In this study, measurement standards with irregular surface topography which can be used for surface texture measuring instruments of various measurement principles are proposed, and the verification system for surface texture measuring instruments is established using the measurement standard. We have generated the software gauge data with 3D irregular surface texture using the non-causal 2D auto-regressive model (2D AR model). This model can generate periodic irregular surface topography data from specified surface texture parameters, and based on the generated software gauge data, the measurement standards were manufactured by machining with a diamond ball end mill. The short wavelength components which cannot be processed by the ball end mill were removed from the original machining data by the morphological filter. Manufactured measurement standards were measured using three types of surface texture measuring instruments. Proposed measurement standards can be used for various types of measuring instruments.

We propose the use of the sinusoidal frequency modulation technique to improve both the frequency stability of an external cavity laser diode (ECLD) and the measurement accuracy and range of a displacement-measuring interferometer. The frequency of the ECLD was modulated at 300 kHz by modulating the injection current, and it was locked to the b 21 hyperfine component of the transition 6-3, P(33), 127 I 2 (633 nm) by the null method. A relative frequency stability of 6.5 × 10 −11 was achieved at 100 s sampling time. The stabilized ECLD was then utilized as a light source for an unbalanced Michelson interferometer. In the interferometer, the displacement and direction of the target mirror can be determined using a Lissajous diagram based on two consecutive and quadrant-phase harmonics of the interference signal. Generally, the measurement range of the interferometer by the proposed method is limited by the modulation index and the signal-to-noise ratio of the harmonics. To overcome this drawback, suitable consecutive harmonic pairs were selected for the specific measurement ranges to measure the displacement. The displacements determined in the specific ranges by the proposed method were compared with those observed by a commercial capacitive sensor. From the comparison, the proposed method has high precision to determine the displacement. The measurement range was also extended up to 10 m by selecting a suitable modulation index and suitable consecutive pairs of harmonics.

This paper describes a concurrent measurement of spindle radial, axial and angular motions using concentric circle grating and phase modulation interferometers. In the measurement, the concentric circle grating with fine pitch is installed on top of the spindle of interest. The grating is a reference artifact in the method. Three optical sensors are fixed over the concentric circle grating, and observe the proper positions of the grating. The optical sensor consists of a frequency modulated laser diode as a light source, and two interferometers. One interferometer in the sensor observes an interference fringe between reflected light form a fixed mirror and 0-th order diffraction light from the grating to measure the axial motion. Another interferometer in the sensor observes an interference fringe between ±2nd order diffraction lights from the grating to measure the radial motion. Using three optical sensors, three axial displacements and three radial displacements of the proper observed position of the grating can be measured. From these six measured displacements, radial, axial and angular motions of the spindle can be determined concurrently. In the paper, a measurement instrument, a fringe interpolation technique by sinusoidal phase modulation and experimental results are discussed.

Currently, the standard length measurement method with nanometre resolution is laser interferometry. However, it is difficult to determine an arbitrary length with an accuracy of sub-nanometre or less order using interferometers because they have a nonlinearity problem in fringe interpolation. A phase modulation homodyne interferometer (PMHI) that can be used to determine the optical path difference of an integer multiple of the wavelength (n × λ) with picometre resolution was proposed by IMGC (former Italian Standard Institute). The lattice spacing of approximately 0.246 nm for graphite regular crystalline lattices is uniform and stable over a long range, when the crystals are stress free. These crystals can be used as a reference scale with sub-nanometre resolution. The scanning tunnelling microscope (STM) is emerging as a powerful tool in surface engineering, and enables us to image atoms on a crystalline surface. Therefore, such a crystalline surface can be used as ‘the crystalline scale’ using the STM.In this study, an instrument for calibrating optical encoders is developed by combining a graphite crystalline lattice as a fine scale and the optical fringe of the PMHI as a coarse scale. The instrument consists of a precise linear X-axis sample stage, on which the reference graphite crystal and the optical encoder scale are set, a head of the STM with a YZ tip scanner and a PMHI. The relative displacement of the X-axis sample stage between optical interference dark fringes (= null points) of the PMHI, which is λ/16 times the integer value in the design, can be measured with picometre resolution using the phase modulation technique. A lattice spacing of 0.246 nm on the graphite crystalline surface is derived as the fine scale from the STM image and the optical fringes of the PMHI. In the experiment, the periodical error of the optical encoder, whose minimum resolution is less than a nanometre, is measured using both the lattice spacing of graphite and the optical fringes of the PMHI. The results show that the proposed instrument has the feasibility to calibrate optical encoders with an uncertainty of 10 pm order.

We present a method for air-refractive-index (nair) fluctuation measurement using a laser interferometer. The method is based on a combination of a phase modulation homodyne interferometer (PMHI), an external cavity laser diode (ECLD) and an ultralow thermal expansion material (ULTEM). The PMHI utilizes a Michelson interferometer which is constructed on the ULTEM plate under the condition of an air temperature fluctuation of less than 10 mK, so that the optical path change or the air-refractive-index fluctuation (Δnair) caused by the thermal disturbance can be neglected. Meanwhile, the ECLD is controlled by adjusting its frequency to track some of the dark fringes of the interferometer, so that Δnair can be derived from the ECLD frequency change. The uncertainty of the Δnair measurement in the experiment is of 10−8 order. However, it will be possible to decrease the uncertainty to 10−9 or less if the signal-to-noise ratio (SNR) of the control system is improved.