document updated 17 years ago, on Aug 21, 2007
Layer math
Layer math in Photoshop & Co
The following are displayed in greyscale mode (otherwise, the operator is applied separately to each color channel). X and y values are considered to range from 0.0 (black) to 1.0 (white). The output of each function is clipped to this range (eg. if they fall below 0.0, they're set to black, and if they fall above 1.0, they're set to white).
While it's useful to visualize these as XY graphs, don't forget that every blend looks at color only, never at position.
| Lower layer ("y") | Upper layer ("x")
|
 | 
|
| Blending Mode | Operator | Equation
|
|---|
| Opacity | Average | a×x + (1-a)×y
|
| Darken | Minimum | min(x,y)
|
| Lighten | Maximum | max(x,y)
|
| Pin Light | | max(min(2x, y), 2x-1) (eg. Darken smooshed into the left half, Lighten smooshed into the right half)
|
| Multiply | Multiplication | x × y
|
| Screen | Negative multiplication | 1 - (1-x)×(1-y)
|
| Linear Dodge | Addition | x + y
|
| Linear Light | | 2x + y - 1
|
| Difference | Subtraction | abs(x-y)
|
| Linear Burn | Negative subtraction
(in the range of 1.0 to 2.0) | x - (1-y)
|
| Exclusion | | x+y - 2×x×y
|
| Overlay | |
| if y≤0.5: | 2×x×y | (eg. Multiply)
| | if y>0.5: | 1 - 2(1-x)×(1-y) | (eg. Screen)
|
|
| Hard Light | Overlay, swapped |
| if x≤0.5: | 2×x×y | (eg. Multiply)
| | if x>0.5: | 1 - 2(1-x)×(1-y) | (eg. Screen)
|
|
| Color Burn | Division | 1 - (1-y)/x
|
| Color Dodge | Division | y/(1-x)
|
| Vivid Light | |
| if x≤0.5: | 1 - (1-y)/2x | (eg. Color Burn, smooshed into the left half)
| | if x>0.5: | y/(2×(1-x)) | (eg. Color Dodge, smooshed into the right half)
|
|
| Soft Light | |
| if x≤0.5: | (2x-1)×(y - y2) + y
| | if x>0.5: | (2x-1)×(√y - y) + y
|
|
| Hard Mix | |
|
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