Sunday, 24 February 2013

Lenses for the DSLR: Crop Factor and Image Circles

(Not to be confused with crop circles)
A few months ago, I wrote about how sensor size affects the way different cameras capture an image when using the same lens. To refine the topic a bit further, I’m going to introduce two terms: crop factor and image circles.
Why bother with this techno-babble? Well, as stated in the earlier article, if you now own a consumer DSLR with an APS-C sized sensor, chances are that when you want to replace it down the road, your next camera will have a full frame sensor. This means that the lenses you have now are going to behave differently on your future camera, or, worst case, will force you to buy at least one new lens.
Now for my definitions:

Crop Factor – The ratio of apparent magnification provided by the same lens when switching between two different-sized camera sensors.

For example, a lens on an APS-C sized sensor will produce an image that appears magnified by a factor of 1.6 times over the image captured by that same lens on a full frame sensor. The actual image projected by the lens is the same in both cases (note that the focal length of the lens is assumed to be fixed), but the smaller APS-C sensor sees fractionally less of the projected image than the full frame sensor. In effect, the APS-C sensor is ‘cropping’ the image, thereby giving the impression that it is magnifying part of the image.

Image Circle – The diameter of a circular image projected by a lens when focused on a surface. It is usually expressed in millimetres.

In this context, the lens is projecting the image from a scene in front of the camera onto the back of the camera. At the back of the camera is the sensor. In order for the image to fully cover the sensor, the image circle must be at least as large as the diagonal measurement of the sensor. Otherwise, we would see a darkening in the corners of the resulting image where the projected image didn’t fully cover the sensor. This is called vignetting.

One important fact to note is that lens manufacturers make two different types of lenses for DSLRs: full frame and digital-only. For example, Canon full frame lenses are designated EF and digital-only are designated EF-S. They may have exactly the same focal length, but the difference is that the full frame version projects a bigger image circle, more than sufficient to cover the full frame sensor. The full frame version works fine on both full frame and APS-C cameras, whereas the digital-only version would cause vignetting on the full frame camera. Note: while the mounts look the same on the EF and EF-S lenses, there is a protruding 'shoulder' on the EF-S lenses that prevents you from mounting them on full frame cameras.
Now, you would be tempted to think that using a full frame lens on an APS-C sensor when compared with the digital-only lens would result in apparent magnification, just like the crop factor, because the smaller sensor is only capturing part of the full frame lens image circle. An important difference, however, is that if you looked at the projected images from the full frame and digital-only lenses (with the same focal length) under the exact same conditions, an object in the scene would be projected at exactly the same size. Why? - because the full frame lens actually captures a wider field of view. In other words, putting the full frame lens on an APS-C camera will project peripheral information outside of the sensor, while the digital-only lens will not project that peripheral information but will adequately cover the sensor.

If that didn’t do it for you, here’s a scenario that might explain the difference between crop factor and image circle. Hopefully, the accompanying graphics will help:
1.  I have an APS-C sensor DSLR in front of me. I also have two lenses – both are 50 mm focal length, but one is designed for full frame and one is designed for digital-only. I have the camera set up on a tripod aimed at an object (X) which sits in the middle of the viewfinder. I try each of the lenses in turn and focus on the X. I notice that the X appears to be the same size in each case, and fills the frame from top to bottom. As long as the focal length on both lenses is the same, there is no change to the size of the image or the apparent angle of view in the captured image. The only difference is that the full frame lens is projecting a bigger image circle with more peripheral information (the dots) that the sensor doesn’t see anyway.
2.  I now take the full frame 50 mm lens and put it on a full frame sensor DSLR. The angle of view now appears wider than it did on the APS-C camera and the X is smaller (doesn’t fill the frame from top to bottom) by a factor of 1/1.6 (62.5%) because of crop factor in reverse. Saying it another way, the full frame lens now just covers the full frame sensor as opposed to the APS-C sensor which cropped the full frame lens image circle and caused apparent magnification. Again, focal length remained the same, but sensor size changed. Note that the full frame sensor captures some of the peripheral image (dots) that the APS-C sensor didn't.

3.  If I put the digital-only 50mm lens on the full frame camera (not generally possible as explained above), the object size is the same as in 2., but I see severe vignetting in the corners. This is because the image circle of the digital-only lens is too small for the full frame sensor.

To tie this discussion up with a nice ribbon, we can summarize where crop factor and image circle come into play as follows:
  • Crop factor is a consideration when using the same lens on two different cameras with different sensor sizes.
  • Image circle is a consideration when using two different lenses with the same focal length but different image circle sizes on the same camera.

Taking this one step further, what if you had a full frame DSLR, but you wanted to use a lens of the same focal length (ie. 50 mm) but with a bigger image circle than the full frame lens provided? Those of us geezers who used to use medium format film know that the lenses for those old cameras projected an even bigger image circle than full frame DSLR lenses because medium format film sizes were larger than a full frame sensor. So, as long as you were comfortable shooting in manual mode, you can adapt your medium format film lenses to your DSLR for reasonable cost. Why would you need a bigger image circle if the full frame lens covered your sensor? Well, with a bigger image circle, you can (with the right adapter) use tilt and shift functions over a wider range than you could with a full frame lens.

But tilting and shifting is another subject for another blog post….