A method for generating one or more functional relationships suitable for correcting projection data acquired by active X-ray sensor pairs to address focal spot misalignment, comprising: emitting X-rays from a focal spot of an X-ray source at a plurality of positions in one or more spatial dimensions; for each position, generating paired response data, wherein the paired response data comprises a first measurement from a first detector element of a sensor pair and a second measurement from a second detector element of the sensor pair, wherein the first detector element and the second detector element of the sensor pair have complementary response functions with respect to movement of the focal spot in the one or more dimensions; wherein the sensor pair comprises an attenuating layer configured to act as an internal collimator within each respective sensor of the pair, wherein the attenuating layer is positioned between the first detector element and the second detector element and separates the first detector element from the second detector element , wherein X-ray attenuation caused by the attenuating layer causes the complementary response functions of the first detector element and the second detector element with respect to position of the focal spot in the one or more spatial dimensions; and wherein the complementary response functions are symmetric about a perfectly aligned focal spot position such that as the X-ray incidence on one of the first detector element or the second detector element decreases, the incidence on the other of the first detector element or the second detector element increases; and associating at least the paired response data and corresponding positions in the one or more spatial dimensions to generate one or more functional relationships . emitting X-rays from a focal spot of an X-ray source at a plurality of positions in one or more spatial dimensions; for each position, generating paired response data, wherein the paired response data comprises a first measurement from a first detector element of a sensor pair and a second measurement from a second detector element of the sensor pair, wherein the first detector element and the second detector element of the sensor pair have complementary response functions with respect to movement of the focal spot in the one or more dimensions; wherein the sensor pair comprises an attenuating layer configured to act as an internal collimator within each respective sensor of the pair, wherein the attenuating layer is positioned between the first detector element and the second detector element and separates the first detector element from the second detector element , wherein X-ray attenuation caused by the attenuating layer causes the complementary response functions of the first detector element and the second detector element with respect to position of the focal spot in the one or more spatial dimensions; and wherein the complementary response functions are symmetric about a perfectly aligned focal spot position such that as the X-ray incidence on one of the first detector element or the second detector element decreases, the incidence on the other of the first detector element or the second detector element increases; and associating at least the paired response data and corresponding positions in the one or more spatial dimensions to generate one or more functional relationships . <EOS>