scanning-microscope-focusing-with-landmark-feature-line-scan

name	scanning-microscope-focusing-with-landmark-feature-line-scan
description	Procedure and instructions for focusing a scanning microscope using the landmark feature line scan method.

Overview

This document describes the procedure to focus a scanning microscope using the landmark feature line scan method. Often, the optics parameters to be adjusted are the positions of focusing devices, such as a zone plate or a lens. The evaluation of the focus is based on the line scan of a thin feature, such as a thin line or a thin spot. The line scan of such features should show a peak, and the FWHM of the peak indicates the quality of the focus. Better focus is associated with smaller FWHM. The goal is to adjust the optics parameters so that the FWHM is minimized.

Tools and information needed

To perform the focusing task, you will need the following tools:

• A tool allowing you to acquire a 2D image of the sample at given locations.
• A line-scan tool allowing you to acquire a 1D line scan at given locations.
• A tool that allows you to adjust the parameters (or motors) of the focusing optics.
• A registration tool that allows you to find the offset between two images, given the paths of their raw data files. This allows you to "track" the landmark feature if the image drifts after optics parameter adjustment.

You will also need the following information:

• The raw image file (NPY or TIFF) of the first 2D scan in the region of interest (ROI) containing the landmark; you need it for later image registration in order to track the feature if the image drifts after optics parameter adjustment. If it is not available, ask the user for the position to conduct a 2D scan to acquire that image.
• The position of the first line scan across the landmark feature. It might be unavailable until the first 2D scan is completed because the line scan coordinates need to be read from the image. If this is the case, ask the user to confirm the line scan positions after the first 2D scan is done.
• The initial parameter(s) of the focusing optics. It might be a scalar number such as the z position of a zone plate, or it can be a vector of multiple parameters.
• The range to adjust the optics parameters for searching for the optimal focus.
• (Optional) A recommended initial step size by which the optics parameters should be adjusted each time at the beginning.
• (Optional) The desired precision of the optimal parameters (e.g., 0.5 micron).

If any of these tools or non-optional information are missing, ask the user.

Procedure

Overall, the procedure consists of the following steps:

1. Conduct a 2D scan of the ROI if it is not yet available. Otherwise, if the user gives you the raw image file of the ROI's 2D scan, check that image. After that, confirm the landmark feature and the positions for the line scan across it.

2. Perform a 1D line scan across the landmark feature.

3. The line scan tool will return a figure containing the following:

   • A line profile plot along the scan line and a Gaussian fit to the line profile. The FWHM of the Gaussian fit will be shown.
   • The scan path of the scan you just did, plotted in the last acquired 2D image (if an 2D image has been acquired previously).
   • The scan path of the first line scan, plotted in the first acquired 2D image (if the current acquisition is not the first). This plot serves as the reference for the relative position of the scan line to the thin feature.

   The goal of a successful line scan is to have a scan line that

   • crosses the same landmark feature at the same location relative to other features in the sample.
   • crosses the landmark feature at the center of the scan line.

4. Adjust the optics parameters using the parameter setting tool.

5. After changing the optics parameters, the sample position relative to the scanning probe might drift. To calibrate, acquire an image of the region using the image acquisition tool again using the same arguments as before. The features of the image may have a translational shift compared to the previous one, but most features should be present in both images.

6. Since the image has drifted, you need to adjust the positions where the next line scan is run. Figure out the offset using the image registration tool. Unless explicitly mentioned otherwise, the registration tool should accept the paths to the raw data files of a moving (sometimes also called "current" or "test") image and a reference image. Denote the returned offset [dy, dx] as registration_offset. Its convention is:

   shifted_current_image = roll(current_image, registration_offset)
   

   where shifted_current_image aligns with the reference image. With this convention, make sure that you use the current image as the moving image, and use the last 2D image as the reference image unless a different reference is explicitly intended. The acquisition tool should return you the paths to the raw data files in NPY or TIFF format.

7. Assuming everything follows the convention mentioned in step 6, define the 2D scan-position difference and the stage-position correction as follows:

   scan_position_difference = current_2d_scan_position - last_2d_scan_position
   stage_position_correction = scan_position_difference - registration_offset
   new_line_scan_position = previous_line_scan_position + stage_position_correction
   

   Use the evaluate_python_expression tool for every drift-correction calculation. Do not calculate the correction mentally. Evaluate each coordinate explicitly when the positions are vectors. State the input values and use the tool's returned result for stage_position_correction, new_line_scan_position, and later new_2d_scan_position. Only calculate manually if that tool is unavailable, and say that you are using the fallback.

   This reduces to simply subtracting registration_offset only when the current and last 2D scans were acquired at the same position. Conduct another line scan at the corrected position. You should see that the scan line crosses the landmark feature at the same location relative to other features in the sample, despite that the absolute positions indicated in the axis ticks may differ.

8. Once you get the new FWHM from the line scan, compare it with the trend of past FWHM values to determine the next optics parameter adjustment. Keep in mind that the goal is to minimize the FWHM, so you should adjust the optics parameters in the direction that makes the FWHM smaller. Then use the parameter setting tool or motor moving tool to make the parameter adjustment.

8.1. Maintain a parameter-versus-FWHM plot during the search. Create the first plot once three points are available. Update and inspect it after every new point near a suspected minimum or whenever the trend changes direction. Use the plot as evidence when choosing the next parameter; do not merely generate it without examining the trend. If you decide to use Bayesian optimization (which is optional), update the model and get its next suggestion in this step.

9. Repeat the process from step 5 (acquire 2D image). When acquiring the next image, update the last 2D scan position by the same stage_position_correction defined above:

   new_2d_scan_position = previous_2d_scan_position + stage_position_correction
   

   This ensures that the previous drift is taken into account before the next registration and line scan.

10. When the FWHM is minimized, conclude the process and report the history of optics parameters and the corresponding FWHM values.

When you finish, generate a plot of the parameter - FWHM data points (if the parameter is 1D or 2D), and fit a quadratic function to it.

Strategies of optimization

Initial direction

The user may suggest to you the initial direction of moving the optics - for example, "we are currently at z = -198, the right focus might be on the positive side". If the user does not suggest that, move around the initial point slightly to figure out the direction along which the FWHM descends. Remember that drift calibration should also be done while collecting these data points.

Advanced search methods

Usually, if the parameter being optimized is a scalar, your own decision of adjusting the parameters should be good enough. However, if the data points of paraemter - FWHM pairs are exetremely noisy, or if the parametes are multivariate, consider the following to help with your search:

• You may use Bayesian optimization to help with your search. Use a high-level BO package such as botorch directly if it is available in the runtime environment, otherwise create a local uv environment and install it. Use the measured data to fit the model, choose a suitable acquisition function (such as expected improvement), and find the optimum of the acquisition function to determine the next step. However, if BO suggests a new parameter that is very far away from the current values, clip the change to a smaller step length to prevent unmanageable drift of the sample images.
• Use fitting. You may use your Python tool to fit the data points (e.g., with a quadratic function) to estimate the optimum. If you use the fit to estimate the optimum, make sure you constrain the step length like in the case of BO.

Use visualization

Plotting is a required diagnostic part of the search, not an optional final-report step. Plot all measured parameter-FWHM pairs in acquisition order, connect adjacent points to make reversals visible, and mark the current best measurement. Once three points exist, inspect the updated plot before declaring a bracket, reversing direction, reducing the step size, or concluding the search. Use it to decide whether an apparent minimum is a noise-induced fluctuation or a supported trend.

Handling noise

The FWHM values may be noisy. If you are searching with very fine step size and find a lot of fluctuations in the data points, do not blindly choose the minimum FWHM. Instead, fit a quadratic function and plot the data points and the fit to help you decide where the true optimum is.

Coase-to-fine search

Use a reasonable step size at the beginning to roughly locate the optimum, then conduct finer search around the vicinity of the optimum to precisely locate it. For example, when focusing a zone plate, you may first step the z-position of the zone plate at 1 mm until you find the optimum with a resolution of 1 mm. If the user wants a finer resolution of 0.1 mm, search within the +/- 1mm window of the optimum with a step size of 0.1 mm following that to locate the precise optimum. See the Criteria for Completion section for more details.

Avoid early termination

Noise and imprecision in line scan positions can cause fluctuations in the FWHM. A single FWHM increase must never be treated as evidence that the optimum has been passed or bracketed. Do not reverse direction, shrink the search interval, or claim that the optimum lies in the last-visited interval based on one increase. Continue in the same direction for at least one additional coarse step, while continuing drift correction and landmark checks. Treat a turnover as credible only when the measurements show a sustained increase at two successive parameter positions beyond the current best, or when repeat measurements near the suspected turnover confirm it. Plot the accumulated points before making this decision.

For example, if you see

zone plate z	FWHM
-190	5.2
-191	3.8
-192	2.3
-193	2.6

The value at -193 may be noise. Do not conclude that the optimum is between -191 and -193, and do not reverse direction. Measure at -194 next. If needed, continue to -195 or repeat a nearby point until the rise is sustained or disproved. Only then bracket the optimum and begin the fine search. A quadratic fit may support this decision, but it does not override the requirement for measurements beyond a one-point apparent turnover.

Handling exceptions

1. The 2D image acquisition tool does not return the raw data path (not PNG)

You need the raw data file to use the image registration tool to accurately decide how much the image and line scan positions should be shifted to track the landmark feature. If the raw path is unavailable, you may try to directly read out the position of the drifted line scan position from the axis ticks of the new image if you are confident. Otherwise, notify the user.

2. The line scan path no longer crosses the landmark feature at the same relative location

This is usually because image registration failed to give an accurate result. Immediately revert to the parameter setting before the last adjustment, and redo a line scan at the same position used at that time. Confirm the state is reverted by checking if the scan line is restored to the same relative location as in the reference image. Then, adjust the optics parameters again in the same direction as you did last time, but with a smaller step size to reduce the drift, which should make image registration easier.

The following images demonstrate a few cases where the line scan path goes "off".

Other Notes

• Tell the user your rationale behind each call to the data acquisition and parameter setting tools. When setting parameters, explain why you are setting them to those values. When running line scan or image acquisition, explain why you are doing them at the chosen positions.
• You should perform the focusing as autonomous as possible. Unless major exceptions happen, do not request human intervention during the process. Before the focusing process concludes, avoid using the bash tool because it would ask for user approval and may cause the process to hang.