## 1 Introduction  
Reference wavefront used in traditional interferometers [1] such as Twyman-Green interferometer and Fizeau interferometer is generated by reflection of a standard reference mirror, so accuracy of the reference wavefront is limited by fabrication accuracy of the standard reference mirror which is usually not better than \(\lambda/40\) (\(\lambda=532\) nm). Different from above interferometers, reference wavefront used in the point diffraction interferometer (PDI) [2; 3; 4; 5; 6; 7] is generated by a diffraction element called reference wavefront source (RWS). RWS generates a nearly ideal spherical reference wavefront by diffraction at a small aperture of micrometer diameter, so accuracy of the reference wavefront is not limited by a standard reference mirror and can reach sub-nanometer scale. To improve the accuracy, numerical aperture (NA), and power of the reference wavefront, and further expand the application of PDIs, researchers have proposed and made various RWSs. Pinhole RWS and fiber RWS are two commonly used RWSs. Pinhole RWS [8; 9; 10; 11] is made by etching a submicron pinhole on the metal film. Such a small pinhole can generate a high accuracy spherical reference wavefront and its NA is up to 0.3, but low light transmittance of this small pinhole (\(<\)0.1%) seriously reduces the power of the reference wavefront [12]. Pinhole RWS can also be fabricated by other materials like liquid crystal [13] or metal wire grid [14], but these pinhole RWSs also have the above problems. Fiber RWS [15; 12; 16; 17] generates the reference wavefront by diffraction at the end face of the single-mode fiber (SMF). Due to high light transmittance of the SMF, power of the generated reference wavefront is high [12]. But due to limitation of the SMF core diameter (3-5 \(\upmu\)m) [17], NA of this reference wavefront is usually less than 0.2, which greatly limits the NA of the optical element to be tested. Using a special SMF with a submicron end face is an effective way to improve the NA of the reference wavefront, but this kind of SMF is difficult to fabricate and clamp. To make the reference wavefront have high accuracy, NA, and power simultaneously, our group has designed a new RWS based on the silicon nitride (SiN) waveguide. Due to high refractive index difference between the SiN core (\(n=1.96,\lambda=532\) nm) and silicon dioxide (SiO\({}_{2}\)) cladding (\(n=1.48,\lambda=532\) nm), light in the waveguide is firmly confined in the core whose cross-section side length is 0.25 \(\upmu\)m, and propagates along the core to the output facet. Then, light is diffracted at the output facet, and spherical reference wavefront is generated. NA of this reference wavefront is more than 0.5, and root-mean-square (RMS) value is less than 0.03 nm. Power of this reference wavefront is mainly determined by coupling efficiency between the SMF and waveguide RWS. To get the maximum coupling efficiency, two fiber-to-waveguide couplers called Y-branch coupler [18; 19; 20] and grating coupler [21; 22; 23] are designed by numerical simulation. Then, coupling efficiency, 3 dB alignment tolerance, 3 dB fabrication tolerance, and polarization-dependent loss of two couplers are compared. Rest of this paper is organized as follows. In Section 2, structure of the waveguide RWS and its operation are first introduced. Then, accuracy, NA and power of the reference wavefront are analyzed. In Sections 3 and 4, Y-branch coupler and grating coupler are introduced in detail, including structure of the coupler, key parameters affecting the coupling efficiency, fabrication difficulty, alignment difficulty, and polarization-dependent loss. Y-branch coupler and grating coupler are compared in Section 5. In Section 6, a summary of this paper is made. In this paper, numerical simulation is performed based on the finite difference time domain (FDTD) method.