Imaging with straight-edge phase plates in the TEM.

Area of Science:

• Optics and Photonics
• Image Formation Theory

Background:

• Phase contrast microscopy utilizes phase plates to visualize transparent specimens.
• Foucault and Hilbert phase plates are common tools for phase manipulation in imaging.

Purpose of the Study:

• To analyze image formation of simple phase objects using Abbe imaging theory.
• To investigate the impact of Foucault and Hilbert phase plates on image characteristics.
• To explore phase relationships between object, plate, and incident wave.

Main Methods:

• Application of Abbe imaging theory for image amplitude determination.
• Utilizing a 2D transform in cylindrical coordinates for analysis.
• Distinguishing contributions from uniform disc objects and azimuthally varying plates.

Main Results:

• The study quantifies image amplitude and phase using cylindrical coordinates.
• It identifies conditions where weak disc object images vanish with standard Hilbert plates.
• A modified Hilbert plate thickness is shown to yield linear intensity contributions from weak phase objects.

Conclusions:

• Abbe imaging theory provides a framework for understanding phase plate effects.
• Hilbert phase plate design critically influences the visibility of weak phase objects.
• Optimizing plate thickness offers a method to enhance the detection of subtle phase variations.