Exponentials of the form e−αr2 , with α a positive constant, are useful for constructing s...

Exponentials of the form e−αr2 , with α a positive constant, are useful for constructing smooth intensity transformation functions. Start with this basic function and construct transformation functions having the general shapes shown in the following figures. The constants shown are input parameters, and your proposed transformations must include them in their specification. (For simplicity in your answers, L0 is not a required parameter in the third curve.)