Holographic focal series: differences between inline and off-axis electron holography at atomic resolution

Electron holography methods allow phase information to be recovered from electron waves at atomic resolution. Focal-series reconstruction, an inline method, and off-axis holography are currently the most commonly employed techniques for this endeavor. By recording and reconstructing data from a holographic focal series of an atomically resolved GaAs crystal, we are able to reconstruct wave functions by means of both methods from the same measurement. Significant differences between these wave functions are found for low frequencies and in thicker specimen parts. Furthermore, in a rigorous treatment, we discuss how the recovered wave functions differ because of fundamental differences in the quantum mechanical measurement.