Diffraction: Resolution taxed to its limits

Many think a higher f-stop automatically means greater detail; they're wrong

By Lloyd Chambers Back to

Chambers1

To fully exploit the sensor resolution of today’s high-resolution digital cameras, photographers must arbitrate the conflict between diffraction and lens performance/depth of field. Understanding how diffraction affects image quality will enable you to extract the best results possible from your camera.

Today’s digital cameras offer steadily improving color accuracy, dynamic range, and bit-depth, together with the crowd favorite— ever-higher megapixel counts. Yet actual image detail is constrained by optical performance: overall sharpness and depth of field require stopping down, but stopping down too far degrades image quality due to diffraction, an optical effect that puts an upper bound on resolution. Even worse, well before the resolution limit is reached, the image has long since been declining in contrast (whites and blacks become grayish), which we perceive as lower resolution, and a loss of “snap.”

For the 21MP Canon EOS 1Ds Mark III, the problem is acute: with a top-performing lens, the loss of contrast from diffraction is already an observable factor by ƒ/8. By ƒ/11, image contrast drops noticeably. By ƒ/22, the degradation is enough that only a critical need for depth of field justifies its use.

Of course, depth of field is not a prerequisite for a good picture; many beautiful and compelling images are made at wide apertures (ƒ/1.4, ƒ/2, ƒ/2.8, etc). But to fully exploit sensor resolution, even a high-quality lens requires stopping down one or two stops down from maximum aperture for optimal performance across the frame.When focus error and field curvature and vignetting are taken into account, the one-to-two-stops figure is almost an inviolate rule, with very few exceptions.

Diffraction is irrelevant when strict technical requirements are not met: focus must be spot-on and camera stability must be rock-solid (high shutter speed and/or mirror lockup on a tripod). Lens optical misalignment must also be ruled out.

Diffraction and Airy’s disc

When rays of light pass around an obstacle (e.g., a lens diaphragm), they scatter, forming a diffraction pattern known as an Airy disc (see Figure 2). As the hole (lens diaphragm) becomes smaller (“stopping down”), the  proportion of image-forming light that is scattered increases; this causes a drop in contrast. At the same time, the Airy disc steadily becomes larger, with its diameter placing a f ixed limit on resolution at any given aperture.

The Airy disc that represents a point of imaged light (Figure 2) offers a bright center portion, surrounded by a series of concentric dark/light rings. At wide apertures, the Airy disc is a tight spot, with the rings being inconsequential by comparison, but at smaller apertures (e.g., ƒ/11, ƒ/16, and so on) it grows much larger and looks less and less like a spot than the pattern of waves one might see from dropping a stone into a still pond. The larger spot and surrounding rings make mush out of image detail when they spill onto more than one photosite.

Pixel (photosite) size and diffraction

Considerations of diffraction need need take into account only the aperture involved and the resolution of the recording device (i.e., the digital sensor’s photosite size). While the sensor design (“fill factor”) along with the anti-aliasing filter and Bayer array do enter into real-world results to some small degree, these factors vary by camera/sensor, and are best ignored. Observe real images to see where the quality limits are found; the results vary little from camera to camera when the relationship of diffraction/aperture/photosite size is considered.

The traditional rule of thumb for resolution (line pairs per mm) is 1600 per f-stop (at minimal contrast). For an aperture of ƒ/8 this means 200 line pairs per millimeter, greatly exceeding the resolution of today’s DSLR sensors (but not those of digicams). But the rule misleads: it yields a resolution figure at which contrast is so low that everything looks gray, soft, and dull.

In practice, it all boils down to a simple rule based on photosite size: ignoring depth-of-field requirements, the aperture for optimal contrast is ƒ/5.6–ƒ/8 for DSLRs and ƒ/2.8–ƒ/4 for digicams, depending on actual photosite size. These figures assume today’s technology and take into account factors such as lens performance and sensor design. Deduct one stop for tomorrow’s 40MP full-frame DSLR (ƒ/4–ƒ/5.6).

The table in Figure 2b assumes lenses of the very best optical performance. Lenses exhibiting modest contrast and/or resolution will maintain their mediocre performance when stopped down further, because they did not offer optimal performance to begin with. In practice, stopping down one stop more than these figures indicate can be appropriate for many images to gain additional depth of f ield, compensate for focus error, and so on.

To understand the relationship between Airy disc size and photosite size, and why it affects resolution and contrast, it is helpful to use a depiction as shown in Figure 2c. It depicts the Airy disc size relative to the pixel (photosite) size of the 21MP Canon EOS 1Ds Mark III. The anti-aliasing f ilter and Bayer array are ignored for this depiction, which approximates the effect. Note how apertures smaller than ƒ/5.6 produce an Airy disc larger than the photosite; this spillage causes the reduction in contrast, and eventually a loss of resolving power.

Diffraction versus depth of field

In classic Greek mythology, the ship of Odysseus is forced between two mortal dangers: the immense whirlpool of Charybdis that swallows whole ships, and the fearsome multi- headed Scylla. Only by steering a precise course between the two could he hope to bring his ship to safety.

Our considerations are not so perilous: we must steer (via aperture) between contrast-robbing diffraction and perceived overall sharpness (depth of field). The irony is that by stopping down to increase overall image sharpness, diffraction degrades the image contrast near the actual plane of focus. To maintain the highest image contrast/resolution, we must find a sweet-spot aperture, in which lens performance is optimal or near- optimal, stopping down further only when depth of f ield requires it. Bear in mind that to double the depth of f ield, stopping down two stops is required, e.g., from ƒ/8 to ƒ/16.

Depth-of-field discussions invariably get technical and often involve print sizes, but ask yourself this question: why shoot that 10- or 12- or 21-MP image in a way that yields only 1 MP of actual resolution for much of the subject matter? That is precisely what you get by consulting traditional depth-of-field tables, or depth-of- field marks on most lens barrels.

Traditional depth-of-field calculations presuppose that “acceptably sharp” means an optical- spot size (circle of confusion) of 30 microns. That’s about 12 times larger than a photosite on the Nikon D3/D700 or EOS 5D, and about 30 times larger than the photosites on 10–12MP sub-full-frame DSLRs (D300, 40D, etc.). Stop down two to three stops more than the depth-of- field marks suggest in order to approach the actual resolving power of the sensor, but remember: what depth of field gives, diffraction takes away— first contrast and then resolution.

Example— resolution chart

Let’s take a look at actual results on high-contrast black-and-white. Note that real-world images often start with much lower contrast; these black-and- white results are as good as can be expected. Also, the limits are reached earlier for red light than for blue, both because of the sensor technology (Bayer array) as well as how diffraction interacts with wavelength.

I used the outstanding Nikon 85mm ƒ/2.8D PC-Micro-Nikkor lens on both the 21MP Canon EOS 1Ds Mark III and the 12MP Nikon D3, at whole apertures from ƒ/2.8 through ƒ/45. In theory, because the Nikon D3 has photosites approximately 32% larger (linearly) than the Canon EOS 1Ds Mark III, it should be possible to stop down about 2/3 stop more before diffraction limits resolution.This is not borne out by this example, however, at least using whole-stop increments. The two cameras are essentially equal in resolving power by ƒ/32.

Apertures ƒ/2.8–ƒ/5.6 are essentially identical. Aperture ƒ/8 shows a slight graying of the whites. By ƒ/11 the trend is clear: lower contrast, followed by a loss of resolution. Future DSLRs with more than 21 megapixels will see the resolution limit earlier, at ƒ/11 or ƒ/16 instead of f/22.

Note that in spite of its nearly 2× resolution advantage, by ƒ/22 the 21MP Canon 1Ds Mark III offers little resolution advantage over the 12MP Nikon D3. Also, apertures ƒ/11 and smaller require more sophisticated sharpening to regain contrast lost to diffraction. Lost resolution cannot ƒ/5.6 be regained.

Please note that magazine reproduction might limit the subtle differences, so please follow the text, or see various other examples at diglloyd.com on your computer monitor.

Does the tried-and-true 1600/f-stop diffraction-limit approximation match up with these examples? The Canon EOS-1Ds Mark III has a sensor that resolves 78 line pairs/mm (5616/36/2). Ignoring the anti-aliasing f ilter, it should be diffraction-limited for resolution at aperture 1600/78 = ~ƒ/21. While the test lens does not offer 1/10 or 1/3 stops to test this precisely, observe that the aliasing observed in the “70” bars at ƒ/16 disappears by ƒ/22, and that some resolution (or perceived resolution) is lost. So the ƒ/21 f igure seems plausible, consistent with the theory. For the Nikon D3 series (59 lp/mm), the diffraction limit should be ƒ/26, which is consistent with the differences observed between ƒ/22 and ƒ/32.


Optimal field conditions

Under optimal conditions with a near- diffraction-limited lens such as the Leica 180mm ƒ/2.8 APO-Elmarit-R (see review at diglloyd.com), superior performance can be observed for aperture ƒ/5.6 versus ƒ/8. Such performance is not the common case; very few lenses can perform to this level. (Canon EOS owners can use many Leica R lenses via an adapter.)

Example–cityscape

Resolution charts are one thing, but a real-world image is instructive. The San Francisco in Progress image at the beginning of this article is used for this example. It represents a real- world image where optimal image quality is not necessarily achievable: atmospheric haze reduces the contrast and atmospheric distortion lends a wavy look to the detail. Other real- world images have limitations as well, especially depth of field. So this image represents an everyday outdoors shooting situation, as a counterpoint to perfect test conditions.

Crops shown are from the center top of the image. Aperture ƒ/8 offers high contrast and detail rendition; aperture ƒ/11 (not shown) is nearly indistinguishable from it. By ƒ/16, however, the trend is clear: contrast drops and the image begins to look flat, though actual resolved detail is still present. Apertures ƒ/22, ƒ/32, and ƒ/45 worsen progressively. In short, a real-world image is highly consistent with the results seen on the resolution chart, except that ƒ/11 is just as good as ƒ/8 when conditions are non-optimal.

Which way is up?

As of mid-2008, the DSLR resolution champion is the 21MP Canon EOS 1Ds Mark III. In spite of its built-in anti-aliasing filter (which many photographers could do without), detail rendition is stunning. Yet within a few years, we should expect a full-frame DSLR in the 30–40 megapixel range. A 40MP full-frame camera means 4.6 micron pixels, plausible in context of existing DSLRs such as Canon’s 12.2MP EOS 450D, with its 5.2 micron pixels. Can 40 megapixels really be used effectively in a DSLR?

The short answer is yes—with the best lenses and perfect technical execution (especially focus accuracy), those 40 megapixels will produce stunning results.

But here are just a few of the caveats:

• The range of working apertures capable of exploiting a 40MP camera will be ƒ/4–ƒ/5.6, perhaps ƒ/2.8–ƒ/5.6 for the very best lenses. Some lenses won’t be up to the task at all—at any aperture.

Focus accuracy is critical.Yetthe tools to achieve perfect focus must improve: autofocus lacks sufficient precision. Manual focus requires Live View coupled with improved LCD resolution, and nearly all AF lenses have awful manual-focus feedback (no precision helicoid as with manual-focus Zeiss ZF lenses).

Field curvature is not uncommon. A curved field means that it is impossible to achieve an in-focus image center and corners simultaneously; stopping down is required. A few lenses require ƒ/8 or even ƒ/11 to overcome field curvature, hitting the diffraction problem head-on. Overcoming even modest field curvature might require stopping down two or three stops on a 40-megapixel camera.

Build quality is essential.Many current cameras suffer from optical misalignment issues (see Brand New Blur at diglloyd.com). On a 12-megapixel camera, less than perfect optical alignment is a problem; on a 40-megapixel camera, fine detail will be obliterated.

Depth-of-field needs won’t go away. Optimal image contrast together with deep depth of field demand the use of special tilt lenses that allow shifting the plane of sharp focus.

Shutter speeds will need to become faster. The “blur circle” caused by camera movement will likely require the 1/4f rule: for a focal length of “f ” millimeters, a shutter speed of 1/(4*f) will be required for 1 consistently sharp images (e.g., 2⁄ 00 sec for a 50mm lens). It might also be that the shutter itself will become a problem, even with mirror lockup. A 40-megapixel camera with a 400mm lens will be a challenging combination.

Lens performance

Most lenses improve their optical performance by stopping down onetothreestops,whichreduces uncorrected optical aberrations.

Initially,this improvement greatly outweighs the negative effects of diffraction, but diffraction soon becomes the dominant factor. A top- quality 50mmƒ/1.4lensperforms well at ƒ/2, then makes incremental improvements until ƒ/4 –ƒ/5.6. After that, image quality declines steadily from diffraction. A diffraction- limited lens is one in which the performance is governed only by physical laws, not by the shortcomings of its design or assembly. Such lenses are rare;the Leica 280mm ƒ/4 APO-Telyt-R is perhaps one example. Of course, many lenses become diffraction- limited when stopped down; the question is whether a lens can perform well when shot wide-open or stopped down only one or two stops.

I’ve explored the performance of a variety of lenses on the CanonEOS- 1Ds Mark III, including the Leica 90/180/280 APO offerings as well as the entire Zeiss ZF line (see diglloyd.com review), as well as numerous Canon and Nikon offerings. In particular, the Leica and Zeiss offerings have a performance reserve (high contrast) that should yield excellent results on even a 40- megapixel camera around aperture ƒ/4. Yet with the possible exception of the Leica 280mm ƒ/4 APO-Telyt-R, all of them require stopping down one to two stops to attain that performance across the frame, and some of them exhibit field curvature, requiring two to three stops to fully overcome.

What is missing is a lens line from any manufacturer that offers near- diffraction-limited performance for apertures from ƒ/1.4–ƒ/4, especially in the wide angle to 60mm range. We can hope that this void will be filled by Zeiss with a “ZF Pro” line, or perhaps Leica will alter strategy and offer their very best designs in Nikon and/or Canon mount. We might even someday see Canon and Nikon offer an ultra-premium lens line. The bad news is that such lenses are likely to be double the price of today’s optics, as well as larger and heavier. In the meantime, photographers serious about extracting the best possible results from their DSLR should be flexible in their choice of lenses.

Conclusions

As megapixels increase, diffraction will become the dominant factor limiting image sharpness, unless and until improved optical designs allow near-diffraction-limited imaging at apertures such as ƒ/2, ƒ/2.8, and ƒ/4. Such lenses are feasible, but will be larger, heavier, and much more expensive than today’s optics. When depth of field is a priority, “tilt” lenses should be used in order to evade the diffraction/depth of field conflict.

To paraphrase an old maxim: ƒ/8 and stop there. That simple rule will maintain optimal or near-optimal lens performance and image contrast resolution with today’s DSLRs, while offering reasonable depth of field for many subjects. Stopping down to ƒ/11 or ƒ/16 is warranted with some subjects, but the contrast compromise should be kept in mind.


About the Author

Lloyd Chambers
LChambers
Lloyd L. Chambers enjoys all-digital photography after shooting film for years in 35mm, 4 X5, 6 X7 and 617 formats. His web site diglloyd.com offers a wealth of material on advanced photographic techniques, and his Making Sharp Images is a reference work on sharpness and blur of all kinds.