Aberration Coefficient Determination via First Derivative Inversion
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Solution Overview
Problem
The existing method for determining aberration coefficients in particle-optical lenses, such as those used in Scanning Transmission Electron Microscopes, is limited by accuracy due to the need for infinitesimal changes in beam position, which are affected by sample drift and spatial resolution issues, leading to relative errors in image registration.
Innovation Solution
Defining the first derivative of the aberration function as a polynomial with coefficients to be determined, using position pairs from multiple Ronchigrams, and solving a set of equations to accurately determine these coefficients, allowing for larger changes in beam position and improved accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the beam position is changed by a large quantity, then the shift in sample features between Ronchigrams is larger, but the accuracy of determining the second derivative of the aberration function deteriorates due to sample drift and spatial quantization noise
Solution Approach 1:
Instead of determining the second derivative of the aberration function by measuring feature shifts (as in the prior art), the patent inverts the approach by determining the first derivative from Ronchigram data. This inversion allows using larger beam position changes while maintaining accuracy, as the first derivative determination is less sensitive to the conflicting requirements of large shifts versus small drift effects
Solution Approach 2:
The patent changes the mathematical parameter being determined from the second derivative to the first derivative of the aberration function. This parameter change enables the use of larger beam position changes (improving signal-to-noise ratio) while avoiding the accumulation of errors from sample drift and spatial quantization that plagues second-derivative methods
2Reliability
If the beam position change is made infinitesimally small, then the accuracy of the second derivative determination is improved, but the shift in sample features becomes too small to overcome sample drift and spatial resolution limitations
Solution Approach 1:
The patent inverts the derivative order being measured, using the first derivative instead of the second derivative. This allows utilizing larger beam position changes that produce measurable feature shifts, thereby overcoming the limitations of infinitesimal changes while maintaining or improving measurement accuracy through appropriate algorithmic processing
Data Source
AI summary
A lens of particle-optical apparatus, such as the objective lens, suffers from aberrations. As is already known since decades Ronchigrams can be used to determine these aberrations of particle-optical lenses.Such methods rely e.g. on the determination of the 2nd derivative of the aberration function on the basis of local magnification in one or a set of Ronchigrams. Being dependent on the 2nd derivative the mathematics of these methods allow only (infinitesimal) small shifts between the Ronchigrams. However, this implies that e.g. the spatial quantization noise of the camera recording the Ronchigrams results in a large error. These conflicting requirements limit the accuracy and thus the usefulness of the known methods.The invention describes a set of algorithms which result in an improved method to quantify the lens aberration coefficients using a set of Ronchigrams.