A radiation imaging apparatus comprising: a radiation detector; a field modulator that modulates the radiation that reaches the detector and is defined by a transmission function; a scanner system for changing the pose of at least the field modulator; and an image reconstruction section that receives a radiation reading from the radiation detector for each of a plurality of angular orientations of the field modulator, and is configured to process the received readings to derive an image representing the amount of radiation originating from each point in an image domain, wherein the transmission function of the field modulator comprises a low transmission region that attenuates radiation incident toward the detector from angular directions defined by that low transmission region, and a high transmission region that transmits to the detector radiation that is incident toward the detector from angular directions defined by that high transmission region, wherein said regions are arranged such that: for each incident angular direction in the high transmission region, there is at least one incident angular direction in the low transmission region that is separated therefrom by less than a first angle, wherein said first angle is 10 degrees; and for each incident angular direction in the high transmission region, the majority of other incident angular directions in the high transmission region are separated therefrom by more than a second angle, wherein said second angle is 20 degrees, characterized in that the image reconstruction section is configured to solve matrix equations relating the radiation readings to the points in the image domain and to the poses of the field modulator. a radiation detector; a field modulator that modulates the radiation that reaches the detector and is defined by a transmission function; a scanner system for changing the pose of at least the field modulator; and an image reconstruction section that receives a radiation reading from the radiation detector for each of a plurality of angular orientations of the field modulator, and is configured to process the received readings to derive an image representing the amount of radiation originating from each point in an image domain, wherein the transmission function of the field modulator comprises a low transmission region that attenuates radiation incident toward the detector from angular directions defined by that low transmission region, and a high transmission region that transmits to the detector radiation that is incident toward the detector from angular directions defined by that high transmission region, wherein said regions are arranged such that: for each incident angular direction in the high transmission region, there is at least one incident angular direction in the low transmission region that is separated therefrom by less than a first angle, wherein said first angle is 10 degrees; and for each incident angular direction in the high transmission region, the majority of other incident angular directions in the high transmission region are separated therefrom by more than a second angle, wherein said second angle is 20 degrees, characterized in that the image reconstruction section is configured to solve matrix equations relating the radiation readings to the points in the image domain and to the poses of the field modulator. for each incident angular direction in the high transmission region, there is at least one incident angular direction in the low transmission region that is separated therefrom by less than a first angle, wherein said first angle is 10 degrees; and for each incident angular direction in the high transmission region, the majority of other incident angular directions in the high transmission region are separated therefrom by more than a second angle, wherein said second angle is 20 degrees, characterized in that the image reconstruction section is configured to solve matrix equations relating the radiation readings to the points in the image domain and to the poses of the field modulator.