2 Interferential Linear Encoder With 270 mm Measuring Length For Nanometrology

The following describes the principle of measurement of the LIP 382 linear encoder from HEIDENHAIN with the measured length error and especially the measurement of the interpolation error. With the aid of a special assembly using a piezo flexure stage and an automatic signal adjustment, an interpolation error of the LIP 382 of ±50 picometers was measured. Principle of function The functional principle of the LIP 382 high-resolution, interferential linear encoder [1] is illustrated schematically in figure 1. The scale of the glass ceramic Zerodur carries on its upper side a phase grating of chromium lines with a grating period of 512 nm with a measuring length of up to 270 mm. The scanning head consists essentially of a light source, an index grating, a cube-corner prism, and three photodetectors. The collimated light beam, which is perpendicular to the direction of measurement but oblique in the line direction, falls on the index grating with a grating period of 1024 nm, where it is diffracted into three orders. The zero order is hidden, and only the ±1st orders strike the scale, where they are diffracted in Littrow arrangement and, inclined in the line direction, are reflected into a cubecorner prism that reflects both beams in parallel offset onto the scale. There they are diffracted once again, reflected, and finally interfere on the index grating at a certain distance from the incident beam. Photodetectors convert the 120°-phase shifted optical signals into electrical output signals which are transformed into quadrature signals. The use of the cube-corner prism has two advantages: First, the two-fold diffraction gives a signal period of 1/4 of the scale pitch, i.e., 128 nm. An electronic interpolation for example by a factor of 128 leads to a measuring step of 1 nm. Second, a relatively large mounting tolerance is achieved in spite of the fine scale pitch. Especially important is the fact that due to this functional principle of pure two-beam interference, the signal has no harmonics, which could cause a short-range nonlinearity error. So the interpolation error depends only on the offset, the amplitudes and the phase difference of the signals, which can be adjusted very precisely as shown below. Figure 2: Length error of LIP 382 Figure 2 shows the length error of an LIP 382 measured with a vacuum interferometer as reference. Over the complete measuring length of 270 mm the length error is less than ±40 nm, which even includes the uncertainty of the vacuum interferometer. Measurement of the interpolation error As the expected interpolation error of the LIP 382 is much less than 1 nm, first of all one has to answer the question of how to measure such very small values. Common heterodyne interferometers cannot be used because their nonlinearity error is in the range of some nanometers [2], [3]. The idea for measuring the interpolation error is the following: a linear nanopositioning system with no intrinsic periodic error moves the scale relative to the scanning head, and an existing nonlinearity error of this positioning system is calibrated by the LIP 382 itself. Only measured values in intervals of the signal period of 128 nm are used, which are free of any periodical error, depend only on the fixed scale pitch. They can be used very well as length reference. For this measuring task a piezo positioning system with a scanning range of 15 μm is used. A flexure stage with a high mechanical stiffness and excellent guidance accuracy provides sub-nanometer resolution by means of an internal capacitance displacement sensor. To achieve an extremely stable setup, the piezo stage with a short scale of the LIP 382 is mounted in a rigid U-section. The scanning head is mounted on a cover plate connected with the U-section. This whole setup is placed on a vibration-insulated laboratory table. An IK 220 PC-board from HEIDENHAIN processes the signals of the LIP 382 with an interpolation factor of 4096, which yields a resolution of 31.25 pm. Figure 3: Noise of piezo system Figure 3 shows the noise of the piezo flexure stage in closed-loop operation measured with the LIP 382. The noise of 0.24 nm (rms) or 1.4 nm (peak-to peak) is caused by both mechanical and electronic components, especially by the servo signal of the piezo translator. This is in good accordance with the technical data of the manufacturer. To reduce the required resolution far below the noise of the piezo system a special setup illustrated schematically in figure 4 was conceived. The basic idea is that the direction of translation of the piezo system with respect to the measuring direction of the LIP 382 is rotated about an angle of 88°. By this means, the scale is moved in an angle slightly oblique to the scale line direction so that the real displacement of ∆L = 15 μm is scaled by the factor of k = cos α ≈ 1/28. This leads to a displacement in the measuring direction of the scale of only about ∆L’ ≈ 530 nm corresponding to slightly more than four signal periods. But 100