## October 6, 2006

### Doing the XDCamHD Math

Please note, this blog has been archived and now lives at www.discretecosine.com

I'm still interested in the XDCamHD product line, and have been doing a bit of investigation regarding lens choices. Both Canon and Fujinon have a few lenses available to work with the 1/2" chips used by the XDCam.

Half-inch is a bit of an odd size for a CCD sensor, so I didn't have a good sense of how to compare focal lengths on the lenses. Most of them have a wide angle of 5.5mm-6.7mm, and I wanted to know if that would be "wide enough."

Since my other hobby is photography of the still variety, I have a pretty good sense of the lenses used in that realm. I shoot with a Canon Digital RebelXT, which has a sensor that is slightly smaller than 35mm film. Because of this, the Rebel (and most other "affordable" digital SLRs) has some amount of magnification as compared to a 35mm still camera.

Let me try to explain why. If you have a lens which is designed to project an image onto a 35mm piece of film, but instead project that image onto a smaller surface, you essentially get a center crop of the image. It's the same image you'd get on the 35mm film if you were to zoom the lens in a bit. In the case of the Rebel, it's a 1.6x zoom factor. Think about it for a bit, it makes sense.

When picking lenses for the Rebel, it's helpful to convert them into "real" 35mm numbers. For example, a while ago I purchased a 12-24mm Tokina lens. This is in the category of "ultra wide angle," and is very nearly a fish-eye. When you do the 1.6x math though, it's the equivalent of a 19-38 lens when shooting to 35mm.

Anyways, this same math applies to video, more or less. Things get a bit fishy because of the different aspect ratios, but we can deal with a center crop of a 16:9 image and get approximations - at least, I'm pretty sure we can.

So, I broke out the ol' whiteboard pen and started doing some geometry and algebra and whatnot.

Just a bunch of triangles, since we know the ratios of the two sides, you can use algebra to find the scaling factor, then do Pythagoras to get the diagonal. Or work backwards from the diagonal. 35mm in film refers to the horizontal, chip dimensions in video refer to the diagonal. Exciting!

After churning through all the math, I came up with the XDCamHD, with its 1/2inch chips, having a 4.25x magnification factor. So, that 6.4mm Canon lens is actually the equivalent of a 27.2mm 35mm lens. So, still moderately wide.

And that's what I wanted to know.

Posted by at October 6, 2006 4:47 PM | Misc