How can digital confocal imaging be achieved in holographic optical coherence tomography?

Full-field OCT trades confocality for speed

Full-field Fourier-domain optical coherence tomography (FF-FD-OCT) images a whole lateral area in parallel with a camera instead of scanning a focused spot. That parallelism delivers very high volumetric rates, but it removes the confocal gate that point-scanning OCT uses to reject out-of-focus and multiply scattered light. Aberrations from the setup or from deep inside the sample distort the point-spread function and lower the signal-to-noise ratio (SNR).

The paper's answer is to rebuild that gate computationally. By acquiring volumes under multiple oblique illuminations, a digital confocal volume can be synthesized in post-processing, an idea originally developed within reflection matrix imaging (RMI). The authors argue that earlier implementations were often time-domain, off-axis, or built around a Michelson interferometer, which reduced sensitivity, speed, and the usable space-bandwidth product (SBP).

A Mach-Zehnder layout preserves usable space-bandwidth product

The system is configured as a Mach-Zehnder interferometer. Light from a swept laser source (880 nm to 805 nm) is split by a fiber coupler into object and reference arms. In the object arm, a dual-axis galvanometric mirror is imaged onto the sample through a 4f system, so the illumination angle can be changed without moving the illuminated area. A separate reference collimator provides a fixed reference wave on the camera.

Acquisition is fast and dense: per sweep and scanner position, 500 interferograms are recorded on 768×768 sensor pixels at 65,000 fps, giving an effective A-line rate of 73 MHz, or 18.3 gigavoxels per second. In total 128 volumes per sample are acquired, each at a different scanner position following a Fermat spiral pattern, plus 128 on-axis volumes for comparison. All data were acquired at a numerical aperture of 0.13. The authors state that this configuration enables optimal use of SBP, providing up to a fourfold increase in effective acquisition throughput.

Shear correction aligns oblique views into one volume

Oblique illumination imposes a phase gradient at every depth, and in the raw reconstruction this appears as a shear: different lateral locations from the same layer are shifted axially by an amount proportional to the illumination direction. Physically this comes from lateral differences in optical path length between object and reference waves at the camera plane.

The authors compensate by applying the conjugate phase gradient before the Fourier transform along the wavenumber axis, which also realigns the object's lateral spatial-frequency content between measurements. Summing these shear-corrected fields over illumination angles produces the digital confocal volume. The paper notes that this shear correction is the computational counterpart to physically scanning the reference pupil, but because the k-space can be zero-padded in post-processing, the apertures can shift without aliasing, yielding up to four times the field of view or resolution.

Least-squares optimization is equivalent to CLASS

The paper poses scattering and aberrations as an overdetermined system, which admits a closed-form solution of an alternating least-squares problem. The resulting iterative optimization is equivalent to the state-of-the-art closed-loop accumulation of single scattering (CLASS) algorithm. CLASS maximizes the coherent sum of aberration-corrected fields, which is only maximal when aberrations are fully corrected.

The unoptimized first estimate, with no corrections applied, equals the earlier CASS image. Each iteration then corrects the observed fields so they better match a common object estimate, which phase-aligns them. In the lens tissue demonstration, optimization typically converged after a couple of iterations but was run for 100 iterations globally and 20 locally.

Resolution doubles and SNR improves in test targets

In a USAF target, the theoretical resolution of the system is λ/4NA = 1.54 µm, corresponding to Group 8 Element 3 (1.55 µm), which is the smallest element still resolvable in the optimized digital confocal enface. Conventional FF-FD-OCT resolves only Group 7 Element 3 (3.10 µm). The paper describes this as the expected doubling of lateral resolution.

In lens tissue, the optimized digital confocal image showed improved image quality and higher SNR, and local optimization over 198×198 µm isoplanatic patches with 49 µm overlap produced consistent quality across the full field of view. The authors attribute a 15 dB SNR gain in the lens tissue almost entirely to correction of input aberrations, since output aberrations were weak there. They also report that the optimized images showed a marked SNR improvement over on-axis coherent averages, which they attribute to better rejection of autocorrelation and multiple-scattering noise whose phase varies with illumination.

Depth-dependent aberrations require sequential estimation

In a PSF phantom, input and output aberrations were first estimated at the surface and applied to every depth. Point scatterers blurred with increasing depth, and the recovered aberrations at in-medium depths of 0.3 mm and 0.6 mm (refractive index n = 1.5) showed a depth-dependent defocus. An off-center defocus in the input aberration indicated misalignment between illumination and detection pupil.

Correcting sequentially from the surface downwards, using pupil functions estimated at depth z as initial estimates for depth z+1, recovered strong signal throughout the volume and made scatterers resolvable at all depths. The paper notes that the least-squares optimization is susceptible to local minima, maxima, saddle points, or local gauge freedom; at maximum depth, aberrations could not be recovered without an initial estimate and instead converged to a speckle-like solution.

Model-eye quality depends on accurate illumination registration

For a model eye, the Fourier transform of the detected object field was set to coincide with the eye's pupil, since most aberrations are expected there. The authors compared theoretical values of the illumination vectors with values obtained through their registration procedure. Using registered values improved the resolution of the estimated aberration and produced an optimized enface with better SNR that revealed the model eye's texture, compared with using theoretical values.

Local optimization over 99 µm × 99 µm patches with 25 µm overlap allowed scatterers to be resolved more clearly, but also pulled up noise in empty regions, shown in a red inset with increased dynamic range. The paper attributes this to the algorithm maximizing the coherent sum without distinguishing signal from noise, and suggests sparsity-promoting regularization or replacing speckle-like output aberrations with estimates from neighboring patches as possible mitigations.

The digital confocal advantage fades without single-scattered signal

The paper's own comparison sets the priority: correcting input aberrations proved as important as correcting output aberrations for optimized digital confocal image quality. In the lens tissue, where output aberrations were weak, the improvement was almost entirely attributable to input correction. Motion gives a random phase to each volume, which prevents coherent summing of the single-scattering component and is in principle indistinguishable from input aberrations.

The advantage of oblique illumination over conventional FF-FD-OCT comes from partial cancellation of multiply scattered and autocorrelation noise during coherent summation, because their phase varies with illumination. That advantage is lost when single-scattered signal is absent or very weak, as observed in the model eye's empty regions. The authors also note that the setup is incompatible with multimode illumination due to its Mach-Zehnder fiber-coupled configuration, that scanning changes the illumination phase front between volumes beyond the expected gradient, that strong in vivo sample motion will uniquely disturb the phases in each aperture, and that the high volumetric rate enabling dynamic applications such as optoretinography is lost to a certain extent. Processing times were under 3 minutes for initial reconstruction, registration, shear correction, and alignment, and under 19 minutes for full optimization of the model eye volume (90 layers, 2304 isoplanatic patches of 32×32 pixels per layer, 20 iterations) on a 128 GB RAM machine with an NVIDIA RTX 4090.

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