Fixed-plane acquisition and reconstruction at four scan spacings

The figures are saved in diagnostics/fixed_plane_sampling_series as PDF, SVG and 600-dpi PNG, with frame arrays in NPZ files and acquisition/reconstruction provenance in manifest.json.

Acquisition figures

acquisition_0.4um, acquisition_0.8um, acquisition_1.2um, and acquisition_1.6um each show seven acquired frames across the sphere's passage through a stationary oblique plane. Columns select the nearest acquired frame to scan positions -10.4, -8, -4, 0, 4, 8, and 10.4 µm, with actual object displacements explicitly labeled. Thus these widely separated snapshots are not consecutive camera frames, and the selected positions vary slightly with acquisition step. The camera display spans -8 to +8 µm in columns and -16 to +16 µm in rows; the small margin outside the saved detector support is displayed black.

The top row illustrates the sphere's lateral translation and the fixed blue detection plane in laboratory YZ coordinates. The middle row independently predicts each frame by translating the Cartesian blurred object past that plane and integrating camera pixels. The bottom row shows the existing noisy camera acquisition. A scan position s corresponds to object displacement -s in the fixed-objective view. Camera images use a shared linear display range of 0–0.5 fluorescence-density units; larger values display white.

consecutive_acquisitions compares all four acquisitions at the same nine consecutive 0.4 µm positions (-1.6 through +1.6 µm). Missing observations are shown as exact zeros, without text overlays on the images. These zeros are display placeholders and are not treated as measured zeros by deconvolution.

Reconstruction figures

reconstruction_0.4_to_0.4um, reconstruction_0.8_to_0.4um, reconstruction_1.2_to_0.4um, and reconstruction_1.6_to_0.4um use the same seven physical scan positions (-10.4, -8, -4, 0, 4, 8, and 10.4 µm) for all acquisitions. The four rows are:

1. Sphere displacement relative to the stationary detector plane.
2. The GC-deconvolved Cartesian microscope reference, sampled onto that plane.
3. OPM GC reconstruction in instrument coordinates, labeled according to whether a camera frame was acquired at that scan position.
4. The final orthogonally deskewed OPM reconstruction, re-sliced onto the same oblique plane to permit a direct frame comparison.

Rows 2 and 4 are trilinear oblique slices of Cartesian volumes, not raw camera measurements or Cartesian projections. No extra optical convolution, camera integration, or noise is added to these reconstructed object estimates. The final re-slicing is a visualization operation; it does not change the saved reconstruction. All reconstruction images share a 0–1 linear display range; larger values display white. Native GC is used for 0.4 µm, and missing-plane GC uses factors 2, 3, and 4 for the other acquisitions. Every reconstruction has a 0.4 µm scan step before unchanged orthogonal deskew.

consecutive_reconstructions shows the corresponding instrument-coordinate GC estimates at the same nine positions as consecutive_acquisitions. "Measured" identifies a location with an acquired camera frame, while "inferred" identifies a location without one; all displayed values are deconvolved estimates, including those at measured locations.

Simulation conditions and limits

The stationary ground truth has 12 meridian arcs on a 10 µm centerline-diameter sphere, 1 µm tube diameter and 50 nm Cartesian sampling. The model uses a 30° oblique plane, NA 1.35, wavelength 637 nm, 115 nm camera pixels and 3 × 3 pixel-area quadrature. Camera noise is Poisson plus 1.5-electron RMS read noise, with 2 background electrons per pixel and a calibration of 500 electrons at the fine Cartesian blurred-object peak. Photon calibration per pixel is fixed across acquisition spacings; total photons per volume are not fixed. Camera seed 42 and Cartesian-reference seed 43 are reused, but differing array shapes give different realizations.

The first three acquisitions cover scan centers from -21.6 to +21.6 µm; 1.6 µm acquisition rounds the padded bounds outward to -22.4 to +22.4 µm. This preserves a centered object and complete optical support, yielding 29 measured and 113 reconstructed planes for 1.6 µm. The other acquisitions have 109, 55 and 37 measured planes and 109 reconstructed planes. The shifted output-grid phase means the 1.6 µm Cartesian reference is sampled on its own recorded Cartesian axes; frame comparisons use physical coordinates for every dataset, without registration or a fitted intensity normalization.

Input electron-data hashes are checked against the hashes recorded by each reconstruction. All reconstructed arrays must be finite, selected planes must land on the recorded 0.4 µm reconstruction grid, and physical settings must agree across cases. The simulations share a spatially invariant optical PSF assumption and do not establish the cause of artifacts in moving live data. No production PSF, GC or orthogonal-deskew code is changed for these figures.

Acquisition-to-reconstruction Cartesian maximum projections

acquisition_reconstruction_mips is a separate figure with one row per acquisition spacing and paired acquisition/reconstruction columns for XY, XZ and YZ. These are true Cartesian maximum-intensity projections through a common object-containing box, with voxel centers restricted to ±7.8 µm in each Cartesian direction, shown within ±8 µm axes. They are not individual frames or projections over raw array indices.

Each acquisition is first placed on a 0.4 µm scan grid, with exact zeros in the unmeasured planes. For display only, its raw cells are assigned to 50 nm Cartesian grid points by nearest neighbor using the inverse physical map row = Z/sin(theta), scan = Y - Z*cot(theta), column = X. This coordinate conversion does not interpolate fluorescence into missing planes, estimate missing data, or call production deskew. The fine Cartesian display grid does not imply finer acquired resolution. Maximum projections are then taken along physical X, Y or Z. Because the missing planes are oblique and parallel to X, their gaps remain diagonal in YZ; projection along Y or Z can cover gaps with signal from other planes.

The reconstruction panels use the saved final orthogonally deskewed GC volumes at their recorded Cartesian sampling, cropped to the same physical box. All panels use a common linear display range 0–1; values above 1 appear white and remain unchanged in exported source data. The acquisition panels retain optical blur and noise; reconstruction panels show deconvolved object estimates. The input hashes, measured/zero-plane counts, physical display grids and projection arrays are saved alongside the figure.

uv run --no-sync --with matplotlib python -m scripts.plot_acquisition_reconstruction_projections --acquisitions diagnostics/meridian_sphere_camera_0p4/scan_0.4um diagnostics/meridian_sphere_camera/scan_0.8um diagnostics/meridian_sphere_camera_1p2/scan_1.2um diagnostics/meridian_sphere_camera_1p6/scan_1.6um --output diagnostics/fixed_plane_sampling_series

Reproduce the figures

uv run --no-sync --with matplotlib python -m scripts.publication_fixed_plane_series --acquisitions diagnostics/meridian_sphere_camera_0p4/scan_0.4um diagnostics/meridian_sphere_camera/scan_0.8um diagnostics/meridian_sphere_camera_1p2/scan_1.2um diagnostics/meridian_sphere_camera_1p6/scan_1.6um --output diagnostics/fixed_plane_sampling_series