Monitoring for the DI process is a very critical consideration, as without accurate monitoring the image being reviewed will look nothing like the final deliverable.
However, the subject of monitoring, calibration, and LUTs has become an confusing area, with many companies and individuals attempting to turn what is really a simple process into a black-art. This is not the view taken by Light Illusion, as with a little understanding, the whole calibration and monitoring procedure can be very simple indeed.
It can be made simpler still by the use of monitoring devices manufactured to meet industry requirements.
Monitoring can be split into two main areas - Display Monitors & Projectors.

The above image show a Cine-tal Cinemàge LCD Monitor, and ProjectionDesign Cineo TI chip based HD/2K Digital Projector.
Monitoring Requirements
The problem with monitoring of any kind today, is the history it has to be compatible with.
What that means is that prior monitoring formats have set presidents that, for better or worse (worse usually) have to be matched to for compatibility and consistency.
For example, CRT monitors have been manufactured with phosphors giving a specific display colourimetry - such as NTSC, PAL, Rec709, etc., while traditional film projectors have display colourimetry specified by the final print film stock - Kodak Vision, Kodak Premier, Fuji, etc, as well as the colour temperature of the projector's bulb.
Because of this history, new display devices have to be able to match to prior display systems - in the same way that NTSC colourimetry was chosen to match prior B&W monitors.
This can limit the capabilities of modern display systems if such 'compatibility' is the basis for display manufacturer...
However, what the majority of manufacturers are attempting to do is to provide a wide gamut display medium - to future proof their systems - and rely on Look Up Tables to modify, or 'limit' the display colourimetry to match historic specifications. And it is here things get all too confusing.
To help with the confusion, some display monitor manufacturers have built displays with variable colourimetry, selectable by the user, often including user definable display LUT capability. In this way, a monitor can be set to 'mimic' the desired final display medium, allowing for accurate colour control, especially during the DI colour correction process.
This makes such monitors very interesting as it enables the user to work with LUTs, as generated by the Light Illusion LightSpace CMS, to provide very accurate display environments.
Digital Projectors can be just as variable, except that unlike display monitors, which tend to use similar LCD 'glass' they can use vary different technologies, resulting in very different colourimetry.
For large projection theatres there is a limited choice for top quality, with Barco, Christie and NEC being the main players (as this is written) with DLP based technology, and Sony with their SXRD projectors.
For DI grading rooms, the choice is a bit larger, with the ProjectionDesign Cineo range being a proven system that can be calibrated very accurately to the final projected print film via LUTs held within third party systems.
The key point with any monitoring system is to ensure the display/projector is set to a known standard and specification prior to attempting any additional calibration via LUTs.
The following diagram should help define monitor/projector calibration in a DI workflow.
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