Robust local thickness estimation of sub-micrometer specimen by 4D-STEM

We present a quantitative four-dimensional scanning transmission electron microscopy (4D-STEM) imaging technique (q4STEM) for local thickness estimation across amorphous specimen such as obtained by focused ion beam (FIB)-milling of lamellae for (cryo-)TEM analysis. Our method is based on measuring spatially resolved diffraction patterns to obtain the angular distribution of electron scattering, or the ratio of integrated virtual dark and bright field STEM signals, and their quantitative evaluation using Monte Carlo simulations. The method is independent of signal intensity calibrations and only requires knowledge of the detector geometry, which is invariant for a given instrument. We demonstrate that the method yields robust thickness estimates for sub-micrometer amorphous specimen using both direct detection and light conversion 2D-STEM detectors in a coincident FIB-SEM and a conventional SEM. Due to its facile implementation and minimal dose requirements, we anticipate that this method will find applications for in-situ thickness monitoring during lamella fabrication of beam-sensitive materials.


Introduction
Scanning transmission electron microscopy (STEM) is a powerful tool for studying thin specimens at high spatial resolution.In conventional two-dimensional STEM modes, such as bright-field (BF), annular bright-field (ABF), annular dark-field (ADF) and high angle annular dark-field (HAADF), images are formed by integrating the total signal over a range of scattering angles in the diffraction plane as the focused STEM probe is scanned over a two-dimensional (2D) area of a specimen.Geometrical sample properties along the image plane can be measured directly from the projection images.Obtaining information about properties along the beam direction is less straightforward.Yet, the ability to obtain 3D information can be highly relevant, for example to accurately determine the sample thickness.A prominent example of the latter is in focused ion beam milling (FIB) of thin, large area lamellae for high-resolution imaging with TEM, where an optimised thickness may be needed to maximise recoverable information and obtain the highest resolution [1][2][3][4][5][6][7] .Determination of sample thickness during the milling process might thus allow the milling process to be stopped at precisely the required endpoint and thereby improve both quality and throughput of sample preparation.
In SEM and TEM instruments, information along the z dimension of electron transparent samples can be obtained by backscattered electron imaging 8 , energy dispersive X-ray spectroscopy (EDX) analysis 8,9 , TEM tomography 10 , zero-loss TEM imaging 11 , the calibration of secondary electron signal intensity ratio in the SEM image to electron energy loss spectroscopy (EELS) measurements 12 , or by comparison of a calibrated STEM image with a simulation of a known sample geometry, which is called quantitative STEM (qSTEM) 13,14 .
Most methods require independent calibration before each imaging session to account for specific imaging settings.An additional disadvantage is that these methods may be difficult to implement in a FIB-SEM to allow for repeated in-situ measurements during sample milling.Very basic calibrations link the image intensities to known sample characteristics originating from other imaging modalities, such as lamella thickness estimation using secondary electrons with STEM/EELS calibration 12 .Thicknessdependent changes in backscattered electron (BSE) signal intensity can also be calibrated via the signal of a standard sample of defined material/thickness 8,[15][16][17] , or by using the differential detector response to a blanked electron beam (lower limit) and standard sample (upper limit) 18,19 .The latter approach is often used for calibration of retractable BSE detectors because the geometry of this detector precludes exposure to the primary electron beam.For STEM detectors with suitable geometry, the detector response to the primary beam can be used for both calibration limits if fluence is chosen such that signal intensity remains within the dynamic range of the detector.This calibration method has been used in most qSTEM studies 13,14,18,20 .For BSE detectors, a reflection of the primary beam on an electron mirror can be used to reverse the direction of the primary beam toward the BSE detector. 21ntensity-based calibration methods have several practical disadvantages.Firstly, the results are dependent on the timedependent beam current or detector contrast/brightness settings, and hence different for each instrument and imaging condition.Secondly, calibration images may cover only a small part of the detector area (e.g.HAADF STEM segment) as its response may vary across the detector.Lastly, rotationally symmetric detectors have to be aligned to the electron optical axis to avoid systematic errors.
In contrast to regular STEM using segmented annular detectors, four-dimensional (4D) STEM involves acquiring a 2D convergent beam electron diffraction pattern at every (x,y) pixel of a 2D STEM raster, yielding a 4D dataset with a spatially resolved diffraction pattern for each position across the specimen.4D-STEM data analysis offers a broad range of methods to extract relevant information about the specimen from these spatially resolved scattering or diffraction patterns [22][23][24] .
Here, we present a local thickness estimation method which can be easily and repeatedly used not only for post acquisition data analysis but also during sample thinning by FIB milling.Our method uses the principles of quantitative 4D STEM (q4STEM) with a 2D STEM detector 25,26 .The method is free of signal intensity calibrations and provides accurate results in a wide thickness range from very thin (<50 nm) lamellae up to rough ones of about one micron thickness.Moreover, the applied electron dose can be reduced to a minimal level to mitigate primary beam sample damage.

Stepped lamella
An epoxy resin block (hard type; H 111 C 115 O 24 , ρ = 1.245 ± 0.013 g/cm 3 ) was prepared as a test sample for lamella thickness estimation.The epoxy resin block was prepared according to manufacturer instructions by mixing epoxy embedding medium (Epon 812 substitute; 20 ml) with the hardeners methylnadic anhydride (MNA; 12 ml) and Dodecenylsuccinic anhydride (DDSA; 9 ml), and the accelerator 2,4,6-Tris(dimethylaminomethyl)phenol (DMP 30; 0.7 ml; Epoxy Embedding Medium kit, Sigma Aldrich).The resin was poured into silicone moulds and cured at 60 • C for 42 hours.The density of cured resin blocks was determined pycnometricly.The cured block was then mounted on a aluminium sample stub using double-sided carbon tape.The stepped lamella was prepared by gallium milling on Helios G4 HP FIB-SEM with a step height of 100 nm and step width of 600 nm.The steps range over thicknesses from 100 nm up to 1200 nm.The final polishing was done at 30 keV beam energy with 18 pA probe current.

Tissue sections
Lung tissue (from female ICR mice) after continuous 12-week exposure in an inhalation chamber containing TiO 2 nanoparticles was embedded in an epon-durcupan mixture and cut to 100 nm sections.

Direct detection 2D-STEM detector
The direct detection 2D-STEM experiments were preformed on a Helios G4 HP FIB-SEM (Thermo Fisher Scientific; located at ISI Brno) equipped with a T-pix pixel array detector.The T-pix detector is composed of 256 × 256 pixels with a physical pixel size of 55 µm.The total active area of the detector is 14 × 14 mm and the detector was mounted at a detector-pole piece distance of 40 mm.The pixel saturation limit is 11,810 counts per pixel.In addition, the microscope is equipped with an annular STEM3+ detector (Thermo Fisher Scientific).All samples were imaged in field-free mode.The in-chamber configuration can be found in Fig. 1c.

Light conversion 2D-STEM detector
The light conversion 2D-STEM experiments were done on a SEM Verios 460 (FEI -Thermo Fisher Scientific; located at TU Delft) equipped with a coincident fluorescence microscope SECOM (Delmic B.V.) equipped with a Zyla 4.2 PLUS sCMOS camera (Andor -Oxford Instruments).The original glass beam stopper was replaced with a YAG:Ce scintillator (thickness 0.15 mm, optical thickness for correction collar 0.18 mm).A Nikon S Plan Fluor 60 × /0.7 objective was used for its long working distance (2.6 -1.8 mm).

Data acquisition settings
Imaging was performed as individual point measurements using spot mode with discrete distances between individual beam positions.Beam shift was used to move the beam across the samples.Data acquisition parameters can be found in Tab. 1.

Electron scattering simulations
Monte Carlo simulations of electron scattering were calculated in MONCA2, an evolution of the original Monte Carlo simulation package MONCA 27 running under MATLAB.1,000,000 electrons with an energy of 30 keV were used in each simulation.Both resulting MCSA (most common scattering angle) and DF/BF (dark field/bright field) ratio dependencies were fitted with low-order polynomial fits (linear and quadratic, respectively).

PXRD simulation
Theroretical powder X-ray diffraction (PXRD) patterns of TiO 2 were computed with the program PowderCell 28 using the crystal structure of TiO 2 (anatase modification) deposited in the Crystallography Open Database 29 .

STEMDIFF settings
Powder diffraction data were analysed in STEMDIFF -powder electron diffraction in SEM available on the MathWorks File Exchange repository 30 .To replicate our results, settings shown in Tab. 2 should be used.3 Results

Principle
The main idea behind our q4STEM method is that electrons passing through electron transparent samples are scattered to higher angles with increasing sample thickness (or mass density).Thus, measuring the extent of electron beam spreading by the transmitted scattering signal allows estimating the local thickness.We present two ways with which this spreading can be quantified: (1) describing the most common scattering angle (MCSA), and (2) the ratio of integral signals in a specific angular range (DF/BF -dark field/bright field).Both can be readily computed from an integral radial profile of intensities in the scattering pattern (Fig. 1a).The resulting descriptors can then be converted into local thickness estimates by comparison to Monte Carlo simulations of electron scattering.Unfortunately, the expected "doughnut" shape of a scattering pattern passing through a thick amorphous sample is not visible directly, because the higher amount of recorded electrons at higher scattering angles is distributed over more pixels (by a factor of 2πr, where r is the distance from the centre).
While we acquire experimental data (MCSA, DF/BF ratio) in pixel units, simulation results are in angular units.To convert pixel position to scattering angles, the position of the 2D-STEM detector relative to the sample has to be known.In the SEM, the detector distance is typically a well-defined, invariable parameter.The use of a pixelated STEM detector has the additional advantage that it does not require detector alignment to the optical axis.When a segmented annular STEM detector is in an off-axis position, the detection geometry does not match that assumed in the simulation, which leads to incorrect thickness estimation.In the case of a 2D-STEM detector, the beam centre can be detected and detector displacement corrections can be applied for each scattering pattern.

Direct detection 2D-STEM detector
For direct detection with a pixelated STEM detector, the detection geometry is straightforward (Fig. 1b).The detector-to-sample distance, and thus the accesible angular scattering range, can be slightly adjusted by a change in working distance as typically the detector is mounted at a fixed distance from the objective lens pole-piece.Fig. 1c shows the in-chamber view in the FIB-SEM.This configuration with a retractable annular STEM detector enables easier and faster navigation across the sample in combination with acquisition of 4D-STEM data, as virtual STEM images based on 4D-STEM data take significantly more time to acquire.The annular STEM detector images are used for region of interest (ROI) localisation at high precision.Subsequently 4D-STEM data cubes are taken at these positions.In our configuration, the original sample stage has to be tilted to 60 • to make sufficient space for 2D-STEM detector.

Light conversion 2D-STEM detector
Implementation of our q4STEM method is not limited to direct detection 2D-STEM detectors.As an example of an alternative approach, we turned a retrofittable integrated light microscope (SECOM; DELMIC B.V.) into a high-resolution 2D-STEM detector, referred to as light conversion 2D-STEM (principle shown in Fig. 1d).The main idea lies in replacing the original glass coverslip protecting the objective lens with a electron-sensitive scintillator (Fig. 1d).
The idea of a scintillator screen together with the SECOM detector is not new.A similar solution is used in the optical STEM method 31 that is used for multibeam detection in the FAST-EM * .In optical STEM, the sample is placed directly on the scintil-* FAST-EM: automated multibeam electron microscope, https://www.delmic.com/en/products/fast-imaging-solutionslator.For q4STEM, a precisely determined free space is introduced between the sample (on a TEM grid) and the scintillator.We achieved this by clamping the TEM grid into an AutoGrid (Thermo Fisher Scientific), which has well-defined dimensions with an inner depth of 300 +0 −20 µm (Fig. 1d).The scintillator is then used as a screen by which the electron scattering patterns are converted to a light signal that can be visualised with the optical microscope.
The light-conversion 2D STEM detection setup allows switching imaging mode from light microscopy to 2D-STEM by changing the objective lens focus.The upper focus plane is at the level of the sample -enabling reflection and fluorescence imaging, while the lower focus plane is located a few microns under the upper scintillator surface -enabling 2D-STEM image acquisition.In this position an image of the interaction volume can be acquired (Fig. 1e) and the scattering pattern of an amorphous sample (Fig. 1f  or the diffraction pattern of polycrystalline samples (Fig. 1g) can be recorded.Diffraction analysis using a fluorescent screen and light detecting camera has been reported previously 32 but in this case the viewing solid angle was significantly lower than that accessible in our system (3.83 × 10 −3 sr compared to 1.54 sr).As a result, our method allows the use several orders of magnitude lower beam currents, enabling application to beam sensitive samples.The in-chamber view on our setup is shown in Fig. 1h.

Data processing
In our q4STEM method, a scattering pattern is recorded for each beam position.In each scattering pattern, the beam centre is detected first (Fig. 2a, usually the pixel with the highest intensity) and the image is cropped to the area containing the scattering pattern (Fig. 2b: smaller size, maximum in the middle).The preprocessed ROI image is then processed differently depending on whether the data comes from a light conversion 2D-STEM detector, where image background subtraction is needed (Fig. 2c-d) or from direct detection 2D-STEM, where the radial profile can be calculated directly.Here, the experimental data are fitted with a polynomial function in order to smooth the noisy raw profiles and to detect the peak position, which we refer to as the most common scattering angle (MCSA) (Fig. 2e).The DF/BF ratio can be calculated directly from the raw data by computing the integral signals in the low angular range (BF, 0-50 mrad) and intermediate angular range (DF, 50-100 mrad; Fig. 2g).Note that these angular ranges are chosen such that they maintain nearly linear dependence in the required range of thicknesses.The descriptors (MCSA and DF/BF ratio) are then compared with results of Monte Carlo simulations of electron scattering with a known sample geometry (Fig. 2f,h) yielding a sample thickness estimate for this beam position.By repeating this procedure for the scattering pattern recorded at each scan beam position, the sample thickness is calculated for each data point.As a result, the above procedure can run in parallel in order to reduce computing time and create position-dependent local thickness maps.
Due to the nature of the thickness descriptors (MCSA resp.DF/BF signal ratio) the results are independent of the absolute intensity values in the initial images.However, there are necessary prerequisites such as a linear detector response to the cumulative electron dose, and homogeneous detector sensitivity across all pixels.Besides, it is mandatory to avoid detector saturation, which can affect the shape of the radial profile.Another prerequisite for the MCSA q4STEM method is for a well-defined peak in the radial profile.For very thin samples, no peak is observed and the scattering profile is monotonically decreasing as shown for a polymer nanosphere sample in Fig. 3a.This limits the lower bound for the thickness estimation using the MCSA method (sample/material dependent; ∼100 nm for latex).
For both methods, the crucial point is the accurate detection of the centre of the scattering pattern during the first processing step.The DF/BF ratio method shows higher robustness to centre mismatch due to signal integration across relatively wide areas.A small error in the true centre position is therefore negligible.On the contrary, the position of the MCSA directly depends on the shape of the radial profile which is highly sensitive to the centre position.
Both thickness estimation methods are based on the same primary data and so can be calculated at once.The final results from both methods should be consistent, allowing detection of possible errors in data processing or data acquisition.For medium/high thickness (> ∼300 nm for nanospheres), the angular range for analysis has to be chosen larger than 100 mrad to avoid unwanted signal changes during background subtraction (a larger range limits the centre dislocation correction).

Optimal beam energy
In addition to the residual error in the primary beam position, the accuracy of thickness estimation by our method depends critically on the primary beam energy, where lower energies result in increased signal modulation (MCSA or DF/BF ratio) with changing thickness.Thus, one may expect that low beam energies lead to higher accuracy in the case of thin samples.This, however, is not generally applicable with light conversion 2D-STEM as shown in Fig. 3, where the scattering pattern becomes blurred for thicker samples and lower beam energies, and affects accuracy of the centre detection step during data processing.Errors in centre position may drastically affect the resulting accuracy of thickness estimation.This effect is more pronounced for the light conversion 2D-STEM detector where background noise is higher compared to direct detection 2D-STEM.Moreover, in order to limit beam damage induced by the transmitted electron beam, a higher beam energy is preferred because less energy is absorbed in the sample from inelastic scattering.For these reasons, we used the maximal SEM energy of 30 keV in all experiments.

Direct detection q4STEM
We applied geometric calibration of local thickness using a FIBmilled stepped lamella after lift-out from a bulk epoxy resin block.The geometric parameters of the stepped lamella were chosen in order to obtain a set of well-defined areas with known thickness.We prepared twelve steps with an individual height of 100 nm and a step width of 600 nm, thus creating a thickness range from 100 nm up to 1200 nm (Fig. 4a).We then mapped an area of interest and estimated the local thickness (Fig. 4b) by direct detection 2D-STEM as described above.The local thickness across the individual stripes was transversely averaged and plotted according to the lateral position of its long axis (Fig. 4c).The cross-sections of linear fits with the border of the lamella give the thickness of the lamella at its edge.In the low thickness region (100-400 nm), the real edge was damaged during milling and thus these values are extrapolated.
The final accuracy as given by comparison of measured and geometrical thickness shows very small deviations, lower than 10 % relative or 25 nm absolute error across the entire thickness range except for the thinnest and thickest step (100 nm and 1200 nm respectively; Fig. 4d).These values are also outside the measuring range of the MCSA method for this epoxy resin sample and 30 keV primary beam.Interestingly, the measured wedge angle is very similar for all stripes and varies around 2 • -the lamella was generated without over-tilting as typically used for bi-planar shape creation.

Light conversion q4STEM
To demonstrate thickness estimation with the light conversion 2D-STEM detector, we mapped a sample of latex nanospheres with varying diameters (Fig. 4e).The chosen area contains nu-merous 95 nm, several 303 nm and two 616 nm beads (nominal diameters).The thickness maps resulting from the individual thickness estimation methods (MCSA -top view in Fig. 4f, side view in h) and DF/BF ratio -top view in Fig. 4g, side view in i) differ in the achieved accuracy.Both methods match the real sample thickness in the case of small and middle beads (diameter = thickness in the centre), but the MCSA map slightly underestimates the largest beads compared to the DF/BF map which shows very good correspondence.The mismatch is possibly caused by imperfect centre detection during data processing or excessive data trimming during cropping of the scattering pattern ROI.This could potentially be improved by extending the angular range beyond 100 mrad.

Combined amorphous/crystalline sample analysis
Our local thickness estimation method can be combined with other 4D-STEM techniques based on the same 4D data cube.For both direct detection and light conversion 2D-STEM modalities, we demonstrate such an application on epoxy resin embedded mouse lung tissue containing inhaled TiO 2 particles in Fig. 5.The same sample was analysed using both detectors, where the areas of interest (a,e) were mapped and analysed with both q4STEM and powder nanobeam diffraction analysis.Resulting thickness maps (b,f) show variation between individual sections (∼30 nm).We note that the thickness retrieved for the nanoparticles is not correct due to their atomic composition, density and crystallinity.Specific information on, and identification of, these nanoparticles can be achieved with the recently-introduced 4D-STEM/PNBD method (powder nanobeam diffraction calculated from 4D-STEM data) 33,34 .Ordinary SEM analytical techniques (such as STEM imaging and EDX analysis) could reveal the presence of TiO 2 , but they could not confirm the crystalline modification of TiO 2 nanoparticles.The new 4D-STEM/PNBD methods yields 2D (two-dimensional) powder electron diffractograms (d,h) and their 1D (one-dimensional) radial profiles (c,g).The comparison of experimental powder electron diffractograms with theoretically calculated powder X-ray diffraction patterns showed that the TiO 2 nanoparticles exhibited the anatase modification, which is a unique additional information from the recorded 4D data cube.

Conclusion and discussion
We have demonstrated the principle and implementation of a robust geometrically calibrated method for lamella thickness estimation by 4D-STEM in a (FIB)-SEM.The combined DF/BF -MCSA method allows mapping local sample thickness at high accuracy in the range up to ∼1 µm and it can be used with any 2D-STEM detector type as shown with both commercial direct detection 2D-STEM and light-converted 2D-STEM detectors.The lower limit for thickness estimation of the MCSA method is dependent on the presence of a discernible peak in the angular electron scattering distribution.As our method measures mass-thickness, this limit is linearly dependent on sample density (e.g.∼100 nm for latex, ∼50 nm for amorphous carbon).
The main advantages of our q4STEM method are the stable and time-invariant calibration given by detection geometry, the simple result interpretation where higher MCSA and DF/BF ratio mean higher thickness, and its applicability over a wide range of relevant sample thicknesses.On the other hand the method requires a priori knowledge on the sample composition as input for simulations of electron scattering, and is limited to measuring only pure matrix material in heterogeneous samples, e.g.resin in case of biological thin sections.In addition, particularly for light conversion 2D-STEM, the short sample to detector distance makes the method sensitive to small deviations such that, for example, large mechanical tolerances of the sample mount or grid curvature may lead to inaccuracies in the estimated thickness.We see the main application for the q4STEM method in combination with FIB-SEM sample preparation for in-situ lamella thickness control.While still to be demonstrated for cryogenic conditions and samples, q4STEM thickness estimation could be integrated into the cryo-ET sample preparation workflow, allowing for sample optimisation before transfer to the TEM for tilt series acquisition.In this case, the 4D-STEM analysis not only allows local thickness estimation, but through its implicit diffraction measurement also provides a quality control mechanism to map regions of vitreous and crystalline ice across the lamella.We foresee a further combination with fluorescence microscopy (FM) in correlative FM modalities integrated in a FIB-SEM 35 and three-beam coincident FM-FIB-SEM instruments 36,37 , where the fluorescence microscope could also be used for in-situ quality control using light-conversion 2D-STEM as we showed here, in addition to fluorescence navigation and ROI localisation.In the final polishing steps, the real lamella thickness can be measured (e.g. at a local spot away from the ROI targeted for TEM analysis) and together with fluorescence-based localisation microscopy produce cryo-ET samples containing the ROI in a lamella of chosen thickness.

Fig. 1 (
Fig. 1 (a) Principle of a geometrically calibrated quantitative STEM measurement using a 2D-STEM detector.The amount of electrons captured by individual pixels is azimuthally integrated according to their position on the detector.The distribution of the integrated signal carries information about the local thickness.Direct detection 2D-STEM: (b) Schematic of the sample/detector geometry in direct detection 2D-STEM.The calibration distance from the sample to the detector is usually in the order of centimeters.(c) In-chamber situation during annular STEM images acquisition.For 2D-STEM data acquisition the annular STEM detector has to be retracted.Light conversion 2D-STEM: (d) Schematic of the sample/detector geometry for light-conversion 2D-STEM.The calibration distance from the sample to the scintillator in this case is given by the depth of TFS Autogrid (300 µm).(e) 2D-STEM image of the single electron beam interaction volume (e-beam in spot mode).(f) Transmission scattering pattern of a semi-thick amorphous sample (latex; ∼300 nm).(g) Transmission diffraction pattern of gold nano-clusters (cropped and contrast-adjusted).(h) In-chamber situation with the SECOM detector.The stage is not in the working position and will be moved under the electron column in operating mode.The optical objective is located below the sample holder on a separate xyz translation stage.
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Fig. 2
Fig. 2 Data processing pipeline for local thickness measurements with q4STEM.(a) In the full-scale image as obtained from the detector, the centre of the scattering pattern is determined (in red) and a region of interest (ROI) is defined such as to cover the entire 100 mrad scattering angle.(b) Data outside the ROI is removed and the cropped ROI is kept for further processing.(c) For light conversion 2D-STEM, a circular mask is used for background subtraction, where the background level is taken as the mean pixel intensity of the corner areas (in green).(d) ROI image after background subtraction.(e) In the MCSA approach, the scattering pattern is azimuthally integrated and its peak position determined.The corresponding scattering angle is then compared to (f) the result of Monte Carlo simulations giving the peak position versus sample thickness up to 500 nm.The comparison yields an estimated local sample thickness.(g) In the DF/BF approach, the integral signals of virtual BF (0-50 mrad) and DF (50-100 mrad) segments are determined and the ratio of DF/BF signal intensity is then compared to (h) the DF/BF ratios obtained from Monte Carlo simulations for a sample thickness up to 500 nm, again to yield a local sample thickness.

Fig. 3
Fig. 3 Determination of optimal beam energy.Simulated angular distribution of scattered electrons: (a) For a 100 nm polymer nanosphere sample, a sharp maximum in the radial profile needed for the MCSA method is only observed at 13 keV, while imaging with 15 keV yields a plateau with non-discernible peak position and for 30 keV electrons a monotonically decreasing profile is observed.(b-d) For 200-500 nm nanospheres, all three electron energies produce recognisable maxima in their angular distributions.Scattering pattern centre detection: (e) Scattering patterns acquired with a light conversion 2D-STEM detector show blurring with decreasing beam energy and increasing sample thickness.(f) Scattering patterns acquired with a direct detection 2D-STEM detector show consistent profiles across all beam energies due to very low background.

Fig. 4
Fig. 4 Demonstration of local thickness measurement on FIB-milled stepped lamella and polymer nanospheres.Direct detection 2D-STEM: (a) Stepped lamella prepared by FIB milling (BF STEM image on top, side-view secondary electron image on bottom).The mapped area is marked in red.(b) Thickness map resulting from MCSA analysis.The original lamella edge is indicated by the white dashed line.(c) Individual step thickness profiles.Symbol colours correspond to stripe numbers in (b), based on intended edge-thickness of each step.Solid lines indicate linear fits to the data for each stripe while the thick black line indicates the lamella edge (their intersections yield the lamella thickness on its original edge).(d) Estimated errors in the determined thickness show high accuracy except for the thinnest and thickest stripes that exceed the MCSA method limits of 200 nm and 1100 nm for this sample.Light conversion 2D-STEM: (e) Three-beads sample on a continuous carbon film, positions indicated with numbered cross marks highlight where the scattering patterns were recorded.(f) Thickness map based on MCSA method.(g) Thickness map based on DF/BF ratio method.(h) Side-view of the MCSA map.(i) Side-view of the DF/BF map.Note: results are corrected for the supporting carbon film; measured diameters of the beads are indicated by black lines (86, 265 and 572 nm respectively) and correspond well with the retrieved thickness profiles, especially for the DF/BF ratio method.

Fig. 5
Fig. 5 Combined analysis of an amorphous-crystalline sample from a single 4D-STEM data cube.Direct detection 2D-STEM in panels (a-d), Light conversion 2D-STEM) in panels (e-h).(a,e) Ultrathin section of mouse lung tissue after TiO 2 inhalation exposure.(b,f) Thickness maps from the areas highlighted with red boxes in (a,e).The line profiles were taken at the position of the solid white line.(c,g) Radial profiles of resulting powder diffractograms.Deconvolution significantly enhances the profile of anatase.(d,h) Powder diffractograms of all points, entropy filtered and entropy filtered + deconvolution respectively.

Table 1
Data acquisition settings for individual experiments.