) equals flens-- the 50% MTF frequency at the sharpest aperture. For the excellent 35mm lens, flens = 61 lp/mm. The f-stop with the same diffraction-limited f50 is N = 0.38/(61*0.0005) = 12.5. We can therefore say with some confidence that good 35mm lenses are relatively unaffected by diffraction at f/8 and below, moderately affected at f/11, and diffraction-limited at f/16 and beyond. Such lenses should only be stopped down beyond f/11 (larger f-stops for larger formats) when extreme depth of field is required. Diffraction in digital cameras is discussed here.
The Imatest program allows you to measure the MTF of digital cameras or digitized film images. You can't measure an individual component in isolation, but you can compare components, such as lenses, with great accuracy. Imatest also measurs other factors that contribute to image quality. |
And relating specifically to digital sensors:
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Pixel size and diffraction
Diffraction, a fundamental physical effect, limits a lens's performance at small apertures (large f-stop numbers). It is approximated by the equation, Rayleigh limit (lp/mm) = 1600/N, where N is the f-stop. At the Rayleigh limit, MTF = 9%; lenses have little response at higher spatial frequencies. At large apertures (small f-stop numbers) lenses are aberration-limited. Aberrations are a function of lens design— not a fundamental effect. Here we only consider diffraction.
The highest spatial frequency a sensor can resolve is its Nyquist frequency, equal to 0.5/(pixel spacing). When a lens is stopped down so its Rayleigh limit is below the Nyquist frequency, the camera is limited by the lens rather than the sensor. For optimum quality (when extreme depth of field is not required), the aperture should be set at least one stop larger than the aperture where the Rayleigh limit equals the Nyquist frequency: NR=N = 3.2 * pixel spacing (µm). For a pixel spacing of 3.4 microns, typical of compact digital cameras, NR=N = 3.2 * 3.4 = f/11, so the aperture should be set at f/8 or larger. The corresponding aperture range for digital SLRs, which have pixel spacings between about 6.8 and 9 microns, is f/16-f/22.
Depth of field at a given f-stop is inversely proportional to a sensor's diagonal dimension, so a compact digital camera with an 11 mm diagonal sensor has the same DOF at f/8 as a 35mm camera at f/32 (plenty).
f-stop Rayleigh Pixel spacing (µm) for
limit (lp/mm) Rayleigh limit = Nyquist
5.6 286 1.75
8 200 2.5
11 145 3.44
16 100 5
22 73 6.87
32 50 10
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Plug the numbers for the E-M5's sensor into those equations and you will get the imperically correct data for diffraction.
However, being a photographer and not an optician or mathematician I'm not that interested, but there is the info you need to reach a concrete figure for the diffraction limitation of the M4/3 sensor and should end any argument if someone who does care does the requisite maths.
What I do know is that the M4/3 sensor does not appeal to me at all because it turns all my favourite lenses into long ones and removes their usefulness to me. I mostly shoot wide angle lenses and therefore the M4/3 sensor is not suitable. The mere fact a 50mm lens becomes a 100mm lens is enough to make me not interested in using any M4/3 camera. I'm not even fond of using APS-C cameras because of the crop factor, my favourite lenses - Tokina 17mm, Konica 21 and 24mm Hexanons are so much more rewarding to use on a film camera because there they are truly wide, on my NEX they are still quite wide but the feeling and the result is inferior, hence I have had to develop stitching techniques. I use APS-C digital cameras because I can't afford a full frame. Therefore, to me, it is irrelevant how good or bad the IQ of a M4/3 camera is, it just isn't any use to me.
Specifically about the E-M5, it sure is a lot of money for a small sensor and to me, it only makes sense if you use it with dedicated M4/3 lenses, for old manual lenses it makes no sense to me at all due to the way the focal length is doubled, that's my view on it, good camera but not for me as I use old manual lenses exclusively.
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I don't care who designed it, who made it or what country it comes from - I just enjoy using it! |
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