Modulation transfer function

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They state elsewhere that performance at 10 line pairs/mm is indicative of the lens contrast while 40 line pairs/mm is indicative of its sharpness.

"The graphs show MTF in percent for the three line frequencies of 10 lp/mm, 20 lp/mm and 40 lp/mm, from the center of the image (shown at left) all the way to the corner (shown at right). The top two lines represent 10 lp/mm, the middle two lines 20 lp/mm and the bottom two lines 40 lp/mm. The solid lines represent sagittal MTF (lp/mm aligned like the spokes in a wheel). The broken lines represent tangential MTF (lp/mm arranged like the rim of a wheel, at right angles to sagittal lines). On the scale at the bottom 0 represents the center of the image (on axis), 3 represents 3 mm from the center, and 21 represents 21 mm from the center, or the very corner of a 35 mm film image. Separate graphs show results at f8 and full aperture. For zoom lenses, there are graphs for each measured focal length."

Kodak publishes MTF data for some color reversal and B&W negative films. Go to Kodak Professional Products or Kodak Consumer Products- Film and navigate from there. Searching for MTF on Kodak's main page also works well. Kodak Germany publishes MTF curves for Gold films, called Farbwelt in German. Ektachrome E200 has f50 = 34 lp/mm. Kodak T-MAX 100 has f50 = 125 lp/mm and T-MAX 400 has f50 = 100 lp/mm with 20% boost. T-MAX P3200 has f50 = 85 lp/mm. These MTF's are quite striking-- far beyond any color reversal film! Photodo's page on 35 mm, medium format, or large format? indicates that T-MAX 100 is indeed a remarkable film. 35 mm T-MAX 100 outperformed medium format Tri-X using very fine equipment. Photodo's articles are worthy of serious study. Kodak also uses a measurement called print grain index for prints.

If you choose to believe manufacturer's data sheets, yes, they are sharper. Thanks to Mitch Mirkin and Jussi Ik�heimo for pointing out data I'd missed. MTF data for Fujicolor Superia 100 color negative film is shown on the right. f50 is around 63 lp/mm. That's about 50% better than Fuji's highly regarded Provia 100F slide film. (Curiously, resolving power, which has less to do with perceived sharpness, is about the same.) Kodak color negative films show a comparable improvement, for example, about 72 cycles/mm for Ultra Color 100UC vs. about 38 cycles/mm for Kodachrome 64 and 40 cycles/mm for Elite Chrome 100 and Chrome Extra Color 100. MTF for Kodak Gold films (Farbwelt in German) are shown on the Kodak Germany site. For Gold 100, shown below,  f50 (extrapolated) is about 110 lines/mm with a 40% adjacency effect boost. (Thanks to Stefan Ittner for directing me to the Kodak Germany site.) This evidently means line widths.  f50 expressed in the more familiar line pairs (or cycles) per mm would be 55.

MTFformula

A condenser lens is an optical component used to converge and focus light onto a sample or specimen in microscopy. It sits beneath the stage and ...

MOXTEK wire-grid polarizing beamsplitter (PBS) plates maintain color uniformity and image contrast over a wide range of acceptance angles.

The adjacency effect increases the perceived image sharpness, though it can become irritatingly obvious if it's overdone. It boosts the the MTF 50% frequency, but it has relatively little effect on the 10% level, which is related to perceived line pairs per mm resolution. Developing technique affects MTF, particularly for B&W films, where there is a large choice of developers and agitation procedures. Development options are more limited for color films.

The MTF curves on the right are from the Photodo (old site) test of the Canon 28-70mm f/2.8L lens. Photodo is an outstanding Internet lens test resource, with 458 lenses optically MTF tested as of June 2000. Photodo curently uses Imatest for its lens tests. In their page, Understanding the MTF graphs, numbers and grades, they state,

As we mentioned earlier,  MTF (sharpness) corresponds to the bandwidth of a communications system while grain corresponds to its noise. Both enter into Shannon's equation for information transmission capacity,

The eyepiece has several major functions: ○ The eyepiece serves to further magnify the real image projected by the objective. ○ In visual observation, the ...

Mtf curveangle

Assuming a 35mm frame is cropped for an 8x10 print, a 4x5 frame is 4 times larger. The ratio of total detail at the 50% level is 4*27.1/36.8 = 2.94. The ratio at the 10% level is 4*49.9/68.6 = 2.91. A 4x5 image can therefore resolve approximately three times the linear detail of 35mm, assuming both employ good technique: excellent lenses and film, optimum aperture, correct focus, sturdy camera support, good atmospheric conditions, etc. Since the passing of the Speed Graphic era, such good technique has been standard practice in large format photography; it's less common with 35mm. A 24x30 inch print from 4x5 would have the same detail as an 8x10 from 35mm. It can be extremely sharp! This result is in substantial agreement with R. N. Clark's scanner detail page. If we are to believe Kodak's T-MAX 100 data, the ratio would be lower: 35mm images would be phenomenally sharp, limited only by the lens.

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Lens performance is typically limited by aberrations at large apertures and diffraction at small apertures. Aberrations depend on lens design and manufacturing quality; they differ markedly for different lenses. Diffraction is a fundamental physical effect; it depends on the aperture alone. A lens is sharpest between the two extremes, near its optimim aperture, 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.

Objective Lenses: Usually you will find 3 or 4 objective lenses on a microscope. ... Rather, the setting is a function of the transparency of the specimen ...

From my former career, I recognized this curve as characteristic of pulse slimming equalizers, widely used in older magnetic disk drives to sharpen readback pulses so more data can be squeezed into a given area. By adding one more parameter, fboost, I was able to fit it reasonably well.

Unlike film, the MTF of lenses don't necessarily match the second order 1/(1+( f / f50)2) equation. MTF rolloff can vary widely, depending on lens design and manufacturing tolerance. To accommodate this, MTFcurve has an input variable for the order of the lens's MTF rolloff, lord, which defaults to 2 if not entered or if entered as 0. The lens MTF equation becomes,

Mtf curvechart

Sep 28, 2022 — The standard magnification bands are as follows: red band = 5x, yellow = 10x, green = 20x, blue = 40-60x, white = 100x. Thus, if a lens has a ...

There is one troubling aspect to some manufacturer's MTF curves, for example Fujichrome Provia 100F. MTF should be 100% at very low frequencies, but it remains flat at 120% from 10 lp/mm down to 1 lp/mm. There are three possible reasons. (1) The adjacency effect extends to extremely low spatial frequencies. Doubtful. 1 lp/mm is awfully low. (2) The graphic arts department took liberties with the plot before sending it out for publication. This happened to me in the old days before I had access to computer tools. (3) The marketing department cheated. It happens.

MTFOptics

shows the combined response of Velvia film and the excellent 35mm lens. The red curve is the spatial response, the blue curve is the combined MTF, and the thin blue dashed curve is the MTF of the lens only.

Lens mount adapters are designed to attach a lens to a camera body with non-matching mounts. Generally, a lens can be easily adapted to a camera body with a smaller flange focal distance by simply adding space between the camera and the lens. When attempting to adapt a lens to a camera body with a larger flange focal distance, the adapter must include a secondary lens in order to compensate. This has the side effect of decreasing the amount of light that reaches the sensor, as well as adding a crop factor to the lens. Without the secondary lens, these adapters will function as an extension tube and will not be able to focus to infinity.

Optical bandpass filters covering 200 nm to 16 µm with bandwidths ranging from 0.3 nm in the UV/VIS to as wide as 4 µm band pass in the IR.

The likely reason that slide film has poorer sharpness is that it's made to be displayed directly. Dark tones must be deep and rich; Dmax is much higher than for negative films, hence more dye is needed. Emultion layers may have to be thicker to accomodate this. .

Mtf curveexample

There is a fairly elementary explanation of how this happens in film. It it particularly noticeable with black & white films developed in highly diluted (one-shot) developers. Visualize a contrast boundary between two areas, one side of which is heavily exposed (a highlight) and the other lightly exposed (a shadow). As the film is developed (particularly in the interval between between agitations), the developer in the heavily exposed area becomes depleted more rapidly than the developer in the lightly exposed area, slowing down the development. Some of the developer diffuses across the boundary, so that the developer in the heavily exposed area adjacent to the boundary is less depleted than in the rest of the region, hence develops more rapidly, and the developer in the lightly exposed area adjacent to the boundary is more depleted, hence develops more slowly. The result is an exaggerated contrast boundary, as illustrated above. This is known as the adjacency effect, and film/developer combinations that exhibit it are said to have high acutance. In Velvia, the diffusion probably takes place inside the film.

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:

X-ray diffraction, phenomenon in which the atoms of a crystal, by virtue of their uniform spacing, cause an interference pattern of the waves present in an ...

The blue curve below the target is the film MTF, expressed in percentage-- the scale on the left applies. It closely approximates the green curve for Ektachrome E100VS. The red curve shows the density of the bar pattern. The 50% and 10% amplitudes are 40 line pairs/mm, as expected, and 120 line pairs/mm.

MTFlens

Mtf curveexplained

The 50% and 10% points for MTF are now 36.8 and 68.6 line pairs/mm. This is the best that can be expected for an excellent lens covering 43mm diagonal, optimum aperture, correct focus, sturdy camera support, and good atmospheric conditions.

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,

Bandpass filters selectively transmit a desired wavelength range. They are characterized by the fact that they connect a region of high transmission (pass ...

Fujifilm publishes MTF data for all their films. Go to Consumer Film Product Line-up or Professional Film Product Line-up and navigate from there. Fujicolor NHGII ASA 800 and NPH 400 color negative films have f50 = 45 lp/mm.

If you are interested in large format photography, Large Format Photography . Info, edited by Quang-Tuan Luong and Bjorn Nilsson, is an outstanding resource.

We can find the lens's 50% MTF value, flens, by modifying the above equation to flens = 20/sqrt(1/MTF20-1), or we can also use the above table by substituting MTF20 for MTF40 and dividing flens by 2. Since MTF20 ~= 66%, we estimate flens to be 28 line pairs per mm. This is just under half the value for the excellent 35mm lens and just slightly under the diffraction limit ( f50 = 32 lp/mm for f/22). Even at optimum aperture (around f/11) a view camera lens is not likely to be as sharp as the excellent 35mm lens; it has to cover about 4 times the image circle (16 times the area). Next we run MTFcurve 45 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 is almost entirely limited by the lens; the film hardly plays a role.

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.

The striking feature of the response, shown in the red curve below the image, is the exaggerated contrast boundaries. Tones overshoot their low frequency (steady state) levels, and the result is plainly visible. The overall effect is that this image appears slightly sharper than the image above for Ektachrome E100VS or Fuji Provia 100F, even though it has slightly lower response at 100 line pairs/mm.