Is the 1.6 Factor on Canon Digital SLRs a Cropping Factor or a Magnification Factor?

When I started working with Canon's EF-lens compatible digital SLRs (DSLRs) -- the line including the Digital Rebel / EOS 300D, Digital Rebel XT / EOS 350D, EOS 20D, Digital Rebel XTi / EOS 400D and EOS 30D -- I constantly came across this factor "1.6."

It referred, I was told by many, to a supposed "magnification effect" of DSLRs.  Screw a 50 mm lens onto a Canon DSLR, and it acts like a 50 x 1.6 mm = 80 mm lens would on a standard film SLR.  The notion was that a lens of Y mm focal length when used on a DSLR would act like a Y x 1.6 mm focal length lens on a film SLR.

As a guy who wants magnification because of the wildlife pictures I like to take, that sounded pretty cool.  Buy Canon's 100-400 zoom lens, and you get a 160-640 lens in reality.  Woo-hoo!

But then I started reading flame wars going on various digital photography forums.  Some disparagingly called the 1.6 factor a cropping factor rather than a magnifying factor.  The reason the pictures looked magnified, the DSLR-haters (isn't it astounding what insignificant things we can find to get apoplectic about on the Internet?) contended, was that the lens was indeed acting as (for example) a 50 mm rather than an 80 mm lens insofar as its degree of magnification... it's just that the "smaller sensor" on the DSLR wasn't using all of the light focused into the camera by the lens.

35 mm Film, DSLR Sensors and APS-C

"Smaller sensor" refers to the fact that most SLRs were designed with 35 mm film in mind; a single shot on a roll of 35 mm film measures 36 mm x 24 mm.  (It's called 35 mm film because the strip is 35 mm wide.  As the picture is rectangular, the 24 mm part comes out of the width aspect of the negative.  The 36 mm part is taken along the longer dimension, the length of the film roll.)  In order for a digital SLR to mimic a 35 mm negative size-wise, the electronic light-gathering sensor would, then, have to measure 36 x 24 mm, which would be kind of expensive, which is where our next term, "APS-C" comes from.

Just about the time that digital cameras were beginning to make point-and-shoot film cameras nearly obsolete, makers of film and point-and-shoot film cameras cooked up a new film format called APS, or Advanced Photo System.  It incorporated an easy-to-use canister approach that could accommodate three kinds of film:  one for standard snapshot-sized photos, one for wider panoramic photos, and one for high-resolution photos.  The beauty of it was that just about any APS camera could use any of the three formats, and contacts on the outside of the film case told the camera which of the three formats of film was in the cartridge.  The run-of-the-mill format (which is the only APS film I've ever run across) shot pictures that were about 25 mm x 17 mm, and that format was called "APS-C."  The "C" stood for "classic," as its width-to-height ratio ("aspect ratio") mimicked that of a 35 mm photograph, even if it was smaller than a 35 mm photo.

The 35 mm aspect ratio was important for anything wanting to call itself an "SLR," but, again, actual 24 mm x 36 mm sensors are expensive.  But inasmuch as the APS-C negatives were smaller but bore the same aspect ratio as the intended-for-35-mm-film lenses, Canon invested in APS-C-sized sensors.  Result:  the length-to-height ratio of DSLR pictures look SLR-ish.  But do you lose something from the smaller sensor?  Well, there must be something to the difference between APS-C-sized sensors and 35 mm film, as Canon also offers a few cameras that sport sensors the size of a 35 mm negative.  (They're sometimes called "full frame" DSLRs.  They've been around for a while but the one that everyone wants is the EOS-1DS Mark II, which you can have for a mere $6800 as I write this.  There are a few other models with the 35 mm sensors, but they're all still expensive.)   But is there real worth in an FF system?

Lenses and Lost Light:  the Case of the Filched Photons

One way to look at it is to consider that in the long run the biggest investment a SLR owner will probably make over the years is in the lenses.  As anyone knows who's ever priced an SLR lens, you can pay as much or (almost) as little for a lens of a given focal length as you'd like.  The difference, of course, lies in the quality of the image produced by the lens as it focuses the light from the subject onto the camera's sensor or film.  In some senses, then, when you pay for a lens, you're "paying for the light" -- every photon's precious, particularly for mere duffers like myself.  The lens produces a good image; it'd be nice to get it all.  But do you get all of the light that you paid for?  No, probably never.

Look at a lens straight-on and you'll notice that it's circular, right?  That means that the image coming out of the back of the lens -- the part hitting your film or sensor -- will have a circular outline.  Hmm... I don't recall ever getting circular photographs back from the Fotomat, so clearly I've been losing at least some of the light that I've been paying for all along.  But how does that apply to taking the same lens and screwing in front of an APS-C sensor versus a full frame (35 mm) sensor?

Well, at first it seemed to me that perhaps smaller sensors/film took care of the "lost light" effect by focusing the image a bit more.  The photons, I supposed, might all be there, but they'd be packed a bit closer by a more tightly focused, brighter circle.  Having the same number of photons hit a smaller area might mean that higher-resolution-but-smaller film might not lose anything.  Reasonable?  Maybe, but in any case it was wrong.  You can prove it yourself the way I did.  Take an SLR lens and use it to project an image onto a piece of white paper.  You'll notice that there is a particular lens-to-paper distance that is the only distance that allows you to focus the image on the paper.

So how do different-sized sensors react to a given SLR lens?  The sad fact is that smaller sensors simply lack the hardware to catch all of the light coming out of the back of the lens, and so those photons are lost.  (That's not the whole story, though, as you'll see later.)  Visualize it like this:

Does this really matter?  I guess it's a matter of taste, but I wanted to find out for sure.  To accomplish that goal, I got ahold of a DSLR that uses a full frame sensor.  I set up a tripod, selected a lens (Canon's f/1.8 28 mm prime), an aperture (F/9) and tried the full frame versus the APS-C.  Here are the results, reduced to 20% of their original size.

APS-C sensor image

35 mm "full frame" sensor image

Of course, these are JPEGs generated by the cameras' processors, and it might be that the software in the APS camera did a better job than did the one in the full frame camera.  So here are two raw files taken at another time but, again, same ISO, aperture, tripod, cable release, lens -- the only difference is the camera bodies (Canon EOS 30D and EOS 5D). For some reason calling them ".cr2" files causes a 404, so I've renamed their extension to ".bin." Just rename the extension back to .cr2 and they'll work fine.

aps raw file (8 megs)

35 mm raw file (12 megs)

So what's the verdict?  Crop or magnify?  It's a bit of both, it seems.

While the 35 mm sensor clearly created a wider picture, it's also a somewhat lower-magnification picture than the APS-C picture.  To see that, grab both photos and crop out the house in the middle.  The APS-C house is about 151x136 pixels, whereas the 35 mm house is about 118x104 pixels.  If the goal here were to grab the largest number of pixels for an image of the house from a given distance on a given lens, then the APS-C camera would give us about 1.6 times -- there's that number again -- the total number of pixels as would the 35 mm sensor.

But why is that?  A smaller piece of film wouldn't create a larger bit of detail on a picture than it would on a larger piece of film.

The Missing Piece:  Sensor Resolution

Clearly there's the two sensors have other differences besides size.  To see that, let's do a bit of arithmetic.  Canon says that the 5D sensor holds 12.8 megapixels, and the 30D sensor holds 8.2 megapixels.  An APS-C sensor is 17 mm x 25 mm, which is 425 mm2.  A full frame sensor is 24 mm x 36 mm, which is 864 mm2.  Aha!  The full frame sensor has about twice the square millimeters' area of the APS-C sensor, but only about 1.5 times the number of pixels.  Calculating the resultant average size of a 5D "megapixel" and a 30D "megapixel," we get

5D pixel size = 864 mm2 / 12.8 million pixels = 68 mm2 per million 5D pixels

30D pixel size = 425 mm2 / 8.2 million pixels = 52 mm2 per million 30D pixels

The 5D pixels, then, are a bit larger, making for a somewhat lower-resolution image.  It's almost as if the 30D has finer grained film than the 5D.  The field of view on the 30D isn't as large, but it can capture any given thing in the field of view better than the 5D can.  Thus, if we were taking telephoto pictures of, say, birds in a nest, then the 30D would provide a somewhat better image than would the 5D.

This apparently isn't the case for all full frame sensors, however.  For example, when I looked up the megapixel values for the EOS-1Ds and the EOS-1Ds Mark II, I found that they offered 11.1 and 16.7 megapixels, respectively.  That would imply that the an EOS-1Ds megapixel would be 78 mm2 in size, worse grain than that offered by the 5D, and the Mark II's megapixel is only 52 mm2, equaling the 30D.

To sum up, then: