A method for the multidimensional directional measurement of gamma radiation in the far field by means of a group of several energy-discriminating, synchronized detectors (1, 2) for detecting radiation, wherein the method uses uni-directional and bi-directional Compton scattering processes and lookup tables LUT SK, a defined functional value f(E1, E2), a list of defined detector pairs with an identification number i for defined detector pairs and one or more frequency distributions Y for detecting the measurement values, and comprising the following steps: a) setting up the detector system for a measurement, wherein the following sequence of steps is performed: - creating a list of defined detector pairs, wherein the defined detector pairs comprise all pairs formed combinatorially from the set of detectors, each pair contains at least one detector made from a material having an atomic number of Z eff > 30 and identifying it with an ID number i; - interconnecting all detectors in a coincidence circuit such that coincidence events are detected in all defined detector pairs i =1,..., I; - identifying both detectors of each defined detector pair i with the numbers 1 and 2, respectively, wherein the detector with the lower atomic number receives the number 1 and the detector with the higher atomic number receives the number 2, both detectors are made of the same material, the identification as 1 and 2 is made arbitrarily; - defining a function f(E1, E2) = (E2-E1)/(E1+E2) which is calculated from two energy values E1 and E2; b) acquiring measured values of coincidence events if interactions take place simultaneously in two respective detectors of all defined detector pairs i, wherein the measured values originate from a radiation distribution in the far field and the measured values are the interaction energies E1 and E2 of the radiation measured in the detectors; c) associating coincidence events with an identification number i; d) calculating the functional value f(E1, E2) from two energy values E1, E2 per coincidence event by means of the function f(E1, E2) defined in step a); e) detecting the coincidence events according to their identification number i and their functional values f(E1, E2) in one or more frequency distributions Y, wherein a separate frequency distribution Y is provided for each radionuclide, f) calculating one or more directional distributions X from the frequency distributions Y by means of a statistical image reconstruction method of emission tomography using lookup tables LUT SK, wherein a separate directional distribution X is provided for each radionuclide. a) setting up the detector system for a measurement, wherein the following sequence of steps is performed: - creating a list of defined detector pairs, wherein the defined detector pairs comprise all pairs formed combinatorially from the set of detectors, each pair contains at least one detector made from a material having an atomic number of Z eff > 30 and identifying it with an ID number i; - interconnecting all detectors in a coincidence circuit such that coincidence events are detected in all defined detector pairs i =1,..., I; - identifying both detectors of each defined detector pair i with the numbers 1 and 2, respectively, wherein the detector with the lower atomic number receives the number 1 and the detector with the higher atomic number receives the number 2, both detectors are made of the same material, the identification as 1 and 2 is made arbitrarily; - defining a function f(E1, E2) = (E2-E1)/(E1+E2) which is calculated from two energy values E1 and E2; - creating a list of defined detector pairs, wherein the defined detector pairs comprise all pairs formed combinatorially from the set of detectors, each pair contains at least one detector made from a material having an atomic number of Z eff > 30 and identifying it with an ID number i; - interconnecting all detectors in a coincidence circuit such that coincidence events are detected in all defined detector pairs i =1,..., I; - identifying both detectors of each defined detector pair i with the numbers 1 and 2, respectively, wherein the detector with the lower atomic number receives the number 1 and the detector with the higher atomic number receives the number 2, both detectors are made of the same material, the identification as 1 and 2 is made arbitrarily; - defining a function f(E1, E2) = (E2-E1)/(E1+E2) which is calculated from two energy values E1 and E2; b) acquiring measured values of coincidence events if interactions take place simultaneously in two respective detectors of all defined detector pairs i, wherein the measured values originate from a radiation distribution in the far field and the measured values are the interaction energies E1 and E2 of the radiation measured in the detectors; c) associating coincidence events with an identification number i; d) calculating the functional value f(E1, E2) from two energy values E1, E2 per coincidence event by means of the function f(E1, E2) defined in step a); e) detecting the coincidence events according to their identification number i and their functional values f(E1, E2) in one or more frequency distributions Y, wherein a separate frequency distribution Y is provided for each radionuclide, f) calculating one or more directional distributions X from the frequency distributions Y by means of a statistical image reconstruction method of emission tomography using lookup tables LUT SK, wherein a separate directional distribution X is provided for each radionuclide.