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Good explo
so there are two types of LUTs - one is the simple 1D LUT and as the name suggests it is a look up table, rarely is anything named so well in this industry.

IF you wanted to convert from one set of numbers - say gamma - to another... you literally have a file with two columns of numbers ... so what is the new value for the old value 104.... look up 104 and read the new number next to it ... say 111 ... thats it. 
Two sets of numbers the from and to numbers ... all integers all very simple, no fractions, no maths , no complexity. There is one really important point if you adjust say red - well there is a RED LUT - only affects RED. You cant for example easily do a complex saturation change with a 1D LUT as the adjustment of Red saturation, may involve some tweaks on Blue and Green as well... but our 1D LUT on Red doesnt allow that - it just gives you back a new RED number - no choices - no variations in Green or Red.. just up or down on the single code value.

The second is a 3D LUT - this is more powerful and more complex. Here if you wanted to adjust Red Saturation ... a 3D LUT is a combination of all three colours... hence there is no 2D LUT - it would make no sense to have a LUT that only works Red+Green but has no Blue... You either work just the RED (1D) or all of them (3D) . The 3D LUT can be thought of as a matrix ... or as a \'forumula\' that given an input change may vary one, two or three of its outputs... 

Who makes them? Well loads of people and products. For example I can turn a grade into a LUT in Scratch - I can then export that and read it into another product. Various companies publish LUTs for operations such as PANA-LOG or other Log curves. 

The uses of a LUT are wide and varied but there are three big uses.

1. LUT conversion. You can use a LUT to move images from one colour space or mapping system to another. This really changes the files/images - but all correctly. So for example if you had something shot on LogC on an Arri - in ProRes you would need to convert that to \"video\" to output as HD video. There is a LUT that converts from LogC to Rec709. That is a conversion that will change the look and actual content of a clip, but it is vital to getting \'sensible\' images out. It is also the case that we often want to convert the images to a \'scene linear\' workspace - a sort of robust neutral place - where all the maths works correctly and where CG is best generated and composited with live action. One of these conversion could be a film LUT where we convert from Cineon DPX, or rather Cineon Printer Density profile to Scene referred Linear ... so that might be 10 bit DPX log Cineon to OpenEXR. It is not done to make the footage \'look\' filmic, it is done to convert the film style encoding to a more CG friendly or accurate encoding.

2. Viewing LUT. In this case I want to look at the LogC on set perhaps but not actually convert the images. This LUT is applied only to the images temporarily... it is like putting on tinted glasses - the underlying image is not changed. And this makes sense since I may want to see if the camera takes look good - but at this stage it is not being processed - more just viewed. Hence the term Viewing LUT.

3. Profiling and calibration. I my use a LUT to calibrate my monitor ... viewing LUT (think of this as a trim on your monitor) and I also make use a 3D LUT to profile what something might look like when projected. This last LUT is I think what you were referring to... it is the LUT that says make this look like it will look when I am projecting in a cinema - which we all know is different to say HD on a Plasma screen.




Links

WIKI
http://en.wikipedia.org/wiki/Lookup_table

ARRI & LUTs
http://www.arri.com/camera/digital_cameras/tools/lut_generator.html

RED & LUTs
http://www.fxguide.com/forums/showthread.php?11251-What-is-a-LUT
http://www.reduser.net/forum/showthread.php?19355-RedLog-to-Redspace-and-or-Rec709-LUT
http://www.reduser.net/forum/showthread.php?58275-Conversion-LUTS

LUT Buddy
http://www.redgiantsoftware.com/news/featured/coloristafreelutbuddy/
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