You are asked to design a spectral filter that practically removes 99.0% of the low energy photons in an X-ray beam. Such photons contribute to the patient dose without contributing to the image and are defined as no more than 1% of these photons making it to the other side of the patient. Assume a patient can be modelled as a 20cm thick homogenous object with linear attenuation coefficients as shown below in Table 1. What is the thickness of the filter needed to eliminate all the energies which satisfy the above requirement? Filter linear attenuation properties are given below in Table 2. Table 1: Lincar attenuation coefficients vs. energy of patient equivalent material Energy [keV] Hjet (mm 20 0.02601 30 0.02407 40 0.02303 50 0.02151 60 0.02013 Table 2: Linear attenuation coefficients vs. energy of filter material Energy (keV Hr mm 20 30 40 50 60 70 0.1225 0.1067 0.0872 0.07541 0.06684 0.06327

You are asked to design a spectral filter that practically removes 99.0% of the low energy photons in an X-ray beam. Such photons contribute to the patient dose without contributing to the image and are defined as no more than 1% of these photons making it to the other side of the patient. Assume a patient can be modelled as a 20cm thick homogenous object with linear attenuation coefficients as shown below in Table 1. What is the thickness of the filter needed to eliminate all the energies which satisfy the above requirement? Filter linear attenuation properties are given below in Table 2. Table 1: Lincar attenuation coefficients vs. energy of patient equivalent material Energy [keV] Hjet (mm 20 0.02601 30 0.02407 40 0.02303 50 0.02151 60 0.02013 Table 2: Linear attenuation coefficients vs. energy of filter material Energy (keV Hr mm 20 30 40 50 60 70 0.1225 0.1067 0.0872 0.07541 0.06684 0.06327

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