Line scales – accuracy for optical metrology tools

VTT MIKES' line scale interferometer [1] uses a dynamic method of measurement with a moving microscope for speed, simplicity, and considerations of space require­ments. The graduation line distances are measured during continuous motion, which makes the system fast and the interferometer insensitive to minor turbulence in the interferometer beam path. Possible problems with speed fluctuations and time delay in observing the lines are avoided by using an electrically shuttered CCD camera as a line detector and synchronous data sampling. The interferometer is constructed on a vibration isolated stone table to eliminate mechanical disturbances. The microscope is fixed on one side of a carriage and the CCD camera.

The displacement of the microscope is followed by a Michelson interferometer utilising a calibrated 633 nm Zeeman-stabilised He-Ne laser. Abbé error is eliminated with a large cube corner, making it possible to adjust the focus point of the microscope and the apex of the cube corner to the same point. This cube corner is constructed from three separate round mirrors adjusted to angles of 90 with each other. Ideal adjustment of the focus point and the apex of the cube corner nearly completely eliminates the Abbé error.


Line scale interferometer at VTT MIKES.

Average profiles of the graduation lines are formed by summing picture element intensities of each row of the CCD. Each image of the CCD camera consists of two fields charged in 1 ms and with time separation of 20 ms. Thereafter, the centre points of the graduation lines are determined from the slopes of the line profile and a correction term needed to superimpose the centre points is applied. The refractive index of air is determined by Edlen's formula updated by Bönsch et al. [2].

 Measuring ranges and uncertainties in line scale calibrations.

Calibration ​Measuring range  ​Expanded               
​Inexpensive calibration0.01…1165 mm ​U = Q[200; 100L] µmL in metres, Q[x; y]=√(x2+y2)
​Normal calibration​0.01…1165 mm U = Q[50; 100L] µm L in metres, Q[x; y]=√(x2+y2)
​High-accuracy calibration *​0.01…1165 mm U = Q[6.2; 82L] µm L in metres, Q[x; y]=√(x2+y2)
​* Requires excellent flatness and quality of line drawing​s.​
 [1]   A. Lassila, MIKES fibre-coupled differential dynamic line scale interferometer, Meas. Sci. Technol. 23, 094011 (2012).

 [2]  G. Bönsch and E. Potulski, Measurement of the refractive index of air and comparison with modified Edlen's formula, 
35, 133–139 (1998).V. Byman and A. Lassila, MIKES’ primary phase stepping gauge block interferometer, 
       Meas. Sci. Technol.26, 084009 (2015).


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

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