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What is the screen blend mode, and why would we want to use it?

Screening one image over another gives an effect that at first glance resembles a double exposure (an arithmetic addition of the digital data), but screening gives more subtle results that don't result in clipped, overexposed overly bright highlights.

The screen blend mode avoids creating overexposures by running the element to be screened as a 3-color holdback matte for itself, before the addition takes place. In this way, a screen resembles a composite. The element to be screened becomes opaque in direct proportion to its brightness.

Mathematically, one inverts ( ~ ) the foreground and multiplies ( * ) it by the background, then adds ( + ) the foreground on top.

One can also achieve a screen blend by printing a positive from two sanwiched negatives. Mathematically, one inverts ( ~ ) both foreground and background, multiplies the two, and inverts the product.

The two approaches are identical because

~ ( ~a * ~b) = 1 - ( (1 - a) * (1 - b) ) = 1 - (1 - b - a + a * b) = 1 - 1 + b + a - a * b = b + a * (1 - b) = b + (a * ~b)

Screening is commutative — it doesn't matter in which order the layers are screened. Screening is a great way to add highlights to shiny objects.

Screening a bright image over a dark one yields results almost indistinguishable from a simple double exposure. Where screening really shines, is when both foreground and background are relatively bright. To see the subtle improvement screening yields over image addition, It's useful to look at some side-by-side comparisons between the action of the screen blend mode and the results obtained simply through the addition (double exposure) of two images.

Screening is a quick way to "open up" a dark image without fear of overexposing and "blowing out" the whites.

Try using "add" in place of "screen" on the same image over itself several times and you'll get a good feel for the difference between the two blend modes.

Anyone with information about other uses for the screen blend mode is welcome to email me with details, if they wish. If it differs enough from what's already posted here, I'll add your information to this page, along with your links and credits.


M. B. wrote on 1/12/2004:
Joseph, Hi. I was just wondering about the mathematical statement that you make in this tutorial (http://www.digitalartform.com/screen.htm ). ~ ( ~a * ~b) = 1 - ( (1 - a) * (1 - b) ) = 1 - (1 - b - a + a * b) = 1 - 1 + b + a - a * b = b + a * (1 - b) = b + (a * ~b) about the screening being commutative. Is this derived from boolean algebra? Can you provide some further mathematical insight/URL's. Thanks, M. B.

I wrote back:
Hi , thanks for writing...

Well, let's see, I haven't gone over that in a while, and a lot of what I write is really part of me sharing my own learning process, so I'll go through it now as I reply, and hopefully I won't have been wrong about what I wrote. Here goes:

1) ALL values are between 0 and 1 -- not between 0 and 255. The way you convert a 255 value to 0 to 1 space is to divide it by 255

2) The ~ symbol is borrowed from boolean algebra, and means "NOT" -- I'm using it sort of as an indication of PHOTOGRAPHIC NEGATIVE.

3) The way you get a photographic negative digitally is to subract the image from 1. Lets say that color "a" is (1 .2 .1) -- a bright red color. Then in that case ~a would be the negative color of (1 .2 .1),  which would be (0 .8 .9) a bright cyan color.

Now, with that groundwork, lets begin --

You take two pictures, a and b

You screen them by negating both, multiplying them together, and negating the result of that multiply.

That means you take a, negate it, which gives you ~a, or (1 - a). Remember, when I say negate it, I don't mean make it negative, I mean make it look like the photographic negative. I should probably say "invert" it, not "negate" it. I mean start with (1 1 1) and SUBTRACT the color from that.

Now that long string of gibberish starts making more sense?

All I'm really trying to say with it is that taking two pictures, inverting each, multiplying both, and inverting the flattened result is the same process as taking one picture, inverting it, multiplying it by the positive of the other, and adding the first one back on as a positive.

When I see multiply I think "Filter with a transparency"

When I see add I think "double expose"

When I say it is commutative, I just mean that it doesn't matter whether you screen a onto b or b onto a, the results will look the same.