The Science of Smoke

Smoke, haze, atmos, whatever you want to call it, anyone who knows me knows that I’m a big fan. But how does it work and what is the purpose of smoking up a set?

 

Aerial perspective

At the most basic level, smoke simulates a natural phenomenon called aerial perspective. If you look at – for example – a range of mountains receding into the distance, the further mountains will appear bluer, lighter, less contrasty and less colour-saturated than the nearer mountains.

An example of aerial perspective

This effect is due to light being scattered by particles naturally suspended in the air, and by molecules of the air itself. It is described by the scary-looking Rayleigh Equation:

We don’t need to get into what all the variables stand for, but there are a few things worth noting:

  • The symbol on the far right represents the angle between the incident light and the scattered light. In practice this means that the more you shoot into the sun – the more the air you’re photographing is backlit – the more scattering there will be. Place the sun behind your camera and scattering will be minimal.
  • is the distance from the particle that’s doing the scattering, so you can see that scattering increases with distance as per the Inverse Square Law.
  • Lamda (the sort of upside-down y next to the x) is the wavelength of the light, so the shorter the wavelength, the more scattering. This is why things look bluer with distance: blue light has a shorter wavelength and so is scattered more. It’s also why shooting through an ultraviolet filter reduces the appearance of aerial perspective/atmospheric haze.

 

How smoke works

An Artem smoke gun

Foggers, hazers and smoke machines simulate aerial perspective by adding suspended particles to the air. These particles start off as smoke fluid (a.k.a. “fog juice”) which is made of mineral oil, or of a combination of water and glycol/glycerin.

In a smoke machine or gas-powered smoke gun (like the Artem), smoke fluid is pushed into a heat exchanger which vaporises it. When the vapour makes contact with the colder air, it condenses to form fog.

A hazer uses compression rather than heat to vaporise the fluid, meaning you don’t have to wait for the machine to heat up. The particles are smaller, making for a more subtle and longer-lasting effect.

As a general rule, you should use only hazers for interior cinematography, unless there is a story reason for smoke to be present in the scene. Outdoors, however, hazers are ineffective. An Artem or two will work well for smaller exterior scenes; for larger ones, a Tube of Death is the best solution. This is a long, plastic inflatable tube with regularly-spaced holes, with a fan and a smoke machine (usually electric) at the end. It ensures that smoke is distributed fairly evenly over a large area.

A Tube of Death in action on the set of “The Little Mermaid”

 

The effects of smoke

Just like aerial perspective, smoke/haze separates the background from the foreground, as the background has more smoke between it and the camera. The background becomes brighter, less contrasty, less saturated and (depending on the type of smoke) bluer, making the foreground stand out against it.

Since smoke also obeys the Rayleigh Equation, it shows up best when it’s backlit, a bit when it’s side-lit and barely at all when front-lit.

Here are some of the other things that smoke achieves:

  • It diffuses the image, particularly things further away from camera.
  • It lowers contrast.
  • It brightens the image.
  • It lifts the shadows by scattering light into them.
  • If it’s sufficiently thick, and particularly if it’s smoke rather than haze, it adds movement and texture to the image, which helps to make sets look less fake.
  • It volumises the light, showing up clear shafts of hard light and diffuse pools of soft light. (For more on this, read 5 Tips for Perfect Shafts of Light.)
  • Backlit smoke in front of a person or an object will obscure them, concealing identity.
Heavy smoke (from an Artem) pops Lyanna (Dita Tantang) out of the background in “Ren: The Girl with the Mark” (dir. Kate Madison).
Backlit smoke through a roof of branches creates magical shafts of light in “Ren: The Girl with the Mark”.
The final day/sunset look. From each side an orange-gelled and a pink-gelled par can light the backdrop. A 2K tungsten fresnel provides backlight, while a 650W fresnel with a cucoloris provides dappled light on the tree and tarsier. An LED panel off right supplies fill, and a second panel is inside the cave with a turquoise gel.
The colour-washed infinity cove in the background of this music promo for Lewis Watson’s “Droplets” (dir. Tom Walsh) is softened and disguised by smoke.
Haze gives the LED panels their glowing appearance in this video for “X, Y & Z Rays” (dir. Tom Walsh) by Revenge of Calculon.
This torch beam in “Above the Clouds” (dir. Leon Chambers) shows up so well because the set is heavily fogged.
Smoke backlit by an HMI creates the blue background glow against which the heroes of “The First Musketeer” (dir. Harriet Sams) stand out.
Haze creates the shafts of light from HMIs outside the windows, and adds to the gothic feel of “Heretiks” (dir. Paul Hyett).
The Science of Smoke

How Big a Light do I Need?

Experience goes a long way, but sometimes you need to be more precise about what size of lighting instruments are required for a particular scene. Night exteriors, for example; you don’t want to find out on the day that the HMI you hired as your “moon” backlight isn’t powerful enough to cover the whole of the car park you’re shooting in. How can you prep correctly so that you don’t get egg on your face?

There are two steps: 1. determine the intensity of light you require on the subject, and 2. find a combination of light fixture and fixture-to-subject distance that will provide that intensity.

 

The Required intensity

The goal here is to arrive at a number of foot-candles (fc). Foot-candles are a unit of light intensity, sometimes more formally called illuminance, and one foot-candle is the illuminance produced by a standard candle one foot away. (Illuminance can also be measured in the SI unit of lux, where 1 fc ≈ 10 lux, but in cinematography foot-candles are more commonly used. It’s important to remember that illuminance is a measure of the light incident to a surface, i.e. the amount of light reaching the subject. It is not to be confused with luminance, which is the amount of light reflected from a surface, or with luminous power, a.k.a. luminous flux, which is the total amount of light emitted from a source.)

Usually you start with a T-stop (or f-stop) that you want to shoot at, based on the depth of field you’d like. You also need to know the ISO and shutter interval (usually 1/48th or 1/50th of a second) you’ll be shooting at. Next you need to convert these facets of exposure into an illuminance value, and there are a few different ways of doing this.

One method is to use a light meter, if you have one, which you enter the ISO and shutter values into. Then you wave it around your office, living room or wherever, pressing the trigger until you happen upon a reading which matches your target f-stop. Then you simply switch your meter into foot-candles mode and read off the number. This method can be a bit of a pain in the neck, especially if – like mine – your meter requires fiddly flipping of dip-switches and additional calculations to get a foot-candles reading out of.

A much simpler method is to consult an exposure table, like the one below, or an exposure calculator, which I’m sure is a thing which must exist, but I’ll be damned if I could find one.

Some cinematographers memorise the fact that 100fc is f/2.8 at ISO 100, and work out other values from that. For example, ISO 400 is four times (two stops) faster than ISO 100, so a quarter of the light is required, i.e. 25fc.

Alternatively, you can use the underlying maths of the above methods. This is unlikely to be necessary in the real world, but for the purposes of this blog it’s instructive to go through the process. The equation is:

where

  • b is the illuminance in fc,
  • f is the f– or T-stop,
  • s is the shutter interval in seconds, and
  • i is the ISO.

Say I’m shooting on an Alexa with a Cooke S4 Mini lens. If I have the lens wide open at T2.8, the camera at its native ISO of 800 and the shutter interval at the UK standard of 1/50th (0.02) of a second…

… so I need about 12fc of light.

 

The right instrument

In the rare event that you’re actually lighting your set with candles – as covered in my Barry Lyndon and Stasis posts – then an illuminance value in fc is all you need. In every other situation, though, you need to figure out which electric light fixtures are going to give you the illuminance you need.

Manufacturers of professional lighting instruments make this quite easy for you, as they all provide data on the illuminance supplied by their products at various differences. For example, if I visit Mole Richardson’s webpage for their 1K Baby-Baby fresnel, I can click on the Performance Data table to see that this fixture will give me the 12fc (in fact slightly more, 15fc) that I required in my Alexa/Cooke example at a distance of 30ft on full flood.

Other manufacturers provide interactive calculators: on ETC’s site you can drag a virtual Source Four back and forth and watch the illuminance read-out change, while Arri offers a free iOS/Android app with similar functionality.

If you need to calculate an illuminance value for a distance not specified by the manufacturer, you can derive it from distances they do specify, by using the Inverse Square Law. However, as I found in my investigatory post about the law, that could be a whole can of worms.

If illuminance data is not available for your light source, then I’m afraid more maths is involved. For example, the room I’m currently in is lit by a bulb that came in a box marked “1,650 lumens”, which is the luminous power. One lumen is one foot-candle per square foot. To find out the illuminance, i.e. how many square feet those lumens are spread over, we imagine those square feet as the area of a sphere with the lamp at the centre, and where the radius r is the distance from the lamp to the subject. So:

where

  • is again the illuminance in fc,
  • is the luminous power of the souce in lumens, and
  • r is the lamp-to-subject distance in feet.

(I apologise for the mix of Imperial and SI units, but this is the reality in the semi-Americanised world of British film production! Also, please note that this equation is for point sources, rather than beams of light like you get from most professional fixtures. See this article on LED Watcher if you really want to get into the detail of that.)

So if I want to shoot that 12fc scene on my Alexa and Cooke S4 Mini under my 1,650 lumen domestic bulb…

… my subject needs to be 3’4″ from the lamp. I whipped out my light meter to check this, and it gave me the target T2.8 at 3’1″ – pretty close!

 

Do I have enough light?

If you’re on a tight budget, it may be less a case of, “What T-stop would I like to shoot at, and what fixture does that require?” and more a case of, “Is the fixture which I can afford bright enough?”

Let’s take a real example from Perplexed Music, a short film I lensed last year. We were shooting on an Alexa at ISO 1600, 1/50th sec shutter, and on Arri/Zeiss Ultra Primes, which have a maximum aperture of T1.9. The largest fixture we had was a 2.5K HMI, and I wanted to be sure that we would have enough light for a couple of night exteriors at a house location.

In reality I turned to an exposure table to find the necessary illuminance, but let’s do the maths using the first equation that we met in this post:

Loading up Arri’s photometrics app, I could see that 2.8fc wasn’t going to be a problem at all, with the 2.5K providing 5fc at the app’s maximum distance of 164ft.

That’s enough for today. All that maths may seem bewildering, but most of it is eliminated by apps and other online calculators in most scenarios, and it’s definitely worth going to the trouble of checking you have enough light before you’re on set with everyone ready to roll!

See also: 6 Ways of Judging Exposure

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How Big a Light do I Need?

Colour Rendering Index

Many light sources we come across today have a CRI rating. Most of us realise that the higher the number, the better the quality of light, but is it really that simple? What exactly is Colour Rendering Index, how is it measured and can we trust it as cinematographers? Let’s find out.

 

What is C.R.I.?

CRI was created in 1965 by the CIE – Commission Internationale de l’Eclairage – the same body responsible for the colour-space diagram we met in my post about How Colour Works. The CIE wanted to define a standard method of measuring and rating the colour-rendering properties of light sources, particularly those which don’t emit a full spectrum of light, like fluorescent tubes which were becoming popular in the sixties. The aim was to meet the needs of architects deciding what kind of lighting to install in factories, supermarkets and the like, with little or no thought given to cinematography.

As we saw in How Colour Works, colour is caused by the absorption of certain wavelengths of light by a surface, and the reflection of others. For this to work properly, the light shining on the surface in the first place needs to consist of all the visible wavelengths. The graphs below shows that daylight indeed consists of a full spectrum, as does incandescent lighting (e.g. tungsten), although its skew to the red end means that white-balancing is necessary to restore the correct proportions of colours to a photographed image. (See my article on Understanding Colour Temperature.)

Fluorescent and LED sources, however, have huge peaks and troughs in their spectral output, with some wavelengths missing completely. If the wavelengths aren’t there to begin with, they can’t reflect off the subject, so the colour of the subject will look wrong.

Analysing the spectrum of a light source to produce graphs like this required expensive equipment, so the CIE devised a simpler method of determining CRI, based on how the source reflected off a set of eight colour patches. These patches were murky pastel shades taken from the Munsell colour wheel (see my Colour Schemes post for more on colour wheels). In 2004, six more-saturated patches were added.

The maths which is used to arrive at a CRI value goes right over my head, but the testing process boils down to this:

  1. Illuminate a patch with daylight (if the source being tested has a correlated colour temperature of 5,000K or above) or incandescent light (if below 5,000K).
  2. Compare the colour of the patch to a colour-space CIE diagram and note the coordinates of the corresponding colour on the diagram.
  3. Now illuminate the patch with the source being tested.
  4. Compare the new colour of the patch to the CIE diagram and note the coordinates of the corresponding colour.
  5. Calculate the distance between the two coordinates, i.e. the difference in colour under the two light sources.
  6. Repeat with the remaining patches and calculate the average difference.

Here are a few CRI ratings gleaned from around the web:

Source CRI
Sodium streetlight -44
Standard fluorescent 50-75
Standard LED 83
LitePanels 1×1 LED 90
Arri HMI 90+
Kino Flo 95
Tungsten 100 (maximum)

 

Problems with C.R.I.

There have been many criticisms of the CRI system. One is that the use of mean averaging results in a lamp with mediocre performance across all the patches scoring the same CRI as a lamp that does terrible rendering of one colour but good rendering of all the others.

Demonstrating the non-continuous spectrum of a fluorescent lamp, versus the continuous spectrum of incandescent, using a prism.

Further criticisms relate to the colour patches themselves. The eight standard patches are low in saturation, making them easier to render accurately than bright colours. An unscrupulous manufacturer could design their lamp to render the test colours well without worrying about the rest of the spectrum.

In practice this all means that CRI ratings sometimes don’t correspond to the evidence of your own eyes. For example, I’d wager that an HMI with a quoted CRI in the low nineties is going to render more natural skin-tones than an LED panel with the same rating.

I prefer to assess the quality of a light source by eye rather than relying on any quoted CRI value. Holding my hand up in front of an LED fixture, I can quickly tell whether the skin tones looks right or not. Unfortunately even this system is flawed.

The fundamental issue is the trichromatic nature of our eyes and of cameras: both work out what colour things are based on sensory input of only red, green and blue. As an analogy, imagine a wall with a number of cracks in it. Imagine that you can only inspect it through an opaque barrier with three slits in it. Through those three slits, the wall may look completely unblemished. The cracks are there, but since they’re not aligned with the slits, you’re not aware of them. And the “slits” of the human eye are not in the same place as the slits of a camera’s sensor, i.e. the respective sensitivities of our long, medium and short cones do not quite match the red, green and blue dyes in the Bayer filters of cameras. Under continuous-spectrum lighting (“smooth wall”) this doesn’t matter, but with non-continuous-spectrum sources (“cracked wall”) it can lead to something looking right to the eye but not on camera, or vice-versa.

 

Conclusion

Given its age and its intended use, it’s not surprising that CRI is a pretty poor indicator of light quality for a modern DP or gaffer. Various alternative systems exist, including GAI (Gamut Area Index) and TLCI (Television Lighting Consistency Index), the latter similar to CRI but introducing a camera into the process rather than relying solely on human observation. The Academy of Motion Picture Arts and Sciences recently invented a system, Spectral Similarity Index (SSI), which involves measuring the source itself with a spectrometer, rather than reflected light. At the time of writing, however, we are still stuck with CRI as the dominant quantitative measure.

So what is the solution? Test, test, test. Take your chosen camera and lens system and shoot some footage with the fixtures in question. For the moment at least, that is the only way to really know what kind of light you’re getting.

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Colour Rendering Index

How Colour Works

Colour is a powerful thing. It can identify a brand, imply eco-friendliness, gender a toy, raise our blood pressure, calm us down. But what exactly is colour? How and why do we see it? And how do cameras record it? Let’s find out.

 

The Meaning of “Light”

One of the many weird and wonderful phenomena of our universe is the electromagnetic wave, an electric and magnetic oscillation which travels at 186,000 miles per second. Like all waves, EM radiation has the inversely-proportional properties of wavelength and frequency, and we humans have devised different names for it based on these properties.

The electromagnetic spectrum

EM waves with a low frequency and therefore a long wavelength are known as radio waves or, slightly higher in frequency, microwaves; we used them to broadcast information and heat ready-meals. EM waves with a high frequency and a short wavelength are known as x-rays and gamma rays; we use them to see inside people and treat cancer.

In the middle of the electromagnetic spectrum, sandwiched between infrared and ultraviolet, is a range of frequencies between 430 and 750 terahertz (wavelengths 400-700 nanometres). We call these frequencies “light”, and they are the frequencies which the receptors in our eyes can detect.

If your retinae were instead sensitive to electromagnetic radiation of between 88 and 91 megahertz, you would be able to see BBC Radio 2. I’m not talking about magically seeing into Ken Bruce’s studio, but perceiving the FM radio waves which are encoded with his silky-smooth Scottish brogue. Since radio waves can pass through solid objects though, perceiving them would not help you to understand your environment much, whereas light waves are absorbed or reflected by most solid objects, and pass through most non-solid objects, making them perfect for building a picture of the world around you.

Within the range of human vision, we have subdivided and named smaller ranges of frequencies. For example, we describe light of about 590-620nm as “orange”, and below about 450nm as “violet”. This is all colour really is: a small range of wavelengths (or frequencies) of electromagnetic radiation, or a combination of them.

 

In the eye of the beholder

Scanning electron micrograph of a retina

The inside rear surfaces of your eyeballs are coated with light-sensitive cells called rods and cones, named for their shapes.

The human eye has about five or six million cones. They come in three types: short, medium and long, referring to the wavelengths to which they are sensitive. Short cones have peak sensitivity at about 420nm, medium at 530nm and long at 560nm, roughly what we call blue, green and red respectively. The ratios of the three cone types vary from person to person, but short (blue) ones are always in the minority.

Rods are far more numerous – about 90 million per eye – and around a hundred times more sensitive than cones. (You can think of your eyes as having dual native ISOs like a Panasonic Varicam, with your rods having an ISO six or seven stops faster than your cones.) The trade-off is that they are less temporally and spatially accurate than cones, making it harder to see detail and fast movement with rods. However, rods only really come into play in dark conditions. Because there is just one type of rod, we cannot distinguish colours in low light, and because rods are most sensitive to wavelengths of 500nm, cyan shades appear brightest. That’s why cinematographers have been painting night scenes with everything from steel grey to candy blue light since the advent of colour film.

The spectral sensitivity of short (blue), medium (green) and long (red) cones

The three types of cone are what allow us – in well-lit conditions – to have colour vision. This trichromatic vision is not universal, however. Many animals have tetrachromatic (four channel) vision, and research has discovered some rare humans with it too. On the other hand, some animals, and “colour-blind” humans, are dichromats, having only two types of cone in their retinae. But in most people, perceptions of colour result from combinations of red, green and blue. A combination of red and blue light, for example, appears as magenta. All three of the primaries together make white.

Compared with the hair cells in the cochlea of your ears, which are capable of sensing a continuous spectrum of audio frequencies, trichromacy is quite a crude system, and it can be fooled. If your red and green cones are triggered equally, for example, you have no way of telling whether you are seeing a combination of red and green light, or pure yellow light, which falls between red and green in the spectrum. Both will appear yellow to you, but only one really is. That’s like being unable to hear the difference between, say, the note D and a combination of the notes C and E. (For more info on these colour metamers and how they can cause problems with certain types of lighting, check out Phil Rhode’s excellent article on Red Shark News.)

 

Artificial eye

A Bayer filter

Mimicking your eyes, video sensors also use a trichromatic system. This is convenient because it means that although a camera and TV can’t record or display yellow, for example, they can produce a mix of red and green which, as we’ve just established, is indistinguishable from yellow to the human eye.

Rather than using three different types of receptor, each sensitive to different frequencies of light, electronic sensors all rely on separating different wavelengths of light before they hit the receptors. The most common method is a colour filter array (CFA) placed immediately over the photosites, and the most common type of CFA is the Bayer filter, patented in 1976 by an Eastman Kodak employee named Dr Bryce Bayer.

The Bayer filter is a colour mosaic which allows only green light through to 50% of the photosites, only red light through to 25%, and only blue to the remaining 25%. The logic is that green is the colour your eyes are most sensitive to overall, and that your vision is much more dependent on luminance than chrominance.

A RAW, non-debayered image

The resulting image must be debayered (or more generally, demosaiced) by an algorithm to produce a viewable image. If you’re recording log or linear then this happens in-camera, whereas if you’re shooting RAW it must be done in post.

This system has implications for resolution. Let’s say your sensor is 2880×1620. You might think that’s the number of pixels, but strictly speaking it isn’t. It’s the number of photosites, and due to the Bayer filter no single one of those photosites has more than a third of the necessary colour information to form a pixel of the final image. Calculating that final image – by debayering the RAW data – reduces the real resolution of the image by 20-33%. That’s why cameras like the Arri Alexa or the Blackmagic Cinema Camera shoot at 2.8K or 2.5K, because once it’s debayered you’re left with an image of 2K (cinema standard) resolution.

 

colour Compression

Your optic nerve can only transmit about one percent of the information captured by the retina, so a huge amount of data compression is carried out within the eye. Similarly, video data from an electronic sensor is usually compressed, be it within the camera or afterwards. Luminance information is often prioritised over chrominance during compression.

Examples of chroma subsampling ratios

You have probably come across chroma subsampling expressed as, for example, 444 or 422, as in ProRes 4444 (the final 4 being transparency information, only relevant to files generated in postproduction) and ProRes 422. The three digits describe the ratios of colour and luminance information: a file with 444 chroma subsampling has no colour compression; a 422 file retains colour information only in every second pixel; a 420 file, such as those on a DVD or BluRay, contains one pixel of blue info and one of red info (the green being derived from those two and the luminance) to every four pixels of luma.

Whether every pixel, or only a fraction of them, has colour information, the precision of that colour info can vary. This is known as bit depth or colour depth. The more bits allocated to describing the colour of each pixel (or group of pixels), the more precise the colours of the image will be. DSLRs typically record video in 24-bit colour, more commonly described as 8bpc or 8 bits per (colour) channel. Images of this bit depth fall apart pretty quickly when you try to grade them. Professional cinema cameras record 10 or 12 bits per channel, which is much more flexible in postproduction.

CIE diagram showing the gamuts of three video standards. D65 is the standard for white.

The third attribute of recorded colour is gamut, the breadth of the spectrum of colours. You may have seen a CIE (Commission Internationale de l’Eclairage) diagram, which depicts the range of colours perceptible by human vision. Triangles are often superimposed on this diagram to illustrate the gamut (range of colours) that can be described by various colour spaces. The three colour spaces you are most likely to come across are, in ascending order of gamut size: Rec.709, an old standard that is still used by many monitors; P3, used by digital cinema projectors; and Rec.2020. The latter is the standard for ultra-HD, and Netflix are already requiring that some of their shows are delivered in it, even though monitors capable of displaying Rec.2020 do not yet exist. Most cinema cameras today can record images in Rec.709 (known as “video” mode on Blackmagic cameras) or a proprietary wide gamut (“film” mode on a Blackmagic, or “log” on others) which allows more flexibility in the grading suite. Note that the two modes also alter the recording of luminance and dynamic range.

To summarise as simply as possible: chroma subsampling is the proportion of pixels which have colour information, bit depth is the accuracy of that information and gamut is the limits of that info.

That’s all for today. In future posts I will look at how some of the above science leads to colour theory and how cinematographers can make practical use of it.

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How Colour Works

The Inverse Square Law

If you’ve ever read or been taught about lighting, you’ve probably heard of the Inverse Square Law. It states that light fades in proportion to the square of the distance from the source. But lately I started to wonder if this really applies in all situations. Join me as I attempt to get to the bottom of this…

 

Knowing the law

The seed of this post was sown almost a year ago, when I read Herbert McKay’s 1947 book The Tricks of Light and Colour, which described the Inverse Square Law in terms of light spreading out. (Check out my post about The Tricks of Light and Colour here.)

But before we go into that, let’s get the Law straight in our minds. What, precisely, does it say? Another excellent book, Gerald Millerson’s Lighting for Television and Film, defines it thusly:

With increased distance, the light emitted from a given point source will fall rapidly, as it spreads over a progressively larger area. This fall-off in light level is inversely proportional to the distance square, i.e. 1/d². Thus, doubling the lamp distance would reduce the light to ¼.

The operative word, for our purposes, is “spreads”.

If you’d asked me a couple of years ago what causes the Inverse Square Law, I probably would have mumbled something about light naturally losing energy as it travels. But that is hogwash of the highest order. Assuming the light doesn’t strike any objects to absorb it, there is nothing to reduce its energy. (Air does scatter – and presumably absorb – a very small amount of light, hence atmospheric haze, but this amount will never be significant on the scale a cinematographer deals with.)

In fact, as the Millerson quote above makes clear, the Inverse Square Law is a result of how light spreads out from its source. It’s purely geometry. In this diagram you can see how fewer and fewer rays strike the ‘A’ square as it gets further and further away from the source ‘S’:

Illustration by Borb, CC BY-SA 3.0

Each light ray (dodgy term, I know, but sufficient for our purposes) retains the same level of energy, and there are the same number of them overall, it’s just that there are fewer of them passing through any given area.

So far, so good.

 

Taking the Law into my own hands

During season two of my YouTube series Lighting I Like, I discussed Dedo’s Panibeam 70 HMI. This fixture produces collimated light, light of which all the waves are travelling in parallel. It occurred to me that this must prevent them spreading out, and therefore render the Inverse Square Law void.

This in turn got me thinking about more common fixtures – par cans, for example.

 

Par lamps are so named for the Parabolic Aluminised Reflectors they contain. These collect the light radiated from the rear and sides of the filament and reflect it as parallel rays. So to my mind, although light radiated from the very front of the filament must still spread and obey the Inverse Square Law, that which bounces off the reflector should theoretically never diminish. You can imagine that the ‘A’ square in our first diagram would have the same number of light rays passing through it every time if they are travelling in parallel.

Similarly, fresnel lenses are designed to divert the spreading light waves into a parallel pattern:

Even simple open-face fixtures have a reflector which can be moved back and forth using the flood/spot control, affecting both the spread and the intensity of the light. Hopefully by now you can see why these two things are related. More spread = more divergence of light rays = more fall-off. Less spread = less divergence of light rays = more throw.

So, I wondered, am I right? Do these focused sources disobey the Inverse Square Law?

 

Breaking the law

To find the answer, I waded through a number of fora.

Firstly, and crucially, everyone agrees that the Law describes light radiated from a point source, so any source which isn’t infinitely small will technically not be governed by the Law. In practice, says the general consensus, the results predicted by the Law hold true for most sources, unless they are quite large or very close to the subject.

If you are using a softbox, a Kinoflo or a trace frame at short range though, the Inverse Square Law will not apply.

The above photometric data for a Filmgear LED Flo-box indeed shows a slower fall-off than the Law predicts. (Based on the 1m intensity, the Law predicts the 2m and 3m intensities as 970÷2²=243 lux and 970÷3²=108 lux respectively.)

A Flickr forum contributor called Severin Sadjina puts it like this:

In general, the light will fall off as 1/d² if the size of the light source is negligible compared to the distance d to the light source. If, on the other hand, the light source is significantly larger than the distance d to the light source, the light will fall off as 1/d – in other words: slower than the Inverse Square Law predicts.

Another contributor, Ftir, claims that a large source will start to follow the Law above distances equal to about five times the largest side of the source, so a 4ft Kinoflo would obey the Law very closely after about 20ft. This claim is confirmed by Wikipedia, citing A. Ryer’s The Light Measurement Handbook.

But what about those pesky parallel light beams from the pars and fresnels?

Every forum had a lot of disagreement on this. Most people agree that parallel light rays don’t really exist in real life. They will always diverge or converge, slightly, and therefore the Law applies. However, many claim that it doesn’t apply in quite the same way.

Diagram from a tutorial PDF on light-measurement.com showing a virtual point source behind the bulb of a torch.

A fresnel, according to John E. Clark on Cinematography.com, can still be treated as a point source, but that point source is actually located somewhere behind the lamp-head! It’s a virtual point source. (Light radiating from a distant point source has approximately parallel rays with consequently negligible fall-off, e.g. sunlight.) So if this virtual source is 10m behind the fixture, then moving the lamp from 1m from the subject to 2m is not doubling the distance (and therefore not quartering the intensity). In fact it is multiplying the distance by 1.09 (12÷11=1.09), so the light would only drop to 84% of its former intensity (1÷1.09²=0.84).

I tried to confirm this using the Arri Photometrics App, but the data it gives for Arri’s fresnel fixtures conforms perfectly with an ordinary point source under the Law, leaving me somewhat confused. However, I did find some data for LED fresnels that broke the Law, for example the Lumi Studio 300:

As you can see, at full flood (bottom graphic) the Law is obeyed as expected; the 8m intensity of 2,500 lux is a quarter of the 4m intensity of 10,000 lux. But when spotted (top graphic) it falls off more rapidly. Again, very confusing, as I was expecting it to fall off less rapidly if the rays are diverging but close to parallel.

A more rapid fall-off suggests a virtual point source somewhere in front of the lamp-head. This was mentioned in several places on the fora as well. The light is converging, so the intensity increases as you move further from the fixture, reaching a maximum at the focal point, then diverging again from that point as per the Inverse Square Law. In fact, reverse-engineering the above data using the Law tells me – if my maths is correct – that the focal point is 1.93m in front of the fixture. Or, to put it another way, spotting this fixture is equivalent to moving it almost 2m closer to the subject. However, this doesn’t seem to tally with the beam spread data in the above graphics. More confusion!

I decided to look up ETC’s Source Four photometrics, since these units contain an ellipsoidal reflector which should focus the light (and therefore create a virtual point source) in front of themselves. However, the data shows no deviation from the Law and no evidence of a virtual point source displaced from the actual source.

 

I fought the law and the law won

I fear this investigation has left me more confused than when I started! Clearly there are factors at work here beyond what I’ve considered.

However, I’ve learnt that the Inverse Square Law is a useful means of estimating light fall-off for most lighting fixtures – even those that really seem like they should act differently! If you double the distance from lamp to subject, you’re usually going to quarter the intensity, or near as damn it. And that rule of thumb is all we cinematographers need 99% of the time. If in doubt, refer to photometrics data like that linked above.

And if anyone out there can shed any light (haha) on the confusion, I’d be very happy to hear from you!

The Inverse Square Law

9 Fun Photic Facts from a 70-year-old Book

Shortly before Christmas, while browsing the secondhand books in the corner of an obscure Herefordshire garden centre, I came across a small blue hardback called The Tricks of Light and Colour by Herbert McKay. Published in 1947, the book covered almost every aspect of light you could think of, from the inverse square law to camouflage and optical illusions. What self-respecting bibliophile cinematographer could pass that up?

Here are some quite-interesting things about light which the book describes…

  

1. SPHERES ARE THE KEY to understandING the inverse square law.

Any cinematographer worth their salt will know that doubling a subject’s distance from a lamp will quarter their brightness; tripling their distance will cut their brightness to a ninth; and so on.  This, of course, is the inverse square law. If you struggle to visualise this law and why it works the way it does, The Tricks of Light and Colour offers a good explanation.

[Think] of light being radiated from… a mere point. Light and heat are radiated in straight lines and in all directions [from this point]. At a distance of one foot from the glowing centre the whole quantity of light and heat is spread out over the surface of a sphere with a radius of one foot. At a distance of two feet from the centre it is spread over the surface of a sphere of radius two feet. Now to find an area we multiply two lengths; in the case of a sphere both lengths are the radius of the sphere. As both lengths are doubled the area is four times as great… We have the same amounts of light and heat spread over a sphere four times as great, and so the illumination and heating effect are reduced to a quarter as great.

 

2. MIRAGES ARE DUE TO Total internal reflection.

This is one of the things I dimly remember being taught in school, which this book has considerably refreshed me on. When light travels from one transparent substance to another, less dense, transparent substance, it bends towards the surface. This is called refraction, and it’s the reason that, for example, streams look shallower than they really are, when viewed from the bank. If the first substance is very dense, or the light ray is approaching the surface at a glancing angle, the ray might not escape at all, instead bouncing back down. This is called total internal reflection, and it’s the science behind mirages.

The heated sand heats the air above it, and so we get an inversion of the density gradient: low density along the heated surface, higher density in the cooler air above. Light rays are turned down, and then up, so that the scorched and weary traveller sees an image of the sky, and the images looks like a pool of cool water on the face of the desert.

 

3. Pinhole images pop up in unexpected places.

Most of us have made a pinhole camera at some point in our childhood, creating an upside-down image on a tissue paper screen by admitting light rays through a tiny opening. Make the opening bigger and the image becomes a blur, unless you have a lens to focus the light, as in a “proper” camera or indeed our eyes. But the pinhole imaging effect can occur naturally too. I’ve sometimes lain in bed in the morning, watching images of passing traffic or flapping laundry on a line projected onto my bedroom ceiling through the little gap where the curtains meet at the top. McKay describes another example:

One of the prettiest examples of the effect may be seen under trees when the sun shines brightly. The ground beneath a tree may be dappled with circles of light, some of them quite bright… When we look up through the leaves towards the sun we may see the origin of the circles of light. We can see points of light where the sun shines through small gaps between the leaves. Each of these gaps acts in the same way as a pinhole: it lets through rays from the sun which produce an image of the sun on the ground below.

 

4. The sun isn’t a point source.

“Shadows are exciting,” McKay enthuses as he opens chapter VI. They certainly are to a cinematographer. And this cinematographer was excited to learn something about the sun and its shadow which is really quite obvious, but I had never considered before.

Look at the shadow of a wall. Near the base, where the shadow begins, the edge of the shadow is straight and sharp… Farther out, the edge of the shadow gets more and more fuzzy… The reason lies of course in the great sun itself. The sun is not a mere point of light, but a globe of considerable angular width.

The accompanying illustration shows how you would see all, part or none of the sun if you stood in a slightly different position relative to the hypothetical wall. The area where none of the sun is visible is of course in full shadow (umbra), and the area where the sun is partially visible is the fuzzy penumbra (the “almost shadow”).

  

5. Gravity bends LIGHT.

Einstein hypothesised that gravity could bend light rays, and observations during solar eclipses proved him right. Stars near to the eclipsed sun were seen to be slightly out of place, due to the huge gravitational attraction of the sun.

The effect is very small; it is too small to be observed when the rays pass a comparatively small body like the moon. We need a body like the sun, at whose surface gravity is 160 or 170 times as great as at the surface of the moon, to give an observable deviation…. The amount of shift depends on the apparent nearness of a star to the sun, that is, the closeness with which the rays of light from the star graze the sun. The effect of gravity fades out rapidly, according to the inverse square law, so that it is only near the sun that the effects can be observed.

 

6. Light helped us discover helium.

Sodium street-lamps are not the most pleasant of sources, because hot sodium vapour emits light in only two wave-lengths, rather than a continuous spectrum. Interestingly, cooler sodium vapour absorbs the same two wave-lengths. The same is true of other elements: they  emit certain wave-lengths when very hot, and absorb the same wave-lengths when less hot. This little bit of science led to a major discovery.

The sun is an extremely hot body surrounded by an atmosphere of less highly heated vapours. White light from the sun’s surfaces passes through these heated vapours before it reaches us; many wave-lengths are absorbed by the sun’s atmosphere, and there is a dark line in the spectrum for each wave-length that has been absorbed. The thrilling thing is that these dark lines tell us which elements are present in the sun’s atmosphere. It turned out that the lines in the sun’s spectrum represented elements already known on the earth, except for one small group of lines which were ascribed to a hitherto undetected element. This element was called helium (from helios, the sun).

 

7. Moonlight is slightly too dim for colours.

Our retinas are populated by two different types of photoreceptors: rods and cones. Rods are much more sensitive than cones, and enable us to see in very dim light once they’ve had some time to adjust. But rods cannot see colours. This is why our vision is almost monochrome in dark conditions, even under the light of a full moon… though only just…

The light of the full moon is just about the threshold, as we say, of colour vision; a little lighter and we should see colours.

 

8. MAGIC HOUR can be longer than an hour.

We cinematographers often think of magic “hour” as being much shorter than an hour. When prepping for a dusk-for-night scene on The Little Mermaid, I used my light meter to measure the length of shootable twilight. The result was 20 minutes; after that, the light was too dim for our Alexas at 800 ISO and our Cooke S4 glass at T2. But how long after sunset is it until there is literally no light left from the sun, regardless of how sensitive your camera is? McKay has this to say…

Twilight is partly explained as an effect of diffusion. When the sun is below the horizon it still illuminates particles of dust and moisture in the air. Some of the scattered light is thrown down to the earth’s surface… Twilight ends when the sun is 17° or 18° below the horizon. At the equator [for example] the sun sinks vertically at the equinoxes, 15° per hour; so it sinks 17° in 1 hour 8 minutes.

 

9. Why isn’t Green a primary colour in paint?

And finally, the answer to something that bugged me during my childhood. When I was a small child, daubing crude paintings of stick figures under cheerful suns, I was taught that the primary colours are red, blue and yellow. Later I learnt that the true primary colours, the additive colours of light, are red, blue and green. So why is it that green, a colour that cannot be created by mixing two other colours of light, can be created by mixing blue and yellow paints?

When white light falls on a blue pigment, the pigment absorbs reds and yellows; it reflects blue and also some green. A yellow pigment absorbs blue and violet; it reflects yellow, and also some red and green which are the colours nearest to it in the spectrum. When the two pigments are mixed it may be seen that all the colours are absorbed by one or other of the components except green.

 

If you’re interested in picking up a copy of The Tricks of Light and Colour yourself, there is one on Amazon at the time of writing, but it will set you back £35. Note that Herbert McKay is not to be confused with Herbert C. McKay, an American author who was writing books about stereoscopic photography at around the same time.

9 Fun Photic Facts from a 70-year-old Book

Choosing an ND Filter: f-stops, T-stops and Optical Density

Imagine this scenario. I’m lensing a daylight exterior and my light meter gives me a reading of f/11, but I want to shoot with an aperture of T4, because that’s the depth of field I like. I know that I need to use a .9 ND (neutral density) filter. But how did I work that out? How on earth does anyone arrive at the number 0.9 from the numbers 11 and 4?

Let me explain from the beginning. First of all, let’s remind ourselves what f-stops are. You have probably seen those familiar numbers printed on the sides of lenses many times…

1      1.4      2      2.8      4      5.6      8      11      16      22

They are ratios: ratios of the lens’ focal length to its iris diameter. So a 50mm lens with a 25mm diameter iris is at f/2. If you close up the iris to just under 9mm in diameter, you’ll be at f/5.6 (50 divided by 5.6 is 8.93).

A stills lens with its aperture ring marked in f-stops
A stills lens with its aperture ring (top) marked in f-stops

But why not label a lens 1, 2, 3, 4? Why 1, 1.2, 2, 2.8…? These magic numbers are f-stops. A lens set to f/1 will let in twice as much light as (or ‘one stop more than’) one set to f/1.4, which in turn will let in twice as much as one set to f/2, and so on. Conversely, a lens set to f/2 will let in half as much light as (or ‘one stop less than’) one set to f/1.4, and so on.

 

If you think back to high school maths and the Pi r squared formula for calculating the area of a circle from its radius, the reason for the seemingly random series of numbers will start to become clear. Letting in twice as much light requires twice as much area for those light rays to fall on, and remember that the f-number is the ratio of the focal length to the iris diameter, so you can see how square roots are going to get involved and why f-stops aren’t just plain old round numbers.

A Zeiss Compact Prime lens with its aperture ring marked in T-stops
A Zeiss Compact Prime lens with its aperture ring marked in T-stops

Now, earlier I mentioned T4. How did I get from f-stops to T-stops? Well, T-stops are f-stops adjusted to compensate for the light transmission efficiency. Two different f/2 lenses will not necessarily produce equally bright images, because some percentage of light travelling through the elements will always be lost, and that percentage will vary depending on the quality of the glass and the number of elements. A lens with 100% light transmission would have the same f-number and T-number, but in practice the T-number will always be a little higher than the f-number. For example, Cooke’s 15-40mm zoom is rated at a maximum aperture of T2 or f/1.84.

So, let’s go back to my original scenario and see where we are. My light meter reads f/11. However,  I expressed my target stop as a T-number though, T4, because I’m using cinema lenses and they’re marked up in T-stops rather than f-stops. (I can still use the f-number my meter gives me though; in fact if my lens were marked in f-stops then my exposure would be slightly off because the meter does not know the transmission efficiency of my lens.)

By looking at the series of f-numbers permanently displayed on my light meter (the same series listed near the top of this post, or on any lens barrel) I can see that f/11 (or T11) is 3 stops above f/4 (or T4) – because 11 is three numbers to the right of 4 in the series. I can often be seen on set counting the stops like this on my light meter or on my fingers. It is of course possible to work it out mathematically, but screw that!

CameraZOOM-20140309092150072_zps94e90ea4
A set of Tiffen 4×4″ ND filters

So I need an ND filter that cuts 3 stops of light. But we’re not out of the mathematical woods yet.

The most popular ND filters amongst professional cinematographers are those made by Tiffen, and a typical set might be labelled as follows:

.3      .6      .9      1.2

Argh! What do those numbers mean? That’s the optical density, a property defined as the natural logarithm of the ratio of the quantity of light entering the filter to the quantity of light exiting it on the other side. A .3 ND reduces the light by half because 10 raised to the power of -0.3 is 0.5, or near as damn it. And reducing light by half, as we established earlier, means dropping one stop.

If that fries your brain, don’t worry; it does mine too. All you really need to do is multiply the number of stops you want to drop by 0.3 to find the filter you need. So to drop three stops you pick the .9 ND.

And that’s why you need a .9 ND to shoot at T4 when your light meter says f/11. Clear as mud, right? Once you get your head around it, and memorise the f-stops, this all becomes a lot easier than it seems at first glance.

Here are a couple more examples:

  • Light meter reads f/8 and you want to shoot at T5.6. That’s a one stop difference. (5.6 and 8 are right next to each other in the stop series, as you’ll see if you scroll back to the top.) 1 x 0.3 = 0.3 so you should use the .3 ND.
  • Light meter reads f/22 and you want to shoot at T2.8. That’s a six stop difference (scroll back up and count them), and 6 x 0.3 = 1.8, so you need a 1.8 ND filter. If you don’t have one, you need to stack two NDs in your matte box that add up to 1.8, e.g. a 1.2 and a .6.

 

Choosing an ND Filter: f-stops, T-stops and Optical Density