Algorithms for the Masses by Julian M Bucknall

I was looking at the following lens, Canon EF-S 18-135mm f/3.5-5.6 IS, on Amazon today. The reason is simple: my favorite zoom is the Canon 28-135mm and I also have a Canon 20-35mm zoom. This could replace both, in theory. At something like $340, it’s affordable too. But how good is it?

The technical description had the following charts to help describe the performance of the lens, both at full telephoto and fully wide-angle:

Riiiight. I’m sure that helps, but I don’t have the decoder ring. What does it all mean?

Back to basics. A lens captures and focuses light onto the camera’s CCD sensor (or film, if you’re still using that). In a perfect world, a lens would let all of the light pass through without hindrance, but it just ain’t so. The focal length of a lens has an effect, as does the aperture. The lenses are built such that the center of the image has the best appearance, but the further you look away from the center the worse the distortions get. At a wide-angle with a wide aperture, the edges of the resulting photo are distorted the most. It could be color fringing or aberration (usually abbreviated to CA for chromatic aberration), it could be vignetting (the edges and corners having a distinct darkening), it could be a myriad other problems. The longer the focal length or the smaller the aperture, the less distortions you get (although at very small apertures, you’ll start to suffer from interference patterns).

For a given lens, these distortion effects will be different than another lens. How to best describe the capabilities of the lens then? Enter the Modulation Transfer Function (MTF) chart.

The two things in a lens we’re interested in are the resolution and the contrast. The resolution of a lens is a measurement of how finely the lens can resolve a set of parallel lines, black lines on a white background. At some point the black lines are thin enough to smear with each other to form a grey-ish color and this point varies with the focal length and the aperture, as well as the distance from the center of the CCD. This is the resolution. Contrast on the other hand is a measure of the difference between pure black and pure white. It’s intimately tied with the resolution, since the resolving power of the lens is correlated to the contrast.

To measure this stuff, the camera and lens are focused on a special card that has a black and white cross-hatching printed on it. There are two types of hatching: one patch at 30 lines per millimeter (in other words, very fine), and another patch at 10 lines per millimeter (that is, coarse). These patches are repeated across the card, some along and parallel to the diagonal of the image (known as sagittal lines), the others perpendicular to those (and known as meridional lines). For each focal length, measurements are taken with the aperture at its widest and with the aperture set to f/8, the aperture that produces the most accurate image. (The image on the right is courtesy and copyright Canon.)

Now we can look at the chart. The X-axis measures the distance in mm along the diagonal from the center of the image. The Y-axis measures the contrast as a percentage from 0 to 100% (or equivalently from 0 to 1.0). 100% contrast is the maximum difference between black and white, anything lower than that indicates that blacks are tending to dark grey and whites to light grey. 0% means you can’t tell the difference between black and white.

On the chart there is a confusion of black lines, blue lines, lines that are solid or dashed, and lines that are thick or thin. Each attribute measures something different:

• Thick/thin — This attribute is a direct measurement of the type of cross-hatching, whether coarse or fine. You’d expect the thicker lines to be above their thinner siblings in the chart.
• Black/blue — This attribute defines a wide-open aperture (black) versus f/8 (blue). You’d expect the blue lines to be above their black siblings.
• Solid/dashed — This attribute measures meridional lines (solid) or sagittal lines (dashed). You’d expect them to be pretty much the same, all other things being equal.

So, using all three binary attributes, you’d expect 8 lines on the chart. If you look at the charts above that’s what you’ll see.

What are you looking for? First of all, a contrast value above 0.8 means you’ll get excellent image quality. Between 0.6 and 0.8, it’s satisfactory; below 0.6, it’s just so-so. Given that, you want the lines to be as high as possible in the chart. Next up, the higher the thick lines are, the better the lens will be at reproducing contrast. Similarly, the higher the thin lines, the better the resolving power of the lens. Finally you’d like the black and blue equivalent lines to be as close together as possible: this means the lens performs just as well wide open as at f/8, the sweet spot, aperture-wise.

Take a look at the telephoto chart above (the left-hand chart). First of all, the lens performs just as well when wide-open or at f/8: all pairs of black/blue lines stick close to each other. Mind you, wide-open telephoto on this lens is f/5.6, only one stop below f/8, so you’d expect the line pairs to track each other closely. Next, the contrast provided by the lens is satisfactory to excellent (the bold lines). The resolution of the lens is equally impressive. The only issue seems to be that the lens exhibits some kind of astigmatism: the differences between meridional and sagittal values is quite marked (solid vs. dashed).

The wide-angle chart is all over the place. For a start you can see that at f/8 the lens resolves much better than when wide-open (the thin lines). Ditto for contrast (the thick lines). There’s also more difference between the meridional and sagittal values. Notice how some of the lines suddenly drop off to the right: at wide-angle the lens suffers from edge distortions.

All in all, I’d say that this lens set to wide-angle should not be used below f/8 and you should expect to crop your photos towards the center to avoid edge distortions. Telephoto is better, but again the best resolution is still close to the center. Given all that, I’d also say that I’m going to stick to my current setup.

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