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01-29-2018, 04:03 PM - 5 Likes   #1
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True Shutter Speeds compared to Nominal Shutter Speeds - Actual Measurements

A week or so ago, partially impelled by this discussion of how our cameras respond to changes in sensitivity (shutter speed or aperture), I used my K-1 to shoot my black/gray/white scale card at various shutter speeds covering the entire range of sensible exposures for all three brightness levels. When I plotted the results, there were some minor kinks in the response curves. After a bit of thought, a plausible explanation was that the claimed shutter speeds were not quite right.

Some web searching lead me to this article, which, while it concentrated on Nikons, suggested that indicated shutter speeds were indeed not necessarily correct. The essence of the argument is that whole exposure step speeds longer than 8 seconds or shorter than 1/8 second are just not right. Rather, our cameras really do change the exposure such that a so-called 15 second exposure is really 16 seconds - the true doubling of the 8 second speed. And, in this scheme, our "30 second" exposure is really 32 seconds.

After reading this, I adjusted the exposure speeds in my plot to the values suggested by a true mathematical sequence, and the results look much smoother. I will report these results elsewhere on the Forum.

This prompted me to try timing a so-called 30 second exposure, since a simple stop watch test should clearly be able to distinguish between 30 and 32 seconds. Lo and behold, I indeed got 32 seconds!

Thus, I started a thread in the Forum asking what folks here knew about this. I also set out to design an electronic way to measure true shutter speeds. In the olden (film SLR!) days, such measurements were ridiculously simple: you opened the camera back, put a photocell behind the shutter curtain, shined a light in the front of the camera, fired the shutter, and measured how long the light came through. You canít do that with DSLRs - you donít have access to the region behind the shutter curtains - the sensor lives there.

Hence, a different approach is needed. A reasonable scheme is to be to create a pattern of lights which flash at a rate such that many of them should be illuminated during an exposure. To make a reasonably accurate measurement (~1%), there should be at least 100 flashes during an exposure. Then you just count how many flashes you see in the image and compare that with how many flashes there "should be" during the exposure. For example, consider a 1 second exposure of lights which flash 100 times per second. You should see 100 flash spots in your image. If you see more than 100, the shutter was open longer than 1 second. Fewer than 100 flashes -> the shutter was not open as long as 1 second.

Itís trivial to flash an LED at appropriate rates - a few times a second to hundred of thousands of time per second. The trick is to have the flashes in separate locations - a picture of a single flashing light tells you nothing about how many times it flashed during an exposure!

So, I need an array of more than 100 LEDs that I can flash at a proper rate. Itís relatively simple to design such a circuit using integrated circuit counter chips and a bunch of LEDs. Unfortunately, wiring this up can be a nightmare - in the simplest circuit, you need at least 100 wires, one for each LED, not counting the rest of the circuitry. A simpler circuit results if you use a grid of LEDs. 8 by 8 arrays (64 LEDs in all) are readily available, and I had already made an exposure tester with one of these years ago. However, to get my 1% target accuracy, I need more than 64 LEDs.

Fortunately, there is another way to spread out the LEDs - you can move a modest LED array during the exposure. An easy way to move it is to hang up the LED array as a pendulum and swing it back and forth. This works nicely, as you will see below, for a range of exposures from around 1 second to about 1/20 second. So, I built a little 10 LED circuit with a decade counter (using a 4017 chip) and hung it up in my house. I have a signal generator that I can use to set the flash rate very accurately to any desired frequency. For some exposures, I set the frequency to produce as many as 400 flashes expected during an exposure.

Hereís a picture of my flasher. One after another, the LEDs are "on" for the duration of a cycle. The clamps hold a battery pack to the back side of the circuit board:



A web search such as "10 LED chaser circuit with 4017" will produce a number of hits if you would like to make something like this on your own. The parts cost with some astute Ebay searching should be well under $10. Here are a couple of examples:

LED Chaser using 4017 Counter and 555 Timer
LED chaser circuit / Sequential LED flasher using 4017 IC and 555 timer - Elonics

These examples include a 555 timer circuit to create the flash rate. This is OK for a simple flasher where you donít particularly care what the flash rate is. To measure shutter speeds, you do need a source of accurate frequency.


Hereís a picture of my flasher shown suspended on a lightweight rope so it can swing back and forth. The wire brings in the frequency signal from my signal generator.





OK - thatís nice, but how about some results!!

Using my K-1, I started at 1 second exposure and a flash rate of 100 Hz (Hz = cycles (flashes!) per second). Hereís one of my first shots, cropped to show just the lights. At this point, I was using only 5 of the LEDs in my array. You can readily count 100 flashes. The sequence starts at far left, with a very faint flash - the exposure started as this LED was going out (the LED array flashes in order from bottom to top - so the pendulum is swinging from left to right in this picture) and ends far right, where the last flash is at the top and a bit fainter than typical - it has not completely illuminated during the exposure. There are 100 flashes (counting the first and last as one, since each is only partly illuminated) as expected for a 1 second exposure.




Then I increased the flash rate to 200 Hz:




I got tired of counting all those cycles of 5, so I activated the rest of the LED array (10 LEDs in all) in the circuit - here are 19 cycles of 10 LEDs and 5 on each end, giving the expected 200 flashes for a correct 1second exposure:




Then itís on to 1/2 second - the lights are not as spread out. With a flash rate of 400 Hz, I get 19 full columns and 4 counts on the left end and 7on the right end - 201 counts in all - one too many for exactly half a second, so my camera shutter is staying open very slightly longer than it should (about half a per cent):




Hereís a shot of my system in action (with the kitchen in the background!). You can see the signal generator in the lower right. I ran a cable from this up to the second floor where the pendulum was swinging from and back down the rope to the circuit.




Hereís 1/4 second, where we again get an extra count:




I then upped the flash rate to give me an expected 400 counts for 1/4 second. And the count is 402. So my K-1 shutter is consistently staying open a bit longer than it should:





So far, everything is as expected. But all these measurements are for changes in shutter speed that are exactly steps of 2.

What happens at 1/15 second? We find that the speed is really 1/16 second, as hypothesized if sensitivity steps really are a factor of two!

First, I set the flash rate to 1500 Hz and took a shot. If the actual shutter speed is 1/15 second, I should see 100 flashes. I donít!! I get 94. Calculating the shutter speed from these counts, I get 94/1500 = 0.0627 second, quite close to what youíd expect for 1/16 second = 0.0625, especially if my shutter speeds are running a bit long:




Then I set the flash rate to 1600 Hz. We find 100+ counts (note the faint glow at the top of the right column), just as expected for a true shutter speed of 1/16 second:




I made a final measurement at a claimed shutter speed of 1/20 second. The result is way short of the expected 100 flashes - only 89 flashes. The resultant shutter speed (based on an average of 9 frames) is actually about 0.0446 second:





Bottom Line

I now firmly believe that the K-1 really is giving mathematically-correct exposure values, rather than the nominal values shown for many exposure lengths. Thus, I expect the 1/20 second exposure should really be (1/16)/sqrt(2), since I had the K-1 set to 1/2 EV steps, where a half EV step corresponds to a change in sensitivity of sqrt(2). The calculated speed for 1/20 second is therefore 0.0442 - very close to measured. (And assuredly different from the value one would get using 1/3 EV steps, where the correct "1/20 second" value is 0.0496 (again, not 0.05).)

To go to shorter shutter speeds, I will have to actually come up with a proper 100 LED flasher circuit. I canít swing my pendulum fast enough! To go to longer shutter speeds (greater than 1 second), I think I can use my existing 10 stage flasher and move it by hand across the camera frame during an exposure - here the pendulum period is too short: the period is less than 2 seconds, so longer exposures will tend to overlap.

When/if I make additional measurements, I will present them here. But for now, I think it is safe to say that actual shutter speeds have an exact mathematical relationship, where we can take the starting point to be a 1 second exposure, and for 1/2 EV steps, the change from one speed to the next is a square root of 2. For 1/3 EV steps, the results should be based on the cube root of 2 (~1.260). this reference (cited earlier) has a nice table of expected shutter speeds for both1/2 and 1/3 EV steps, about half-way down the page (the 1/2 and 1/3 EV values are interleaved - be careful!).

I will make some similar measurements for my K-3.

I will also try to find the old data taken with my 8x8 flasher - that was for my long-gone Canon Rebel XT (or XTi) and (I think) my also-long-gone K-10 (maybe K-20). Those results should be accurate enough to shed some light on actual versus nominal shutter speeds over a wider range of speeds.


I have embedded my images in with text where I want them above by reference to a web site. Is there any way to actually put images in the middle of text by attaching them? My experience on attaching images is that they always go at the end of a post. At some point in the future, the embedded images will disappear (i.e. when I die and my web sites disappear!).

01-29-2018, 06:06 PM   #2
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Having dabbled extensively in microprocessor programming in Assembly, I think the simplest explanation for this is that overall processing speed (therefore latency) during shutter release is a greater concern than absolute precision in the timing. All MCUs are at their basic level binary. Even when programmed in C (which most are at this level) the instructions are rendered in assembly, using binary calculations that make very short work of factors of two. Any calculations involving an integer in between necessitates multiple repititions of large chunks of code which, while trivial for CPUs, will introduce a significant latency in simple MCUs as would be used as the timer for this purpose.

Shutter lag, especially for those that moved from mechanical bodies with zero lag, is a greater sin than a few percent error in shutter speed, which was never remotely that accurate in mechanical bodies. This would I expect be the engineering decision behind using binary rather than decimal timings.
01-29-2018, 06:17 PM   #3
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Awesome work and extremely interesting results.

It definitely confirms that the K-1 accurately preserves reciprocity -- ensuring, for example, that 8 sec @ f/4 really is the same as "30" sec @ f/8.

That said, it seems to imply that a "20" sec exposure might either be 20.16 seconds or 22.63 seconds depending on whether the camera is in 1/3 or 1/2 stop increment mode which is kind of confusing for setting up interval shooting.
01-29-2018, 08:55 PM   #4
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Really, really interesting. So it just boils down to the fact that the camera display of the shutter speed has been idealized and that the exposures are right on the money (even mathematically)?

Suggest that for the high speed test, you use a single stationary LED and a rotating mirror in front of the lens (90 degrees relative to the LED). Synchronizing it might be tricky - maybe just a bunch of runs until you get a centered set of pulses.

Alternately, you can also use a CRT if you know the vertical (and horizontal) sweep speeds accurately. Shoot a picture on the CRT and by observing the lighted lines, you should be able to deduce the shutter speed (if you can find a CRT display).

Great work - I already saw it referenced in another forum.

01-29-2018, 11:11 PM   #5
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So it also looks like there is nothing in the EXIF data that specifies the more precise version of the shutter speed; just the "traditional" shutter speed shown on the camera's display and knobs.
01-30-2018, 11:20 AM   #6
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Maybe there's something I'm not taking in to account, and I don't mean to be rude, but do you think there's anybody who can tell the difference between a 32s and a 30s exposure? or a 1/16s and 1/15? or a 1/256 and 1/250?

I always thought that the actual speeds were multiples of two (1/4, 1/8, 1/16, 1/32, 1/64, 1/128, 1/256, etc.) as is demonstrated by the OP, and the labels in camera were rounded for simplicity. With all respect, what is the relevance of all this?
01-30-2018, 11:24 AM - 2 Likes   #7
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QuoteOriginally posted by CarlosU Quote
Maybe there's something I'm not taking in to account, and I don't mean to be rude, but do you think there's anybody who can tell the difference between a 32s and a 30s exposure? or a 1/16s and 1/15? or a 1/256 and 1/250?

I always thought that the real speeds were multiples of two (1/4, 1/8, 1/16, 1/32, 1/64, 1/128, 1/256, etc.) as is demonstrated by the OP, and the labels in camera were rounded for simplicity. With all respect, what is the relevance of all this?
This a dup of my post in Actual shutter speeds versus "standard" values - Page 2 - PentaxForums.com

For 99% of images, you are right that the difference is irrelevant. But there are at least a three scenarios where it does matter:

1. Interval shooting: Intervalometers (including the ones built into the K-1) work by "pressing the shutter button" on a schedule of timed intervals. If you set the intervalometer to 30 seconds, then every 30 seconds it will try to take a picture. Now if the shutter speed is set to "30" but the exposure time is really 32 seconds long, then the next intervalometer button press will happen during the previous exposure and do nothing. Instead of getting one shot every 30 seconds, you'll get a shot, then a 28 second delay, then another shot, then a delay , etc. and half the number of shots you expected. Successful use of interval shooting depends on knowing the true exposure time and this work shows that the true exposure time (which is mathematically calculated for accuracy) is different than the dial time.

2. Interactions with artificial lights: Many types of artificial lights (fluorescent, CFL, LED, etc.) flicker stroboscopically in time with the power line or some internal clock. Often this flicker frequency is exactly twice the line frequency (e.g., 2*60 Hz = 120 flickers per second in the US). If you set the shutter speed to "1/60" you'd expect to always get an exposure illuminated by exactly 2 flickers of light. But we now know that the camera is actually shooting at 1/64 so it's not getting two full flickers. Because the intensity of the light source and color of the light source varies during the flicker cycle, shooting at 1/64 in a place lit by a 120 flicker/second light source may have weird color and image brightness variations between the shots.

3. Measurement: In technical photography, you can estimate the velocities of objects from the length of the blur they create in the image. But to get an accurate velocity estimate, you need to know the true exposure time which might be up to 13% different than the dial time.


Besides, it's a interesting foray into science and engineering to try to figure out exactly what the camera is doing. It's fun exercise for the little grey cells to figure a way to accurately measure the true exposure time of the camera as AstroDave has done.
01-30-2018, 12:24 PM   #8
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For film cameras, I have an old Calumet branded timer that can measure focal plane or leaf shutter speeds from 4 seconds to 1/8000" to a degree of accuracy of 1/100,000". Plus or minus 1/6 EV was considered normal and acceptable. Plus/minus 1/3 EV or greater was considered unacceptable (depending of course on if you're shooting slides or negs, and the ISO).

In testing film camera focal plane shutters, there are always plus/minus errors. I would hope that's not the case on electronic shutters, but it's always there on DSLRs with mechanical shutters.

Also one can't forget the inaccurate nature of apertures measured in f/stops which are purely theoretical and do not take into account variables such as light transmission of the glass. T/stops are accurate, but overkill for most of us not shooting a movie with the need and expense to color and density correct thousands of feet of film.

Thanks for sharing your research and findings Dave!

01-30-2018, 01:01 PM   #9
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QuoteOriginally posted by CarlosU Quote
what is the relevance of all this?
Relevance is not always necessary in such things.
01-30-2018, 01:10 PM   #10
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QuoteOriginally posted by photoptimist Quote
This a dup of my post in Actual shutter speeds versus "standard" values - Page 2 - PentaxForums.com

For 99% of images, you are right that the difference is irrelevant. But there are at least a three scenarios where it does matter:

1. Interval shooting: Intervalometers (including the ones built into the K-1) work by "pressing the shutter button" on a schedule of timed intervals. If you set the intervalometer to 30 seconds, then every 30 seconds it will try to take a picture. Now if the shutter speed is set to "30" but the exposure time is really 32 seconds long, then the next intervalometer button press will happen during the previous exposure and do nothing. Instead of getting one shot every 30 seconds, you'll get a shot, then a 28 second delay, then another shot, then a delay , etc. and half the number of shots you expected. Successful use of interval shooting depends on knowing the true exposure time and this work shows that the true exposure time (which is mathematically calculated for accuracy) is different than the dial time.

2. Interactions with artificial lights: Many types of artificial lights (fluorescent, CFL, LED, etc.) flicker stroboscopically in time with the power line or some internal clock. Often this flicker frequency is exactly twice the line frequency (e.g., 2*60 Hz = 120 flickers per second in the US). If you set the shutter speed to "1/60" you'd expect to always get an exposure illuminated by exactly 2 flickers of light. But we now know that the camera is actually shooting at 1/64 so it's not getting two full flickers. Because the intensity of the light source and color of the light source varies during the flicker cycle, shooting at 1/64 in a place lit by a 120 flicker/second light source may have weird color and image brightness variations between the shots.

3. Measurement: In technical photography, you can estimate the velocities of objects from the length of the blur they create in the image. But to get an accurate velocity estimate, you need to know the true exposure time which might be up to 13% different than the dial time.


Besides, it's a interesting foray into science and engineering to try to figure out exactly what the camera is doing. It's fun exercise for the little grey cells to figure a way to accurately measure the true exposure time of the camera as AstroDave has done.
Thanks Photoptimist. Those are scenarios that I wouldn't have considered. The work of AstroDave is commendable, and yes, it feels grate to put your mind to work and solve problems like these, even if its just for fun.
01-30-2018, 07:27 PM   #11
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very impressive work, Dave!
02-01-2018, 02:58 PM   #12
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QuoteOriginally posted by CarlosU Quote
Maybe there's something I'm not taking in to account, and I don't mean to be rude, but do you think there's anybody who can tell the difference between a 32s and a 30s exposure? or a 1/16s and 1/15? or a 1/256 and 1/250?
That's what I was thinking. It strikes me as a tremendous waste of time when I could be doing something useful, like watching Oprah.
02-07-2018, 11:03 AM   #13
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QuoteOriginally posted by photoptimist Quote
2. Interactions with artificial lights: Many types of artificial lights (fluorescent, CFL, LED, etc.) flicker stroboscopically in time with the power line or some internal clock. Often this flicker frequency is exactly twice the line frequency (e.g., 2*60 Hz = 120 flickers per second in the US). If you set the shutter speed to "1/60" you'd expect to always get an exposure illuminated by exactly 2 flickers of light. But we now know that the camera is actually shooting at 1/64 so it's not getting two full flickers. Because the intensity of the light source and color of the light source varies during the flicker cycle, shooting at 1/64 in a place lit by a 120 flicker/second light source may have weird color and image brightness variations between the shots.
@AstroDave, can you try the test with any other cameras, like the K-5 or K-3? I assume they would use the same "binary" shutter speeds, but I seem to see fluorescent light banding only on the K-1 whereas I hadn't noticed it before on older cameras.
02-07-2018, 12:07 PM   #14
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QuoteOriginally posted by leekil Quote
@AstroDave, can you try the test with any other cameras, like the K-5 or K-3? I assume they would use the same "binary" shutter speeds, but I seem to see fluorescent light banding only on the K-1 whereas I hadn't noticed it before on older cameras.
I checked the K-5 and it definitely has a shutter time of 32 seconds when set to "30" but I don't have AstroDave's amazing setup to test short shutter times for power-of-two effects.

Banding within a frame is typically an artifact of using an electronic shutter (which is an option with the K-1 but not the K-5). In theory, banding could occur with the mechanical shutter but would really only be noticeable with very short shutter speeds (e.g., 1/1000) and only with very high frequency lights (some CFLs and LEDs). Under those conditions both the K-5 and K-1 should have similar artifacts although the difference in sync speed (1/180 vs. 1/200) means the K-5 would probably see 10% more high-frequency bands across the frame than the K-1.
02-08-2018, 02:07 PM   #15
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QuoteOriginally posted by photoptimist Quote
I checked the K-5 and it definitely has a shutter time of 32 seconds when set to "30" but I don't have AstroDave's amazing setup to test short shutter times for power-of-two effects.

Banding within a frame is typically an artifact of using an electronic shutter (which is an option with the K-1 but not the K-5). In theory, banding could occur with the mechanical shutter but would really only be noticeable with very short shutter speeds (e.g., 1/1000) and only with very high frequency lights (some CFLs and LEDs). Under those conditions both the K-5 and K-1 should have similar artifacts although the difference in sync speed (1/180 vs. 1/200) means the K-5 would probably see 10% more high-frequency bands across the frame than the K-1.
Oh yeah, duh, i could have checked the longer shutter speeds myself.

The difference is probably due to the proliferation of (bad?) LEDs and CFLs around the same period the I got the K-1. I recall in high school I was able to measure the fluctuation of the fluorescent lights with a light sensor, but I have never noticed a photographic issue until recently.
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