For MTF, why does 10 represent contrast while 30 represent resolution?

I'm trying to learn to read MTF charts. Everything is making sense to me, except why most explanations of MTF will refer to the 10 l/mm line as a measure of contrast while referring to the 30 l/mm line as a measure of resolution?

Aren't they both a measure of contrast? That's what the Y axis is measuring. How I understood the graph is: At a specific resolution (10, 30, etc), how much contrast will it retain at a specific distance away from the center. Both lines are actually a measure of contrast, is it not?

-

First off, the use of 10lp/mm and 30lp/mm are not really a standard. Depending on the market for the lenses, the brand, and possibly the rough timeframe when a specific approach to producing MTF charts was formulated, the specific resolution of the features of a test chart can vary. Larger format cameras often used 40-50lp/mm test charts, and manufacturers of modern lenses still use 40lp/mm (Zeiss/Leica come to mind.) Ultimately, the resolution (spatial resolution, in this context) of the test chart is somewhat arbitrary. That said, current test charts, be it 10 & 30 lp/mm or 20 and 50 lp/mm, may not even be sufficient for modern lenses and digital sensors, which are theoretically capable of resolving finer details with higher microcontrast than even the best lenses of decades past. When part of a total optical system, however, most systems (lens + sensor, for this discussion) rarely resolve more than 50-70 lp/mm due to how "real images" with high analog precision transfer to the discrete pixel grid of a sensor.

It really helps to fully understand what MTF really is. Modulation Transfer Function. That second word is key here...transfer. The MTF measures how well information "transfers" from one medium to another. In the case of a lens, the original medium is reality, an original analog signal of, for all intents and purposes, "infinite" resolution. (Obviously there might be a finite resolution if you photograph atoms or molecules...but we'll ignore those cases for the moment.) That original signal is transferred to, and through, the lens. The result on the other side of the lens is a modulated function of that transfer. Similarly, in the case of a sensor, information projected by the lens is again transferred.

In any and every transfer, there is a loss of information. To fully and very accurately measure the performance of a full optical system, one would need to compute the MTF of each and every element that affects the transmission of light from its origin in the scene to its reception by the sensor. If we break down an entire scene...we would have the air between our subject and the lens. The lens is a complex entity, containing anywhere from a few to well over a dozen elements. Between each element or element group is some other medium...air, an optical glue, the diaphragm. Between the rear-most element and the sensor is another pocket of air. Between that air and the sensor itself is a stack of filters, one designed to cut off infrared frequencies, and a matched pair to blur spatial frequencies in proximity to a certain threshold. The sensor itself has a layer of microlenses, and below the microlenses is a layer of RGB filters. Additionally, the orientation of the image projected by the lens relative to the orientation of the pixels on the sensor ALSO factors into the transfer function. Only after light has passed through this entire stack of transfer mediums is the final signal realized.

Generally speaking, we don't perform MTF "testing" on that level. Most MTF charts today are generated mathematically using original, precise computer models. These same computer models are also the basis for the actual manufacture of a lens. With a proper understanding of the materials used in a lenses actual manufacture, one can mathematically generate a very accurate MTF of a lens, within some fairly small margin of error.

MTF of a sensor is usually some derivative of its physical spatial resolution...the spacing of each pixel, factoring in loss due to a bayer design, spatial incongruence between green and red/blue pixels, optical low pass filter strength, etc. A good rule of thumb is that the spatial resolution of a CMOS image sensor (CIS) is ~73% of its base spatial resolution as derived by it's pixel pitch, although one might adjust that if they have no OLPF, or think they have a strong one, or have a sensor that does not use gapless microlenses, etc.

If we take Canon and Nikon, both of whom I believe use a 10 & 30 lp/mm "test" for their lenses, I believe the choice to use those particular detail frequencies is a hangover from original decisions decades ago. The continued use of those frequencies is to likely maintain consistency between MTF charts generated for modern lenses, allowing them to be directly compared against MTF charts for lenses 20, 30, maybe even 50 years old. So, why 10lp/mm and 30lp/mm? The general idea is to have one set of detail elements in the test scene which are, in relative terms, much larger than the resolving power of the imaging system, and one set of detail elements in the test scene which are, in relative terms, very similar to the resolving power of the imaging system.

In real-world terms, a "large" element of detail is 0.1mm in size (10lp/mm), while a "small" element of detail is 0.0333mm in size (30lp/mm). A large element is expected to be fully resolved, where as a small element may not fully resolve, depending on the resolving power of the lens. A large element is thus capable of being used to measure global contrast (more on this in a moment), and a small element is thus capable of being used to directly measure the resolving power of a lens.

Note: Depending on the lens, these days, many at wider apertures (f/4 or wider) are quite probably capable of resolving 100lp/mm, 150lp/mm, possibly even more. One has to question, then, the validity of using a 10 & 30 lp/mm test chart to evaluate the true resolving power and contrast of such a lens. It seems to me that 30lp/mm increasingly becomes a contrast factor, rather than a resolving power factor, for such lenses. Then again, not all lenses can resolve that much detail, and if a manufacturer wishes to use a common means of measuring the quality of their lenses, there is little option than to use the lowest common denominator.

Global contrast is the measure of a system's ability to transfer enough information to maintain relative difference. If a thick black line neighbors a thick white line, a lens with high contrast (regardless of it's resolving power) should transfer white as white and black as black. The transition between the black and white line may blur, thus producing a soft transition between the two rather than a hard transition...but a lens capable of high contrast will transfer white as white and black as black. A lens that is not capable of high contrast may transfer white as a bright gray, and black as a dark gray. A particularly poor lens may transfer both white and black as a middle toned gray. The part of the test chart responsible for testing the contrast of an optical system must be larger than the smallest element of detail the system can resolve in order to be useful for this purpose.

Resolving power is the measure of a system's ability to separate fine elements of very small detail. If a thin black line neighbors a thin white line, a lens with high resolving power will be able to accurately separate the two. Both lines should be observable in the projection from the lens. A lens with low resolving power will begin to blur the lines together, making it difficult to determine which part of the image is the black line, and which is the white line.

How is resolving power different from contrast? As resolving power drops, so does contrast, so why measure both? A loss of contrast does not necessarily come from a loss in resolving power. A lens may indeed be capable of resolving the hard edges between every line in a test chart, be it 10lp/mm, 30lp/mm, 50lp/mm, or 100lp/mm. A lens with low contrast, however, will still be incapable of transferring white as white and black as black...those sharply resolved line pairs may all be light and dark gray, instead of white and black. So, a properly designed MTF test will use elements of relatively large detail as well as elements of relatively small detail, in order to measure both aspects of a lens, or sensor, or full optical system.

If we use one of Canon's MTF charts as an example. A standard Canon MTF chart is plotted with quality being the Y axis, and point along the lens from center to corner being the X axis. Canon's standard indicates that 0.6 is the baseline...any line on the plot that drops below 0.6 is poor quality. Between 0.6 is good quality. Above 0.8 is excellent quality. Solid lines represent "meridional" test chart line pairs, while dotted lines represent "sagittal" test chart line pairs. Both meridional and sagittal line pairs are 45 degrees diagonal, however they are perpendicular to each other by 90 degrees. (There is a specific reason for this, which I'll get into later.) Thick lines represent the 10lp/mm test, thin lines represent the 30lp/mm test. Black lines are the MTF when the lens is tested wide open, blue lines are the MTF when the lens is stopped down to f/8.

In the case of Canon's 14mm f/2.8 L II lens, the MTF chart looks like this:

There are a lot of things we can garner from the MTF chart above. Ignoring the dotted lines for the moment, both wide open and at f/8, this lens performs extremely well (by the standard established when Canon first put their 10 & 30 lp/mm test chart into use). At f/8 (blue lines), the lens continues to perform quite well right into the corner, with the exception of the sagittal test case, where IQ drops to 0.6 and below by the corner. Resolving power (thin lines) is near maximum for f/8, however it drops off fairly quickly for both meridional and sagittal planes, producing results that are only good or poor anywhere but the center.

There are quite a few other things one can glean from an MTF chart like this as well. By using perpendicularly opposed sets of line pairs, meridional and sagittal, additional factors about a lens can be tested. Diagonal line pairs test the lens from center to corner, for all four corners. This allows astigmatism, which is a discrepancy in the point at which a lens resolves that is dependent on the rotational angle of the lens. In a lens with astigmatism, something that resolves properly at the sensor plane (focus plane) at 45 degrees may resolve forward or backward of the focus plane at 135 degrees.

The same rotational factor of the meridional and sagittal lines also allows Canon's MTF test to determine field curvature, which is the result of a lens focusing at a curve at focal point, rather than a literal plane, as the object being resolved moves towards the corner.

The quality of background blur (boke) can also be gleaned from an MTF chart like this. The quality of falloff for the MTF curves as they approach the edge is an indication of how smooth a blur circle will be. If the curves oscillate up and down as they fall off, the quality of a blur circle will probably be poor. A smooth falloff would indicate better blur circles.

This standard has been in place for years (at least 20 years, although I believe much longer than that.) While the use of diagonal line pairs still applies to test astigmatism, field curvature, and indicate boke, it is entirely possible the 30lp/mm factor is insufficient to adequately measure resolving power for lenses wide open. It is likely sufficient to measure resolving power at f/8, although something around 70lp/mm would probably be better (as maximum diffraction limited resolution at f/8 is 86lp/mm.)

-
It should be noted that my sample image is particularly "exaggerated" compared to an actual 10lp/mm + 30lp/mm test chart. If you think about those measures...ten line pairs PER MILLIMETER. The highest frequencies in my sample image probably don't even meet the requirement for 1lp/mm, let alone ten or thirty. Also keep in mind, a line pair is one white and one black line...so you actually have 20 or 60 lines total per millimeter. – jrista Apr 25 '13 at 4:19
Also recognize that the most recently released modern equipment is capable of resolving FAR more than 30lp/mm. To put things in perspective...the Canon 7D sensor, and 18mp APS-C, is capable of resolving at its best, 116lp/mm (luminance only). Factoring in the bayer CFA, it can resolve ~80lp/mm in full color, interpolated detail. A new Canon L-series Mark II lens such as the EF 300mm f/2.8 L IS II, can resolve around 160-170lp/mm at f/4. On a relative scale...10lp/mm would be like the big fat lines to the left of my chart, while 30lp/mm would be like the lines in the middle. – jrista Apr 25 '13 at 4:22
Modern real-world tests always test optical systems. MTF charts produced for lenses tend to be theoretical, generated by computers from the computer models used to actually manufacture the lenses. They are quite accurate, and extrapolating them theoretically is really the only way to determine the actual resolving power of a lens. Trying to use any kind of equipment, especially digital equipment, will limit the results, as the resolving power of an optical SYSTEM is the RMS of all the system components combined (which tends to be quite a bit lower...~20-55lp/mm most of the time.) – jrista Apr 25 '13 at 4:25
@mattdm: I've rewritten my answer. Hopefully this is better – jrista Apr 29 '13 at 16:09
That's a very useful answer but I'm still not sure how to distinguish between contrast and resolution. For example, if you look at your graph, you can see that wide open (black solid lines) the lens does well with 10l/p but struggles with 30l/p at the mid range (10 away from center). But what does that mean? Is the lost in contrast because the lens has low resolution power at that distance? Your last paragraph is most interesting (lost in contrast vs lost in resolution) but you haven't explained how the graph gives you that information. – erotsppa Apr 30 '13 at 1:14

They are indeed both a measure of contrast; one is simply measuring it at a much higher frequency than the other so they are measuring for different qualities.

The 30 lines per mm test will test the limits of the resolution of your lens, while the 10 lines per mm measurement will not really do so; your lens should have plenty of resolution to get a good measurement at that much lower granularity test. What generally affects the 10 lines per mm test is more general contrast reduction in the lens which may be caused by flare, fogging/impure surfaces or any reflections.

-

It may be helpful to consider the numbers (10 line pairs per millimeter and 30 line pairs per millimeter) as being related to the size of the features in the scene they can reproduce. In the same way it would be difficult to reproduce fine details when drawing with a fat magic marker, 10 lp/mm may be too coarse to reproduce fine image details like hair and cloth texture.

But yes, despite this difference in how we perceive their effect in an image, with an MTF graph, both figures do measure contrast reproduction.

It's also worth noting that 30 lp/mm and 10 lp/mm are fairly arbitrary (but common) choices made by some lens manufacturers. There are also plenty of optics manufacturers who use other values (such as 5, 20 and even 40 lp/mm), including Leica (Leitz), Rodenstock, Schneider and Zeiss.

-