QUESTION: 4k 3840x2160 is only 2x more than 1080p, so it is really 2k?

Well first, the "4K" or "2K" refers to the horizontal resolution, not the vertical resolution. 

Here's a fun little fact: years ago, when we first started using Cineon/DPX 10 bit* frame containers, a piece of real film would be scanned full aperture at 2k, which was 2048x1556. However, the actual "useable frame" of this was actually only 1828x1332. Note that this was also referred to as 2k (sometimes Cineon 2k), but in fact was slightly less than HD's 1920x1080. (Note also the 1334 was bigger, as real film was typically shot 4 perf, for a more square aspect ratio, despite that most was cropped and not used).

So max 4K (DCI theater projection) is 4096x2160, 2k is 2048x1080 (smaller resolutions are actually used depending on the aspect ratio). Consumer / broadcast HD is close enough to 2K for practical purposes, and is 1920x1080. Plenty of feature films are actually shot at this "HD" resolution. Scaling wise, it is most easy to double or half an image in size, so when developing the higher rez consumer format, they doubled HD creating 3840x2160. Again "close enough" to 4K for practical purposes.

IMAGE FIDELITY

4K is really a marketing gimmick - the truth is you get better image fidelity going from 8 bit to 10 bit and using a wider gamut, than you do going from 2k to 4K. When you go from 8 bit to 10 bit, you increase data rate 1.25 times. When you go 2k to 4K, you increase data rate 4 times. Yet people at home don't have screens large enough to even have a really noticeable difference at 4K, but they would see better image fidelity with a higher bit depth and a wider gamut**. (Screens really need to be theater size to get the benefit of 4K). What I see instead is these 4K TVs add a very lame motion interpolation*** to bump the effective frame rate up to 60. Personally I find it nauseating, but consumers perceive it as "sharper" – and it has nothing at all to do with 4K. 

 

 Footnotes:

* As a side note, DPX is a 10 bit format, while most HD is 8 bit, particularly broadcast. DPX can retain the dynamic range of film, while 8 bit HD cannot.

** Using a wider gamut requires also using a greater bit depth than 8 bit. 8 bits per color channel is not enough to accurately represent color in wider gamut colorspaces. 8 bpc should only be used for sRGB/Rec709 sized colorspaces. DCI P3, Adobe RGB, etc \. need to be 10 bits or more to gain any benefit in terms of image fidelity from the wider gamut.

*** I, and most other filmmakers, would love it if display manufacturers would turn off this terrible motion interpolation or remove it altogether, as it severely and negatively affects the "film" feeling of 24P, making 24P features films look like cheap video. If you own such a display, I implore you to turn off motion interpolation, especially when viewing feature films.

 

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