Methods, apparatus and systems for detecting charged particles and obtaining tomography of a volume by measuring charged particles including measuring the momentum of a charged particle passing through a charged particle detector. Sets of position sensitive detectors measure scattering of the charged particle. The position sensitive detectors having sufficient mass to cause the charged particle passing through the position sensitive detectors to scatter in the position sensitive detectors. A controller can be adapted and arranged to receive scattering measurements of the charged particle from the charged particle detector, determine at least one trajectory of the charged particle from the measured scattering; and determine at least one momentum measurement of the charged particle from the at least one trajectory. The charged particle can be a cosmic ray-produced charged particle, such as a cosmic ray-produced muon. The position sensitive detectors can be drift cells, such as gas-filled drift tubes.