Theoretical analysis of performance limitation of computational refocusing in optical coherence tomography

TL;DR

The paper develops a two-dimensional, pupil-based framework to analyze defocus and computational refocusing in OCT, comparing point-scanning OCT and spatially-coherent FFOCT. It derives two key criteria: a Nyquist-based lateral-sampling limit applicable to both modalities and a confocality-limit that constrains point-scanning OCT, yielding an analytic expression z_c = z_R sqrt(10^{SNR_dB/10} - 1) for the maximum defocus at a given SNR. The core finding is that point-scanning OCT is ultimately limited by confocal energy loss with defocus, while SC-FFOCT can in principle correct defocus indefinitely provided sampling density meets the Nyquist bound, making SC-FFOCT particularly well-suited for optical coherence microscopy. These results guide system design and highlight practical strategies (e.g., off-axis modulation, MFA) to mitigate performance limits and extend high-resolution imaging deeper into scattering samples.

Abstract

High-numerical-aperture optical coherence tomography (OCT) enables sub-cellular imaging but faces a trade-off between lateral resolution and depth of focus. Computational refocusing can correct defocus in Fourier-domain OCT, yet its limitations remain unaddressed theoretically. We formulate the lateral imaging process of OCT by using pupil-based imaging theory and the constraints of the computational refocusing in point-scanning OCT and spatially-coherent full-field OCT (FFOCT) are analyzed. The constrains in lateral sampling density and the confocality are considered, and it is shown that the maximum correctable defocus (MCD) is primarily limited by confocality in point-scanning OCT, while spatially-coherent FFOCT has no such constraint and can achieve virtually infinite MCD with a proper and reasonable sampling density. This makes spatially-coherent FFOCT particularly suitable for optical coherence microscopy.

Figures (5)

• Figure 1: Diagram illustrating the interrelationship among the conceptual pupils, spots, aperture, and point spread function. $(x,y)$ and $(k_x, k_y)$ are the lateral spatial coordinates and their corresponding spatial frequencies, respectively. FT stands for Fourier transform.
• Figure 2: Configurations of (a) point-scanning OCT and (b) spatially-coherent FFOCT.
• Figure 3: Schematic diagrams of probe optics used in (a) point-scanning OCT and (b) spatially-coherent FFOCT.
• Figure 4: The phase increments per the sampling distance at the periphery of the PSF, which corresponds to Eq. (\ref{['eq:MaxPsXi']}) and Eq. (\ref{['eq:MaxScXi']}) but without absolute operations. The blue and orange curves correspond to the cases of point-scanning OCT and spatially-coherent FFOCT, respectively. The horizontal axis corresponds to the normalized defocus distance $\zeta_d$, which takes a value of $\pm 1$ when the absolute defocus distance is equal to the Rayleigh distance. The phase increments takes its maximum and minimum values when $\zeta_d$ approaches to $+\infty$ and $-\infty$, respectively. For the figure plot, we assumed $w_0$ = 3 $\muup$m.
• Figure 5: Intensity profile of the peak intensity of the refocused signal. The orange line and the red dashed line indicate the noise level and the critical defocus distance, respectively. The signal becomes observable after refocusing if the defocus distance is less than the critical defocus distance.