There is provided an optical encoder with alignable relative positions between elements including an encoding medium, a sensor package and a memory. The sensor package includes a photodiode array and two alignment photodiodes opposite to the encoding medium. The memory records an alignment pattern associated with output signals of the two alignment photodiodes when the encoding medium and the sensor package are at nominal operating positions. When the encoding medium and the sensor package are not at the nominal operating positions, the relative position alignment is performed by adjusting current relative positions between the encoding medium and the sensor package to cause a current pattern associated with output signals of the two alignment photodiodes to be identical to the alignment pattern.

A method is given for finding a reference correction value of an index mark of an angular encoder. The angular encoder includes a first read head, a second read head, and a patterned element having incremental marks and an index mark. In a first instance and in a second instance, the patterned element is rotated relative to the read heads to obtain incremental readings from the first read head and the second read head and an index mark from the first read head. Based on these readings, a processor determines, in the first instance, a first reference position and, in the second instance, a second reference position. The processor determines the reference correction value based at least in part on the first reference position and the second reference position.

A reference signal generation circuit generates a reference signal from a reading result of the reference point detection pattern. The first light-receiving element array includes a first light-receiving element that outputs a first signal, and a second light-receiving element that is disposed in a first direction of the first light-receiving element and outputs a second signal. A second light-receiving element array includes a third light-receiving element that outputs a third signal, and a fourth light-receiving element that is disposed in the first direction of the third light-receiving element and outputs a fourth signal. The second light-receiving element array is disposed in a second direction of the first light-receiving element array. The reference signal generation circuit outputs a reference signal that starts at a period when levels of the first and second signal become equal and ends at a period when levels of the third and fourth signal become equal.

An encoder includes a scale including an origin detecting pattern, an origin detector, and a processor. The origin detector includes a plurality of detecting element groups including a first, second, third, and fourth detectors. The first and second detectors and the third and fourth detectors are symmetrically arranged to a center of each detecting element group, respectively. A part of the origin detecting pattern having a physical characteristic different from an origin peripheral part is shorter than each detecting element group. The origin detector outputs a first signal from the first and third detectors, and a second signal from the second and fourth detectors. The processor outputs a fifth signal based on a third signal from the first signal and a first threshold, and a fourth signal from the second signal and a second threshold as an origin signal.

A method and a system for arbitrary optical waveform generation from an optical input, the system comprising an optical shaper comprising unbalanced interferometers with at least one delay, the delay being selected of at least 0.1 ps, an optical sampling readout selected for measuring optical waveforms of at least 0.1 ps; and an electronic processing unit; wherein the optical input is a picosecond pulse; with a minimal pulse duration before the optical shaper equal to a minimal delay of the optical shaper; the optical shaper splitting and interfering optical pulses; the optical sampling readout collecting data at an output of the optical shaper; and the electronic processing unit comparing the collected data with a preset target and updating the optical shaper from results of the comparison until a maximal match between the output of the optical shaper and the preset target output, wherein the maximal match is determined iteratively using one of: machine-learning, optimization algorithms and iterative search algorithms.