# Shutter Maths: Flicker-free Screens and Exposure Compensation

In last week’s post I mentioned the minor trouble we had on Harvey Greenfield is Running Late with a flickering TV screen in the background of shot. In today’s post I’m going to look at the underlying maths, find out why the 144° shutter angle I ultimately chose gave the best results and how to calculate the exposure compensation when you change your shutter angle like this.

If you haven’t already read my exposure series, particularly the posts about shutter and ISO, I suggest you look at those before diving into this one.

### Working out the shutter interval

Harvey Greenfield was shot at 24fps here in the UK, where the mains current alternates at 50Hz (i.e. 50 cycles per second). To avoid certain light sources and any screens in shot from flickering, you generally want to match your shutter interval – the period of time during which light is allowed to charge the sensor’s photosites – to the AC frequency, i.e. 1/50th of a second in the UK. That works out to a shutter angle of 172.8° because…

frame rate x (360 ÷ shutter angle) = shutter interval denominator

… which can also be stated as…

frame rate x shutter interval x 360 = shutter angle

24 x (1 ÷ 50) x 360 = 172.8

So, as with all features I shoot in the UK, I captured most of Harvey at a shutter angle of 172.8°.

Going back to the TV problem, I scrolled through the Red Gemini’s available shutter angles until I found the one that gave the least flicker: 144°. With the twin wonders of hindsight and maths I can work out what frequency the TV was operating at, using the first version of the formula above.

24 x (360 ÷ 144) = 60

144° with a frame rate of 24 meant that the Red was capturing 1/60th of a second’s worth of light each frame. To produce (almost) no flickering at this camera setting, the TV was evidently operating at 60Hz.

### Working out the exposure compensation

Reducing your shutter angle reduces the amount of light captured by the sensor each frame, i.e. it reduces the exposure. I was happy with the depth of field and didn’t want to change the aperture, so instead I compensated by increasing the ISO from 800 to 1280. This was a guess made under time pressure on set, but now I can calculate the right exposure compensation at my leisure.

Fortunately, unlike f-stops, shutter angles and ISO are linear scales. Double the shutter angle or ISO and you double the exposure; halve the shutter angle or ISO and you halve the exposure. This makes the maths relatively easy.

172.8° was my original shutter angle. Let’s think of this as 100% exposure. When I went down to 144°, what percentage of the original exposure was that? I still remember the mantra from calculating maths workbook scores in secondary school: “What you got divided by what you could have got, times 100.”

(144 ÷ 172.8) x 100 = 83%

Now we turn to the ISO. At its original value, 800, the camera is only providing 83% of the desired exposure, thanks to the reduced shutter angle. What must we increase the ISO to in order to hit 100% again?

(800 ÷ ?) x 100 = 83%

800 ÷ ? = 0.83

800 ÷ 0.83 = ? = 960

So I should have been at ISO 960 ideally. The closest available setting on the Red is ISO 1000, not 1280 as I selected, so I was actually over-exposing by a third of a stop. Given that we were shooting in RAW, so the ISO is only metadata, and I could see from the false colours display that nothing was clipping, this is a very minor error indeed.

### Letting the meter do the maths

One more thing. My Sekonic L-758D light meter assumes a 180° shutter (so I set it to 25fps when I’m actually shooting 24fps at 172.8°, as both work out to 1/50th of a second). Another way I could have worked the correct exposure out, if I’d clocked the 60Hz frequency of the TV at the time, is to have set the meter to 30fps (1/60th of a second at 180°) and then changed the ISO until it gave me the stop I wanted.

# “A Cliché for the End of the World”

In August 2019 Jonnie Howard, director of The Knowledge, approached me about shooting an unusual short film with him. A Cliché for the End of the World is only two minutes long, but Jonnie wanted to shoot it as two unbroken takes which would be presented side by side. Each take would follow one character, starting and ending with them next to each other, but separating in the middle.

My first thought was that the two takes would have to be shot concurrently, but to squeeze two cameras into the small location and keep each out of the other’s frame would have been impossible. Instead, we settled on shooting with a single camera. After capturing 18 takes of the first side, Jonnie reviewed the footage with his editor Kat and selected one to use. We then shot the other side, with Kat calling out cues that would keep the actors in sync with the selected “master” take. (It took 18 takes to get this side in the can as well, partly because of getting the cues right and partly because of the difficulties Steadicam op Luke Oliver had in manoeuvring up the narrow staircase.)

The film had to be lit in a way that worked for both sides, with the camera starting in the living room looking towards the kitchen, moving up the stairs, through the landing and into the bedroom.

Working as usual to the general principle of lighting from the back, I set up a 2.5K HMI outside the kitchen window to punch a shaft of sunlight into the room. I angled this steeply so that it would not reach the actors directly, but instead bounce off the floor and light them indirectly. (See my article on lighting through windows.)

Gaffer Jeremy Dawson blacked out the living room windows to keep the foreground dark. He used an LED panel set to 6,600K (versus our camera’s white balance of 5,600K) to simulate an off-screen TV, waving a piece of black wrap in front of it to create dynamics.

Next we needed to bring up the light levels for the actor’s journey up the stairs, which were naturally darker. Jeremy and spark Gareth Neal opened the loft hatch on the landing and rigged an LED Dedo inside, aimed at the darkest part of the staircase. They diffused this with some kind of net curtain I think.

To brighten the landing we set up a diffused 2×4 Kino Flo in the spare room and partially closed the door to give the light some shape. Both this and the loft Dedo were a couple of stops under key so as not to look too artificial.

All that remained was the bedroom. The characters were to end up sitting on the bed facing the window. Originally the camera in both takes was to finish facing them, with the window behind it, but this would have meant shadowing the actors, not to mention that space between the bed and the window was very limited. After some discussion between me, Jonnie, Luke, the cast, and production designer Amanda Stekly, we ended up moving the bed so that the camera could shoot the actors from behind, looking towards the window. This of course made for much more interesting and dimensional lighting.

The window looked out onto the street, and with a narrow pavement and no permission from the council, rigging a light outside was out of the question. Furthermore, we knew that the sun was going to shine right into that window later in the day, seriously messing with our continuity. Unfortunately all we could do was ask Amanda to dress in a net curtain. This took the worst of the harshness out of any direct sun and hopefully disguised the natural changes in light throughout the day at least a little.

When the sun did blast in through the window at about 6pm, we added a layer of unbleached muslin behind the net curtain to soften it further. We doubled this as the angle of the sun got more straight-on, then removed it entirely when the sun vanished behind the rooftops opposite at 7pm. About 20 minutes later we rigged a daylight LED panel in the room, bouncing off the ceiling, as a fill to counteract the diminishing natural light. We wrapped just as it was becoming impossible to match to earlier takes.

We were shooting in RAW on a Canon C200, which should give some grading latitude to help match takes from different times of day. The split-screen nature of the film means that the match needs to be very close though!

As I write this, the film is still in postproduction, and I very much look forward to seeing how it comes out. I’ll leave you with the start and end frames from slate 2, take 17, with a very quick and dirty grade.

# Exposure Part 3: Shutter

In the first two parts of this series we saw how exposure can be controlled using the lens aperture – with side effects including changes to the depth of field – and neutral density (ND) filters. Today we will look at another means of exposure control: shutter angle.

### The Physical Shutters of Film Cameras

As with aperture, an understanding of what’s going on under the hood is useful, and that begins with celluloid. Let’s imagine we’re shooting on film at 24fps, the most common frame rate. The film can’t move continuously through the gate (the opening behind the lens where the focused light strikes the film) or we would end up recording just a long vertical streak of light. The film must remain stationary long enough to expose an image, before being moved on by a distance of four perforations (the standard height of a 35mm film frame) so that the next frame can be exposed. Crucially, light must not hit the film while it is being moved, or vertical streaking will occur.

This is where the shutter comes in. The shutter is a portion of a disc that spins in front of the gate. The standard shutter angle is 180°, meaning that the shutter is a semi-circle. We always describe shutter angles by the portion of the disc which is missing, so a 270° shutter (admitting 1.5x the light of a 180° shutter) is a quarter of a circle, and a 90° shutter (admitting half the light of a 180° shutter) is three-quarters.

The shutter spins continuously at the same speed as the frame rate – so at 24fps the shutter makes 24 revolutions per second. So with a 180° shutter, each 24th of a second is divided into two halves, i.e. 48ths of a second:

• During one 48th of a second, the missing part of the shutter is over the gate, allowing the light to pass through and the stationary film to be exposed.
• During the other 48th of a second, the shutter blocks the gate to prevent light hitting the film as it is advanced. The shutter has a mirrored surface so that light from the lens is reflected up the viewfinder, allowing the camera operator to see what they’re shooting.

### Intervals vs. Angles

If you come from a stills or ENG background, you may be more used to talking about shutter intervals rather than angles. The two things are related as follows:

Frame rate x (360 ÷ shutter angle) = shutter interval denominator

For example, 24 x (360 ÷ 180) = 48 so a film running at 24fps, shot with a 180° shutter, shows us only a 48th of a second’s worth of light on each frame. This has been the standard frame rate and shutter angle in cinema since the introduction of sound in the late 1920s. The amount of motion blur captured in a 48th of a second is the amount that we as an audience have been trained to expect from motion pictures all our lives.

A greater (larger shutter angle, longer shutter interval) or lesser (smaller shutter angle, shorter shutter interval) amount of motion blur looks unusual to us and thus can be used to creative effect. Saving Private Ryan features one of the best-known examples of a small shutter angle in its D-day landing sequence, where the lack of motion blur creates a crisp, hyper-real effect that draws you into the horror of the battle. The effect has been endlessly copied since then, to the point that it now feels almost mandatory to shoot action scenes with a small shutter angle.

Large shutter angles are less common, but the extra motion blur can imply a drugged, fatigued or dream-like state.

In today’s digital environment, only the Arri Alexa Studio has a physical shutter. In other cameras, the sensor’s photo-sites are allowed to charge with light over a certain period of time – still referred to as the shutter interval, even though no actual shutter is involved. The same principles apply and the same 180° angle of the virtual shutter is standard. The camera will allow you to select a shutter angle/interval from a number of options, and on some models like the Canon C300 there is a menu setting to switch between displaying the shutter setting as an angle or an interval.

### When to Change the Shutter Angle

Sometimes it is necessary to change the shutter angle to avoid flickering. Some luminous devices, such as TV screens and monitors, or HMI lighting not set to flicker-free mode, will appear to strobe, pulse or roll on camera. This is due to them turning on and off multiple times per second, in sync with the alternating current of the mains power supply, but not necessarily in sync with the shutter. For example, if you shoot a domestic fluorescent lamp in the UK, where the mains AC cycles at 50Hz, your 1/48th (180° at 24fps) shutter will be out of sync and the lamp will appear to throb or flicker on camera. The solution is to set the shutter to 172.8° (1/50th), which is indeed what most DPs do when shooting features in the UK. Round multiples of the AC frequency like 1/100th will also work.

You may notice that I have barely mentioned exposure so far in this article. This is because, unlike stills photographers, DPs rarely use the shutter as a means of adjusting exposure. An exception is that we may increase the shutter angle when the daylight is fading, to grab an extra shot. By doubling the shutter angle from 172.8° to 345.6° we double the light admitted, i.e. we gain one stop. As long as there isn’t any fast movement, the extra motion blur is likely to go unnoticed by the audience.

One of the hallmarks of amateur cinematography is that sunny scenes have no motion blur, due to the operator (or the camera’s auto mode) decreasing the shutter interval to avoid over-exposure. It is preferable to use ND filters to cut light on bright days, as covered in part two of this series.

For the best results, the 180° (or thereabouts) shutter angle should be retained when shooting slow motion as well. If your camera displays intervals rather than angles, ideally your interval denominator should be double the frame rate. So if you want to shoot at 50fps, set the shutter interval to 1/100th. For 100fps, set the shutter to 1/200th, and so on.

If you do need to change the shutter angle for creative or technical reasons, you will usually want to compensate with the aperture. If you halve the time the shutter is open for, you must double the area of the aperture to maintain the same exposure, and vice versa. For example, if your iris was set to T4 and you change the shutter from 180° to 90° you will need to stop up to T2.8. (Refer back to my article on aperture if you need to refresh your memory about T-stops.)

In the final part of this series we’ll get to grips with ISO.

Learn more about exposure in my online course, Cinematic Lighting. Until this Thursday (19/11/20) you can get it for the special price of £15.99 by using the voucher code INSTA90.