How many pixels in a 35 mm frame?
There is a lot to understand about image resolution.
If there are 3000 pixels per inch on film, that is equivalent to 118 pixels per mm. (I have heard the film can go to 4000 pixels per inch which is 157.48 pixels per mm.) I will use 3000 dpi for now.
19.4 mm x 29.1 mm = 7.860.655 pixels per frame. (13.9M pixels with the 4K figure)
Now the HDTV display standards call for 720×1280 ( .9M px/F) or 1080×1920 (2.1M px/F) the main difference being that the 720 rate can display a frame every 60th of a second and the 1080 rate only displays a frame every 30th of a second. There are progressive and interlaced display differences as well.
So, if a movie frame has 8 M pixels, then HDTV can display a quarter of the resolution, at best. a movie projector that is going to display a 2.33:1 picture. I need to work this out. Using a 35 mm frame, a movie director want to project a 2.33:1 ratio so that the width is over twice the height. I know I have seen a page somewhere that define how much of a frame is used for the different aspect ratios in a 35 mm frame.
I found one place that scans in 5200×3500 pixels so that is 18.2M pixels per frame. That is 1.5 ratio. for a 2.65:1 aspect ratio we would have 5200×1962 pixels or 10.2 M pixels per frame.
So lets assume that a movie needs to project 10M pixels at 5200×1962 ratio so they need to come up with some advanced projectors and not try to replicate the HDTV displays. And they will want to project at least 24 frames per second, shuttered to repeat the frame twice for an apparent 48 frames a second (this avoids a flickering effect). Although, digital projection can give the director the option of displaying more the 24 frames a second to get different effects. A 72-frame-per-second image looks different than a 24-frame-per-second image, especially if there is motion involved.
To get a 5200×1962 display, you can take an array of DLP chips (currently 1280×720) and synchronize them into a coherent display. 5 chips x 3 chips gives you a potential display of 6400×2160 ( 2.96:1 13.8 Mpx). Turn the chip sideways and an 8×2 matrix gives a 5760×2560 pixel display (2.25:1 14.7 Mpx).