DPC/CoM

Quant4D can generate Differential Phase Contrast (DPC) and Center of Mass (CoM) images from the 4D-STEM dataset. In CoM mode, the center of mass is calculated from within the circular or round mask on the diffraction pattern. In DPC mode, the circular/annular mask is subdivided into a user-defined number of sectors both radially and azimuthally (default = 4 quadrants).

Scan rotation estimation

It is critical to estimate the rotation angle between the scan direction in real space and the diffraction pattern on the detector. The user can explicitly set this angle in the main UI window, or it can be estimated automatically by minimizing the curl as a function of the rotation angle. When the user first enters either DPC or CoM mode, the Scanning Direction panel on the main UI window will be highlighted in orange, indicating that the angle has not yet been set. The user can enter or estimate the angle by first clicking the lock icon to enable the inputs. If the user clicks the Auto button, the curl minimization routine will run, using the estimated rotation angle and automatically locking the Scanning Direction panel to avoid accidental changes. In addition to the rotation angle, the handedness of the scan direction can be swapped by enabling or disabling the swap_y icon, which inverts the y-axis scan direction.

Images

Many images are calculated in DPC/CoM modes; however, most are not immediately made visible to the user to avoid opening too many windows at once. The user can show any/all of the following images by clicking the corresponding icon in the Show Image Windows panel of Windows tab in the Settings UI. When the user is enters DPC or CoM mode, this tab is automatically activated. The name of the images will automatically update to reflect the current mode (i.e. CoMx or DPCx, etc.).

diffraction - Main diffraction space image.
diffraction_mask - Diffraction space mask used to generate images.
bfdf - Main real space image.
bfdf_mask - Real space mask (i.e. if an ROI is used)
CoMX - CoM/DPC image in the x-direction.
CoMY - CoM/DPC image in the y-direction.
CoM_magnitude - CoM/DPC magnitude image.
CoM_phase - CoM/DPC phase image.
colorwheel - Color wheel legend for phase images.
CoM_phase_mag - CoM/DPC phase image with opacity based on the magnitude image
dCoM - Differential CoM/DPC image.
iCoM - Integrated CoM/DPC image.

Vector overlays

DPC and CoM imaging generates a vector field, which can be selectively overlaid on any/all real space images. The user should first select the desired image by either clicking the relevant button above, clicking the image window, or selecting the image from the Image dropdown on the Display tab in the Settings UI. After the desired image is selected, the user can click the Vector Sampling dropdown in the Windows tab of the Settings UI. Vectors can be displayed at each pixel (1:1), or subsampled by a factor of 2, 4, 8, or 16. This is especially helpful when the vector field is highly oversampled compared to its rate of change. Additionally, the user can change the color of the vector overlay independently on each image using the colorpicker icon next to the vector sampling dropdown.

iDPC/iCoM

Integrated DPC/CoM images are generated automatically using the detector chosen by the user. Integration of the DPC/CoM signal retrieves the phase of the specimen transmission function. The maths are thoroughly described by Lazić et al. [1]

dDPC/dCoM

Differentiated DPC/CoM images are generated automatically using the detector chose by the user. Differentiation of the DPC/CoM signal retrieves the charge density distribution of the specimen. [1]

Filtering

Because the integration step can amplify noise at low spatial frequencies, while differentiation can suffer from noise at high spatial frequencies, a bandpass filter is made available to the user in the Windows tab of the Settings UI. The user can independently change the low and high frequency cutoff values (in pixels) to apply a bandpass, lowpass, or highpass filter. The filter is only applied to the iCoM/iDPC and dCoM/dDPC images.

  1. Ivan Lazić, Eric G. T. Bosch, and Sorin Lazar. “Phase contrast STEM for thin samples: Integrated differential phase contrast.” Ultramicroscopy 160 (2016): 265-280. https://doi.org/10.1016/j.ultramic.2015.10.011