Abstract
A convenient and powerful method is proposed and presented to find the unknown phase shifts in three-step generalized phase-shifting interferometry. A slight-tilt reference of 0.1 degrees is employed. As a result, the developed theory shows that the unknown phase shifts can be simply extracted by subtraction operations. Also, from the theory developed, the tilt angle of the tilt reference can also be calculated, which is important as it allows us to extract the object wave precisely. Numerical simulations and optical experiments were performed to demonstrate the validity and efficiency of the proposed method. The proposed slight-tilt reference allows the full and efficient use of the space-bandwidth product of the limited resolution of digital recording devices as compared to the situation in standard off-axis holography where typically several degrees for off-axis angle is employed.
Highlights
Phase-shifting interferometry (PSI) has been developing for decades and applied to many fields [1,2,3,4,5,6]
The phase shift of the reference beam introduced into the PSI is typically affected by environmental interference and phase shifter errors [9]
In order to improve the convenience and stability of the phase-shift extracting algorithm further in three-step PSI, we propose a simpler and more reliable method to extract the unknown phase shifts with a slightly tilted reference beam during the recording process
Summary
Phase-shifting interferometry (PSI) has been developing for decades and applied to many fields [1,2,3,4,5,6]. The phase shift of the reference beam introduced into the PSI is typically affected by environmental interference and phase shifter errors [9]. To further simplify the measurement procedures and avoid the negative effects of the environmental disturbances and phase shifter errors, Cai et al have introduced generalized phase-shifting interferometry (GPSI), where the phase shifts are generally arbitrary, unequal and unknown values, but can be extracted from several interferograms [10,11]. In order to improve the convenience and stability of the phase-shift extracting algorithm further in three-step PSI, we propose a simpler and more reliable method to extract the unknown phase shifts with a slightly tilted reference beam during the recording process. Three-step generalized phase-shifting interferometry (TGPSI) uses three interferograms to extract phase shifts and retrieve the original object wave. We derive the theory behind the proposed method and carry out numerical simulations as well as optical experiments to verify our idea
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