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# Macro the 1/f rule and flash duration

Started Sep 8, 2008 | Discussions thread
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Macro the 1/f rule and flash duration

My apologies for the double post - the first time through the title was clipped.

Among the many things I've learned from the macro experts on this forum is that motion blur can have a particular severe impact on image sharpness in the regime of high magnification. So much so that even using a flash in close proximity to the subject may not entirely freeze motion.

As a recovering physicist, though, I had to try to quantify this. First the theoretical part:

A standard maxim for handheld photography is the "1/f rule" stating that for sharp images shutter speeds (in seconds) should always be faster than the reciprocal of the focal length (in mm). While some folks feel that this should really be more like 1/2f or 1/5f in practice, the basic scaling rule holds. The angle you need to rotate the camera to shift the image by one pixel is roughly a/f where a is the width of the physical pixel on the sensor. So lets say you can limit the jitter in your camera to an angular velocity of w. One pixel of blur will result when your shutter speed is (a/fw). So indeed the required shutter speed to achieve a given level of blur is proportional to 1/f (and to the pixel size and the steadiness of your hands).

In any case, this is as far as the analysis usually goes, but we can easily extend this to the macro world. At high magnifications the distance from the sensor plane to the image is the sum of the image and object distances or: [(1+M) + (1+1/M)] f = [(1+M) 2 / M] f where M is the magnification and f the focal length. Since the image is magnified by a factor of M this means if we shift our view laterally by a distance of a/M (where a is again the sensor pixel width) we will shift the image by one pixel on the sensor. So the angle required for this 1 pixel shift is:

(a/M) / {[(1+M) 2 / M] f} = a/[f (1+M) 2]. This is exactly the same as the non-macro case above except for the factor of (1+M) 2 - and in fact the earler results is just the limiting case for small M.

So the upshot is that the 1/f rule is still valid for macro, but must now be modified by multiplying f by the factor of (1+M) 2. So for example at 1:1 (1+M) 2 =4 and the shutter speed for sharp handheld imaging needs to be 1/4th as long as would ordinarily be the case for the focal length.

But most folks tend to use flash at high magnifications for this very reason - which brings me to the experimental part of my post.

I'd been wondering how well flashes actually freeze motion. So I set up my MR-14 ring flash, pointed it at a photodiode and recorded the result under a few different conditions. The longest and the shortest flash duration I was able to get are shown below:

First stopped way down (f/16 on an MPE at 5:1 for an effective f/96 at ISO 100) we get about 1/1000 sec. I got the same result by recording a test flash by hand with the flash not connected to the camera.

Next open wide at minimum magnification at ISO 1600 (and yes, the actual image was totally overexposed). Here we get a duration of about 1/3000 sec.

So at least for the MR-14EX flash the effective exposure time is always going to be between about 1/1000 - 1/3000 sec. The actual amount of light can vary by a lot more than just this factor of 3 as the peak light intensity is also changing when these durations change, but the key result here is that the flash exposure is fast - but not insanely fast.

Let's put this in the context of the modified 1/f rule derived earlier. For a 65mm MPE lens at 4:1 the modified 1/f rule would say we need a shutter speed of 1/(25*65) or about 1/1600 sec to freeze motion as well as a speed of 1/f would in conventional photography. This speed is right around what the MR-14 will provide. So in this case, even with the flash you still need steady hands to produce a sharp image. Furthermore, if you have shaky enough hands or are enough of a perfectionist that you need 1/4f or 1/5f handheld, the MR-14 is simply not short enough in flash duration to provide the equivalent suppression of motion blur.

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