Digital Light & Color

Another analogy that helps me thinking about it - perhaps simpler than the slide projectors metaphor:

Go from the bottom up, in two steps:

Step 1: the Input image is blended with the Overlay image, with the Overlay Amount slider controlling the Overlay image content in the mix.

Step 2: the output of the Step 1 blend is blended again with the Input image, with the upper Amount slider controling the Step 1 blend content in the final Composite output image.

To me, the logic of all this is that the Composite, just like most other transformations, does something to the Input image to create an Output. It this case it mixes the Input image the Overlay image according to the Operation method and the Overlay slider.

The Amount slider does what it always does in all other cases: it allows to water down the transformation output by blending its result with the virgin input to balance the final output.

The recent addition of the equations to Help really helps me.

So if those Blend formulas are translated to Composite scenario with and extra Overlay Slider in between, would this be true?:

L Overlay amount value
O' Intermediate output after applying Overlay Amount Slider, but before applying the Amount Slider

O' = A * (1 - L) + R * L
O = A * (1 - X) + O' * X

Yes, the overlay amount is applied first and then the base amount.