1. Introduction

The development of optical design and fabrication such as projection optics for extreme ultraviolet lithography (EUVL) and laser fusion, etc. places ultrahigh requirement on the optical testing precision and accuracy. In the EUVL operating at a wavelength of 13.5 nm [1–4], the projection optics is composed of 4–6 aspheric mirrors and each mirror needs to be

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

finished with the figure error less than 0.2–0.3 nm (RMS), requiring a higher testing accuracy (e.g., 0.1 nm RMS). The optical interferometers, including the Twyman-Green [5] and Fizeau interferometers [6], have been widely used in the testing lenses and mirrors for figure metrology, in which standard lenses are applied to produce the necessary reference wavefront. Due to the fabricating error of the reference optics, the achievable measurement accuracy of the traditional interferometers is generally limited within λ/50 (λ is the operating wavelength). As a novel optical technique, the point-diffraction interferometer (PDI) [7–12] has been developed to overcome the accuracy limitation in traditional interferometers, and it can reach the measurement accuracy in the order of subnanometer. The PDI method employs point-diffraction spherical wavefront as ideal measurement reference, and it can achieve the accuracy better than 10−<sup>3</sup> λ. The PDI does not require precise and costly standard parts, and it provides a feasible way to overcome the accuracy limitation of the reference optics in traditional interferometers. The process of point diffraction determines the reachable accuracy of PDI, thus, a good reproducibility of the measurement accuracy can be achieved with PDI. The ideal spherical wave can be generated from the point-diffraction source such as circle pinhole [13–15] and optical fiber [16–18]. Nikon realized that the high-precision testing of spherical and aspherical surfaces with the pinhole PDI [14, 15], and the Lawrence Livermore National Laboratory measured surface figure with the single-mode-fiber PDI [16]. The diffracted wave in both PDI systems serves as testing wave as well as reference wave. To extend the aperture of the optics, a fiber PDI with two optical fibers serving as point sources was proposed for large optics measurement [18], in which the diffracted wave from one fiber acts as testing wave and that from the other fiber as reference wave. Considering the fact that the diffraction light power from pinhole is poor (transmittance <0.1‰) and the numerical aperture (NA) of diffracted wavefront with single-mode fiber is quite low (<0.20), both approaches limit the measurement range of the existing PDIs. A submicron-aperture (SMA) fiber with cone-shaped exit end has been proposed to obtain both the high diffraction light power and high-NA spherical wavefront [19–21], and it is considered as a feasible way to extend the measurement range of the system. Due to the fact that the achievable testing accuracy of PDI is mainly determined by the sphericity of diffracted wavefront, the analysis of the diffracted wavefront error has become a fundamental way to evaluate the performance of PDI. In our research, both numerical analysis and experimental measurement have been performed to reconstruct the point-diffraction wavefront aberration. Besides, various setups of PDI have been developed to realize the precise surface testing with adjustable contrast [12, 22] and three-dimensional (3D) coordinate measurement [20, 23, 24]. The new PDI for three-dimensional (3D) coordinate measurement avoids the measurement uncertainty introduced by the imperfect target in multilateration and allows the target (made of two point-diffraction sources) to take free movement within a volumetric space over NA of point-diffraction wave. Section 2 presents a brief review of the PDI for testing of wavefront and the optical surface. Section 3 presents the basic theory of the SMA fiber PDI for 3D coordinate measurement. Sections 4 and 5 explain the numerical method and the experimental measurement method for the evaluation of diffracted wavefront sphericity, as well as the corresponding analyzing results.
