Diffraction wavefront analysis of computer-generated holograms

Abstract

Computer-generated holograms (CGHs) use diffraction to create wavefronts of light with desired amplitude and phase variations. The amplitude control is well known. But the sensitivity of phase, which is most important for some applications, such as interferometry, is less known. This dissertation studies phase errors resulted from design and fabrication limitations of CGHs. Fabrication uncertainties of CGHs are primarily responsible for the degradation of the quality of wavefronts generated by CGHs. In this dissertation, the binary linear diffraction model is introduced to study wavefront phase errors caused by substrate figure errors, pattern distortion, grating duty-cycle and etching depth errors. Wavefront sensitivity functions derived from diffraction model provide analytical solutions to estimate phase deviations due to duty-cycle or phase depth variations. The results of the wavefront sensitivity analysis also enable us to identify hologram structures that are the most sensitive, as well as the least sensitive to fabrication uncertainties. Experiments were conducted to validate the diffraction model. Example error budgets for common CGH optical testing configurations are demonstrated. In addition, a graphical representation of the diffraction fields is introduced. It provides an intuitive way for diffraction wavefront analysis and explains phase discontinuous observed in the diffraction model. Scalar diffraction models are commonly used in CGH analysis and modeling due to their computational simplicity compared with rigorous diffraction models. The validity of the scalar diffraction models becomes unclear when they are used to analyze diffractive elements with wavelength-scaled features. This dissertation discusses the validity of the scalar diffraction models with giving emphasis to wavefront phase. Fourier modal method (FMM) derived from rigorous diffraction theory is used to study a binary zone plate. The result of this analysis is compared with experimental data, This study shows that polarization sensitivities of the hologram are almost negligible for the chrome-on-glass zone plate with a minimum ring spacing of 2lambda. This result implies that scalar diffraction models may still be sufficient for modeling the phase from holograms with wavelength-scaled diffraction features for the case studied in this dissertation.