Getting alpha channel/opacity working for lighting

Question

I have two pixel arrays, foreground and lighting. When I draw a white radial gradient (blurry circle) onto the lighting array, I want it to make the foreground visible - much like a torch in terraria/starbound. However, I also want to be able to mix different colors of lighting, rather than be stuck with black to white.

So how do I manipulate the pixel arrays so that they 'multiply' (I believe it's called)? Or is there an easier way using RGBA which I have not been able to get to work (flickering black on white or image getting ever more posterized)?

So far most responses regarding alpha channels / opacity have been using libraries from java which for this project I want to refrain from using.

Any help much appreciated!

Answer 1

If you want to know how the blending modes (such as "multiply") work in image editing programs on the pixel-value level, read this: How does photoshop blend two images together?.

Note that if you want to make the image lighter, you need a mode like "screen", because "multiply" makes it darker.