Encoder and apparatus using the same

An apparatus comprising:

• an encoder;
• and
• a movable member whose position is detected by using the encoder,
• wherein the encoder comprises:
• a scale provided with a first track and a second track each including at least one periodic pattern;
• a sensor relatively movable with the scale and configured to read the periodic patterns in the first and second tracks to output periodic signals respectively corresponding to the read periodic patterns with a relative movement of the sensor and the scale;
• and
• a processor configured to calculate a detection position in a relative movement direction of the scale and sensor by using the periodic signals,
• wherein:
• the first track includes a first periodic pattern and a second periodic pattern whose periods are mutually different, and the second track includes a third periodic pattern whose period is different from that of the second pattern and is one of an integral multiple and an integral fraction of that of the first periodic pattern,
• the sensor is configured to output a first periodic signal corresponding to the first periodic pattern, a second periodic signal corresponding to the second periodic pattern and a third periodic signal corresponding to the third periodic pattern, and
• the processor is configured (a) to calculate an error by using a phase difference between the first and third periodic signals, the error being due to a relative displacement between the first and second tracks and the sensor, and (b) to calculate the detection position after correction of the error, by using the error and at least the first and second periodic signals.