Imaging of weak phase objects with a Zernike phase plate

TL;DR

This paper analyzes how Zernike phase plates image weak phase objects, showing that sharp phase transitions are well transmitted while low-frequency components are attenuated, affecting image quality based on object size and plate parameters.

Contribution

It provides a theoretical analysis of Zernike phase plate imaging, characterizing the effects of phase transitions and low-frequency attenuation on image formation.

Findings

Sharp phase transitions are well transmitted by Zernike plates.

Low-frequency components are attenuated, affecting image contrast.

Maximum object size for accurate imaging is inversely related to the phase plate hole diameter.

Abstract

Analysis of the imaging of some simple distributions of object phase by a phase plate of Zernike type shows that sharp transitions in the object phase are well transmitted. The low-frequency components of the complete object function are attenuated by the plate. The behaviour can be characterised by a cut-on parameter defined as the product of the cut-on frequency of the plate and a characteristic dimension of the object. When this parameter exceeds a value of the order of unity, a sharp boundary in the object is imaged by a Zernike plate as a dark lining inside the boundary with a white outline or halo outside the boundary, in agreement with reported observations. The maximum diameter of objects that can be imaged accurately is inversely proportional to the diameter of the hole for beam transmission in the phase plate.