Lucky Sampling in STM Measurement

This repository contains the code used in a project in collaboration with Prof. Dr. Fabian Natterer, focused on applying lucky sampling to STM (Scanning Tunneling Microscopy) measurement data.

Major Takeaways

• Using color mapping based on the mean ± 3 standard deviations is the most effective approach.
• Adjusting the median and standard deviation has no noticeable impact on the results.
• Root Mean Squared (RMS) provides a different perspective compared to the mean or median.
• Important information is not encoded in periodic points but is spread over a given time frame. Further investigation is needed to confirm this.
• Reducing the time spent on each pixel by up to 50% might be possible depending on the variation in the time spread. Further analysis is required for longer and shorter time experiments.
• To better compare results numerically, it would be useful to look at matching 2D Fourier Transform (FT) features across the spectrums. Removing background noise might assist in this analysis.

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Data Information

• Data collected by: Dr. Berk Zengin
• Date of experiment: 18/06/2021
• Dataset: Contains 24.8 million points or 155,000 after averaging.
• Experiment details:
  • 50x50 pixels with 31 real and complex coefficients
  • Each pixel has 160 data points captured over 0.1 seconds
• Plots: Represent the mean value of pixels for each coefficient, with color mapping bound by ±3 standard deviations.

Coefficients plotted are from 1 to 12 real components.

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Visuals

Sliced Spectrums

• Sliced spectrums, at intervals compared to the full spectrum:

2D Fourier Transformed Spectrum

• 2D Fourier Transformed sliced spectrum, compared to the full 2D Fourier Transformed spectrum:

Dice Coefficients (Sliced Up to the Middle Point)

• Dice coefficients across all coefficients when data is sliced up to the middle (80 data points):

Dice Coefficients (Sliced From the Middle Point)

• Dice coefficients across all coefficients when data is sliced from the middle point (80 data points):

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Future Work

• Conduct further experiments to analyze the variation in the time spread.
• Investigate matching 2D FT features across spectrums.
• Explore ways to remove background noise to improve the clarity of results.

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Raw Fourier Signal Analysis

While Fourier analysis on the raw spectrum was initially explored, it turned out to be a dead end. However, I encourage the reader to take a look at the code for further insights.

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General Steps

The following are the general steps used for signal analysis:

1. Correlate Coefficient 1 with other coefficients and subtract off Coefficient 1.
2. Apply a Fourier Transform (FT) on the data to extract the major frequencies.
3. Create a new signal in the frequency domain using these frequencies.
4. Reverse the newly created signal back into the time domain.
5. Slice the original data based on this signal and plot the result.

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FT Coefficients plotted are from 1 to 12 real components.

Feel free to explore the code and experiment with different approaches based on these steps!