The design of log curve

Before the article……

There are a lot of popular tutorial on how to expose with which camera on Youtube and all kinds of review websites. Long tiem ago before I learned all necessary things I’ve seen massive similar articles and video tutorials. The more I read and the more confusion I had. There are a lot of “Should” but nobody explains “why” so it becomes a mystireous topic and then people invented ETTR.

I come from the camera side and learned post process from scratch. So I tried to understand every step of the process and then come back to camera to design the curve.

1. What is log and why we need to shoot log?

Nowadays, nearly all cameras are digital. The light signal comes from the optical parts will be sensed by the image sensor and that will be converted as voltage. Between 0 and maximum voltage the voltage shows the lights LINEARLY. Then the analog voltage will be converted to digital via AD convertor and read out to the processor. The processor(ISP) will process the data and then compress with codec and then store to mediums. This is the simple explanation of how the lights are finally stored to your disks.

The keyword is LINEAR(the magenta line in below chart). For those who doesn’t understand it a simple explanation is the output response to input is dedicate. The input output response is a line instead of a curve.

When the analog signals are converted to digital, and we use 10bit to express the voltage, it will be from 0 to 1024. 0 means no signal response(darkest), 1024 means overflow(brightest).

Here before I start to talk about the curve, I need to explain stops first. We often talk about stops of the dynamic range, and that’s important concept to have. Let’s check the following numbers:

0,1,2,4,8,16,32,64,128,256,512,1024.

So the first stop is 0–1 and second is 2–4…… the last stop is 512–1024. Then you can see the problem we face:

We are so sensitive to the shadow but with linear 10bit we only use 0–128 to describe the prvious 8 stops and 128–1024 for the last 3 stops. We are wasting most of the data to describe the highlights which we are not sensitive.

That’s why log is designed. IT IS A STORAGE FORMAT. The log curve is generated with some parameters and it amplifIes the shadow greatly and compress the highlights greatly and this solves the problems. So basically log is a curve to compress lights and reallocate the bits between shadow and highlights. Different log design means different allocation between the light and shadow.

2.What’s the important infomation we should know with log?

So for log design, the MOST IMORTANT infomation is how it allocate the lights: how many stops above middle grey and how many stops below it.

So here comes how middle grey affects your shots:

Middle grey is the anchor point where the color correction happens. All the color correction(The so called color science) happens there. A standard shot needs to get middle grey chart exposed to the designed level(normally around 40% for most of the cameras). So if I gives the shadow one more stop it means that the log curve will not amplify the linear data from sensor as much and the camera operator will increase the exposure one stop to make sure the middle grey will be at 40% level. Stop here and just think about how you expose with grey card and you will understand it. Then if you have one more stop lights into the camera of course you will have better SNR and clearner shadow but you will lose the upper one stop of the highlight. So when you test the camera, you can under expose it some stops to check what you can recover and also you need to check how many stops you can over expose to recover. It’s a design choice. So for the same sensor, if you choose to reserve more stops in the curve for highlights, it will be dangerous to under expose and if you choose to reserve more for shadow, it is easy to over expose for highlights. Some cameras choose to satisfy people from mirrorless camera field or those who used to shoot RAW stills, and they only reserve 4 stops over middle grey and that will lead to great shadow noise performance but hard highlight roll over. We choose the opposite.

If you understand this segment, then it is easy to understand that some cameras are very noisy with log. Those cameras reserve a lot stops with a small dynamic range sensor and when they amplify the shadow it’s noisy. But if you use LUTs to reover the image back to rec709 it is much better. This is also the reason why with a bigger sensor you can have worse SNR comparing to another camera with different log design. It’s wrong to compare in this way.

When we design Zlog, we only considered the mathimatical part of the log so Zlog 1 is noisy with above reasons. Then we realized that there are still a lot of people who will never follow the workflow and grade the footage directly. Then the SNR performance with log is important. We balanced the stops between shadow and highlight and we considered the user habits so we compressed the noisy stops but still retained 7 stops above middle grey.

3. how to start testing your camera with log?

The first thing is you should get a grey card and expose it to the designed level and check the LUTs or the designed workflow(for Zlog2, please try our plugin).

Then you need to understand when you under expose and over expose what will happen. Please don’t grade the under exposed or over exposed image directly. Images will have correct white balance and color response only in linear space and all these adjustment can only happen in that space. Simple explanation is you need to get the image back to what the sensor output by reverse curves and then do white balance adjustment and exposure adjustment(digital amplification or reduction). That’s how ACES works. For Zlog2, our plugin is doing this job. So if you over expose the image 3 stops and you can use the plugin to bring them back and see what’s result.

After this test, you will be understand the curve design and you will be able to know once you are in a rush shot, should you over expose or under expose to be safe.

One more comment for direct grading of the footage which isn’t correctly exposed: If you adjust white balance directly, if the middle grey is neutral the tint of shadow will change. If you use LUTs directly, it will be over saturated when under exposed and under saturated without contrast when over exposed.

*I will add more charts and polish this article in the coming a few days but I’d like to see the feedback and collect questions now.