## 3 Results  
Based on the above geometric optical design, a batch of proposed QFP prisms were fabricated by a lens manufacturing company (Union Optic Incorporated, Wuhan, China) and the parameters were measured and given as shown in Figure 3a. It should be noted that a cuboid base was added onto the bottom of the QFP prism so that the prism can be mounted onto the plate base of the grating ruler, which also benefits the prism manufacture process. Figure 2: (**a**) The 3D structure diagram of the integrated quadrangular frustum pyramid prism and the optical route; (**b**) the optical configure of the defection diffractive beams in the design. In order to test the effectiveness of the QFP prism, a fundamental grating ruler optical path using interferometric measuring principle is constructed, as shown in Figure 3b,c. This optical layout is the same as the optical path principle shown in Figure 1c. The incident beam with a calibrated wavelength of 660 nm was divided into two beams and are projected to the reference grating and the scale grating after passing through the QFP prisms, respectively. The scale grating is mounted onto a moving table and the reference grating is stable. First of all, performance of the QFP prism in diffraction beams propagation directions modulation was evaluated by observing the beam spots on the screen. The observation as shown in Figure 3c was placed at a distance about 150 mm, a similar distance with that of a real grating ruler. Figure 4a illustrated the beam spots on the screen. It can be seen that the four diffraction beams from the reference grating coincided well with those from the scale grating. The distance between these four diffraction beams from the central beam (reflective beam, also called zero-order diffraction beam) are consistent with the designed values. These results verified the geometry accuracy of the fabrication process. It should be noted that there are many undemand spots on the screen which are caused by the non-orthogonal diffraction beams from the grating and can be easily blocked by setting a physical holes aperture. In order to further verify the effectiveness of the proposal in terms of optical property, such as polarization, the interference signal was tested. As shown in Figure 4b, clear diffraction stripe structure can be observed in all four interference spots and these represent that they have almost same order of interference intensity, while in previous separated prism layouts this was always the most challenging task. The results can preliminarily prove that the QFP prisms based interferometric grating ruler optical configuration is feasible and effective. To further test the optical path, the scale grating was  
Figure 4: **(a)** The diffraction beams spots on the observation screen; **(b)** the interference fringe on the observation screen. Figure 3: **(a)** The picture of the fabricated deflection prism; (b) the light path of the deflection of the diffractive beams; (c) the grating interferometry testing system with the fabricated deflection prism. driven by the micron motion platform (PI-M112.1 DG, Physik Instrumente (PI) GmbH & Co. KG, Karlsruhe, Germany), as shown in Figure 3c. As the principle of grating interferometry, the movement of the scale grating brings a periodic change of the interference signal. In this demonstration, two interference signals, \(I_{\text{X+1}}\) and \(I_{\text{X-1}}\), were recorded by a photodiode. The interference signals are given in Figure 5. It can be seen that the visibility of the interference signal almost remains stable, which is essential for the grating ruler application. The direct current components in the interference signal can be eliminated optically. The results show that the given QFP prisms based optical layout can form a good interference signal, the signal is in good sinusoidal shape under constant speed drive and can be used for bit shifting calculation.