Math behind Photoshop linear density (add) blending mode

Yes, I know this sounds like a stupid question, because the web is littered with answers him, say, he adds just two components. But this is only justified if there is no transparency involved. As soon as there is transparency involved, it becomes more complex. So, what's the math behind the linear density, blending mode, if the top layer is semi-transparent pixels (= less than 1 alpha)?

I need only the math for the RGB values.

Your fifth line is the expected result when the intermediate result of the (high + low) is tight with a maximum of 1.

Tags: Photoshop

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