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Abstract

Shutter angle

I recently realised that some people are actually quite confused when I talk about exposure time and frame rate. Recently, someone told me: "If you increase the frame rate, images will be less blurry.". Although this is totally wrong, I understand why people can get confused.

Frame rate

Recording a video is somewhat equivalent to taking a lot of photographs with a constant time between each picture. Experiments show that the minimum frame rate, for a human being to sense a smooth motion, is 16 frames per second (fps). However, it depends a lot on the images content, that's why common frame rates are 24, 25 or 30 fps. You can also find higher frame rates, like 60 fps for 720p videos with the Nikon 1 J1, or even more with newer versions of the Nikon 1 (120 fps for a 720p video).
So why is a higher frame rate better ? I can give you three different reasons for that:

• A higher frame rate gives you a better time resolution. You can see fast motion clearly, and more details in dynamic scenes. As an example, when I play drums, I see my cymbals vibrating after I hit them. In the real world, this is pretty clear, in a 30 fps video, I can't really see the same thing, the vibrations are sort of filtered or averaged. With a 60 fps video, I can see these vibrations more clearly.
• Another advantage of higher frame rate is that you can make slow motion videos. For instance, if you record a video at 60 fps, you can play it back to 30 fps and see the video as if things where moving twice slower. With recent cameras, you can record a 120 fps video and play it back at 24 fps, which gives a five-times slower video.
• Finally, recording videos at a high frame rate is good because you can still convert them to a lower frame rate. Of course, you will need more space on you hard drive or SD card, but it's always better to have more information (more frames!).

Exposure time/Shutter speed

If you understand what exposure time is, the rest of this article will be pretty straightforward. The exposure time, or shutter speed, is the amount of time that the camera shutter is open when you take a photograph. The longer the exposure time, the brighter the image but, the blurrier the moving objects! Indeed, whilst the shutter in open, if an object moves between a point A and a point B, the motion is averaged and, on the final image, we see that the object is actually blurry. The amount of blurriness depends on the shutter speed, as this is illustrated on the next figure.

The question is: How can we quantify the amount of blurriness in a video? As we will see in the next section, the shutter angle partially answer that question.

Shutter angle

The shutter angle explains why people get confused. Indeed, the shutter angle is used to control the amount of motion blur as the function of the frame rate. It is defined as: $$\mathrm{\text{<mi>S</mi> <mi>h</mi> <mi>u</mi> <mi>t</mi> <mi>t</mi> <mi>e</mi> <mi>r</mi> <mi>A</mi> <mi>n</mi> <mi>g</mi> <mi>l</mi> <mi>e</mi>}}={360}^{\circ }\times \frac{\mathrm{\text{<mi>E</mi> <mi>x</mi> <mi>p</mi> <mi>o</mi> <mi>s</mi> <mi>u</mi> <mi>r</mi> <mi>e</mi> <mi>T</mi> <mi>i</mi> <mi>m</mi> <mi>e</mi>}}}{\mathrm{\text{<mi>F</mi> <mi>r</mi> <mi>a</mi> <mi>m</mi> <mi>e</mi> <mi>I</mi> <mi>n</mi> <mi>t</mi> <mi>e</mi> <mi>r</mi> <mi>v</mi> <mi>a</mi> <mi>l</mi>}}}.$$ Following that definition, the shutter angle varies from 0° to 360°. Thus, we can have very different situations in which the shutter angle is close to 0°, close to 180°, or close to 360°, as shown on the following figure.

To illustrate these situations I found a great example, as shown on this figure:

Okay, now it's time for some practical examples. I faced the problem of shutter angle when I tried to record drum covers, so let's illustrate the problems with some captions from these videos. The first problem that I had was a too low shutter angle. I configured the camera in shutter priority mode, so the camera was trying to have a high shutter speed (short exposure time). Here's the result, as you can see on the figure 1.3, there is almost no motion blur. The counterpart of this is that the motion was very crispy, and I was very disappointed by these videos.

To fix the problem, I read some articles about shutter angle, and I found that the common shutter angle that is used in cinematography is 180°. So, I recorded new videos with a 180° shutter angle, as shown by the next figure.

Having a look at a still frame is a bit weird, since the drum sticks are very blurry, but the video looks a lot better. We now have all the necessary background to understand why people often get confused. Let's consider the case where the shutter speed is constant and equal to 1/60 seconds. The next video shows what happens when the camera records a video at 30 fps, which corresponds to a shutter angle of 180°.


If you take a careful look, you should see a sort of "crispy" motion. To see this effect more clearly, you can watch the middle of the screen, while the video is being played, don't try to follow the moving object. If you don't see that effect, have look at the next video, it should look more "smooth". This video is recorded at 60 fps, with the same shutter speed of 1/60 seconds, which leads to a shutter angle of 360°.


I don't know if it works for you, but for me it does, in the second video, the object looks more blurry, hence the smoother motion. The question is: why is the motion smoother, and the motion blur seems to be stronger ? Of course, these two things are related because they depend on the shutter angle.
Because a human being is sensitive to the shutter angle, the object looks more blurry in the second video. That's because the shutter angle is 360° whereas it is 180° in the first video. However, the shutter speed is exactly the same in both videos (1/60), so if we isolate an image of each video, the motion blur will be exactly the same! Let's check that... We take some snapshots of the two previous videos, when the object is approximately in the centre of the image. The top part of the next figure show the result for the 60 fps video, the bottom one for 30 fps.

The blurriness is exactly the same! Of course, this is because the shutter speed is the same in both videos (1/60). So let's give a conclusion to that in the next section...

Conclusion: shutter speed or shutter angle ?

When we look at a video, our eyes and brain are sensitive to the shutter angle. Therefore, the blurriness that we perceive in a video is related to both the shutter speed and the frame rate. We can give some very important conclusions to that:

• For a constant shutter speed, the higher the frame rate the blurrier the video will look.
• For a given shutter angle, the blurriness of the video will always be almost similar if the frame rate is not changing too much (it has to be more than 16 fps).
• Last but not the least: the motion blur that we see in an isolated frame of a video only depends on the shutter speed, not the shutter angle. It is thus independent of the frame rate.

I thinks that this last point is really important because it explains the difference between still image and video. More importantly, it shows that what we see is a combination of frame rate and shutter speed, and the shutter angle formula explains how we perceive things. In other words, it shows the link between photographs and videos.