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# Macro the 1/f rule and flash duration

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

fred vachss wrote:

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.

Well, Fred... Your relapse is our gain. Thanks for the info.

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Re: Macro the 1/f rule and flash duration

Great info Fre, tks very much!

Where did you find the flash duration rates? I'm interested on duration of MR14-EX and 430EX that I own.

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Re: Macro the 1/f rule and flash duration

Eyvind wrote:

Let's not jump to conclusions, Fred. According to the manual, a total discharge
of the MR14 lasts 1.4ms i.e. about 1/700s. In addition, you can cut off the

blast by 1/64th, at least. So, I would tend to believe that the shortest possible
flash duration with the MR14 should be at least 1/45000s, and with the MT24
even shorter (more powerful flash).

You also said the 1/3000s shot was grossly overexposed, so we do not really
know how long a properly exposed one would last.

Eyvind,

As you can see from the scope traces there is some noise in these measurements and some question of how to define the duration. I used Full Width at Half Maximum and got 1.0-1.1 ms in various tries. If you define the width a bit differently I could easily see this being stated as 1.4 ms.

On the short duration end remember that peak intensity as well as duration is being varied to control total exposure. For the shortest duration shots I saw peak values as little as 1/10th those obtained with the max duration. While 1/10th peak times 1/3 duration gets a range of 30:1 not 64:1 that's at least in the ballpark of the expected range. To be fair I didn't accurately control distance from flash head to detector from shot to shot, so I don't really have a quantitative measure of how much peak intensity varied.

The point I was making about overexposure was that I believe I was close enough, at wide enough aperture and high enough ISO that the flash was cutting to its minimum power and still overexposing. I guess I am making the (unverified) assumption that when the exposure is clearly too great for the flash ETTL will limit the flash to the minimum power it can produce. I strongly suspect that f/2.8, ISO 1600 and 2-3 inches subject distance puts one in that regime.

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Re: Macro the 1/f rule and flash duration

Agreed, Fred. There are many factors deciding the minimum duration. Many of us also have found that the ETTL on the 40D is a bit inconsistent when used with the MT24 (ref. numerous threads on the misbehaviour of the 40D + MT24 combo). It could well be a similar scenario you're seeing here.

And I have to say I admire your approach and the willingness to try to measure things instead of just speculating and theorizing, as the rest of us are doing, incessantly

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Re: Macro the 1/f rule and flash duration

Very interesting. I am surprised that the minimum duration is only 1/3000 sec. I'll take your word for the maths (or math as you would say). I haven't got my mathermatical head on at the moment. I think with freezing motion it is not one of those dichotomies where it is sharp or not type things. It is probably more degrees of sharpness. Actually the figures you come up with suggest a lot of photos with the MPE and flash at high magnification are in an area where motion blur could but will not always effect sharpness.

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I did the same sorts of experiments.

A while back, I did the same kinds of experiments, but I used the MT-24EX and a 580EX.

I used a very high-speed photodiode of the sort optimized for visible light.

I tested the photodiode and measuring system using a purpose-built pulse generator driving an LED. I found that I needed to use a fast FET to drive the LED at a high enough speed to even be able to approach testing the speed of the photodiode.

In any case, I was able to satisfy myself that the photodiode, its circuit, and the rest of the measuring system was orders of magnitude faster than the flash pulses being measured. So the waveforms I was capturing truly represent the actual light output from the flashes I was testing.

The photodiode lived up to the claims of the manufacturer of having a 50 nanosecond response time, which was nice to see

I posted some threads about this, and I'll try to find them. In those threads, I calculated the flash durations using both a full width at half maximum method and a different method that I came up with that I hope better represents the periods of time where visible blurring of an image might occur.

I think what I did was to measure the widths of the pulses down to 3 stops below the peak brightness. In any case, we're on the same track here

Here are the results I got for the MT-24EX and the 580EX:

http://www.flickr.com/photos/98036178@N00/sets/72157603894160312/

1. MT-24EX Flash, One head only firing at 1/64 power.
2. MT-24EX Flash, One head only firing at 1/32 power.
3. MT-24EX Flash, One head only firing at 1/16 power.
4. MT-24EX Flash, One head only firing at 1/8 power.
5. MT-24EX Flash, One head only firing at 1/4 power.
6. MT-24EX Flash, One head only firing at 1/2 power.
7. MT-24EX Flash, One head only firing at full power.
8. MT-24EX Flash, both heads firing. A = 1/16 power, B = 1/8 power
9. MT-24EX Flash, both heads firing. A = 1/16 power, B = 1/4 power

1. 580EX Flash, Firing at 1/128 power.
2. 580EX Flash, Firing at 1/64 power.
3. 580EX Flash, Firing at 1/32 power.
4. 580EX Flash, Firing at 1/16 power.
5. 580EX Flash, Firing at 1/8 power.
6. 580EX Flash, Firing at 1/4 power.
7. 580EX Flash, Firing at 1/2 power.
8. 580EX Flash, Firing at Full power.

1. 580EX Flash, Firing at 1/32 power, high speed sync mode, 1/1000th shutter speed.

2. 580EX Flash, Firing at 1/16 power, high speed sync mode, 1/1000th shutter speed.

3. 580EX Flash, Firing at 1/16 power, high speed sync mode, 1/2000th shutter peed.

4. 580EX Flash, Firing at 1/16 power, high speed sync mode, 1/4000th shutter speed.

5. 580EX Flash, Firing at 1/16 power, high speed sync mode, 1/8000th shutter speed.

6. 580EX Flash, Firing at 1/16 power, high speed sync mode, 1/4000th shutter speed, partial trace at higher sweep speed to show detail of waveform.

7. 580EX Flash, Firing at 1/16 power, high speed sync mode, 1/4000th shutter speed, partial trace at an even higher sweep speed to show better detail of waveform.

Based on my testing, I'm wondering if perhaps the photodiode you used, or the circuit for it, might not be too slow to see the true waveforms from the flash.

I come up with a similar figure for the full-power flash duration, but at the lower output levels, I see considerably faster pulses.

Then again, I was not testing the MR-14, but instead, the MT-24 in one case, and the 580EX in the other.

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Jim H.

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Re: I did the same sorts of experiments.

Thank you very much for showing these results.

I agree that they do show faster response for the 580EX and MT24 than I appear to get with the MR14. In particular, it appears that the fastest response (of 350us) that I got from the MR-14 is similar to what you got at between 14 and 1/8 power on the MT-24.

Perhaps this is the result of my using ETTL and exposure to control duration rather than explicitly varying flash power and perhaps it is the true behavior and flashes like the MR14 with lower guide numbers don't allow for as much modulation of duration as the high GN flashes like the 580EX - and indeed you get shorter minimum durtation out of the 580 than the MT24.

That said, I don't think it's a problem in my instrumentation. I used the same photodiode and scope that I routinely use to characterize laser pulses down in the 10 ns regime. While it's not optimized for visible light and doubtless produces more noise than a properly optimized detector would I'm pretty certain that detector/circuit response time is not at issue.

Regardless, it looks like I should explicitly vary the flash head powers and repeat to remove this ambiguity.

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Do you have another flash to test with?

You might try it with a different flash, and using manual mode with the MR-14, too.

I have not tried it in ETTL mode, myself yet. But I may. In fact, that has been requested by a few people

The thing is, in ETTL mode, I'll have to trigger on the pre-flash and then use the 'scope's delayed trigger mode to find the "real" flash pulse.

And that brings something up:

Are you sure that you're not just seeing the pre-flash that is emitted when shooting in ETTL mode? Avoiding that is the main reason that I did my tests using the manual mode of the flash. But I also wanted to be able to explicitly dial in the exact flash power repeatedly, so it helped me in both of those ways.

I will try to do a search to find the threads where I posted about this before. In those threads (somewhere), I have the numbers I came up with for the flash durations.

It really is an interesting question as to what is the best or appropriate way to characterize the flash pulse widths. If they were nice rectangular pulses, it'd be easy.

But the rising edge is a typical cap-charge kind of waveform, and the falling edge is sharp (when the flash terminates the pulse to lower the output power). And for long pulses, we see a very long cap discharge curve for the trailing edge.

So we're forced to try to assign a "pulse width" figure to an odd waveform that is not of a constant shape.

So that's why I tried to come up with an arbitrary value for relative brightness above which, we get visible image creation (thus adding to blur) and below which, things will be insignificant. So that's sort of a judgment call, I guess.

In any case, though, I do think that this is important because it IS so hard to get really sharp images when shooting macros hand-held.

I've often wondered if camera shake is a big part of problems people have with the MP-E (or other high magnification set-ups) even when they are using flash. And when we use diffusers, and such, that cut down on the flash power, we might pay a penalty of increased susceptibility to blur due to the longer flash pulses that must result.

It'd be neat to design a very high speed flash system using multiple flash tubes, each of which emits only a very brief pulse. We could make up for flash duration with large numbers of flash tubes

One of the contributors to the FM "macro world" forum has built some very high-speed LED illuminators. With those, you can precisely control the flash durations.

Anyhow, this is a good subject to explore, I think!

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Jim H.

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Here's the funny thing

I did some similar measurements, but I added a step. I also tried automatic mode (ETTL) where I knew even 1/128 was way more power than asked for. Surprisingly, the 580EX seems to be able to go about 2 stops faster than manual mode 1:128. I measured that at about 1/60,000th of a second (16 uS).

Strange huh?

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Jim: to spare you the search, here it is

JimH wrote:

I have not tried it in ETTL mode, myself yet. But I may. In fact,
that has been requested by a few people

I certainly was among them :), and here is the link:

One of the contributors to the FM "macro world" forum has built some
very high-speed LED illuminators. With those, you can precisely
control the flash durations.

could you please post a pointer to this one @FM?

good luck with the ETTL setup, and if you'd ever do it, pls. test also just
a plain, on-board flash of the 40d (with and without diffusers - if
you happen to have one of these, the Puffer would standardize it a bit).

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Re: I did the same sorts of experiments.

Whoa, thanks Jim - this test is even more relevant for us MT24EX owners. The most realistic scenario is no 8, I believe, and it looks like 15 us duration of both flash heads, i.e. 1/67000s, no less. Motion blur at that level? Sounds far fetched to me.

And the shortest duration you measured is only 4us in no 1, which is 1/250000s (!).

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Ooops, I should have posted one important point.

The time period shown in the upper right corner of the oscilloscope is expressed as time / division.

And the screen divisions are very hard to see. There are ten divisions across the screen. So the actual times are ten times what you were lead to believe.

In shot 1, for example, the time is 20uS/division. So the actual duration of that flash pulse is more like 40uS (1/25,000th).

Sometime, I'd like to get a good digital oscilloscope. In this case, I was using a good-old analog storage scope which makes things a bit harder to read, particularly when looking at photos of its screen and not seeing it "in the flesh".

I think in my original thread about this, I did mention all of that. But I failed to say it this time.

Sorry for the confusion, it's my fault for just posting the photos without the proper annotations!

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Jim H.

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That's interesting.

They might have just gotten lazy and not provided the additional manual steps when they were designing the flash. It's a shame that they didn't provide access to that extra capability in the manual mode, but they might have felt that nobody would ever use them.

It's interesting that your tests show that in ETTL mode, when the flash is free to set itself, it's capable of producing those even shorter flash pulses. To me, it'd be handy to have those available in manual mode for some uses.

I remember, years ago, taping a piece of paper to an auto-thyristor type flash so that it guided a portion of the flash's output directly back into the sensor. This yielded extremely brief flash pulses that I used to try to freeze flying bullets and things like that.

I was actually somewhat gratified to find that the 580 does seem to be capable of fairly brief pulses. I wonder just how brief its flash pulses can be when it's in ETTL mode.

It really is a shame that the manual settings don't go lower since the flash itself is capable of generating the shorter pulses. I might use them even if almost nobody else would

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Jim H.

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This guy is amazing :)

Here is one of the threads. This is amazing work. Read through that thread and you'll see his LED devices mentioned throughout, and particularly near the end of the thread:

http://www.fredmiranda.com/forum/topic/609566/0

And here's a link to one of his pages on pbase:

http://www.pbase.com/fotoopa/water_figures_2008

At some point, if I get the time, I'd like to test various speedlites and the on-board flash of the 20D or 40D to see what the pulse widths look like.

I don't have a puffer, but I've been thinking of getting a few anyhow, so I may well do that too.

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Jim H.

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Re: Macro the 1/f rule and flash duration

I know, not from math or physics, but from experience that getting razor sharp images means shooting with insanely fast shutter speeds -even if you have everything on a tripod. A lot of what people call diffraction I call macro motion blur induced by a flash duration that's too long...

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Re: Macro the 1/f rule and flash duration

oldfartwitha5d wrote:

Agreed, Fred. There are many factors deciding the minimum duration.
Many of us also have found that the ETTL on the 40D is a bit
inconsistent when used with the MT24 (ref. numerous threads on the
misbehaviour of the 40D + MT24 combo). It could well be a similar
scenario you're seeing here.

I'm beginning to wonder if the E-TTL II metering in the 40D isn't compatible with the first generation of E-TTL flash units. I had to completely re-learn how to use the MT-24EX this year after switching to the 40D...

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Re: Ooops, I should have posted one important point.

JimH wrote:

The time period shown in the upper right corner of the oscilloscope
is expressed as time / division.

And the screen divisions are very hard to see. There are ten
divisions across the screen. So the actual times are ten times what
you were lead to believe.

In shot 1, for example, the time is 20uS/division. So the actual
duration of that flash pulse is more like 40uS (1/25,000th).

Sometime, I'd like to get a good digital oscilloscope. In this case,
I was using a good-old analog storage scope which makes things a bit
harder to read, particularly when looking at photos of its screen and
not seeing it "in the flesh".

I think in my original thread about this, I did mention all of that.
But I failed to say it this time.

Sorry for the confusion, it's my fault for just posting the photos
without the proper annotations!

There seems to be some confusion Jim when people see your results in that they think the whole "motion blur with flash problem" is over rated because your pulse widths are so short. But the problem is that you'll never get those short duration pulses when shooting a photo in the real world -you need a lot more light than a 1/25,000 of a second pulse can provide. I wish there was a way to measure the pulse width when shooting a standard gray card at different magnifications -still not an accurate test of real world conditions but it would be a little better than just testing each power level.

Since most commercial diffusers block at least one full stop I've switched to using some engineering samples that a company sent to me (sorry, can't name them) and the plastic that I'm currently testing only blocks 2% of the light passing through it (a full stop would be 50% light transmittal). So far the level of detail that I'm getting has been excellent...

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Re: Jim: to spare you the search, here it is

jpr2 wrote:

could you please post a pointer to this one @FM?

I posted a link at the macro forum: http://www.fredmiranda.com/forum/topic/685753/0#lastmessage

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