How to apply light map?

Question

Shaders

There is a medium sized tile map, let's say 1024*1024 tiles. The tiles are square, 48*48 pixels. There is an illumination map for the entire map, sized 1024*1024 pixels. Those. each tile has one pixel. Due to linear interpolation between tiles, illumination is interpolated. The viewport size is 960*540 pixels, so at least 20*11.25 tiles are visible on the screen. The viewport moves pixel by pixel in any direction (scrolling). I can't figure out how to make it so that only a piece of the light map is applied, depending on the visible tiles?

I drew an example in the picture: the entire shadow map was projected onto the screen, not a small piece of it.
I could not formulate the question in such a way that Google gave out something appropriate. It needs to be implemented using a pixel shader or a sprite (on sfml, the size of the sprite is equal to the size of the rectangle inside the texture and the most obvious option did not work because of this).