In the displacement measurement of the wafer stage in lithography machines, signal quality is affected by the relative angular position between the encoder head and the grating. In this study, a two-degree-of-freedom fiber-coupled heterodyne grating interferometer with large operating range of rotation is presented. Fibers without fiber couplers are utilized to receive the interference beams for high-contrast signals under the circumstances of large angular displacement and ZEMAX ray tracing software simulation and experimental validation have been carried out. Meanwhile, a reference beam generated inside the encoder head is adopted to suppress the thermal drift of the interferometer. Experimental results prove that the proposed grating interferometer could realize sub-nanometer displacement measurement stability in both in-plane and out-of-plane directions, which is 0.246 nm and 0.465 nm of 3σ value respectively within 30 s.

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A method for measuring the relative phases (RPs) among the three beams in the case of homodyne three-beam interference (TBI) is proposed and verified by the ZEMAX simulation in this paper. The method requires that the interference beams are not on the same plane, that is, any two of the three beams interfere at an angle in different planes. Based on the phase delay of the beam in space, the inclined beams have different phases at different positions within the beams’ range. By arranging the photodetector array within the interference area, the RPs can be calculated using the intensity of the interference light received by specific photodetector units. The application of the algorithm for the displacement measurement of the homodyne three-beam interferometer (TBIR) has been verified by simulation. The beam number of three-beam interference is one less than that of two two-beam interference when measuring two relative phases. Compared with the two-beam interferometer, the TBIR applied to two-degree-of-freedom displacement measurement is more compact in structure due to the more compact phase measurement components.

Laser interferometers and grating interferometers based on optical interferometry are widely used in displacement measurement of precision machining and testing equipment, such as the measurement system of integrated circuit equipment, due to their high precision, noncontact, and large dynamic measurement range. The ghost reflection in optical elements may lead to the periodic nonlinear error of the interferometer and also reduce alternating current/direct current. We propose a general method for automatic ghost reflection interface identification. It can analyze the influence weight of ghost reflection for each interface of any interferometer. In addition, the manufacturing cost of the interferometer is effectively reduced by optimization algorithms that enable ghost reflection avoidance in the interferometer design. Experimental results prove the influence weight of ghost reflection at different positions in the interferometer and provide the parameter selection of the most suitable interface reflection of the interferometer.