I have read two documents on panasonic professionalThere is a white paper out there for the VLOG-L have a look it gives all the details. Can't upload files here or don't know how to.
One is the varicam VLOG/VGamut this applies to the varicam cameras that are professional level recorders here there is the full low down on dynamic range color gamut etc
The second is a paper on production considerations for the DVX200 that shares the same processor of the GH4 there is no mention of what the color space is and clearly this implementation of vlog is a castrated version of the varicam
To finish off Panasonic only provides LUTs for REC709 so this looks like the camera uses vlog l gamma to compress within rec709 and then uses the LUT to decompress gamma back into rec709
I have found out a company called mysterybox that provides custom LUT to capture BT.2020 HDR10 using inferno or other monitors
Without that workflow you can only convert to REC709
I suppose using a set of 3 LUTs to accomplish a few more colours is out of reach for your normal underwater production and you might as well use HLG that requires no LUTs
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