Extract Signal

The next step in quantification requires extracting edge intensities from the spectrum while disregarding the underlying background intensity.

To separate the edge intensity, you must fit, extrapolate, and subtract a background model. It is essential to consider the following items when you perform this critical extraction step:

• Which background model should I use?

• Where should I fit the background model to the data?

• What are the optimal width and position for the signal integration window?

Theory               Step-by-step

Background modeling

To extract the edge intensity, you must determine a model for the background of your spectrum. First, identify a pre-edge fitting region that allows you to determine the parameters of the fit. Then, extrapolate this fit to estimate the background intensity below the edge signal. However, an accurate background subtraction may become difficult below 100 eV due to a large number of scattering processes in this region (e.g., plasmons tails, plural scattering).

Typically, the model is determined using linear least-squares methods using a single pre-edge region. \(\Gamma\).

where

• \(\Gamma\) = Background fit window

• \(\Delta\) = Signal integration window

• \(I_{b}\) = Background intensity

• \(I_{k}\) = Signal intensity

Power law

A power law is the most common background model.

\(J\left ( E \right )=AE^{-r}\)

where

• \(A\) = Scaling constant

• \(r\) = Slope exponent (usually 2 – 6)

When interpreted as the long energy tails of the preceding energy loss events, this model has a physical basis. 

Background model placement

When you choose the optimal background placement, it is important to consider these parameters:

• The high-energy side \(E_{be}\) should be as close to but still preceding the edge (e.g., 5 eV) to avoid chemical shifts and broadening detector tails

• To limit statistical error, the fit region \(\Gamma\) should be as wide as possible

• To limit systematic error, you need to limit the fit region to 10 – 30% \(E_{k}\)

Rules of thumb to follow

• Background window end should be 5 eV from edge onset

• Background window width should be at most 30% edge energy

• May need to limit window size to avoid preceding edges where necessary

Troubleshoot background extrapolation errors

Once background placement is made, it is important to review common errors.

• Unphysical

  • Symptom – Obvious error where the background model crosses the spectrum and may cause the signal to become negative

  • Solution – Increase the window size and/or offset it from the edge onset; you may need to limit the extrapolation distance of your analysis
    

    

• Systematic errors

  • Symptom – Small changes in the background window width or position have significant effects on the background model

  • Solution – Ensure minor variations in window position do not change background fit significantly; increase the size of window
    

    
    
    

• Overlapping edges

  • Symptom – Background extrapolation is ineffective for instances where the pre-edge region is obscured by the preceding edge

  • Solution – Reduce the window size or placement as well as limit the signal window size and offset; a multiple linear least-squares (MLLS) fitting or model-based approach may be necessary

    

Width and position of the signal integration window

When you choose the optimal signal integration window placement, it is important to consider the following:

• Statistical error – The region \(\Delta\) should be as wide as possible and start at the steepest intensity increase of the spectrum

  • Hydrogenic edges (e.g., K-, some L-edges) – Place the window at the threshold

  • Delayed edges (e.g., L-, M-, N-, O-edges) – Offset by a few tens of eV

• Systematic error – Limit fit region to about 10%, but it should cover all of the significant energy loss near edge structure (ELNES) changes
  

  

White lines – Best to avoid inclusion for quantitative evaluation as their intensity can vary with chemical state and are not well modeled in cross-section calculations

Signal extraction with DigitalMicrograph 3 software

With DigitalMicrograph^® 3 software, the signal extraction process is highly automated. However, the guidelines and concepts above still must be considered. DigitalMicrograph 3 quantification utilizes a model-based approach where the spectral background and the edge intensity are treated as a single model. If overlapping edges are present, they are also added to the model to allow separation of the overlap. Follow the below steps for EELS signal extraction in DigitalMicrograph 3 software.

1. Identify the edge features within the spectrum.
2. Show fit regions on the spectrum using the Show signal setup button in the Elemental Analysis window.
3. The edge model will be shown on the spectrum. Default values are typically adequate, but the user can dynamically change the regions of interest if needed.
4. The EELS edge setup button allows a specific setup for each edge:
   1. Exclude ELNES – Removes the near-edge structure from the analysis.
   2. Include plural scattering – Enables linking to low-loss spectrum and is required for absolute quantification.
   3. Most settings dynamically update if the fit region is adjusted on the spectrum.

6. Edges that are close in energy are automatically tagged for overlap analysis. The Overlaps checkbox in the edge setup dialog allows you to change this default.
7. The fit to the edge model is less than the models for the background, and any proceeding edges yield the extracted signal intensity for that edge.