Don't worry. It's the enormous amount of light which makes it look far worse than it actualy is. I just cleaned mine with lens cleaner and when the lamp is off it looks as clean as can be but when I turn it on it looks just like the one in your picture.
As long as you dont use anything abrasive, and blow or gently brush any large dust particles off first, there is absolutely no problem with touching a lens. It's better to moisten the lens first, your breath works just fine for this if you can get your mouth close enough.
I use something called a lens pen to clean mine every once in a while when I am feeling anal, but to be honest, I can't see any difference after I do.
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