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The MP4 file format does not support an Alpha Channel. If you require an Alpha Channel for your MP4, you will need to render the Alpha Channel as a separate movie. IOW, One movie for the RGB Channels and another movie for the Alpha Channel. Use QuickTime Animation or DNxHD CODECs if you want a single file output with both the RGB and Alpha Channels.
Quicktime JPEG 2000, Cineware - free from GoPro, and several other formats support alpha channels. Compressed formats are 8 bit color per channel for a with a total of 24 bits. For a video format to support Alpha Channels you need at least 8 bits per channel and four (4) channels for a total of 32-bits. I know that's confusing because it is easy to think of 32-bit formats as trillions of colors but when you are describing video formats a 32-bit file is a format with four 8-bit color channels, the fourth one being a grayscale alpha channel. There are formats that support 10-bit, 12-bit, 16-bit and even 32-bit color per channel that also support 4 channels.
It is even more complicated than that. Red Green Blue and Alpha channels are just the beginning. It is common in professional 3D rendering to also include things like depth, occlusion, specularity and other things in the rendered files. Some formats like Open EXR support even allow you to assign a bunch of random things to the available channels:
OpenEXR's multi-resolution and arbitrary channel format makes it appealing for compositing, as it alleviates several painful elements of the process. Since it can store arbitrary channels—specular, diffuse, alpha, RGB, normals, and various other types—in one file, it takes away the need to store this information in separate files. The multi-channel concept also reduces the necessity to "bake" in the aforementioned data to the final image. If a compositer is not happy with the current level of specularity, they can adjust that specific channel. (from Wikipedia)
If you want to dabble in video, there is a lot you need to learn about video formats and standards to produce predictable and consistent results when you render.