Step gauges – most accurate interferometric calibrations

The VTT MIKES interferometer for step gauge calibration [1] is constructed on a vibration isolated stone table to eliminate mechanical disturbances. The interferometer has two parallel beams in measuring arm allowing the adjustment of the measuring probe ball to the actual effective measuring line to minimize the Abbé error. The beams are reflected back by two corner cubes fixed to the same stiff measuring head frame with the probe. The probe ball (d=5 mm) is of sapphire to avoid magnetic effects during probing. The measuring head is constructed so that it is possible to lift the probe ~13 mm by tilting it without disturbing the interferometer signals. The measuring head is fixed to a carriage with air bearings and can be moved on stone guide using a stepper motor. The position of the probe is measured using a homodyne laser interferometer. During probing the measuring head and probe is moved by piezo actuator to have few micrometres deep bending of probe ball and simultaneously analogue voltage signal from probe electronics and interferometer readings are recorded. The edge position is extrapolated to zero force. The standard deviation of the probing is 20 nm. The probe is lifted up and down using a linear actuator and kevlar line.


Step gauge interferometer at VTT MIKES.

Ambient conditions (air and material temperature, air pressure and humidity) are measured continuously online. Humidity and pressure are measured using Vaisala PTU200 meter. Four Pt100 sensors are used for material temperature measurement and three for air temperature measurement. The temperature sensors are connected via 4-wire scanner to Isotech TTI-2 High Accuracy Thermometer. All sensors and laser wavelength are calibrated against higher accuracy reference standards of VTT MIKES. Refractive index of air is calculated using updated Edlen’s equation by Bönsch [2].

The calibration sequence is fully controlled by a PC. Before measurement the positioning of the step gauge is done with integrated 2D-CMM using 3D edge detector and Heidenhein linear encoder scales with <1 µm resolution. The probe ball diameter is calibrated using a stack of three calibrated gauge blocks wrung so that both external and internal measurements can be done. For high accuracy measurement, the same step gauge is measured four times: in two different positions with two orientations. Each measurement consists of several (n=~3) back and forth measurements of full scale. The average of 4 runs gives the final results.

Measurement uncertainties for different calibrations.

​Calibration ​Measuring
Inexpensive calibration *5...2020 mm U = Q[0.17; 0,28L] µmL in metres, Q[x; y]=√(x2+y2)
​Normal calibration *5...2020 mm U = Q[0.090; 0,14L] µm L in metres, Q[x; y]=√(x2+y2)
High-accuracy calibration **5...2020 mm U = Q[0.064; 0,088L] µm L in metres, Q[x; y]=√(x2+y2)
​​*  Within MRA-agreement, MRA = Mutual recognition agreement
** not yet in MRA​ ​
  1. V. Byman and A. Lassila, MIKES’ primary phase stepping gauge block interferometer, Meas. Sci. Technol.26, 084009 (2015).
  2. G. Bönsch and E. Potulski, Measurement of the refractive index of air and comparison with modified Edlen's formula, Metrologia 35, 133–139 (1998).


  • Antti Lassila, Research Team Leader, tel. +358 40 767 8584, email antti.lassila(at)

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