## 3 Experimental Results  
To verify the measurement performance of the proposed differential quadrature Fabry-Perot interferometer, a commercial interferometer with the resolution of 1 nm is employed as a reference standard to carry out the comparison experiment simultaneously. After the experiment, the deviation can be obtained by the difference between the measured values of two interferometers. For determining the measurement repeatability, the experimental standard deviation is calculated by 10 deviations (10 repeated cycles) at each position, and then the linearity can be confirmed through dividing three times the maximum standard deviation by the whole measuring range [20]. The experimental arrangement is demonstrated in Figure 9. In this experiment, the measurement structure of PM type in the small measuring range and that of CCR type in the large range have been utilized. Results can be gained in both structures. The Fabry-Perot interferometer and the commercial interferometer are installed on the left and right sides of the linear stage, and the corresponding measurement mirror is fixed on it to carry out the measurement procedure.  
In the comparison experiment between the Fabry-Perot interferometer of the PM type with the resolution of \(\lambda\)/8 and commercial interferometer, the forward displacement is regulated from 0 mm to 150 mm with a step interval of 15 mm, and each cycle is repeated 10 times. According to the  
Figure 8: Comparison of nonlinearity error between polarized and proposed differential Fabry–Perot interferometer.  
Figure 9: The optical arrangement of the comparison experiment between the commercial and proposed interferometer.  
measurement result (Figure 10), the maximum deviation between the two interferometers is 0.219 \(\upmu\)m, the maximum standard deviation is 0.076 \(\upmu\)m, and the linearity is \(1.52\times 10^{-6}\) F.S. in the whole range.  
The comparison experiment between the Fabry-Perot interferometer of the CCR type with the resolution of \(\lambda\)/16 and commercial interferometer is similar to the above-mentioned procedure. The measuring range is extended to 600 mm, which is conducted with a step interval of 60 mm. The measurement results, shown in Figure 11, demonstrates that the maximum deviation, the maximum standard deviation, and the linearity are 0.427 \(\upmu\)m, 0.120 \(\upmu\)m, and \(6\times 10^{-7}\) F.S., respectively. From these comparison results between two measurement types demonstrated in Table 2, the linearity of CCR type is better than the PM type. Because of CCR bearing large tilt angles of the measurement mirror, the linearity of CCR type would be better than that of the PM type within the same measuring range.  
In order to evaluate the improvement of the measurement performance in the large measuring range, comparison results between the published polarized Fabry-Perot interferometer in reference 11 and the proposed differential Fabry-Perot interferometer of CCR type are illustrated in Table 3. It reveals that the linearity in the published structure within the range of 500 mm is \(8.76\times 10^{-7}\) F.S.,  
Figure 11: The comparison result between the commercial interferometer and proposed Fabry–Perot interferometer of CCR type.  
Figure 10: Comparison result between the commercial interferometer and proposed Fabry–Perot interferometer of PM type.  
and the linearity in the proposed structure within the extended range of 600 mm is \(6\times 10^{-7}\) F.S. In summary, the maximum deviation and linearity can be improved by 48% and 32%, respectively by the proposed measurement system. This measurement performance can be utilized for the linear displacement measurement to meet the high-precision industrial demand.