Dimension and layout of the integrated-optics 4T-nuller. Top left: NOTT’s 4T-nuller photonic chip with the network of waveguides manufactured by ULI (see Sect. 3.2 for details). Top right: cross-section of the input-output facet of a triplet waveguide. Bottom left: schematic of the 4T-nuller showing the four inputs, the side-step S-bends, and the three cascaded directional couplers. Bottom right: visualization of the different outputs of the 4T-nuller (photometry and interferometry) observed on the testbench camera (Sect. 4.5.1). The photometric signals from each input are extracted by the Y-junctions and routed to photometric outputs P₁, P₂, P₃, and P₄. The remaining signals pass through the interferometric section consisting of three directional couplers, producing the four circled interferometric outputs I₁, I₂, I₃, and I₄. In the configuration of Fig. 1, I₁ and I₄ correspond to constructive outputs, while I₂ and I₃ yield isolated nulled signals. We note that l is the interaction length of the coupler, s is the center-to-center separation between the waveguides or pitch, A is the amplitude of the lateral offset, and r is the radius of curvature.