The first thing to realise about LUTs is that they have different applications that require a different level of understanding, and a different type of LUT!
LUTs being used to make an image visually 'pretty', often called Viewing LUTs, are very different to LUTs used to show an image accurately calibrated to another display format, referred to as Calibration LUTs.
Calibration LUTs
We'll start with Calibration LUTs as it then easier to understand why Viewing LUTs are so different.
Calibration LUTs started life, and in many cases still exist, to match a film print image projected via the traditional format of 35mm celluloid film in your local flea-pit.
This obviously means that the LUT has to display the image matched to the final film print, and this in turn means that there has to be a set of known parameters for the digital image to be accurately calibrated, and it is here that some confusion starts.
Initially all digital images for film projects that were going to be put back to film for projection came from a 35mm film source, which needed to be scanned to digitize the image.
This first step fixed the relationship between the original film image being scanned at the digital image generated, and very quickly the Kodak Print Density (Log) based Cineon image format became the standard for such film scanning.
This Cineon image format later became the SMPTE DPX format, and is now the basis for all 'digital film' work...
As a result, all film recorders now expect to be presented image data for film-out recording in this DPX Log format, and if presented with tv gamma images will internally convert to DPX Log, using inbuilt LUTs, before film recording commences.
This default calibration for all film recorder is a key point to remember.
Note: It is possible for film recorders to be user calibrated to different specifications, but to do this make the recorder an island in the digital film world, and can cause major problems when moving projects between different facilities.
So, with this digital film image format fixed one of the variables in LUT operation is removed. As a result, any calibration LUT can be built based on the digital image source being Cineon/DPX Log.
This means the actual LUT is now only looking at the variables for the actual film recorder calibration, film stocks being used, and the celluloid film projection environment, plus the digital display system and environment being used to show the digital images.
In an ideal world all these variables would also be locked-down, with every film recorder in the world being accurately calibrated to take into account its local variables (the actual film recorder being used, the negative film stock, and the chemical negative processing lab calibration), while the film lab would be running accurately calibrated film baths so the neg and print processing is accurate. This accurate film print would then be displayed on an accurate film projector in an accurately set-up theatre... And the digital viewing environment would equally be accurately set-up, with known monitor or digital projection settings, including illumination, colour temperature, colour gamut, etc.
If all these stages and processes were accurate as described a single LUT would work throughout the world. 
But, life just isn't like that... 
Having said that, the variables in the film process chain can be 'within tolerance', and still be visually different. This is just the way life is, and sometimes a call has to be made on how accurate 'accurate' needs to be.
See these print calibration examples to see the problem. All the images shown are 'accurate' to film lab tolerances, as specified by Kodak. Just because your 'answer print' is good and accurate, doesn't mean the bulk release prints will look anything like the same... In all likelihood, they wont! And actually, your answer print will change on a day-by-day basis, so to be really accurate you'll need to be generating a Calibration LUT on at least a daily basis...
But, the DPX source file is a given standard that can be assumed for all LUT building, and means that Calibration LUTs don't care about the source file - they simply show what the film print would look like if the image being displayed were to be film-out recorded and processed as it presently exists - within the lab tolerances described above.
Grading Through a Calibration LUT
So, if you have understood the above correctly, you should now understand that taking any digital image - regardless of its format - and grading it to look correct while viewing through a Calibration LUT, will 'push' the image into becoming a Cineon/DPX format image...
make sense?
This approach is discussed here with examples of View and Print LUTs, and here with just View LUTs, but it's worth going over again.
The following image is a Viper original frame shot in FilmStream mode, which is nothing like the Cineon/DPX Log format. It could just as easily be a Red captured image.
Viper Original image with no LUT
The next image is the same one, but with a Calibration 'Print' LUT applied. As can be seen, the image looks 'wrong' as the underlying format is not Cineon/DPX Log...
Viper Original image viewed through a Calibration Print LUT
However, by grading the image while viewing through the Calibration Print LUT the image can be 'corrected'...
Viper image graded while being viewed through a Calibration Print LUT
And if we remove the LUT the underlying image now looks as we would expect for am accurate Cineo/DPX Log image...
Viper image after grading with LUT removed - now a Cineon/DPX Log format image!
This approach to working with LUTs works with any image that is not initially a Cineon/DPX Log format image... and that includes images shot with any of the Digital Cinematography cameras, such as Red, SI-2K, Sony CineAlta (especially those images shot with extended DR Gamma Curves), VariCam, etc...
Cool, huh?
Viewing LUTs
Ok, so you get Calibration LUTs - but what of Viewing LUTs - those things that get used a lot on-set to make Viper, Sony CineAlta cameras with user Gamma Curves (see here), Red in non-Rec709 form, VariCam Cinegamma, etc., look good during shooting?
Well, a Calibration LUT is totally useless, as can be seen above.
As none of the Digital Cinematography cameras (well, none, unless using a Sony CineAlta camera with my Cineon Gamma Curves!) outputs a Cineon/DPX Log format image, a Calibration LUT will look totally wrong on-set with the raw images.
So, what are needed are ViewLUTs, so approximate what the images will look like after grading using a real Calibration LUT...
Make sense? It really is that easy!
But, what does this mean when getting into the DI suite for grading?
In simple terms, the ViewLUT is useless, other than to show the direction in which it is desired for the grade to head...
Grading On-Set
So, what of all those system that offer grading on-set? How can decisions taken on-set be moved into the DI grading room?
Ah, glad you asked that!
What do you think?
Next Page - On-Set Grading
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