The suppression of phase error by applying window functions to digital holography

• The application of digital window functions to digital hologram to reduce the phase/axial error in digital holography, is proposed. The mechanism of this application is analyzed.
• The specific feature of window function related to the axial error, the side lobe energy to main lobe energy ratio (SMER), is pointed out.
• Both simulation and experiment results validate that the application of appropriate window function helps to reduce the axial error of digital holography and SMER is an effective indicator to select the appropriate window function.

Digital holography (DH) is a 3D imaging technique with a theoretical axial accuracy of around 1–2 nm. However, in practice, the axial error is generally quoted as tens of nanometers. Previous studies on sources of axial error mainly focused on the phase error introduced by lens. However, it was later shown that other factors such as the limited CCD aperture size also contribute to axial error. Based on this study, further investigation approaches to suppress the axial error caused by the limited CCD aperture size is discussed in this paper. Use of a window function to modify the shape of the hologram aperture after the recording process is proposed to reduce the axial error. The mechanism of how this window function reduces axial/phase error is analyzed. Specific features of this window function related to the axial error, namely the side lobe energy to main lobe energy ratio (SMER), is postulated. Both simulation and experiment are performed to validate that the selection of an appropriate window function helps to reduce the axial error of digital holography and SMER is an effective indicator in selection of an appropriate window function.