Line scales are used as a working standard of length for the calibration of optical measuring instruments such as profile projectors, measuring microscopes and video measuring systems. The authors have developed a one-dimensional calibration system for line scales to obtain a lower uncertainty of measurement. The scale calibration system, named Standard Scale Calibrator SSC-05, employs a vacuum interferometer system for length measurement, a 633 nm iodine-stabilized He-Ne laser to calibrate the oscillating frequency of the interferometer laser light source and an Abbe's error compensation structure. To reduce the uncertainty of measurement, the uncertainty factors of the line scale and ambient conditions should not be neglected. Using the length calibration system, the expansion and contraction of a line scale due to changes in ambient air pressure were observed and the measured scale length was corrected into the length under standard atmospheric pressure, 1013.25 hPa. Utilizing a natural rapid change in the air pressure caused by a tropical storm (typhoon), we carried out an experiment on the length measurement of a 1000 mm long line scale made of glass ceramic with a low coefficient of thermal expansion. Using a compensation formula for the length change caused by changes in ambient air pressure, the length change of the 1000 mm long line scale was compensated with a standard deviation of less than 1 nm.

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.