Understanding Resolution, MTF and Contrast Charts

Many photographers have great difficulty in interpreting lens test data. In particular, how does one interpret resolution, and either contrast or MTF charts for a given lens? How is contrast related to resolution? Moreover, how and why does MTF contrast data differ in the tangential and sagittal plane, and what does this this data mean in terms of the overall sharpness of a lens? For that matter, what is MTF and what are the tangential and radial planes? And even in more depth, what do various terms such as spherical aberration, coma, longitudinal aberration or axial color, lateral color and off-axis astigmatism refer to?

These are the many questions which photographers ask themselves when reading test reports for various lenses. This first article will only answer questions about interpreting resolution tables, MTF tables and graphs, and contrast tables.

MTF (Modulation Transfer Function)

(Bear with us, this definition of MTF is a long one, but modulation transfer function is absolutely the most important lens test, aside from resolution, which you need to understand.)

Most lenses are not perfect optical systems. Light, when passing through a lens, undergoes a certain degree of degradation. The question is how can this degradation be evaluated? Before we can answer this question we need to define "modulation." Modulation is basically a measure of the len's contrast at a given frequency. We could try to analyze real world images taken through a lens in order to determine modulation or contrast for details of different sizes or frequency (spacing), but this is very impractical to do. Instead, it is much easier to measure the modulation or contrast for pairs of alternating white and dark lines. These alternating white and dark lines are referred to as a square wave grating. The spacing of the lines in the square wave grating is the frequency (v) for which we will be measuring the modulation or contrast function of the lens. Here are two examples of square wave gratings, the right one having three times the frequency of the left one:

Note that in a square wave grating there are dark bars and light bars. We can measure the amount of light coming from each. The maximum amount of light will come from the light bars, and the minimum amount of light will come from the dark bars. If the light is measured in terms of luminance (L) we can define modulation according to the following equation:

modulation = (Lmax - Lmin ) / (Lmax + Lmin)

where Lmax is the maximum luminance of the white lines in the grating, and Lmin is the minimum luminance of the dark lines in the grating. When modulation is defined in terms of light, it is frequently referred to as Michelson contrast. Indeed, when one takes the ratio of the illumination from the light and dark bars, one is measuring contrast.

Now, let's assume that you have a square wave grating of a specific frequency (v) and modulation (inherent contrast between the dark and light areas), and that we image light reflecting from this grating through a lens. The modulation of the image, and thus the contrast of lens, can now be measured for the given grating frequency (v).

The modulation transfer function (MTF) is defined as the modulation, Mi, of the image divided by the modulation of the stimulus ( the object), Mo, as shown in the following equation.

 MTF(v) = Mi / M0

We print our USAF test gratings on 98% bright laser paper. Our laser printer's black laser toner has a reflectance of about 10%. Thus our value for M0 is 88%. But since film has a more limited dynamic range compared to the human eye, we can safely assume that M0 is essentially 100% or 1. Thus the above formula reduces to the following simpler equation:

 MTF(v) = Mi

Thus a len's MTF for the given grating frequency (v) is simply the measured modulation of the grating (Mi) when photographed through the lens onto film.

Okay, maybe you grasped most of the above information regarding MTF. Perhaps it will be simpler to look at a few practical examples:

Lets assume that you have a theoretically "perfect" lens. Such a lens does not exist anywhere in the real world because every lens has inherent aberrations, internal reflections, and suffers the effects of diffraction due the wavelike nature of light. This "perfect" lens would perfectly transmit an image of our square wave grating with no loss of sharpness or contrast. Thus, if we took a picture with our "perfect" lens, the resulting image would look exactly like the square wave gratings shown at the top of this page.

Instead, light in fact behaves like waves and quite similarly to ocean waves. Light waves can merge to create stronger light waves, and light waves can collide and cancel each other out. Light waves can hit an obstruction, such as the edges of a lens's aperture blades, and create numerous smaller ripples which are similar to the ripples you see when a ocean wave passes a post which supports part of an oceanside pier. Another analogy is the wavelets produced on the surface of a pond by small and large raindrops. Most of us, as children, grew up noticing these phenomena but likely didn't give it much thought since it was much more fun to play in the surf or splash around in the pond. Lets move on.

Assume that your camera lens has a limiting resolution which is equal to the spacing of the lines in the square wave grating shown at the upper right. Lets also assume that the upper right square wave grating has lines which, when photographed on film, have a spacing of 90 lines per millimeter. Lets also assume that 90 lines per millimeter happens to be the maximum resolution of your very nice lens, perhaps a really good macro lens. So, what would the above two gratings look like if you photographed them with your camera and your really good macro lens? The gratings would theoretically would look like this:

In the above right grating, you can just distinguish that there are very close light and dark line pairs. We assumed that the above right grating has a line spacing of 90 lines per millimeter, and that your really good macro lens also has a maximum resolution of 90 lines per millimeter. It should be obvious that, if the upper right grating were any finer (having closer spaced lines) then we would not be able to distinguish the individual lines at all. The left grating shown above, which is at 1/3 the spatial frequency or 30 lines per millimeter compared to the 90mm frequency in the above right grating, resolves the line pairs rather nicely. This is a good example of why Modern Photography chose to test lens contrast using a modulation frequency of 30 lines per millimeter, as this frequency is very good for subjectively evaluating the quality of a lens optical design and manufacture. At 30 lines per millimeter, really good lenses will image the line pairs with very good contrast (at least 50% or better), and really bad lenses will display the line pairs with extremely low contrast. Looking at the upper left grating, you can visually guess that our sample macro lens exhibits approximately 60% contrast for a spatial frequency of 30 lines per millimeter.

There is another reason why a frequency of 30 lines per millimeter is a good choice for measuring contrast. Why? Because the contrast results at this frequency provide you with a quick evaluation of how sharp a poster sized print, viewed from about four feet away, will appear to the human eye. The average human eye has a resolution of 2 arcminutes or about 1/30 of a degree. At four feet, this translates to about 7/10 of a millimeter. Note that a poster sized print represents a 22x enlargement of the film negative after allowing for a 5% crop of the film edges. Thus 30 lines per millimeter on the film translates to, again, about 7/10 of a millimeter.

MTF Conclusions

We can conclude that any 35mm format lens which has approximately 50% contrast at 30 lines per millimeter will produce a poster sized print which appears to be sharp when viewed from four feet away — period! So this is the long and the short of it as far as MTF is concerned, and the results can be stated as follows for either contrast tables or MTF tables or graphs measured at a spatial frequency of 30 lines per millimeter:

• Lenses with greater than 60% contrast at 30 lines per millimeter are very sharp to razor sharp.
• Lenses with approximately 40% to 60% contrast at 30 lines per millimeter are moderately sharp to very sharp.
• Lenses with approximately 30% to 40% contrast at 30 lines per millimeter contrast are slightly soft to moderately sharp.
• Lenses with approximately 20% to 30% contrast at 30 lines per millimeter are moderately soft to slightly soft.
• Lenses with than 20% contrast at 30 lines per millimeter are extremely soft to moderately soft.

In conclusion, any 35mm format camera lens with contrast of 40% or better at 30 lines per millimeter is at least moderately sharp — perhaps not razor sharp, but moderately sharp nevertheless.

So there you have it! Just look at contrast tables, MTF tables or MTF graphs for a lens and note whether the lens achieves 40% or better contrast or MTF. If the lens achieves 40% or better contrast or MTF results at 30 lines per millimeter, then the lens is a good lens at that tested aperture setting. If the lens achieves 60% or better contrast or MTF at 30 lines per millimeter, then the lens is razor sharp at that tested aperture setting.

Film and CCD Limitations Which Affect MTF

Both film and the CCD sensors in digital cameras impose their own inherent limitations on MTF or contrast for line pairs which are spaced progressively closer together (increasing frequency). Why? For film, the problems are the film's inherent grain and the fact that light striking the film scatters sideways within the fim's emulsion. Film grain and light scatter within the emulsion rapidly lower contrast as line frequencies increase. For CCDs, the problems are somewhat similar to film in that light is scattered, due to diffraction, when light strikes the edges of the CCD sensor's overlying gate structure. This problem is rather evident with the smaller multi-megapixel CCDs used in current digital cameras. This is the primary reason why several camera manufacturers and CCD chip manufacturers are working towards producing true 35mm format CCD sensors.

In any event, the limitations of film and current CCD sensors do have serious effects on the MTF at frequencies greater than 20 lines per millimeter. For example, we attached a fully baffled 10mm eyepiece to the back of a fully refurbished Tamron SP 24-48 zoom lens, set the zoom to 48mm, and then visually examined our USAF lens test target from 8 feet 2 inches distance. Visually, our lens nicely resolves 100 lines per millimeter at the film plane, with an apparent visual contrast of about 50%, and with the aperture wide open at F/3.8! Yet Modern Photography's test of this lens at 48mm and at the maximum aperture of F/3.8 indicate a maximum resolution of only 50 lines per millimeter, and contrast of only 50% using their standard grating of 30 lines per millimeter. So why the huge difference? The inherent deficiencies of film (due to film grain and light scattering within the emulsion), and the inherent light scattering off of the black painted surfaces within a camera's mirror box are the answers. The gate structure in CCD sensors imposes similar deficiencies. The point of all this is that many vintage camera lenses do truly provide extremely good and sometimes exceptional performance compared to modern lenses.

We look forward to eventually using one of the true 35mm format CCD sensors which are now in development since these new sensors will finally have the capacity to significantly surpass the performance limitations of fine grain films and to allow the inherent performance of many really good lenses to really stand out. Hopefully one of the OEM camera manufacturers will build a camera body which can accept older manual focus lenses (and thus Tamron Adaptall-2 lenses with an appropriate mount) and will include full automatic aperture operation.

Lens Resolution

Charts for lens resolution are just that. These charts indicate the maximum resolution obtainable by the lens at each aperture, as recorded on film. In other words, if a chart indicates that a lens has a resolution of 60 lines per millimeter, then this means that the lens is just barely able to distinguish two high contrast details (such as a black line on a white background) which are spaced only 1/60 millimeter apart at the film plane. In other words, this is the closest spacing limit for high contrast details at the film plane for which one can say, "I just am able to see that there are two details which are spaced 1/60 millimeter apart on the film. Lens resolution charts may be presented either as tables, showing center and corner resolution (corner resolution usually being measured at about 2/3 or 3/4 of the distance from the center to the extreme corner), or as a graph which shows how the resolution changes from the center to the edge of the film plane.

At the center of the focal plane (the axial or center portion of the image), a good lens should have equal resolution regardless of which direction our black and white lines are oriented. It shouldn't matter if we are photographing vertically oriented black and white lines, horizontally oriented lines, or lines oriented at any angle in between the horizontal and the vertical. If there is an obvious difference in axial resolution, depending on how these lines are oriented, then this means that the lens has axial astigmatism where the lens is sharper for lines at some given orientation compared to lines which are oriented at other angles. The screen on a window or a screen door makes an excellent target for this test. Axial astigmatism can only be due to one or a combination of manufacturing defects. If your lens has axial astigmatism, then you should seek to exchange it for another one.

Lens Contrast

Lens contrast tables are simply tables of a lens's MTF function, which were explained above. Lens contrast tables for 35mm format lenses are only valuable in determining a lens's optical quality and apparent sharpness if the contrast charts are for contrast measurements taken at 30 lines per millimeter spatial resolution.

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