Mtf For Large Format Lenses
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Large format lenses are that provide an large enough to cover large. Large format lenses are typically used in cameras and.Photographic optics generally project a circular image behind the. On smaller format cameras the image circle generally covers only the intended film size with little room to spare. Large format lenses are an exception. For large format use the circular patch of image light usually extends beyond the minimum size circle needed to fully cover the rectangle of the film. The extra image offers room to spare to make use of camera movements that re-align the lens away from dead center on the film.
Resolution and MTF curves in film and lenses Understandingimage sharpness part 1A:Resolutionand MTF curves in film and lensesby NormanKoren updated March 1, 2007SearchWWW Searchwww.normankoren.comTableof contentsfor theimage sharpnessseries Inthis page we illustrate how MTF is used to characterize theperformance of film and lenses.Green is forgeeks. Do you get excited by a goodequation?
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Were you passionateabout your college math classes? Then you're probably a math geek- amemberof a maligned and misunderstood but highly elite fellowship. The textingreen is for you. If you're normal or mathematically challenged, youmayskip these sections.
You'll never know what you missed.Film. LensesMTFfor film is rather simple- it's the same in all directions and uniformthroughout the film surface. Not so lenses. MTF is a function of thedistancefrom the image center, the aperture (f-stop), the spectrum of thelight, the focal length (for zooms), and eventhe focusing distance (macro lenses are designed to maintain good MTFatclose focus).
Not only that, but there are twoMTF's at each point:one along the radial (or sagittal) direction (pointing away from theimagecenter) and one in the tangential direction (along a circle around theimage center), at right angles to the radial direction. Because ofthis,the MTF curve cannot be displayed in the same way as for film.The MTF curves on the right are from thetest of the lens.
Photodo is an outstanding Internet lenstest resource, with 458 lenses optically MTF tested as of June 2000.curently usesfor its. In their page, they state,'The graphs show MTF in percent for the three linefrequencies of 10lp/mm, 20 lp/mm and 40 lp/mm, from the center of the image (shown atleft)all the way to the corner (shown at right). The top two lines represent10 lp/mm, the middle two lines 20 lp/mm and the bottom two lines 40lp/mm.The solid lines represent sagittal MTF (lp/mm aligned like the spokesina wheel). The broken lines represent tangential MTF (lp/mm arrangedlikethe rim of a wheel, at right angles to sagittal lines). On the scale atthe bottom 0 represents the center of the image (on axis), 3 represents3 mm from the center, and 21 represents 21 mm from the center, or theverycorner of a 35 mm film image. Separate graphs show results at f8 andfullaperture. For zoom lenses, there are graphs for each measured focallength.'
They state elsewhere that performance at 10 linepairs/mm is indicative ofthe lens contrast while 40 line pairs/mm is indicative of its sharpness.Lens performance is typically limited by aberrationsat large apertures andat small apertures. Aberrations depend on lens design and manufacturingquality; they differ markedly for different lenses. Diffraction is afundamental physical effect; it depends on the aperture alone.
A lensis sharpest between the two extremes, near its optimimaperture,which tends to be around f/8 or f/11 for the 35mm format. It is smaller(as low as f/4) for compact digital cameras and larger (f/11 to f/22)for large format cameras.Unlike film, the MTF of lenses don't necessarilymatch the second order1/(1+( f / f 50) 2)equation. MTF rolloff can vary widely, depending on lens design andmanufacturingtolerance. To accommodate this, MTFcurve has an input variable for theorder of the lens's MTF rolloff, lord, whichdefaults to 2 if notentered or if entered as 0. The lens MTF equation becomes,MTF lens(f)= 1/(1+ f/ f lens lord)( lord defaults to 2 in MTFcurve if not entered) F lens is the frequency wherelens MTF = 0.5 = 50%, corresponding to f 50in film. We use lord = 2, which appears to be anadequate approximationfor typical lenses, until better information is available.
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It's noteasyto derive lord from Photodo's data because most ofthe curves areabove MTF = 50%; you need to look at MTF below 30% to get a clearpictureof the rolloff. Flens can be estimated by interpolating between curvesif MTF at 40 line pairs/mm (MTF 40) is below 50%.Or it can be estimatedfrom MTF 40 using the following table, which isbased on theinverse of the second order equation, flens = 40/sqrt(1/MTF 40-1),where MTF 40 is expressed as a fraction ratherthan a percentage.Sqrtcan be replaced by exponentiation to the 1/ lordpower ( flens =40/(1/MTF 40-1)^(1/lord) ) when lordis not 2. MTF 4020%30%40%50%60%70%80%flens(1/mm)2026.280Estimatingflens(50% MTF) from MTF at 40 lines/mm (MTF 40)(second order rolloff). Thelens in this test is an outstanding performer,achievingaratingof 3.9 out of a possible 5, about as good as zoom lenses for the 35mmformat (covering 43mm diagonal) get. At 40mm,f/8, it's as sharp as a first rate prime (single focal length) lens.WithMTF 40 around 70% at f/8, flens is around 61 linepairs/mm The downside: it's expensive (over $1000 US), large, and heavy. Theis full of hypebole like, 'one.bleeping.
sharpzoom!,' 'sharpnessand contrast is spectacular,' 'a stunning piece of glass,' etc. Since35mm lenses don't get much better I use this lens as the standard forthe'excellent 35mm lens' for the remainder of this article.The plot on the right, generated byMTFcurve2 45 13 61shows the combined response of Velvia film and theexcellent 35mm lens.The redcurve is the spatial response,the bluecurve is the combined MTF,and the thin bluedashed curve is theMTF of the lens only.The 50% and 10% points for MTF are now 36.8 and 68.6line pairs/mm. Thisis the best that can be expected for an excellentlens covering 43mm diagonal, optimumaperture, correct focus, sturdy camera support, and good atmosphericconditions.Lens linksA excellent short text onlenses witha fine description of factors that affect resolution and MTF. Fairlytechnical.has an excellent description of lens aberrations.A mathematical description of theSeidel aberrations from,U.C. Berkeley Professor of Astronomy. A great source of MTF tests for 35mmlenses. Optical MTF tests on the were discontinued in 2000, but usesfor its.hasa page on that includes an explanation of MTF.
Ifyou readthis page carefully, you'll find a minor error in their MTF diagram.Theyalso publish MTF data for their andlenses. The curves look like Photodo's except that they're done at 5,10,and 20 line pairs per mm instead of 10, 20, and 40. I suppose this ismore appropriatefor large format. Unfortunately these curves are based on computersimulationrather than real measurements, which will always be a little worse.Theirarch competitorhas unkind things tosay about this technique.has MTF curves for Rollei medium format lenses- similar to lenses usedby Hasselblad.has MTF data its for EOS lenses, measured at.
It's evidently calculated rather than measured;it tendsto be a bit more optimistic than.Compare, for example, the. Similar data is available on a.has publishedMTF data for several of its outstanding(rangefinder) and(SLR) lenses as PDF Product information, linked on the lower right ofthesetwo pages. MTF data is for 5, 10, 20, and 40 lp/mm. They state that the5 and 10 lp/mm data relates to large object contrast while the 20 and40lp/mm data relates to small object resolution. It's instructive tocompareLeica's data with detailed lens performance observations by.page contains some serious discussionaboutimage sharpness issues and links to test targets.DiffractionLensesare sharpest between about two stops down from maximum apertureand the aperture where diffraction, an unavoidable consequence ofphysics,starts to dominate. For 35mm lenses, this is typically between f/5.6(f/8for slow zooms) and f/11.
At large apertures, resolution is limited byaberrations (astigmatism, coma, etc.), which lens designers workvaliantlyto overcome. MTF wide open is almost alwayspoorer than MTF at f/8.Diffraction worsens as the lens is stopped down (the f-stop isincreased).The equation for the Rayleigh diffraction limit, adapted from, is,Rayleigh limit(line pairs per mm) = 1/(1.22 N ω ) N is the f-stop setting and ω=the wavelength of light inmm = 0.0005 mm for a typical daylight spectrum. (0.00055 mm is thewavelengthof green light, where the eye is most sensitive, but 0.0005 mm may bemorerepresentative of daylight situations.) I've seen a simple rule ofthumb,Rayleigh limit = 1600/ N, which correspondsto ω= 0.000512mm.
The light circle formed by diffraction, known as theAiry disk,has a radius equal to1/(Rayleigh limit).The MTF at the Rayleigh limit is about 9%. SignificantRayleigh limitsare 149 lp/mm @ f/11, 102 lp/mm @ f/16, 74 lp/mm @ f/22, and 51 lp/mm @f/32.,an experienced lensdesigner, finds these numbers to be somewhat conservative because theRayleighlimit is based on a spot, which has lower resolution than a band. Hisnumbersof 125 lp/mm @ f/16 and 64 lp/mm @ f/32 are derived from a Kodak charthe contributed to page. Most lenses areaberration-limited(relatively unaffected by diffraction) at f/8 and below. The OTF(opticaltransfer function) curve in shows how MTF (the magnitude of OTF)varieswith spatial frequency for a purely diffraction-limited lens at f/22.We can derive some interesting relationships fromDavid Jacobson's graph.At the Rayleigh diffraction limit of 68 lp/mm (for f/22, ω= 555nm = 0.000555 mm), MTF is approximately 9%.
Restrictions and limitations of a sharepoint documemt library. It is 10% at about 64 lp/mmand 50% at 32 lp/mm. LargeformatThanksto Schneider's, we can compare large format image qualityto 35mm.The MTF curve on the left is for the 150mm f/5.6 Schneider Apo-Symmarlens,focused at infinity at f/22. It could be a little better than actuallensperformance because it's derived from computer simulation. But it'salmostcertainly worse than optimum because the lens is diffraction-limited atf/22; it is almost certainly sharper at f/11 and f/16.
Its image circleis u' = 110mm, more than sufficient to cover the 4 x5(inch) format with room for camera movements. The principal differencebetween this curve and the Photodo curves (above) is that the threelines(top to bottom) represent 5, 10, and 20 lines per mm (instead of 10,20,and 40). This is a first class view camera lens; hence we'll refer toitas an 'excellent 4 x5lens.' We can find the lens's 50% MTF value, flens, by modifying theaboveequation to flens = 20/sqrt(1/MTF 20-1), or wecan also use theabove table by substituting MTF 20 for MTF 40and dividingflens by 2. Since MTF 20 = 66%, we estimateflens to be 28 line pairsper mm. This is just under half the value for the excellent 35mm lensandjust slightly under the diffraction limit ( f 50= 32 lp/mm for f/22).
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Even at optimum aperture (around f/11) a viewcameralens is not likely to be as sharp as the excellent 35mm lens; it has tocover about 4 times the image circle (16 times the area). Next we run MTFcurve45 13 28, (Velvia film + lens) and we find that the 50%and 10%MTF values of the film + lens are 27.1 and 49.9 line pairs/mm.Sharpness isalmost entirely limited by the lens; the film hardly plays a role.Assuming a 35mm frame is cropped for an 8x10 print,a 4 x5frame is 4 times larger.
The ratio of total detail at the 50% level is4.27.1/36.8 = 2.94. The ratio at the 10% level is 4.49.9/68.6 = 2.91. A4 x5 image cantherefore resolve approximately threetimesthe linear detail of 35mm, assuming bothemploy good technique:excellent lenses and film, optimum aperture, correct focus, sturdycamerasupport, good atmospheric conditions, etc.
Since the passing of theSpeedGraphic era, such good technique has been standard practice in largeformatphotography; it's less common with 35mm. A 24x30 inch print from 4x5wouldhave the same detail as an 8 x10from35mm.
It can be extremely sharp! This result is insubstantial agreementwith. If we are to believe Kodak'sT-MAX 100data, the ratio would be lower: 35mm images would be phenomenallysharp,limited only by the lens.If you are interested in large format photography, edited by and, is anoutstandingresource.Back to Next:Imagesand text copyright © 2000-2013 by Norman Koren.
Norman Koren livesin Boulder, Colorado, where he worked in developing magnetic recordingtechnology for high capacity data storage systems until 2001. Since 2003 most of his time has been devoted to the development of. He has been involved with photography since 1964.