Digital Defocus Aberration Interference (DAbI)

• DAbI is a physics-based defocus sensing method that digitally combines Fourier transforms of two LED images to encode defocus as interference-like fringes.
• It achieves autofocus and digital refocusing across wide depth ranges—up to 212× to 300× the depth-of-field—by mapping fringe modulation to defocus distance.
• The method employs a simple dual-LED setup with FFT-based processing, delivering rapid, robust performance across multiple imaging modalities.

Searching arXiv for papers on Digital Defocus Aberration Interference and closely related methods. Digital Defocus Aberration Interference (DAbI) is a physics-based defocus sensing method introduced for automated optical microscopy in which two intensity images acquired under two oblique illumination angles are Fourier transformed, digitally summed, and analyzed in an overlap region whose interference-like fringe modulation encodes defocus (Zhou et al., 15 Jul 2025). The method was developed for automatic, efficient, and generalizable defocus detection with a simple two-LED setup, and it is used both for autofocus, where the sample or objective is moved to the correct focal plane, and for digital refocusing, where defocus is estimated and then corrected numerically. In the reported demonstrations, DAbI was applied to brightfield, complex-field, refractive index, confocal, and widefield fluorescence imaging, with autofocus ranges reported as $212\times$ the depth-of-field (DoF) for thin samples and $300\times$ DoF for thick specimens (Zhou et al., 15 Jul 2025).

1. Definition, scope, and problem setting

DAbI addresses a longstanding bottleneck in automated microscopy: reliable focus control across diverse specimens and imaging modalities. The method is defined by four steps: sequential illumination of a sample by two LEDs at two different incident angles, acquisition of two intensity images, digital summation of their Fourier transforms, and estimation of defocus from the fringe modulation appearing in the Fourier-domain overlap region (Zhou et al., 15 Jul 2025). In this formulation, autofocus and digital refocusing are distinct tasks. Autofocusing estimates the sample’s defocus distance $\Delta z$ and then physically moves the sample or objective to the correct focal plane, whereas digital refocusing estimates defocus and numerically reconstructs an in-focus image without mechanical $z$-motion (Zhou et al., 15 Jul 2025).

The method was positioned against several existing autofocus families. Deep learning autofocus can be fast, but often has limited range, needs training data, and may not generalize across sample types or modalities. Passive image-based focus metrics require $z$-stacks or multiple trial positions, are slow, and often use sample-dependent sharpness metrics. Active hardware methods such as phase detection, interferometry, triangulation, and tilted sensors can be effective but usually need extra hardware and may not transfer well between modalities. Dual-illumination displacement methods are simple and useful, but fail at small defocus when the two shifted images cannot be separated, and they suffer from sign ambiguity; the paper specifically highlights failure at small defocus, for example $<46\times$ DoF for a $20\times/0.75$ NA objective, in prior image-separation dual-angle methods (Zhou et al., 15 Jul 2025).

A common misconception is that the “interference” in DAbI is optical interference measured directly at the camera. The paper explicitly rejects that interpretation: the effect is a digital interference-like phenomenon that emerges after Fourier processing of two intensity images. The fringes arise from the phase difference between the defocus aberration terms associated with the two illumination angles, not from direct path interference at the detector (Zhou et al., 15 Jul 2025). This distinction is central to the method’s compatibility with ordinary microscope hardware.

2. Fourier-domain mechanism and thin-sample theory

The physical intuition begins with two-angle illumination by oblique plane waves,

$$e^{-j\mathbf{k}_{in,i}\cdot \mathbf{r}_\perp}, \qquad i=1,2,$$

where $\mathbf{r}_\perp=(x,y)$ is the transverse coordinate and $\mathbf{k}_{in,i}$ is the transverse illumination wavevector for LED $300\times$0 (Zhou et al., 15 Jul 2025). Each illumination angle shifts the sample spectrum differently relative to the objective pupil. In the Fourier transform of each intensity image, the paper identifies four terms: $300\times$1 with $300\times$2, where $300\times$3 is the shifted scattered sample spectrum and $300\times$4 is the coherent transfer function (Zhou et al., 15 Jul 2025).

For weakly absorbing and weakly scattering thin samples, the fourth autocorrelation term is negligible in a specially useful overlap region of the summed spectrum. There the magnitude of the digital sum becomes

$300\times$5

where $300\times$6 and $300\times$7 is the phase of the coherent transfer function containing the defocus aberration (Zhou et al., 15 Jul 2025). This is the central DAbI equation: the overlap-region amplitude is modulated by a cosine term, so the observed fringes directly reflect the phase difference

$300\times$8

The paper states that this formulation is valid when defocus is the dominant aberration. In that regime, the pupil phase has the familiar scalar-diffraction dependence

$300\times$9

up to sign convention and additive constants (Zhou et al., 15 Jul 2025). Because the two illuminations sample this phase at shifted pupil locations, defocus produces a predictable fringe spacing. Larger defocus produces a larger phase gradient and therefore denser fringes.

The retrieval equation is derived from fringe valleys, defined by odd multiples of $\Delta z$0. The paper gives

$\Delta z$1

where $\Delta z$2 is a spatial-frequency coordinate at which a valley is evaluated and $\Delta z$3 correspond to the two illumination-angle frequency shifts (Zhou et al., 15 Jul 2025). This formula provides the explicit physics-based mapping from fringe location to the magnitude of the defocus distance.

3. Acquisition, computation, and sign determination

The implementation is intentionally minimal. The reported DAbI setup consists of a standard microscope, two LEDs placed off-axis for transmissive illumination, and sequential acquisition of two images at one axial position (Zhou et al., 15 Jul 2025). In most demonstrations, the authors used a $\Delta z$4 NA objective and chose the two LEDs at equal radial distance from the optical axis, with illumination angles slightly smaller than the system’s maximum acceptance angle. The design rules stated in the paper are that each illumination angle must be no larger than the system NA acceptance angle, the separation between the two angles should lie in a suitable range, and equal-angle symmetric geometry simplifies processing (Zhou et al., 15 Jul 2025).

The processing pipeline is entirely FFT-based. First, compute

$\Delta z$5

then form the digital sum

$\Delta z$6

Next, locate and crop the overlap region, select a smaller rectangular subregion based on signal level and fringe contrast, apply a Fourier transform to that fringe-bearing subregion, and estimate the fringe period or frequency. The main computation therefore scales as

$\Delta z$7

where $\Delta z$8 is the pixel count (Zhou et al., 15 Jul 2025).

A notable feature of DAbI is its explicit handling of small defocus. When defocus is small, roughly less than $\Delta z$9 DoF, the fringes are too sparse or are distorted by other aberrations. The reported procedure is to digitally apply a known large virtual defocus to both intensity spectra, thereby creating denser and more measurable fringes, then include amendment terms to compensate for curvature due to high-order terms of defocus, especially at high NA, estimate the total defocus, and subtract the added defocus (Zhou et al., 15 Jul 2025). The same mechanism resolves sign ambiguity. In the Methods section, the authors describe adding a known virtual defocus corresponding to $z$0 DoF or $z$1; if the total estimated defocus after virtual addition is $z$2, then the physical defocus is

$z$3

For defocus larger than about $z$4 DoF, the fringe frequency can be extracted directly, and sign is determined by trying positive and negative virtual defocus additions and checking which direction produces denser fringes (Zhou et al., 15 Jul 2025).

The method is mostly model-based and does not require sample-specific training. Calibration is limited to system geometry such as objective NA, wavelength, pixel size, magnification, and LED positions or illumination wavevectors; one-time system aberration pre-calibration is required if non-defocus aberrations such as spherical aberration, astigmatism, or coma are strong (Zhou et al., 15 Jul 2025).

4. Thin and thick specimens, operating range, and performance

For thin samples, the overlap region is a relatively broad area in the 2D Fourier plane, the second terms in the image-spectrum model dominate, and the defocus relation above applies directly (Zhou et al., 15 Jul 2025). For thick samples, the paper invokes the Fourier diffraction theorem: the relevant terms are distributed over 3D spherical caps rather than a thin 2D support, the overlap region shrinks to a narrow line in frequency space, and fringe visibility decreases away from that line (Zhou et al., 15 Jul 2025). The authors compare this to a coherence-area effect in interferometry. Under these conditions, DAbI fringes correspond to an average defocus aberration across the 3D volume, which makes the method well-suited to finding the central plane of a thick specimen rather than a single exact in-focus section (Zhou et al., 15 Jul 2025).

The reported autofocus range is unusually large relative to conventional microscopy DoF. For thin samples, DAbI quantified defocus over a range of about $z$5, equivalent to $z$6 DoF, using a $z$7 NA objective (Zhou et al., 15 Jul 2025). For thick samples roughly $z$8–$z$9 thick, the reported range is about $z$0, equivalent to $z$1 DoF, again with $z$2 NA optics (Zhou et al., 15 Jul 2025). For the $z$3 NA setup with $z$4 pixels and green illumination, the paper reports

$z$5

which is the basis for the quoted thin-sample multiple (Zhou et al., 15 Jul 2025).

The temporal budget is likewise small. The demonstrated experiments used only 2 images, total capture under $z$6 ms, and illumination power density around $z$7 at the sample plane (Zhou et al., 15 Jul 2025). Reported feedback time was $z$8 s on CPU using an Intel i7-14700KF and $z$9 s on GPU using an NVIDIA RTX4090 (Zhou et al., 15 Jul 2025). For thin samples, the paper states that DAbI achieved errors within the system DoF in the reported experiments.

When integrated with complex-field imaging, DAbI also functions as a defocus prior for digital refocusing. The reported mechanism is to estimate $<46\times$0 from two LED images, encode that estimate as a Zernike defocus aberration in the pupil phase, and reconstruct the sample with the corrected pupil (Zhou et al., 15 Jul 2025). In that setting, the paper reports a 20-fold extension of natural DoF over conventional brightfield or phase contrast microscopy and a $<46\times$1-fold improvement over the state-of-the-art APIC method alone (Zhou et al., 15 Jul 2025). Using a USAF1951 phase target, the reported achieved resolution was $<46\times$2, compared with the theoretical resolution

$<46\times$3

while the measured phase step was $<46\times$4 versus an expected $<46\times$5 (Zhou et al., 15 Jul 2025).

5. Demonstrated applications and methodological limits

The demonstrations span several microscopy workflows. In a bi-modality microscope for imaging HEK cells transfected with self-assembling $<46\times$6-synuclein constructs, DAbI was used to autofocus in a multi-well slide before widefield fluorescence and phase imaging; one reported well had $<46\times$7 before correction (Zhou et al., 15 Jul 2025). In live mouse embryo imaging, the method was used to focus thick samples for refractive index tomography via analytic Fourier ptychotomography and for brightfield transmission microscopy, with one reported central-plane defocus estimate of $<46\times$8 (Zhou et al., 15 Jul 2025). The same paper reports automated prefocus alignment for confocal imaging of an $<46\times$9-thick mouse brain section with four fluorescence channels, as well as DAbI-assisted APIC whole-slide imaging of unstained human lung cancer tissue, unstained colon cancer tissue, and H&E-stained non-small-cell lung cancer tissue (Zhou et al., 15 Jul 2025).

The method’s advantages are explicitly tied to its operating assumptions. Because DAbI is based on image-formation physics rather than a learned sample prior, it does not require training data and is described as robust across 2D and 3D samples, stained and label-free specimens, and multiple modalities (Zhou et al., 15 Jul 2025). At the same time, fringe visibility depends on sample properties. Highly scattering, highly absorptive, or very thick samples reduce contrast in the overlap region, and the paper specifically notes difficulty for very thick or highly scattering samples, for example $20\times/0.75$0, where fringe visibility can become too low for reliable estimation (Zhou et al., 15 Jul 2025). Proposed mitigations in the paper are optical clearing and longer illumination wavelengths to reduce multiple scattering.

Several additional limits are stated directly. Non-defocus aberrations can distort fringes, so one-time system aberration pre-calibration is needed if spherical aberration, astigmatism, or coma are strong. The autofocusing range is upper-bounded by the sampling rate in frequency domain, mainly determined by the field of view; larger field of view improves range but increases computational cost. The LED angles must lie within the objective acceptance and have suitable separation. For 3D samples, DAbI yields a volume-center-like defocus rather than a unique local best focus for every depth (Zhou et al., 15 Jul 2025). This suggests that DAbI is best understood as a model-based autofocus and refocusing primitive whose thick-sample output is an average defocus estimate adapted to volumetric workflows, rather than a universal single-plane focus metric.

6. Relation to adjacent research

DAbI sits within a broader landscape of methods that use defocus, sub-aperture diversity, or interference-derived artifacts as computational signals. In dual-pixel imaging, the paper “Learning Dual-Pixel Alignment for Defocus Deblurring” shows that left and right dual-pixel observations are physically meaningful sub-aperture views linked to defocus and depth, and that explicit multiscale alignment improves reconstruction (Li et al., 2022). That work does not study aberration asymmetries such as coma, astigmatism, chromatic effects, or interference or phase analysis, but it is directly relevant to DAbI-style settings in which dual-view differences arise from defocus-induced sub-aperture shifts rather than being treated as mere auxiliary channels.

In self-interference digital holography, the paper “Three-dimensional neural network driving self-interference digital holography enables high-fidelity, non-scanning volumetric fluorescence microscopy” studies a different but adjacent phenomenon: a 3D fluorescent object is encoded into a 2D self-interference hologram, conventional numerical back-propagation produces strong axial blur, out-of-focus crosstalk, and “defocus noise,” and a 3D U-Net is trained to suppress those artifacts (Man et al., 15 Apr 2025). The overlap with DAbI is conceptual rather than terminological. The holography paper is not an autofocus method, but it shows that digitally reconstructed defocus-interference artifacts can be treated as structured volumetric degradations rather than as simple 2D blur.

Aberration-aware depth-from-defocus and defocus-assisted pupil estimation provide another adjacent line. “Self-Supervised Spatially Variant PSF Estimation for Aberration-Aware Depth-from-Defocus” calibrates field-dependent PSFs from real sharp and blurred image pairs without ground-truth PSFs, explicitly addressing spatially variant blur and focus breathing (Wu et al., 2024). “Self-Bayesian Aberration Removal via Constraints for Ultracold Atom Microscopy” uses differing degrees of defocus and density-density correlations to estimate even-order aberrations and then performs support-constrained digital aberration removal without additional hardware (Altuntas et al., 2021). These works suggest that DAbI belongs to a larger class of physics-based strategies in which defocus is not merely a nuisance parameter but an informative perturbation for calibration, estimation, or reconstruction.

A more distant but conceptually revealing comparison is “Quantum, Nonlocal Aberration Cancellation,” which models defocus as a quadratic phase and demonstrates recovery of spatial resolution by introducing complementary aberrations in a correlated optical path (Black et al., 2019). That experiment uses two-photon coincidence measurements rather than ordinary microscopy images, so it is not a DAbI implementation. A plausible implication is that DAbI’s digital fringe mechanism and the quantum cancellation result share a deeper phase-based viewpoint: defocus becomes measurable or correctable when paired channels sample related aberration phases under a known coordinate mapping.