An encoder interferometry system comprising: an encoder head (300, 500) configured and arranged to direct a measurement beam, from the encoder head (300, 500) to an encoder scale (305, 505), to give rise to a plurality of diffraction orders of the measurement beam as once-diffracted measurement beams (503a, 503b), and change directions of the once-diffracted measurement beams (503a, 503b) back toward the encoder scale (305, 505) in a way that deviates slightly from a retro-reflection to produce a plurality of twice-diffracted measurement beams, wherein two of the plurality of twice-diffracted measurement beams propagate along non-parallel beam paths having an angular separation α, and the non-parallel beam paths of the two twice-diffracted beams at least partially overlap; a first detector arranged to receive one of the two twice-diffracted measurement beams and a first reference beam; a second detector arranged to receive the other of the two twice-diffracted measurement beams and a second reference beam, wherein the non-parallel beam paths of the two twice-diffracted measurement beams overlap one another as they propagate toward the first and second detectors; and an electronic processor configured to receive an interference signal from each of the first and second detectors, each interference signal comprising a phase related to the relative displacement between the encoder scale (305, 505) and the encoder head (300, 500), and to determine information about a degree of freedom of the encoder head (300, 500) or the encoder scale (305, 505) based on the phase for each interference signal. an encoder head (300, 500) configured and arranged to direct a measurement beam, from the encoder head (300, 500) to an encoder scale (305, 505), to give rise to a plurality of diffraction orders of the measurement beam as once-diffracted measurement beams (503a, 503b), and change directions of the once-diffracted measurement beams (503a, 503b) back toward the encoder scale (305, 505) in a way that deviates slightly from a retro-reflection to produce a plurality of twice-diffracted measurement beams, wherein two of the plurality of twice-diffracted measurement beams propagate along non-parallel beam paths having an angular separation α, and the non-parallel beam paths of the two twice-diffracted beams at least partially overlap; direct a measurement beam, from the encoder head (300, 500) to an encoder scale (305, 505), to give rise to a plurality of diffraction orders of the measurement beam as once-diffracted measurement beams (503a, 503b), and change directions of the once-diffracted measurement beams (503a, 503b) back toward the encoder scale (305, 505) in a way that deviates slightly from a retro-reflection to produce a plurality of twice-diffracted measurement beams, wherein two of the plurality of twice-diffracted measurement beams propagate along non-parallel beam paths having an angular separation α, and the non-parallel beam paths of the two twice-diffracted beams at least partially overlap; a first detector arranged to receive one of the two twice-diffracted measurement beams and a first reference beam; a second detector arranged to receive the other of the two twice-diffracted measurement beams and a second reference beam, wherein the non-parallel beam paths of the two twice-diffracted measurement beams overlap one another as they propagate toward the first and second detectors; and an electronic processor configured to receive an interference signal from each of the first and second detectors, each interference signal comprising a phase related to the relative displacement between the encoder scale (305, 505) and the encoder head (300, 500), and to determine information about a degree of freedom of the encoder head (300, 500) or the encoder scale (305, 505) based on the phase for each interference signal.