Need help with creating maps for the Displace modifier

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Hi, I'm looking for some info on how best to use the max precision of my data as a map to displace geometry. I have raw data that ranges from 0-1 with 16-bit precision in a huge array. My intent was to create an image where each pixel in the image corresponds to a data point in that array.
At this point I'm unsure of how to store the values in the image itself. Should I be storing 16-bit floats in a single color channel? Should I store 3 copies of the 16-bit floats in each channel of a RGB image? Should I be storing ints 0-65535 instead of floats like .017368 etc?
So yeah, I'm really just not sure how to go about creating the appropriate image to use as a map. I should mention that I'm currently creating PNG files, though I suppose I could create tiffs. I'd prefer PNG simply because I already coded for creating PNGs.
Thanks!