Displacement Measurement of Planar Stage by Diffraction Planar Encoder in Nanometer Resolution Kuang-Chao Fan, Bo-Hsuan Liao, Yi-Cheng Chung, Tien-Tung Chung Dept. of Mechanical Engineering National Taiwan University Taipei, Taiwan, ROC fan@ntu.edu.tw Abstract— This paper presents a novel planar diffraction grating interferometer (PDGI), which is based on the principle of diffractive interferometry. The PDGI is composed of two linear diffraction grating interferometers (LDGIs) arranged in orthogonal configuration for simultaneously measuring the two- dimensional displacement of the planar grid, which is mounted on the bottom surface of an XY stage. It adopts a special design in optical path that can increase the alignment tolerance between the optical head and the grid. The signal process circuit and software are also developed, including the pulse count and phase subdivision. The fabricated planar grid has 55 mm×55 mm size and 1740 line/mm. The resolution can reach to 1 nm. Experimental results on an air bearing XY stage showed that even in the normal laboratory environment the standard deviation of measured values can be controlled to within 15 nm for a long stroke up to 25 mm in both axes. Keywords-planar encodert; XY stage; diffractive interferometry; displacement measurement I. INTRODUCTION In recent years, many linear displacement sensors based on grating interferometry with long-stroke and nano-scale resolution have been developed [1-3]. Compared with the commonly used laser interferometer that is bulky, expensive and sensitive to the environment, the grating interferometer features the advantages of small, low cost and immune to the environment. However, the alignment tolerance of the sensor head to the scale is crucial as all stages have angular errors. Therefore, developing a high resolution and high accuracy 2D displacement sensor which possesses high alignment tolerance is urgently needed. Mitutoyo Co. used three linear gratings in each dimension to form a planar encoder that is deemed a complicated design [4]. Lee [5] developed a special conjugate optical design to achieve nano-scale resolution. Gao [6] proposed a surface encoder which is composed of a slope-sensor and a grid and has the ability to measure multi-DOF. Kao [7] proposed a double diffraction optical design using conjugate optics to achieve nano-resolution. Gao [8] developed a three-axis displacement sensor composed of Michelson interferometry and grating interferometry by using two planar gratings. Akihide [9] proposed a two-DOF linear encoder that can measure the X-directional position and the Z-directional straightness simultaneously. It is noted that most of the above- mentioned researches could not successfully demonstrate the capability of long-stroke and nano accuracy by experiments. A preliminary study of a novel planar diffraction grating interferometer (PDGI) module was carried out by the author’s group, but only on a 25×25 mm 2 planar encoder and at a low speed motion [10]. In this report, the PDGI is modified to allow measuring fast speed motion of an air bearing XY stage driven by linear motors to the range of 50 mm×50 mm. The fabricated planar grid has 55 mm×55 mm size and 1740 line/mm. The DSP- based signal process circuit and software of PDGI are also developed, including the pulse count and phase subdivision. The resolution can reach to 1 nm. Experimental results showed that even in the normal laboratory environment the standard deviation of measured values can be controlled to within 15 nm for a long stroke up to 40 mm in both axes. II. PIINCIPLE OF THE PDGI A. Principle of LDGI Figure 1 shows the principle of the LDGI system [3]. The laser diode emits a linearly polarized beam and split by a polarization beam splitter (PBS) with equal intensity. The P- polarized beam propagates along the right side of the optical path. The quarter waveplate (Q2) converts the P-polarized beam into a right-circularly polarized beam. Simultaneously, the S-polarized beam propagates along the left side of the optical path, and then converted into a left-circularly polarized beam after Q1. These two circularly polarized light beams are reflected by mirrors (M1~M3) and diffracted by the grating. Designed with Littrow configuration, the two incident angles equal to the grating’s ±1th order diffraction angles, each input beam will be diffracted back through the same path to the corresponding mirror. The left-arm beam is changed to a P- polarized beam after it transmits through Q1. Similarly, the right-arm beam is changed to a S-polarized beam after it transmits through Q2. After passing through the quarter waveplate Q3 these two beams are retarded to the left- circularly polarized and right-circularly polarized beams,  894