Modular Transfer Function (MTF)

Courtesy of Norman Korman (http://www.normankoren.com/Tutorials/MTF.html)

I was going to post this long time ago but today I'm motivated to finish it because a friend asked me "I have a 15MP Canon T1i camera, should I buy a Canon 18-200mm f/3.5-5.6 IS to replace my 18-55mm version?" Well, it depends. If the lens will give flexibility when shooting kids from wide to zoom, AND it's only going to be used on the internet (1600 pixel width), AND you don't care about optical quality, then by all means get the 18-200mm lens. On the other hand, the results may be disappointing when zoomed in to 1:1 resolution or printed at 8x10 or 11x14 and above because super zoom lenses like the 18-200mm get convenience and trade-off with inferior optical quality. So if one must use the 18-200mm lens, one might as well as shoot it on a 8-10MP camera because at full 15MP, pictures will have a tendency to look "soft" and "mushy"... they will look not much better than shooting with a lower megapixel sensor and then upsize it later in Photoshop.

Let me just say that when I need convenience, I'll simply use my wife's Canon SD750 point-and-shoot, which is a superb camera to shoot casual events... kids, pets, what not. I don't usually care about optical quality for casual events. In fact I don't expect the quality of the SD750 to remotely match that of modern DSLRs+pro-lenses. On the other hand if I'm serious about something, I'll get SLR equipments but not just any SLR equipments-- pro-lenses. There's no point of buying a toy consumer 18-200mm lens when a point-and-shoot will shoot just as well. Having that said, two years ago I bought the Canon equivalent-- back then a spanking brand new Nikkor 18-200mm f/3.5-5.6 VR. I had it for about 2 months. I sold it (on eBay) after only using it for 2 months because I was very disappointed with its optical quality. In fact, eBay today is full of used 18-200mm lenses-- people are now starting to discover that super zooms don't project good quality images, and are dumping them back to the used market.

So let's assume now that optical quality is in fact of high concern, how should one determine in general whether a lens is well matched for a particular MP sensor? You compare technical specs. However unlike looking at a single MP value, lenses are a bit more complicate. Lenses are usually characterized using the Modular Transfer Function (MTF).

Originally MTF started from USAF in the 50s when the air force wanted to know how much "lines PAIRS per millimeter" (lp/mm) a lens can resolve (this is different than l/mm!). The higher details, the more information they can get from the Soviet Union using high altitude spy planes and spy cameras. In the old film days, lp/mm was used commonly because there were only a few common formats: 35mm, medium format (45, 67, etc) and it made sense to talk about lines per millimeter projected on film. Today with a plethora of digital sensor sizes, people use lw/ph or lwph (line width per picture height) in favor of the older lpmm unit. Keep in mind, the two aren't equivalent and requires calculations to get from one to another, but for the sake of simplicity, let's just agree that the higher MTF value, the more details a lens can resolve. By the way there are a bunch of good technical MTF information online. My favorite is the following URL. Is this really necessary to read? Yes, absolutely, especially if you're a pixel peeping/engineering/math type of person:

http://www.luminous-landscape.com/tutorials/understanding-series/understanding-mtf.shtml

So going back to the question "I have a 15MP camera, should I get a 18-200mm f/3.5-5.6 IS lens to replace my 18-55mm vesion?" Unlike the camera body, we can't simply look at one single MTF value on a lens. What makes lens comparison complicated is that the center resolution will be different than the corner resolution because unlike a uniform sensor/film density, the projected optic quality isn't uniform throughout the area. To make things more complicated, lens resolution varies with aperture as well; subject to the laws of optics engineering and design, the higher the aperture, the higher resolution, and likewise the wider-open the aperture, the lower resolution. So we have two basic things to worry about now: 1) how much resolution in the different areas a lens projects 2) how much resolution using different apertures. In fact to make things even more complicated there are a bunch of other factors to consider (but we won't get into it here): contrast vs. resolution, color, chromatic aberration, vignette, distortion, and bokeh (BTW I hope I've made pixel peepers happy by mentioning all of these other issues).

Unfortunately, most manufacturers have their own MTF values derived from theoretical/calculated results. In fact, they don't make it easy for consumers to access that information. In addition, manufacturers' MTF is a lot lower than the theoretical values due to manufacturing variations, and subject to real world conditions (heat, humidity, calibration, irreproducible lighting levels, etc). Luckily however, there are numerous MTF charts published by independent testers online. Photozone is one very good European company that publishes optical results. Let's look at the MTF for the following two lenses:

18-55mm 55-250mm	18-200mm

Go to both pages, scroll to MTF for 18mm at f/3.5. You'll see that for center MTF value (middle of projection), both lenses resolve almost the same lp/ph. Now, look at border MTF value (edge of projection), and you see while the 18-55mm resolves at 2182 lw/ph, the 18-200mm resolves at an abysmal 1703 lw/ph. Extreme corner is another story to be told. Based on this MTF, one can say that the 18-200mm lens often yields mushy looking images. "This lens at f/3.5 and 18mm isn't very sharp" is what photographers would say. You can look at other apertures and other zoom ranges and see that aperture-for-aperture, zoom-for-zoom, the cheaper 18-55mm lens usually out-performs the much more expensive 18-200mm lens! (see footnote 1)

In short, lens engineering is about trade-offs, and one of the big trade-offs is convenience vs. optical quality. I understand that the 18-200mm lens is much more convenient for shooting pets and kids. It's certainly more convenient than having to switch between 18-55mm and 55-250mm lenses. So if convenience is the primary issue at hand, the 18-200mm is a fine lens. Just don't expect crystal sharp pictures.

If on the other hand optical quality is of importance (portrait, event, wedding, poster, etc), then don't get the 18-200mm. Instead get a better lens that can also resolve just as much resolution as the sensor has. MTF is your friend.

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Footnotes:

1) One can make the argument that you can just close up the aperture to f/5.6 and beyond and both lenses will perform superbly. As good as that sounds, f/5.6 is 1.5 stop lower than f/3.5. That means the lens opening at f/5.6 is roughly 1/3 (1/(2^1.5)) than at f/3.5. Shooting f/5.6 under anything but bright day will yield a lot of disappointments.