Super-resolution imaging of azimuthal features with illumination carrying OAM

TL;DR

The paper addresses surpassing the Rayleigh resolution limit by structuring illumination in the azimuthal coordinate with orbital angular momentum (OAM) to resolve azimuthal features. It develops a theoretical framework and validates it experimentally on azimuthal objects like an azimuthal double-slit and a Siemens star, revealing an optimal OAM mode index $l_{opt}$ that maximizes contrast or minimizes the CRLB for a given angular separation $2\theta_0$; specifically, $l_{opt}=\frac{(2n+1)\pi}{2\theta_0}$. The work shows that azimuthal features can be super-resolved with OAM illumination, while non-azimuthal features may not benefit, and that a rigorous metric (Fisher Information and CRLB) confirms the optimal $l$ (e.g., $l=10$ for $2\theta_0=0.1\pi$). These findings offer a practical route to image azimuthal structures with enhanced resolution, with potential implications for biological objects exhibiting predominantly azimuthal features, such as centrosomes. The study integrates analytical derivations, simulations, and experiments to establish a principled link between OAM structure and azimuthal super-resolution.

Abstract

Super-resolution imaging refers to imaging techniques that surpass the Rayleigh resolution limit. One standard way to achieve super-resolution is by structuring the phase of the field illuminating the object. Although super-resolution techniques are already employed in commercial imaging devices, intense research efforts continue to enhance the resolution even further. In this work, we show that if the field illuminating the object is structured in the azimuthal coordinate--such as a field carrying orbital angular momentum (OAM)--the azimuthal features of the object can be imaged with enhanced imaging resolution. We experimentally demonstrate it with two objects, namely, an azimuthal double-slit and a Siemens star. We find that for a given azimuthal feature, there is an optimum OAM mode index of the illumination that gives the best imaging resolution. Super-resolution imaging of azimuthal feature can have important implications, especially for some biological objects that are known to have predominantly azimuthal features.

Figures (7)

• Figure 1: Illustrating how structuring the wavefront of the illumination in a particular coordinate helps super-resolve the object features in that coordinate. The object present in (a), (b), and (e) is in the form of a transverse double-slit, with two slits in both $x$- and $y$-directions. The slit-width and slit-separation of the object is $0.0625$ mm and $0.125$ mm, respectively. The object present in (c), (d), and (f) is an azimuthal double-slit, with the angular slit width being $0.02\pi$ and the angular slit separation being $0.1\pi$. The focal length of the lens is $400$ mm. For each sub-figure, we have explicitly shown the transmission function of the object at $z=0$ and the corresponding image-plane intensity at $z=4f$ calculated numerically using Eq. (\ref{['I4f']}).
• Figure 2: (a) Schematic of the experimental setup. (b) The azimuthal-double-slit object. (c) The Siemens star object. For the objects shown in (b) and (c), the angular slit width is $0.02\pi$ and the angular slit separation is $0.1\pi$. SF: spatial filter, SLM: spatial light modulator, A: aperture, L: lens, M: mirror.
• Figure 3: Experimental results. (a) Image intensity $I(r, \theta, z=4f)$ of the azimuthal-double-slit object shown in Fig. \ref{['fig2']}(b) for various OAM mode index $l$ of the illumination. (b) The plot of the radially averaged intensity $I(\theta)$, defined in Eq. (\ref{['avg-Int']}), as a function of $\theta$ for various plots shown in (a). The visibility $V$ of the intensity pattern $I(\theta)$ is indicated on each plot.
• Figure 4: Experimental results. (a) Image intensity $I(r, \theta, z=4f)$ of the Siemens star object shown in Fig. \ref{['fig2']}(c) for various OAM mode index $l$ of the illumination. (b) The plot of the radially averaged intensity $I(\theta)$, defined in Eq. (\ref{['avg-Int']}), as a function of $\theta$ for various plots shown in (a). The visibility $V$ of the intensity pattern $I(\theta)$ and the Cramér–Rao Lower Bound $C$ are indicated on each plot.
• Figure 5: Schematic of a setup to image an object using a $2f-2f$ imaging system.