Supplementary Figure 6: SLAP motion tracking and registration.

Reconstruction of SLAP data requires precise and accurate detection of sample position, and appropriate compensation by the imaging model. We perform motion registrations using 3D grid search to identify the sample displacement that minimizes an alignment cost function (Methods). (a-e) We characterized registration precision by introducing known 3D displacements to a static sample of beads embedded in agarose gel. X-Y displacements were made by moving the stage and collecting a raster image to determine the precise lateral displacement. Axial displacements were made with a calibrated piezo objective stage. As in all experiments, 2D SLAP frames are aligned in 3D to a 3D reference image. b) Actual vs. estimated displacements from center of reference image for lateral (X,Y) axes. ‘Actual’ displacements were computed from raster scan images acquired after each stage movement. c) Histogram of alignment errors when aligning single SLAP frames (top) or mean of 100 frames (bottom). Lateral alignments were performed at 50 nm grid spacing. d) Actual vs. estimated displacements from center of reference image for vertical (Z) axis. e) Histogram of alignment errors for single SLAP frames (top) or mean of 100 SLAP frames (bottom). Axial alignments were performed at 375 nm grid spacing. (f-i) We demonstrated kHz-framerate sub-micron 3D brain motion tracking in awake headfixed mice implanted with fluorescent beads. g) Example SLAP recording. Despite head fixation, significant brain motion occurs during movements. Dashed boxes denote zoomed regions at right. h) Estimated 3D displacements for the same recording. i) Histograms of frame-to-frame displacements. Each frame was aligned independently to the 3D reference image. Estimated displacements between consecutive frames never exceeded a single pixel of the reference image (200nm lateral, 750 nm axial; frames were aligned at 0.5 pixel precision, n=2000 frames). This indicates that sample motion within a single 1-ms frame is negligible even in actively moving mice, and that SLAP motion alignment is precise and reliable. (f-i) this experiment was repeated 5 times in 2 mice with similar results. j) SLAP measurements (average of 100 frames) and Expected SLAP measurements before (left) and after (right) global position alignment. The Expected measurement is the product of the measurement matrix (P) with the rigidly-aligned reference image. This example is typical of all in vivo recordings in the study.