In general, an X-ray radiograph is a transformation of attenuation coefficient u to image intensity I. Argue why this transformation of attenuation coefficient to intensity is not a linear imaging system. X-ray radiography becomes a linear system when transforming to logarithmic intensities: I = I,e-Hx -> In = -ux. The logarithmic intensities are obviously behaving linear. This fact is used in so called dual- energy radiography. An example is shown below, in which two X-rays a) and b) of a chest are shown. This example is very similar to the application in DXA=Dual X-ray Absorptiometry (see class notes). Using picture a) as a reference: how were tube voltage (higher, lower, same?) and tube current (higher, lower, same?) changed for picture (b)? Explain. The logarithmic intensities of pictures a) and b) are combined (summed) using different weighting factors k and kp to form pictures c) and d). We assume a simple model with monoenergetic X-rays with different energies for a) and b) and assume that no Compton scattering takes place. We also assume that the body is only made of tissue (thickness xt and attenuation coefficient H;) and bone (thickness Xp and attenuation coefficient Hb). Express the ratio ka/kp through the attenuation coefficients t and ub in order to obtain pictures c) and d), respectively. b