Filtering Chromatic Aberration for Wide Acceptance Angle Electrostatic Lenses

Abstract

Chromatic aberration is a major issue for imaging mainly with large acceptance angle electrostatic lenses. Its correction is necessary to take advantage of the outstanding spatial and angular resolution that these lenses provide. We propose a method to eliminate the effect of chromatic aberration on the measured images by determining the impact resulting from higher and lower kinetic energies. Based on a spectral image sequence and a matrix, which describes the transmission function of the lens, a system of linear equations is solved to approximate the 2D spectral intensity distribution of the sample surface. We present the description of our method and preliminary test results, which show significant contrast and image quality improvement. The presented algorithm can also be applied as a software-based energy analyzer.

Filtering Chromatic Aberration for Wide Acceptance Angle Electrostatic Lenses II—Experimental Evaluation and Software-Based Imaging Energy Analyzer

“…1) where a matrix (A), whose elements describes the transmission function of the lens system, acts on the vector of the ordered intensity values of the pixels of the aberrations and distortions free spectral image sequence (b) resulting the vector of the ordered intensity values of the pixels of measured and aberration distorted spectral image sequence (c) (see ref. [18]). …”

“…This strongly nonlinear 3D deconvolution-like method can enhance not only the real-and k-space image quality, sharpness, contrast as well as the position-, angular-and spectral information contents, but it can be applied as a Software Based Imaging Energy Analyzer (SBIEA). Furthermore, it is also possible to utilize the method to correct other, different types of aberrations [18]. The present paper is the sequel of the previous article [18], which discusses the theoretical concepts and model calculations of the filtering method on a simulated image sequence.…”

“…Furthermore, it is also possible to utilize the method to correct other, different types of aberrations [18]. The present paper is the sequel of the previous article [18], which discusses the theoretical concepts and model calculations of the filtering method on a simulated image sequence. Here, the ability of FECA method and its application as SBIEA are demonstrated on a spectral image sequence that have been measured by the High Voltage (HV) ±45° (0.59π sr) WAAEL based DELMA (Fig.…”

“…However, the effect of chromatic aberration in first order is proportional to the electron energy that on the one hand makes possible the measurement of spectral images at different pass energies, but on the other hand it also has disadvantages especially by mixing the 3D angular-, spatial and spectral information (Figs. 1,3) [9,11,12,14,17,18]. It occurs by the phenomenon that the higher and lower kinetic energy electrons emitted from different points can also hit on the same pixels of the images of desired specific pass energy Therefore, in the case of WAAEL based lenses the elimination of the distortion effect of the chromatic aberration is unavoidable to take the advantages that these types of electrostatic lenses provide.…”

“…This method resulted in quite good filtering close to the optical axes or in the case of Gaussian beams. The latest and also general method is the Filtering the Effect of Chromatic Aberration (FECA) for WAAEL [18] solves a system of linear equations (Eq. 1) where a vector (b), determined by the intensities of the image points of the aberrations and distortions free clear spectral image sequence is multiplied by a matrix (A) resulting the vector (c) of the intensities of the image points of the measured image sequence (Fig.…”