## 2 Materials and Methods  
The interferometric techniques by their very nature include a reference that is an important feature of any radiometric measurement. Furthermore, the shearing interferometry incorporates a temporal element under control of an Earth user that allows the development of a causal relationship in the detected pattern when the planet is within the instrument field of view. Originally, the theoretical analysis was developed by substantiating that the rotationally shearing interferometer (RSI) may detect an invisible distant planet orbiting a bright, large star [27; 28; 29; 30; 31; 32; 33; 34; 35]. The traditional Mach-Zehnder interferometer, that requires a reference surface for its functioning, is transformed into an RSI when a rotated Dove prism is inserted in one of its arms, as illustrated in Figure 2. A Dove prism is an optical component that rotates the wavefront by twice its own angle of orientation [36; 37; 38; 39; 40; 41; 42]. Thus, a wavefront in one interferometer arm is compared, that is subtracted and interfered, with the duplicated and rotated copy of itself in the other arm. Therefore, the need for an external radiometric reference is eliminated.  
Using this technique, the presence of an invisible off-axis planet may be detected by observing straight fringes. The planet presence is confirmed unequivocally by the RSI feature that a change in one parameter produces a change in the detected fringe pattern, but only in the presence of an off-axis point object. This critical parameter is the orientation angle of the Dove prism. When its angle of orientation is changed, the fringe density and the fringe inclination change, but only in the presence of the planet, as illustrated in Figure 3. In the absence of a planet, the fringes do not arise when the interferometer is bore-sighted on the star. The star wavefront features the azimuthal symmetry, so the RSI does not detect it. As a derivative device, the RSI ignores a constant quantity.  
The experimental work was also performed to verify the feasibility of this concept. Both a solar system simulator and the RSI were designed and built. The proposed technique of using an RSI to detect a planet in a nearby solar system was indeed experimentally demonstrated in the laboratory environment. Experimental results are presented in Figure 4. For the laboratory demonstration, a single-aperture instrument was designed and developed. It meets the stringent conditions of the Mach-Zehnder configuration.  
Figure 3: Interference fringes of tilt simulated in an RSI when the shear angle is increased from 0\({}^{\circ}\)-rotation angle (blank field) to 8\({}^{\circ}\) in increments of 1.6\({}^{\circ}\) (axis of rotation is normal to the page). The shear angle is the angle of the orientation of the Dove prism, or the wavefront rotator in Figure 2. The density of fringes increases, and the fringe inclination angle decreases with increasing wavefront rotation angle. The fringe angle is defined as the angle that the straight line through the bright fringe makes with the horizontal axis.  
Figure 2: (**a**) An RSI implemented in a Mach–Zehnder configuration with two Dove prisms. A Dove prism DP that is rotated by an angle about the optical axis introduces the wavefront shear in the RSI. The symbols are interpreted as follows: M, mirror; BS, beam splitter; and OP, observation plane. (**b**) Conceptual design of an RSI with an electro-opto-mechanical delay module in one arm and a compensation module in the other arm. A computer-controlled two-mirror assembly in each arm is used to precisely adjust the paths in both interferometer arms for increased wavefront coherence.