Microscopes trade resolution, field of view and frame rate against the sensor's limited pixel throughput. The authors build and experimentally demonstrate a microscope that treats a 6 × 8 array of 48 sensors as one large 'super sensor' (active pixels cover only ~22% of its area) and place a fabricated 64-level diffractive optical element in the pupil that turns each point into 15 spots, so every sample position sends light to at least one sensor. A sparsity- and total-variation-regularized reconstruction with a fully shift-variant convolutional forward model then recovers a gap-free image, ext

Forty-eight camera chips, tiled into one “super sensor”, leave about 78% of the image plane uncovered. For sparse worm scenes, this microscope can recover what falls in the gaps: a diffractive element splits each point of light into 15 copies, and a sparse solver untangles them.

Companion to Zhou, Gu, Ikeda, Hayward, Antipa, Menon, Horstmeyer, Kato & Waller, “Large-scale compressive microscopy via diffractive multiplexing across a sensor array”, Nature Photonics 20, 1240–1246 (2026).

The gap bench

Below is the paper’s real sensor layout: 6 × 8 chips, each 3.45 × 4.51 mm, on a 9 mm grid. Light that falls between chips is simply lost. Drag the worm, swap what sits in the microscope’s pupil, and ask the solver to rebuild the scene.

What the 48 sensors record

Reconstruction

Why that odd pattern of 15 spots?

The authors searched for a spot pattern meeting two tests. Pan-visibility: wherever a point sits, at least one copy lands on a chip. No translational ambiguity: no two positions may produce the same recorded pattern. Drag the spots, try the classic candidates, or mis-scale the pattern as a slightly wrong lens focal length would.

Spot pattern

Every position around one gap

Spots: 15. More spots split the light further and add read noise, so the authors wanted as few as possible: 13 sufficed, but 15 tolerated scale errors better (robustness ~1.15 vs <1.05).

What the real instrument recorded

Wild-type C. elegans crawling through a 2 cm × 2 cm pillar arena, filmed at 120 fps in dark-field mode. Left: the 48 sensor readouts (static background removed), shown edge-to-edge so the gaps are hidden. Each worm appears as several overlapping copies. Right: the authors’ gap-free reconstruction with tracked worms.

Clips from Zhou et al. (2026), Supplementary Videos 1 and 2, CC BY 4.0. Modified: downscaled and re-encoded as WebM; Video 1 resampled from 120 to 30 frames per second, and Video 2 (published at quarter speed) sped up 4×, so both play in real time and in step.

Throughput, by the numbers

Every microscope trades resolution, field of view and frame rate against the sensor’s pixel budget. The array multiplies the budget; the diffractive gap-filling multiplies it again.

Each frame took under 5 s to reconstruct (50 gradient-descent iterations) on a 24 GB GPU. The fluorescence mode is limited by lens aberrations; vignetting and aberrations also degrade the corners of the field, which the authors identify as the main limitation of using one large lens pair.

Model notes

The bench uses the paper’s forward model: the recorded image is the object convolved with a 15-impulse PSF, then masked by where chips exist (Eq. 3):

and reconstructs by minimising a sparsity-regularised least-squares loss with non-negativity (Eq. 7):

The impulse positions Δri are the paper’s Supplementary Table S1. Sensor size, pitch and array layout come from the main text. The designer recomputes the authors’ two key criteria (Supplementary Section S1) over one periodic 9 × 9 mm cell, which the authors note is sufficient because the array is “periodically shift-invariant”.

Simplifications in this companion

Image-plane grid of 0.1 mm (the instrument samples at 4.4 µm after binning), so worms are coarse and the full field is 734 × 565 cells.

All 15 copies are given equal brightness; the real amplitudes Ai, lens distortion (Eqs. 4–6), aberrations, chromatic blur and noise are omitted.

Solved with an accelerated proximal-gradient method (FISTA), 120 iterations, L1 + non-negativity only; the paper also uses a total-variation term and plain gradient descent.

Worms are synthetic, ~2.8 mm long in the image plane (about 1 mm at 2.78× magnification). “Found / missed / ghost” use a 0.4 threshold, echoing the overlay convention of the paper’s Supplementary Fig. S6.

The crowding trend mirrors the paper’s finding that recovery is reliable below a density of about 10−2 and fails near 10−1 (Supplementary Figs. S5–S7), but the exact numbers here come from this simplified simulation.

Ambiguity is counted when two positions give identical recorded spot sets (the paper’s strict-ambiguity test); “worst overlap” is the normalised column correlation (mutual coherence).

Source & credits

Kevin C. Zhou, Chaoying Gu, Muneki Ikeda, Tina M. Hayward, Nicholas Antipa, Rajesh Menon, Roarke Horstmeyer, Saul Kato & Laura Waller. “Large-scale compressive microscopy via diffractive multiplexing across a sensor array.” Nature Photonics 20, 1240–1246 (2026). doi.org/10.1038/s41566-026-01974-4

The article and its supplementary material are published under a Creative Commons Attribution 4.0 International License. Video clips are adapted from Supplementary Videos 1–2 (modifications noted above). Sensor geometry and PSF coordinates are taken from the main text and Supplementary Table S1. The interactive simulations are reconstructions for explanation, not the authors’ code; their reconstruction code is at github.com/kevinczhou/diffractive-compressive-array-microscopy and raw data at doi.org/10.5061/dryad.tmpg4f5b6. The illustration at the top is an AI-generated conceptual illustration.