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# D3S focus testing

Started Feb 14, 2010 | Discussions thread
Focus hyperbola

Grevture wrote:

Now I have sometimes shot dogs in action, and that is in my experience quite tricky.

Most lenses are, again in my experience, YMMW, distinctly slower to focus the closer you are to the subject. And for small dogs like terriers etc ... They are very small compared to a running athlete, a speeding motorcycle or any of the other stuff you shoot at high speeds. I mean if you were tracking focus on a race car at 20 feet distance ... You are in trouble

I think this very critical point deserves some additional emphasis. Exactly how much more difficult is it to follow focus on a close subject? The answer may surprise you.

It's a result of optical principles that the focus ring position varies as the reciprocal of subject distance. In other words, move your subject in to half its distance, and the rotation required on the focus ring (starting at infinity position) doubles. [Actually, at close distances, it's even more than this, but we can neglect that for this discussion.]

Let's call the focus ring position A, measured in degrees from the infinity position. If D is subject distance, we have
Eq. 1) A = k/D (k is a proportionality constant, determined by the lens)

Now bring in a subject moving at constant speed V:
Eq. 2) D = V*t (t is time)

Combining Eq. 1) and 2):
Eq. 3) A = k/(V*t)

Let W be the rotational speed of the lens ring, required to track our subject. W is the time derivative of A:
Eq. 4) W = dA/dt = -k/(V*t^2)

Use Eq. 2 to substitute out t:
Eq. 5) W = -k*V/(D^2)

Now, it's no surprise that the focus ring speed is proportional to subject speed, V. But that 1/(D^2) relationship is Trouble in Doggieland.

Let's apply this to a practical comparison. Suppose our camera/lens is capable of successfully tracking a race car speeding toward us at 200mph, when it's as close as 200ft. [Let's also assume that we survive this encounter.] Will Fido then be trackable, when he is coming toward us at 20mph, and he's 40ft. away?

Relatively, Fido's V has dropped by a factor of 10, which may give us comfort. However, D has decreased by a factor of 5, so (1/D^2) increases by a factor of 25. Oops. Tracking Fido will require 2.5 times as much speed as our camera is capable of!

It turns out that we need to move Fido all the way out to a minimum of 63ft., before he will be trackable by AF in this example. Clearly, intimate Fido action photography will pose a serious challenge.

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