A magnetic field sensor includes a back bias magnet to generate a DC magnetic field. First and second magnetic field sensing elements of the magnetic field sensor are disposed proximate to at least one ferromagnetic surface of a ferromagnetic target object. The first and second magnetic field sensing elements generate first and second electronic signals, respectively, in response to first and second sensed magnetic fields corresponding to the DC magnetic field but influenced by the at least one ferromagnetic surface. The magnetic field sensor generates a difference signal that is a difference of amplitudes of the first and second electronic signals. The difference signal is indicative of a rotation measurement of an absolute relative rotation of the ferromagnetic target object and the magnetic field sensor about a rotation axis.

Apparatus and associated methods relate to measuring position and displacement of a 2D surface magnet array of at least three adjacent magnetic north and south tracks with an acute angle versus its motion displacement relative to a magnetic field sensor (e.g., magnetic sensing probe). In an illustrative example, the geometry of the 2D surface magnet array may be planar with adjacent and alternating north and south pole regions. In some embodiments, the 2D surface magnet array geometry may take the form of (1) an axial cylindrical helical multipole magnet array having individually magnetized layers that are oriented in helical shape, or (2) a radial disk spiral multipole magnet array with at least three adjacent north and south tracks oriented as a spiral shape.

A system includes a helically polarized magnet having a plurality of north and south poles circumferentially and helically patterned along a linear axis. Magnetic flux varies at different positions along a linear path in a direction aligned with the linear axis. A multi-axis magnetometer and/or magnetometer array is configured with at least two sensing coils to detect the position of the helically polarized magnet by sensing the magnetic flux variations at the different positions along the linear path.

A system includes a helically polarized magnet having a plurality of north and south poles circumferentially and helically patterned along a linear axis. Magnetic flux varies at different positions along a linear path in a direction aligned with the linear axis. A multi-axis magnetometer and/or magnetometer array is configured with at least two sensing coils to detect the position of the helically polarized magnet by sensing the magnetic flux variations at the different positions along the linear path.

A system includes a helically polarized magnet having a plurality of north and south poles circumferentially and helically patterned along a linear axis. Magnetic flux varies at different positions along a linear path in a direction aligned with the linear axis. A multi-axis magnetometer and/or magnetometer array is configured with at least two sensing coils to detect the position of the helically polarized magnet by sensing the magnetic flux variations at the different positions along the linear path.

An angle sensor is disclosed. The angle sensor has a disc, a first magnetic pattern disposed on a side of the disc and including a number N1 of first portions of spirals regularly distributed in a first ring, and a second magnetic pattern disposed on a side of the disc and including a number N2 of second portions of spirals regularly distributed in a second ring. The numbers N1 and N2 are coprime and N1 is different from N2, N21, and N2+1.

A stroke sensor is provided with two disk-shaped rotors configured to rotate with a stroke of a measuring object, a rotation detecting unit that detects rotations of the two rotors, respectively, and a stroke position detecting unit that detects the stroke position of the measuring object based on the rotations of the two rotors detected by the rotation detecting unit. At least one of the two rotors is in direct contact with the measuring object. The two rotors are provided side by side in an arrangement direction perpendicular to an axial direction of the measuring object and are provided so as to be adjacent to the measuring object in an arrangement perpendicular direction perpendicular to the axial direction and the arrangement direction. Each of the two rotors is provided in such a manner that its rotation axis direction is inclined with respect to the arrangement direction.