The 1Dplus encoder is a 2-D encoder that allows measurement of linear guiding and thermal drift errors during movements of a stage or machine, allowing the processing and immediate compensation of guiding and thermal drift errors. The encoders are frictionless and have gratings in 2-D, with models featuring two or three scanning units for simultaneous measurement of both the X and Y directions. Three scanning units allow the calculation of the angle of rotation of the bracket that houses the scanning units. The X-axis measurement of the encoder has an accuracy grade of ±1 micrometer and includes a reference mark. The grating period of the encoder is 8 micrometers; the signal period is 4 micrometers.