A Mathematical Model for Detection of Back-Scattered Radiation during Diagnostic Scanning with a Narrow X-Ray Beam

摘要

In this work, the triangle openN signal for detection of foreign impurities using back-scattered radiation is defined as the difference between the number of quanta reflected from a control object in the presence (N_1) and in the absence (N_2) of foreign impurities in the object: The quantum noise is described by the Poisson distribution:The signaloise ratio (S/N) determines the probability of detection of foreign impurities in the object: Scheme for detection of foreign impurities in an object using back-scattered radiation beam is shown in Fig. 1, where F_1 is distance from radiation source to input plane of control object (m); b is focal spot size of X-ray radiation source (m); a is distance from focal spot to col-limator of scanning beam (m); S_(ca) is cross-section area of scanning beam at control object input (cm~2); mu is radiation extinction coefficient in control object (cm~2/g); Hmd is radiation extinction coefficient in detected material (cm~2/g); p_(ob) is object material density (g/cm~3); p_(md) is detected material density (g/cm~3); N_0 is radiation yield as calculated from number of quanta in scanning beam (quanta.m~2/sec.cm~2); N_1 is radiation beam reflected from control object (quanta/sec-cm~2); S_d is cross-section area of detector input window in control object (cm~2); S_(do) is cross-section area of detected object (cm~2); H_t is scanning beam geometric unsharpness (m); F_2 is distance from scanning site to input plane of detector of back-scattered radiation (cm); is angle of radiation back-scattering from control object; d is distance from input plane of control object to detected object (for forward scattered radiation beam this distance is in m; for scattered radiation beam this distance is in cm).