An optics preprint describes a neural-network method for designing arbitrary three-dimensional point-spread functions (PSFs), the light patterns associated with point sources. In simulations and tabletop experiments, the authors reported reproducing several specified patterns, including rotating helixes and an extended-depth-of-field design. In a single-helix task, the neural-field run was reported to use fewer optimization iterations and produce a smoother phase profile than pixel-wise methods.
The proposal treats 3D PSF engineering as a phase-retrieval problem: the goal is to find a pupil phase mask that makes light form a chosen distribution in depth. Rather than assigning a phase value independently to every pixel, it parameterizes that mask with an MLP-based implicit neural representation, a neural model for the pupil phase.
A continuous map for the pupil
Target PSF stacks are first preprocessed to mimic the optical transfer function’s band-limited response—the limit on spatial detail imposed by the optical system. The MLP is then trained with a differentiable Fourier-optics model, and its coordinate input is encoded with Fourier features.
Patterns tested on the bench
In the reported experiments, single- and double-helix PSFs rotated over axial ranges of 80 micrometres and 100 micrometres, respectively. An extended-depth-of-field design maintained its extension over 400 micrometres. The measured axial behavior was reported to agree qualitatively with the simulations.
The method was also used to shape the intensity balance through depth. Giving more weight to slices farther along the positive z direction was reported to be associated with more even focal-point intensity, especially at farther axial positions. Other demonstrations included an alternating three-focus design with staggered axial spacing and a 2 × 2 multifoci pattern.
A reported edge in one benchmark
The benchmark compared the neural-field approach with direct pixel-wise phase optimization and a threshold-based pixel-NOVO cost; MSE loss was used for the other methods. For the single-helix task, the neural-field run was reported to converge in fewer iterations and produce a smoother phase profile. NOVO reached a functional solution without initialization but took more iterations and had higher loss than the MSE-based methods.
These are reported comparisons, not a blanket result across optical systems. Exact iteration counts, repeated-run variability, numerical error measures, confidence intervals and formal statistical tests were not reported. The preprint therefore does not establish superiority across all PSF tasks or experimental conditions.
Evidence still comes from a narrow test
Experimental validation used fluorescent beads reported as 1 micrometre in diameter as point sources. Bead counts, axial scans, measurements and independent replicates were not reported. The test therefore does not show whether the approach improves biological or in vivo imaging, or how it performs under scattering and aberrations.
The document is identified as arXiv:2608.20277v1 in physics.optics and dated 20 August 2026. It is a preprint, and peer-review status is not reported. Underlying results data and trained checkpoints are not publicly available, although the authors say they may be obtained on reasonable request. The remaining question is whether agreement at the PSF level translates into better localization, 3D imaging or biological imaging outcomes.
Paper data and sources
Original title: Point Spread Function Engineering Using Implicit Neural Representations
Authors: Suet Ying Chan, Mitchell Gilmore, Qilin Deng et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text