More pixels do not always yield better resolution — especially when photographing small things, like snowflakes

Snowflakes photographed by the author in Yellowknife, Northwest Territories, using a custom-built low-temp, high-resolution microscope system. Copyright Modernist Cuisine Gallery

Let me start out by saying that I have huge respect for Don Komarechka’s snowflake photos. They have been an inspiration to me. I am new to snowflake photography, and having seen his photos — as well as those of Ken Libbrecht, Alexey Kljatov, and many others — I would never even dream of boasting that I’ve made the best snowflake photos.

So I am a bit dismayed that a flurry of controversy has erupted around a claim that I thought would be simple and objective: that my new snowflake microscope makes the highest-resolution snowflake photos ever taken. That isn’t an empty boast; it’s supported by math and basic optics. I don’t see why it should be so threatening to Mr. Komarechka that he has to try one-up me, but that apparently is the situation.

Resolution is all about details, so the technical details matter.

Mr. Komarechka’s immediate claim is that he made a snowflake photograph containing 187 million pixels (megapixels) — more than the 100 megapixels in my snowflake image files. So let’s examine this in detail.

First, the photo in question isn’t even a picture of a snowflake. Instead, it is an image of a “cast” or replica of a snowflake made by covering the snowflake with a clear resin (some people use superglue for this) and then making a permanent microscope slide. The slide can then be taken indoors and photographed at room temperature. Indeed you can buy snowflake casts on Etsy.

It’s obviously more convenient to work with a permanent replica than to labor to take your shot out in the cold, where time is your enemy because snowflakes literally vanish into thin air, through the process of sublimation. But if I pointed my camera at my TV set during a BBC wildlife show, would be it be fair for me to then say that I shot a photo of a snow leopard, because one was on the screen?

Despite the convenience of replicas, there is a good reason that serious snowflake photographers these days avoid them: replicas look bad. Mr. Komarechka himself commented that his “high-resolution” photo of the replica is not that great. And I’d agree, especially comparing it to his photos of real (non-replica) snowflakes on his site Sky Crystals or to Ken Libbrecht’s excellent photos on his site SnowCrystals.com.

A second important issue with the claim that this 187-megapixel photo is a very high-resolution image is that pixels and resolution are different things, particularly in macro photography and microscopy. Mr. Komarechka explained that he used a Panasonic Lumix S1R digital camera, a model that has a feature known as pixel shift. This feature allows it to shoot eight images in quick succession, with the sensor shifted sideways by a fraction of a pixel before each shot. Software then processes the eight images to make a large composite photo — which yields a whopping big file containing lots of pixels.

But that is not the same thing as resolution because the optics (the lenses and apertures and focal distances) also limit the smallest details in the subject that are captured in the photo. If the optics aren’t up to the job, you’ll just make a big, high-megapixel image that fails to resolve tiny details.

Mr. Komarechka’s photo was taken at just over 2x magnification with a camera macro lens, which he says was set to f/5.6. Basic optics tells us that, under these circumstances, the effective f-stop is approximately

where f_stop is the setting on the lens (5.6 here), and mag is the magnification (2). (See this site for a good explanation of the physics.) Mr. Komarechka’s setup yields an effective f-stop of about f_eff/16.7.

That’s quite different from f/5.6, and that matters because of the effects of diffraction: the higher the f-stop, the more that the wave nature of light limits resolution. (The Cambridge in Color site also has a good explanation of diffraction effects.) The minimum size detail resolved in an image — and thus its maximum resolution — is limited by the diameter of the so-called Airy disc, which at an effective f-stop of f/16 is 21.3 microns (0.0213 mm).

Mr. Komarechka used a full-frame sensor in his camera that is 36 mm by 24 mm, which works out to about 1690 by 1127 in units of Airy discs. Multiply those two numbers together, and we get an effective resolution for his setup of 1.9 million details resolved in the picture. In other words, the image is very close to what you would capture with a 2-megapixel sensor and roughly the same resolution as HDTV.

Though one can argue that you’d need a few more than 2 million pixels to capture a couple million details resolved in Airy discs, there is simply no possible way that Mr. Komarechka’s optical system exploited 187 megapixels.

A third factor at play is the low 2x magnification used for his photo. Most snowflakes are just 3 mm to 6 mm in diameter. At 2x magnification, the image on the sensor was probably 12 mm across at most. That’s just 1/6th of the frame size, so most of the pixels in the photo contain background rather than snowflake. Because of these effects, the snowflake replica proper probably occupies fewer than 0.4 megapixels.

The technical term for a system like this one is “optics limited.” Although the Lumix S1R camera can use pixel-shift processing to create pixels that are 2.1 microns across — even though its sensor has a pixel pitch of 4.3 microns — the smallest details are actually 21.3 microns across, due to diffraction. So that ought to dispose of the claim that his photo is higher resolution than mine. It’s closer to the resolution of the rearward-facing selfie camera on most new phones.

These optical limitations apply as well to Mr. Komarechka’s other snowflake work. On his website, he notes that most of his serious snowflake photos are taken with a Canon 1DX with a Canon macro lens that goes to 5x magnification and a maximum aperture of f/2.8. Setting that Canon lens wide open at f/2.8 and 5x produces an effective f-stop of 16.7. Again, the Airy disc will be about 21.3 microns across, and the full-frame sensor on the Canon 1DX should cover about 1690 by 1127 details, equivalent to about 1.9 million pixels, or HDTV resolution. These days, for professional still photos, that would qualify as quite low resolution.

A funny thing about that setup is that one can actually get higher-resolution photos by using lower magnification. Using the lens at 1x magnification yields an effective f-stop of 5.6 and Airy discs 7.5 microns across — comparable in size to the 6.9 micron pixels on the Canon 1DX sensor, which has a full-frame resolution of 18.1 megapixels. Because typical snowflakes at 1x magnification will form an image just 3 mm to 6 mm wide on the sensor, the useful resolution will be around 3 megapixels, but that’s actually better than the scenario above.

It’s pretty clear that Mr. Komarechka’s approach to snowflake photography is quite different than mine.

He uses a camera, often handheld, to take pictures of a snowflake perched on a mitten. I use a Phase One camera back with a medium-format, 100-megapixel sensor to photograph snowflakes on an optically flat piece of chilled artificial sapphire. Instead of standard camera lenses, I use Mitutoyo microscope objectives, and most of my snowflake pictures are taken with a 10x objective.

Microscope objectives are not described in terms of f-stops; instead one uses a term called numerical aperture, or NA. My 10x objective has an NA of 0.28. This corresponds (at a wavelength of 550 nanometers) to an Airy disc diameter of 1.198 microns at the objective. The tube lens I use makes the actual magnification 12x, so at the sensor the Airy disc is 14.38 microns across. With a Phase One IQ3 sensor that is 53.7 by 40.4 mm, this means the effective resolution is about 3735 by 2810 details, resolved by about 10.5 million pixels. Here is a table for all of the objectives I use:

The 5x, 7.5x, and 10x objectives come out to the same resolution by design — the manufacturer planned that would happen in their choice of NA and magnification.

Even though my medium-format sensor has 100 megapixels, it records far fewer than 100 million details: each of those objectives can resolve about 10.5 million details. The physical size of the sensor is actually more important here than its pixel count. If I had instead used a full-frame 35 mm sensor (dimensions 36mm by 24mm), then the 5x thru 10x objectives would give me only about 4.2 megapixels of detail.

By the way, this is also how I knew that my photos were the highest resolution around. Everybody else taking snowflake photos is using camera sensors that are physically smaller. Ken Libbrecht also uses Mitutoyo objectives but in a set up with a smaller-sensor camera. Others, like Mr. Komarechka, use inferior optics as well as smaller sensors.

The analysis above should make it clear why it is silly that the Maclean’s article challenges me to provide an image file to “prove” that my snowflake photos have higher resolution. File size does not mean resolution; it means file size. To measure resolution, you need to account for both the effects of diffraction (the size of the Airy discs) and the sensor size.

Now one might ask what does it matter? Is picture resolution worth squabbling over?

The answer depends entirely on what you want to do with the pictures. For web sites, it really doesn’t matter at all. Most photos published online are 1 to 2 megapixels, so there is no difference between a 100-megapixel shot and one that is natively shot with 1 megapixel. In fact, because smaller files load faster, extra resolution can be a negative. Low-resolution photos (of about 2 megapixels or less) are also fine for most books, magazines, and newspapers.

But when you start making prints larger than 10 to 12 inches, the limits of low-resolution images become easily visible. I like to make big prints — sometimes many feet across — that you can walk right up to and still see intricate details. That’s a personal choice of mine, and I don’t expect everybody (and perhaps not even most people) to agree.

That said, I’m apparently not the only one who likes higher resolution. Although HDTV was supposed to be as much resolution as we would ever need, almost all large flat-screen TVs these days are “4K” resolution (8.3 megapixels in a 16:9 picture), and most streaming services now support 4K programs. Most viewers seem to like them better. Now 8K TVs coming to market cram more than 33 megapixels into a frame. The same is happening with cell-phone cameras: they are marketed aggressively on the basis of their megapixel counts.

The bottom line is that resolution can limit the practical uses of a photo, but it does not by itself make the photo good or bad. Many of the greatest photos ever taken were of low resolution, either because the film on which they were shot had inherent resolution issues, or because they were taken with less sophisticated digital cameras. On the flip side, nobody cares that you can’t make a big print of a bad photo!

Considering how much effort it took to develop our snowflake microscope and lug it to Ontario and the Yukon and Fairbanks, I can certainly understand Mr. Komarechka’s decision to use smaller and lighter equipment. Easy to use, nimble equipment lets you take more pictures in a session, and that usually translates into better pictures overall.

For my part, I labor away with more clumsy equipment because our use case requires it. The resolution distinction for a photo is not the whole prize, but it is an interesting footnote that in some cases can be important.

That’s why I was so surprised that Mr. Komarechka went on the attack. His pictures are beautiful, even if they are low resolution. There is no reason for him to feel threatened by me. It would be easy to dismiss his jabs as just a misunderstanding, but I have to believe that Mr. Komarechka understands all these crucial technical points about diffraction and resolution. He has written a forthcoming book on macro photography that, according to his promo blurb,

“aims to cover every challenge that a macro photographer might encounter, from beginner problems like focus and motion blur, to more complex issues with magnification and diffraction, lighting and composition, and so much more.”

So he must know that the actual resolving power of his own photos is quite low. And though I’ve elaborated here on the technical details of my setup, the basics have been widely reported in the media.

This isn’t a case of a usurper making false claims and getting, as Maclean’s put it, “taken to task.” Nor is it some kind of Canada vs. U.S. rivalry, as they suggested. It’s just a case of deliberately deceptive statements to gin up self-promoting controversy. I find that unethical and really unfortunate, because snowflake photographers are a tiny community who should be sharing tips and techniques rather than smacking each other around.

As a newcomer to that community, I look forward to learning more from its pioneering photographers, including Mr. Komarechka. And given continuing advances in technology, I have no doubt that both better and higher-resolution snowflake photos will be made in the future.

Addendum 03–01–21

Although this note on resolution is long, it is nevertheless a grossly simplified account and doesn’t cover a variety of relevant factors.

First, the discussion above assumes perfect lenses; of course no real lens is perfect. Next, it ignores color. In reality, the size of the Airy disc varies with color — that is, it depends on the frequency of light. The convention when estimating resolution is to use green light, which is near the center of the visible spectrum, but red, green, and blue light actually diffract in different patterns.

Color is further complicated by the Bayer filter array, which is a mosaic filter overlaid on most camera sensors to produce separate pixels for red, green, and blue light. A third subtlety ignored in the analysis is contrast. Our ability to see resolution in a photo depends in part on how much contrast the lens provides in the final image.

Equating the number of Airy discs directly to the pixel count is also a gross simplification. It is inspired by the Rayleigh criterion, which states that two point sources are just barely resolved when the edges of their Airy discs just touch without overlapping. While that has some intuitive support, it is not a precise relationship.

Mathematically, the effect of diffraction on an image is very similar to applying a Gaussian blur in Photoshop. But really there is no simple algorithm you can run on a severely blurred image to calculate the equivalent number of sharp pixels. Cambridge in Color has a good simulation that illustrates how diffraction destroys details in an image.

None of these subtler factors change the overall conclusions above. Nor do they alter the relative standing of the resolution of different approaches to snowflake photography.

The official Medium account of Nathan Myhrvold, CEO of @IVInvents, @ModCuisine author, scientist, inventor, and photographer. FaceBook: @NathanMyhrvoldOfficial.