Well, 14-bits runs from 0 to 16383...
Actually it's complicated. In simply going from 14-bit to 16-bit you would increase the number of POSSIBLE colours (though I have heard that in Photoshop 16-bit only has 15-bits of precision). But if you also convert colour space, the number of colours in your original may be reduced. This is a little hard to explain, but here is a very exaggerated example.
Suppose you take 14-bit values in the range 0 to 16383 into 15-bit values in the range 0 to 32767. How many values are possible? 32768. How many could you have? 16384. But suppose that when we take our values from 14-bit to 15-bit we also divide all the numbers by 2. How many values are possible? Still 32768. How many could you have? Now it is only 16384. In the same way, converting colour spaces does maths which will reduce the total number of colours.
If this doesn't make sense or seems too advanced to meet your needs, ignore it!
Those two cannot be related in this way.
A raw file is a grayscale image. It doesn't contain color information at all - that happens in the demosaicing stage in the raw converter. And a lot of things happen to the file between that and final encoding into an output color space.
Either way it's not really a question of any importance or relevance. You have enough bits.
A RAW file contains groups of four adjacent sensor pixels
with (e.g.) 14 bit for each sensor pixel.
This group contains the information
4 x 14 bit = 56 bit.
The reconstruction for an image (demosaicing) delivers four pixels
with three channels R,G,B each
with (e.g.) 16 bit per channel R, G, B, with the information
4 x 3 x 16 bit = 192 bit.
The increased information, 192 bit instead of 56 bit, is a result
of cute interpolation, taking into account as well neighbour
sensor pixels beyond the actual group, and maybe inherent
If the reconstructed image is represented by 8 bit per channel
(instead of 16 bit per channel), then we have this information:
4 x 3 x 8 bit = 96 bit,
which is still more than the original 56 bit, therefore partly fantasy.
By the way: 14 bit per channel in the RAW image is by no means
relevant in the sense of accuracy and precision.
Thank you Gernot!
So returning to the main question I asked, there is no difference in working on a raw file or on a a PSD file 16 bit Prophoto?
There is no difference in the sense that it's moot in either case. There's plenty enough bit depth to handle any data manipulation without visual effects or artifacts.
The way you phrase the question makes me suspect you have other specific problems? If you do, this isn't it. For instance, if you have banding on screen, that's in your display system, not in the image data.
Thank you D Fosse!
So if my understanding is correct, there is no difference in working on a raw file or working on a raw file converted in PSD 16 bit Prophoto.
I simply want to understand how it works, I am curisous persion.
Well, of course there is a difference. A raw file is 14 bit grayscale, a 16 bit RGB file is 15x3 = 45 bits. Yes, that's 15 bits and not 16, but that's a different story.
But that's just a small piece of the whole picture. Processing a raw file vs. processing an RGB file is so different that they can't be compared in this way. There is no 1:1 linear relationship between them. That was my original answer and that is still my answer. The question rests on false assumptions.
Thank you D Fosse! I think I should study something more in deep, I have searched on the net of course, but there are many different opinion. If you know some link or some book about the argument, please, feel free to tell me.