Error contributor of defocus and quadratic caustic in line scale measurement

Measurement error resulting from the defocus and quadratic caustic of a line-detecting microscope in line scale measurement was investigated. The relationship between the lateral shift and defocus was clarified and a procedure for measuring the lateral shift without changing the tilt of the line scale under measurement was proposed. An experiment was performed on line scale measurement to demonstrate the proposed measurement procedure using a line scale calibration system. The calibration system used in this experiment was a one-dimensional, laser-interferometric length measurement system for line scales developed by Nikon. The calibration system features a reduced Abbe's error, laser interferometer paths installed in vacuum and real-time calibration of the wavelength of the Zeeman laser, which is used for length measurement, using a 633 nm iodine-stabilized He–Ne laser. The line scale used for the experiment was 300 mm in length, and made of glass ceramics. The experimental result of the lateral shift stemming from the defocus and quadratic caustic of the optics of the line-detecting microscope was approximately 4 nm for a defocus range of ±10 µm. The possibility of reducing this type of error was also discussed.