## 2 Reference Wavefront Source Based on SiN Waveguide  
In this section, structure of the waveguide reference wavefront source (RWS) and its principle to generate the reference wavefront are introduced firstly. Then, important parameters of the waveguide RWS that influence the accuracy, numerical aperture (NA), and power of the reference wavefront are mentioned.  
As shown in Figure 1, structure of the waveguide RWS is similar to the buried waveguide: silicon nitride (SiN) core with a thickness of 250 nm in the \(y\) direction is buried between the silicon dioxide (SiO\({}_{2}\)) bottom cladding of 2.52 \(\upmu\)m thickness and SiO\({}_{2}\) top cladding of 2 \(\upmu\)m thickness. SiO\({}_{2}\) bottom cladding is located on the silicon (Si) substrate of 3 mm thickness. This waveguide RWS can be divided into four parts and each part has its function. Part A\({}_{1}\) (Y-branch Coupler) or Part A\({}_{2}\) (grating coupler) is used to improve the coupling efficiency between the single-mode fiber (SMF) and waveguide, and further increase the power of the reference wavefront. Therefore, fiber-to-waveguide coupler is the most important part in the design of the waveguide RWS. Part B and Part C are the straight waveguide. Part C is a bent waveguide with the sector angle of 90\({}^{\circ}\). This bent waveguide makes the reference wavefront perpendicular to the incident light, which avoids the interference between them.  
Waveguide RWS generates the spherical reference wavefront by diffraction at the output facet of the SiN core. This process is as follows: 532 nm incident light provided by the laser propagates to the fiber-to-waveguide coupler along the SMF. This incident light can be coupled into the waveguide either by the Y-branch coupler (Part A\({}_{1}\)) or the grating coupler (Part A\({}_{2}\)) and then propagates along the core. Due to high refractive index difference between the SiN core and SiO\({}_{2}\) cladding, light in the waveguide is strongly confined in the sub-micron core during the propagation. Finally, light arrives at the output facet and spherical reference wavefront is generated by diffraction.  
Accuracy and numerical aperture (NA) of the reference wavefront are determined by the size of the core cross-section (\(y-z\) cross-section of the core in Figure 1). SiN core of the waveguide RWS has a square cross-section of 0.25 \(\upmu\)m in length, which satisfies the single-mode propagation condition. Accuracy and NA of the reference wavefront generated by this waveguide RWS are calculated by numerical simulation and results are shown in Figure 2. When NA of the reference wavefront is 0.3, peak-to-valley (PV) value and root-mean-square (RMS) value are \(1.07\times 10^{-4}\lambda\) and \(1.72\times 10^{-5}\lambda\) (\(\lambda=532\) nm), respectively. When NA increases to 0.5, PV value and RMS value are \(2.86\times 10^{-4}\lambda\) and \(4.83\times 10^{-5}\lambda\), respectively. Even if NA of the reference wavefront reaches 0.5, RMS value is still less than 0.03 nm. Such a high accuracy reference wavefront cannot be generated by a pinhole RWS or fiber RWS.  
Power of the reference wavefront is determined by the coupling efficiency between the SMF and waveguide. Therefore, an optimal fiber-to-waveguide coupler must be designed to improve the coupling efficiency. To provide a reliable reference for the selection of a fiber-to-waveguide coupler, Y-branch coupler and grating coupler are compared in detail, including their max coupling efficiency, 3 dB fabrication tolerance, 3 dB alignment tolerance and polarization-dependent loss.