If you are using XNA 4.0, you can pass the object BlendStateto SpriteBatch.Begin.
You want to install BlendState.ColorBlendFunctionin BlendFunction.Max. The documentation lists the actual mixing features.
To achieve the effect, I think, you might also want to set ColorSourceBlendand ColorDestinationBlendequal Blend.One.
You can do the same in earlier versions of XNA, but you must use SpriteBatch with SpriteSortMode.Immediateand change the corresponding members GraphicsDevice.RenderStateafter calling Begin and before calling Draw for the first time.
Read this blog post for more details.
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