Fig. 1. Schematic of principle of diffracted-grating displacement measurement

Fig. 2. Variation of normalized diffraction intensity of the first three orders with displacement d

Fig. 3. Principle of Twyman-Green interference

Fig. 4. Arctangent algorithm Simulink simulation. (a) Modeling of arctangent algorithm in Simulink; (b) Simulink simulation of sine/cosine function; (c) Simulink simulation of absolute value; (d) Simulink simulation of tangent function; (e) Simulink simulation of arctangent function

Fig. 5. Effect of offset error on arctangent. (a) Comparison of arctangent value of without offset error and with 1% offset error; (b) arctangent error value with 1% offset error

Fig. 6. Experimental setup of resolution verification (L:laser; PL: polarized light polariscope; PI: P-611 linear piezoelectric ceramic positioning system; IC: interpolation circuit)

Fig. 7. Displacement error analysis of interpolation circuit. (a) Comparison of the feedback of linear piezoelectric ceramic positioning system and displacement output of interpolation circuit; (b) error distribution curve