Displacement detecting device and scale

A displacement detecting device comprising:

• a scale having marks whose pitch interval can be approximated to a quadratic or higher-order polynomial along a measurement direction, or changes randomly;
• a first displacement detecting unit arranged facing the scale and configured to detect a displacement in the measurement direction;
• a second displacement detecting unit arranged facing the scale and with a predetermined distance in the measurement direction from the first displacement detecting unit, and configured to detect a displacement in the measurement direction;
• a first displacement computing unit configured to output first relative position information based on the displacement in the measurement direction detected by the first displacement detecting unit;
• a second displacement computing unit configured to output second relative position information based on the displacement in the measurement direction detected by the second displacement detecting unit;
• a comparing unit configured to calculate a difference between the first relative position information and the second relative position information per unit displacement in a position where the first displacement detecting unit is arranged and also, to calculate absolute position information with respect to the measurement direction of the scale based on the calculated difference, and to output the absolute position information;
• and
• an absolute position computing unit configured to compute an absolute position in the measurement direction with respect to the scale based on the absolute position information from the comparing unit and the relative position information of at least one of the first relative position information and the second relative position information and to output the absolute position.