# S-Log. A Further In Depth Look.

Well I posted here a few days ago about how Data was distributed across the S-Log curve. David williams (thanks David) questioned some of the things in my post raising some valid questions over it’s accuracy, so I withdrew the post in order to review it further. While the general principles within the post were correct (to the best of my knowledge and research) and I stand by them, some of the numbers given were not quite right and the data/exposure chart was not quite right.

Before going further lets consider the differences between the a video sensor works and the way our eyes work. A video sensor is a linear device while our own visual system is a logarithmic system. Imagine you are in a room with 8  light fittings, each one with the same power and light output. You start with one lamp on, then turn on another. When you turn on the second lamp the room does not appear to get twice as bright even though the amount of light in the room has actually doubled. Now with two lamps on what happens when you turn on a third? Well you wouldn’t actually notice much of a change. To see a significant change you would need to turn on 2 more lamps. Now with 4 lamps on to see a significant difference you would need to turn on a further 4 lamps. Only adding one or two would make little visual difference. This is because our visual system is essentially a logarithmic system.

Now lets think about F-Stops. An f stop (or T-stop) is a doubling or halving of exposure. So again this is a logarithmic system. If with one light bulb your scene is one stop then to increase the scene brightness by one stop you must double the amount of light, so you would add another light bulb. Now to increase the scene brightness by a further stop you would have to take your existing two light bulbs and double it again to 4 light bulbs, and so on… 2, 4, 8, 16, 32, 64….

Now going back to a video sensor, take a look at the illustrative graph below. The horizontal scale is the number of lightbulbs in our hypothetical room and the vertical scale is the video output from an imaginary video sensor in percent. Please note that I am trying to illustrate a point, the numbers etc are not accurate, I’m just trying to explain something that is perhaps miss-understood by many, simply because it is difficult to understand or poorly explained elsewhere. The important thing to note is that the plotted blue line is a straight line, not a curve because the sensor is a linear device.

Now look at this very similar chart. The only difference now is that I have added an f-stop scale to the horizontal axis. Remember that one f-stop is a doubling of the amount of light, not simply one more lightbulb. I have also changed the vertical scale to data bits. To keep things simple I’m going to use something close 10 bit recording which actually has 956 data bits or steps (bits 64 to 1019 out of 1024 bits), but lets just round that up to 1000 data bits to keep life simple for this example.

So we can see that this imaginary  video sensor uses bits 0-50 for the first stop, 50-100 for the second stop, 100-200 for the third stop, 200-400 for the fourth and 400-800 for the fifth. So it is easy to see that huge amounts of data are required to record each stop of over exposure. The brighter the image the more data that is required. Clearly if you want to record a wide dynamic range using a linear system you need massive numbers of data bits for the highlights, while the all important mid tones and shadow areas have relatively little data allocated to them. This is obviously not a desirable situation with current data limited recording systems, you really want to have sufficient data allocated to your mid-tones so that in post production you can grade them satisfactorily.

Now look what happens if we allocate the same amount of data to each stop of exposure. The green line is what you get if, in our imaginary camera we use 200 data bits to record each of our 5 stops of dynamic range. Does the shape of this curve look familiar to anyone? The important note here is that compared to the sensors linear output (the blue line) as the image brightness increases less and less data is being used to record the highlights. This mimics the way we see the world and helps ensure that in the mid ranges where skin tones normally reside there is lots of data to play with in post. Our visual system is most acute in the mid range. that’s because some of the most important things that we see are natural tones, plants, fauna and people. We tend to pay much less attention to highlights as these are rarely of interest to us. Because of this we can afford to reduce the amount of information in video highlights without the end user really noticing. This technique is used by most video cameras when the knee kicks in and compresses highlights. It’s also used by extended gamma curves such as cinegamma’s and hypergamma’s.

Anyone that’s seen a hypergamma curve or cinegamma curve plot will have seen a similar shape of curve. Hypergammas and Cinegammas also use less and less data to record highlights (compared to a linear response) and in many ways achieve a similar improvement in the captured dynamic range.

Hypergammas are not the same as S-Log however. Hypergammas are designed to be useable without grading, even if it’s not ideal. Because of this they stay close to standard gammas in the mid range and it’s only really the highlights that are compressed, this also helps with grading if recording using only an 8 bit codec as the amount of pushing and pulling required to get a natural image is less extreme. However because the Hypergammas allocate more data in the 60 to 90 percent exposure range to stay close to standard gamma the highlights have to be more highly compressed than S-Log so there is less highlight data to work with than with S-Log.  If we look at the plot below which now includes an approximate S-Log curve (pink line) you can see that log recording has a much larger difference from a standard gamma in the mid ranges, so heavy grading will be required to get a natural looking image.

Because of the amount of grading that will normally be done with S-Log, recording the output using a 10 bit recorder is all but essential.

When I wrote this article I spent a lot of time studying the Sony S-Log white paper and reading up on S-Log and gamma curves all over the place. One thing that I believe leads to some confusion is the way Sony presents the S-Log data curve in the document. The exposure is plotted against the data bits using stops as opposed to image brightness. This is a little confusing if you are used to seeing traditional plots of gamma curves like the ones I have presented above that plot output against percentage light input. It’s confusing as Sony forget that using stops as the horizontal scale means that the horizontal scale is a log scale and this makes the S-Log  “curve”  appear to be a near straight line.

I have not used S-Log on an F3 yet. It will be interesting to see how it compares to Hypergamma in the real world. I’m sure it will bring some advantages as it allows for an 800% exposure range. I welcome any comments or corrections to this article.

# More on S-Log and Gamma Curves

A lot of the issues with any camera and the dynamic range it can record are not due to limitations of the cameras hardware but to retain compatibility with existing display technologies, in particular the good old fashioned TV set that has been around for half a century. The issue being that in order for all TV owners to see a picture that looks “natural” there has to be a common standard for the signal sent to the TV’s that will work with all sets from the very oldest to the most recent.

As even the most recent TV’s and monitors often struggle to display a contrast range greater than 7 stops there is no point in attempting to  feed them with more, Taking 12 stops and simply squashing it into 7 stops will create a disappointing, flat and dull looking image. So for productions where extensive grading is not taking place, it is not desirable to record information beyond that which the existing broadcast system can handle. This is why the vast majority of modern camcorders with the knee off and using a standard gamma curve all exhibit very similar dynamic ranges (7 to 8 stops typically), because the limitation is generally not that of the sensor, but that of the gamma curves used in broadcast television. By adding a bit of highlight compression through a cameras knee circuit we can stretch out the dynamic range a bit as our visual system is most acute to inaccuracies in the the mid ranges of an image where faces, people and natural subjects normally appear so we don’t tend to notice strong compression occurring in highlights such as the sky or reflections. A well designed knee circuit can help gain an extra 2 or 3 stops by compressing the hell out of highlights, but as most of us are probably aware it can create it’s own issues with the near complete loss of real detail in clouds and the sky as well as color saturation issues on skin highlights, this is gamma curve compression rearing it’s ugly head. Moving on, we come to cinegammas, hypergammas and other similar extended range gammas. One of the issues with a traditional aggressive knee circuit is that it is either on or off, compressing or not compressing, there is no middle ground and this makes grading problematic as it is all but impossible to extract any meaningful data from very highly compressed highlights. Cinegammas etc address this by slowly increasing the amount of compression used as image brightness increases. In addition the gamma curve compression starts much earlier, long before you get to what would traditionally be regarded as “highlights”. This slow and gentle onset of compression grades in a more pleasing manner than a conventional knee. If you don’t grade the added mid-to-highlight compression results in a picture that looks a little flat and lacks “punch”, but is not overly objectionable to view. There is however a limit to just how much data you can cram into a compressed codec or recording system. Cinegammas and Hypergammas are tailored to give optimum performance with existing 8 bit and 10 bit high compression systems and workflows so the design engineers chose to only record a range of about 11 stops as trying to extract more than this from systems essentially designed to only record 7 to 8 stops will lead to visible compression artefacts. Technologies have continued to advance and now it’s remarkably easy (compared to just a couple of years ago) to record 10 bits of 4:2:2 or 4:4:4 data without compression or with only minimal compression. By eliminating or at least significantly reducing the compression artefacts it’s now possible to extract more meaningful data from a compressed gamma curve than was possible previously. S-Log is in effect nothing more than a heavily modified gamma curve, taking cinegammas and hypergammas to the next level. S-Log needs 10 bit recording to work as the curve compression starts much lower in the curve, so when grading those crucial skin tones and natural objects will need to be un-compressed to look natural and 8 bits of data just would not give enough range. As the image brightness increases the amount of gamma curve compression is increased logarithmically. If you look at the data being recorded this means that the majority of the 10 bit data is allocated to shadow areas then mid tones with less and less data being used to record highlights.
Most modern cameras, not just the XDCAM’s simply ignore highlight information beyond what can be recorded, this results in the image getting clipped at a given point depending on the gamma curve being used. Interestingly using negative gain on a camcorder can act as a low end clip as very small brightness changes will be reduced by the negative gain, possibly to the point where they are no longer visible. This  normally results in a reduction in dynamic range (as well as noise). I suspect this is why the F3 has less noise using standard gammas because the sensor has excess dynamic range for theses curves and good sensitivity, so Sony can afford to set the arbitrary 0db point in negative space without impacting the recorded DR but giving a low noise floor benefit. For S-Log however it’s possible to record a greater dynamic range so 0db is returned to true zero and as a result the noise floor increases a little.
LUT’s are just a reverse gamma curve applied to the S-Log curve to restore the curve to one that approximates a standard gamma, normally REC-709. They are there for convenience to provide an approximation of what the finished image might look like. However applying an off the shelf LUT will impact the dynamic range as an assumption has to be made as to which parts of the image to keep and which to discard as we are back to squeezing 12 bits into 7 bits. As every project, possibly every shot will have differing requirements you would need an infinite number of LUT’s to be able to simply hit an “add LUT” button to restore your footage to something sensible. Instead it is more usual for the colorist or grader to generate their own curves to apply to the footage. Most NLE’s already have the filters to do this, it’s simply a case of using a curves filter or gamma curve correction to generate your own curves that can be applied to your clips in lieu of a LUT.

# When should I use a Cinegamma or Hypergamma?

Cinegammas are designed to be graded. The shape of the curve with steadily increasing compression from around 65-70% upwards tends to lead to a flat looking image, but maximises the cameras latitude (although similar can be achieved with a standard gamma and careful knee setting). The beauty of the cinegammas is that the gentle onset of the highlight compression means that grading will be able to extract a more natural image from the highlights. Note than Cinegamma 2 is broadcast safe and has slightly reduced recording range than CG 1,3 and 4.

Standard gammas will give a more natural looking picture right up to the point where the knee kicks in. From there up the signal is heavily compressed, so trying to extract subtle textures from highlights in post is difficult. The issue with standard gammas and the knee is that the image is either heavily compressed or not, there’s no middle ground.

In a perfect world you would control your lighting (turning down the sun if necessary ;-o) so that you could use standard gamma 3 (ITU 709 standard HD gamma) with no knee. Everything would be linear and nothing blown out. This would equate to a roughly 7 stop range. This nice linear signal would grade very well and give you a fantastic result. Careful use of graduated filters or studio lighting might still allow you to do this, but the real world is rarely restricted to a 7 stop brightness range. So we must use the knee or Cinegamma to prevent our highlights from looking ugly.

If you are committed to a workflow that will include grading, then Cinegammas are best. If you use them be very careful with your exposure, you don’t want to overexpose, especially where faces are involved. getting the exposure just right with cinegammas is harder than with standard gammas. If anything err on the side of caution and come down 1/2 a stop.

If your workflow might not include grading then stick to the standard gammas. They are a little more tolerant of slight over exposure because skin and foliage won’t get compressed until it gets up to the 80% mark (depending on your knee setting). Plus the image looks nicer straight out of the camera as the cameras gamma should be a close match to the monitors gamma.