Crop Factor versus Teleconverter

An interesting argument broke out over the last few days on a forum on DPReview. The whole thing started when someone posted a comment that the 2.7x crop factor of the new Nikon 1 system provides some serious crop magnification so that, when the new adapter for F Mount lenses arrives, we be able to carry the equivalent of a Bigma (Sigma’s 50-500 lens) in a small bag. Wow …

I had not spent any time pondering that because the camera is not compact enough to be useful as a concert cam (or is it … hmmmm) and therefore it’s real value is as an enthusiast’s replacement for a dSLR. Well … perhaps I did not think that through.

I own the D7000 and the 18-200VR and 70-300VR along with a selection of primes and a few other zooms. I will be reshaping this over time, but for now it suffices. Imagine, though, that I felt like birding in a place where I could not get all that close to the birds. Bigmas are quite suitable for that because on a 1.5x crop like the D7000 they give a nice effective 750mm focal length.

So with the Nikon 1, my 70-300VR suddenly gives me a field of view to match a 190-810mm lens in a much smaller package than the Bigma. Now that’s quite interesting … if one carries a Nikon 1 in the bag, one is always ready to get some pretty amazing reach, providing that the light is adequate. And note that the Nikon 1 is showing serious promise with sample images being quite clean at 6400 ISO … it gets better and better.

Now, back to the argument. One person in particular is pushing the idea that the crop of the Nikon 1 is the same as if you had attached a teleconverter to a camera to achieve the same field of view on the same lens. Thus, he suggests (rather stridently in fact) that the aperture must be multiplied for more than just the depth of field effects (which is always true.)

Well, he’s made a complete hash of the argument because in fact no such effect exists. You multiply the aperture to see what sort of depth of field in full frame terms you can expect. So shooting at f/5.6 on a 2.7x crop factor means that your depth of field will be approximately equivalent to that achieved on a fill frame camera at f/15. Of course, the magnification is so strong by this point that there is plenty of subject isolation anyway.

But when we try to apply this to the noise generated by the exposure shift, the argument hits a wall. What follows is my analysis of the differences … please let me know in the comments if you find a fundamental error.

So … when you draw it out, things start to get a whole lot clearer. Here we have the identical lens on the identical system, let’s presume an F mount or EF mount … it really doesn’t matter, so long as we change only one thing in each case to achieve our crop to the new field of view.

In the top case, all we did was to insert a smaller sensor in place of the larger sensor. Basically, take a D3 body and place an APS-C sensor inside it in place of the FF sensor it came with. That would give you the moral equivalent of a D2Hs. In fact, both would be 12mp sensors, giving you the same effective quantization as well.

Now, what have you done? The amount and density of the light is the same (aperture has not changed.) Therefore, you are merely cropping the middle out of the frame, exactly as if you had captured the same image on a larger sensor and then cropped that image to the same dimensions. In other words, the aperture and exposure are the same, so the noise will be the same in that portion of the image …

The bottom case is very different. Here, you have inserted a teleconverter to magnify the image and therefore crop using the original sensor in place. Thus, you have spread the light to make it cover a larger image circle. You have therefore reduced the light density and therefore reduced the effective aperture, since nothing else has changed.

So the exposure must be rebalanced by slowing the shutter or increasing ISO. If you increase ISO, you are adding more noise to this portion of the image.

There is really nothing similar about these two cases except for the fact that you can match the field of view. The light density received across the whole image is quite different, so the exposure will be different.

Bottom line: When mounting a full frame 50mm 1.8 lens on an APS-C camera, you still get full value for the f/1.8 aperture despite the narrower field of view.

Edit:

Here is another way to think about this “dilution of light density” concept … take a magnifying glass and hold in such a way that it concentrates sunlight in a tight circle. Point the light at a piece of paper. What happens? Almost anyone knows that answer … fire and a hole in the paper.

Now, reverse the lens to spread the light out instead. What happens? Nothing. The light is much less dense and there are far fewer photons hitting any one area of the paper. It would take all the time in the world to set fire to the paper with the light spread out.

That’s all a teleconverter does. Spreads the light out to cover a larger area. Hence, it takes more time to capture the same number of photons in each pixel.