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In this exercise I'll show you the formulas for the remaining Darken modes and we'll also see the Lighten modes and how closely they're related. I'm still working inside that document Blend mode math.psd. Notice down here the Color Burn formula. Now this becomes the first one of what I consider to be kind of the brain twisters, but one that's a little hard to figure out when you see it for the first time. Anytime, however, you see 1- like this that means that you're inverting something. So in this case, we're inverting the background image and I do truly mean inverting.
We're inverting all the luminance levels and then we are dividing that inverted background by the active layer which would normally give us a very bright effect, which is why Color Burn then turns around and inverts the entire thing with this 1- upfront. So, as you can see here, we get invert, divide, and invert. Not surprisingly, because divide is involved, we have a caution icon that's telling us there is going to be some clipping. And Color Burn is one of those modes that almost always results in clipping inside Photoshop.
Next, we have Linear Burn which provides us with a simplified equation, we are still going to get clipping out of it, but we do get smoother results as well. So Photoshop starts by adding the pixels together, which would normally brighten the heck out of the image. Bear in mind that Linear Burn is a Darken mode which is why we have a -1 at the end. Any time you're subtracting 1, you're not inverting. Instead what you're doing is you're taking the wind out of the sails. So 1 is an awfully big number to subtract where a blend mode is concerned, because after all, if you subtract 1 from what would normally be a composite white pixel, it's going to become black.
So you might think looking at this equation, well, how is it that anything survives, why doesn't the entire composite image become black? And the reason is that A+B often results in numbers that are larger than 1 and the sum may be as large as 2. So in any case, we add the luminance levels together and then we sink that sum in order to create a darker image. The next group of four modes here are the Lighten modes, starting with Lighten which just finds the maximum luminance level where pixels A and B are concerned.
So whichever pixel is lighter ends up winning on a pixel-by-pixel basis. Next drop down to Screen and notice, if you will, that every one of these Lighten formulas actually includes the Darken formula inside of it. So right there we've got multiply at work inside of Screen. So we've got A+B, we go ahead and add those pixels together which gives us a very bright image indeed, but to avoid any clipping because Screen never clips luminance levels inside of Photoshop, it goes ahead and subtracts the multiplied result.
So what's really happening here, just to give you a sense, because this is a simplified equation, what's really happening here is Photoshop inverts the background then it inverts the active layer, it multiplies them together and then it turns around and inverts the result. And so what that mean is Screen is absolutely the inverse of multiply; it is that awesome brightening mode that always delivers smooth results and never clips luminance levels. Next we have Color Dodge and notice this time around instead of inverting the background image, Photoshop goes ahead and inverts the active layer and then it divides the background by that inverted foreground.
This time, however, because it does not invert the result the way that Color Burn did, we get a bright result because you may recall from a couple of exercises ago, division always results in brightness inside of Photoshop. So we are taking the background, we are dividing it by an inverted version of the foreground layer. As a result, we get a very bright image and of course, we get clipping. And then finally, one of the simplest equations of them all, Linear Dodge (Add), all Photoshop does is it adds the luminance levels across the board on a pixel-by-pixel basis and because those values are frequently going to add up to more than one, we get clipping in some portions of the composition.
So that's how the Darken and Lighten modes work and in next exercise, we'll take a look at the more complicated contrast modes.
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