Metrology with a twist: probing and sensing with vortex light

Abstract

Optical metrology is a well-established subject, dating back to early interferometry techniques utilizing light's linear momentum through fringes. In recent years, significant interest has arisen in using vortex light with orbital angular momentum (OAM), where the phase twists around a singular vortex in space or time. This has expanded metrology's boundaries to encompass highly sensitive chiral interactions between light and matter, three-dimensional motion detection via linear and rotational Doppler effects, and modal approaches surpassing the resolution limit for improved profiling and quantification. The intricate structure of vortex light, combined with the integration of artificial intelligence into optical metrology, unlocks new paradigms for expanding measurement frameworks through additional degrees of freedom, offering the potential for more efficient and accurate sensing and metrological advancements. This review aims to provide a comprehensive overview of recent advances and future trends in optical metrology with structured light, specifically focusing on how utilizing vortex beams has revolutionized metrology and remote sensing, transitioning from classical to quantum approaches.

Fig. 1. Creation and detection of vortex beams.

a OAM beams are defined by their twisted wavefronts and azimuthal phase, giving rise to donut-shaped intensity patterns, illustrated here for topological charges from 0 to ±2, the sign determining the direction of the phase change. b Some examples of optical transformations for tailoring OAM beams from an input Gaussian beam, shown from left to right as a pie-shaped amplitude mask, a meta surface, a diffractive optic, and a digital hologram of a forked grating. c Phases and amplitudes can be swapped by noting that two phase-only functions can produce an amplitude-only function, shown here for the example X = 3ϕ + k_xx. d The detection of OAM is possible by running the creation in reverse for modal decomposition, requiring a hologram and an on-axis measurement in the far-field with the aid of a Fourier transforming lens, i.e., at (k_x, k_y) = (0, 0). An input OAM mode is untwisted back to a Gaussian when the SLM has the complex conjugate of the incoming mode, returning a modal spectrum (∣c_l∣²) of the initial beam, shown here for an l = 1 input mode

Fig. 2. Evolution of optical metrology capabilities.

This progression highlights the transition from utilizing basic intensity attributes to leveraging a broader spectrum of light’s physical properties, ultimately leading to the full exploitation of available data. A significant driver of this evolution is the application of vortex beams, which possess unique phase structures and OAM properties, which enhance measurement precision and resolution. Vortex beams facilitate precise micro-scale engineering, biomedical research such as advanced imaging and probing, and deep-space exploration, including improved black hole measurements through OAM, increased precision surveillance, quantum sensing, and environmental monitoring. This ongoing journey toward fully utilizing light’s physical properties promises unprecedented improvements in optical metrology’s precision, accuracy, comprehensiveness, and sensitivity

Fig. 3. OAM Doppler metrology.

Enhancing Doppler metrology with a helical phase of vortex beams, by integrating superposition, dual-frequency, time, polarization, spatial structures, and array configurations, improves signal amplitude, accuracy, and robustness while enabling rotational direction and acceleration analysis. Amplified RDE arises when opposite OAM modes interact with a rotating object. Dual-frequency vortex beams elevate Doppler signals to higher frequencies, reducing noise and enhancing rotational direction analysis. Time-frequency analysis allows dynamic monitoring of angular velocity and acceleration, while polarization and OAM within a vector RDE framework support simultaneous evaluation of velocity and direction. Exploring the spatial structure of probing beams enhances detection accuracy and efficiency for complex radial targets, and an array of superimposed optical vortex beams increases the signal amplitude and robustness against non-coaxial incidence. References given in the insets

Fig. 4. Advances in Doppler metrology.

Doppler metrology technology has evolved from assessing the 2D rotational velocity to covering 3D velocity assessment, determination of rotational direction and acceleration, geometric symmetry analysis, and detection of axis orientation. 3D velocity trajectories of particles can be analyzed by revealing both translational and rotational velocities, including helical motions. The rotational axis and direction can be determined by using dynamic structured light, dual-frequency vortex beam, or vector RDE with oppositely polarized vortex beams. Time-frequency analysis dynamically tracks rotational velocity and obtains acceleration. RDE measurements exhibit high sensitivity to geometric symmetry and rotation axes of objects, enabling analysis of geometric symmetry and determination of rotation axes. References given in the insets

Fig. 5. Applications of the rotational Doppler effect (RDE) metrology.

RDE metrology with vortex beams exhibits exceptional adaptability across various conditions, ranging from ideal to complex scenarios such as micro-object rotation detection, tiny rotations, oblique incidence, and lateral misalignment. Utilizing vortex beams with opposite-sign OAM in both reference and measurement paths, this approach accurately identifies micro displacements, the direction of micro-object rotation, and minute velocity changes. The central frequency remains stable despite variations in incident angle and lateral displacement, while the rotational Doppler signal broadens, ensuring extraction of rotational velocity even in cases of oblique incidence and lateral misalignment. References given in the insets

Fig. 6. Utilizing the OAM spectrum of probe beams for complex object assessment.

a The distinct OAM spectrum provides an additional degree of freedom and conserved quantities, facilitating high-precision measurements at micro- and nano-scale levels. Vortex light serves as an exceptionally sensitive probe. b Leveraging the OAM spectrum allows for rapid and accurate identification of geometric structures by correlating the positions of intensity minima to the object’s aperture angle and the gradient of the OAM phase spectrum to the object’s angular orientation. c Asymmetry in the OAM spectrum, induced by a moving obstructing object, directly reveals the object’s rotational and lateral motions, with phase differences in the OAM spectrum providing the determination of its rotational dynamics. References given in the insets

Fig. 7. Observation of twisted waves from the black hole Einstein ring.

a, b Normalized magnitudes of the electric field component along the observer’s direction, reconstructed through the transport of intensity equation analysis of the brightness temperature within a finite frequency bandwidth for epoch 1 and epoch 2. c, d The corresponding OAM spectrum. Adapted with permission from ref.

Fig. 8. Leveraging vortex beam propagation characteristics for enhanced environmental monitoring.

As vortex beams propagate through the atmosphere, turbulence disrupts their intensity distribution and modifies their spiral phase structure, leading to the formation of speckle patterns and the dispersion of the OAM spectrum. Analyzing these effects provides valuable insights into atmospheric properties, aiding in the retrieval of key environmental parameters. Moreover, combining two-dimensional speckle patterns with one-dimensional OAM spectrum data enables deep learning models to accurately classify and reconstruct turbulent atmospheric conditions

Fig. 9. Atmospheric parameter inversion and correction based on vortex beam speckle patterns.

a–c The influence of atmospheric turbulence (AT) on vortex beams with different OAM mode numbers (l = 2, 4) at Δz = 50 meters. a Intensity and phase distributions of undisturbed light beams. b Simulated AT equivalent phase screen. c Intensity and phase distributions of the vortex beams after disturbance. d Schematic diagram of the CNN framework used for AT compensation. Conv convolutional layer, Mp Max-pooling layer, Deconv deconvolution layer. e The simulated, predicted, and compensated phase screens under different ATs. Adapted with permission from ref.

Fig. 10. Experimental results for beam width measurement and modal coupling in two distinct turbulence regions.

a The experimental setup utilizes two longitudinally structured beams, each with narrow beam widths at 0 < z < 0.3 m and 0.3 m < z < 0.6 m, respectively. b Experimentally measured intensity and phase profiles, along with the normalized modal spectra of Beams 1 and 2, for two different turbulence cases where regions 1 and 2 have different r₀ values. Adapted with permission from ref.

Fig. 11. OAM entanglement.

a OAM entanglement is generated via Spontaneous Parametric Downconversion (SPDC) in a nonlinear crystal, where the OAM of the two SPDC photons, adding to that of the pump, l_pump = l_A + l_B, e.g., if the pump has zero OAM, then if l_A = 1 corresponds to l_B = −1, and so on, as shown in the insets. This process results in an infinite superposition state, represented by $∣\mathrm{\Psi }⟩$. b Measurement process involves a quantum version of the previously discussed modal decomposition method, typically employing holograms encoded onto SLMs, with the resulting light coupled into single-mode fibers, and the outcomes are then measured in coincidence using a coincidence counter. For OAM measurements, the holograms correspond to the standard azimuthal phases, as depicted in the insets. c Experimental validation confirms that OAM naturally forms a Schmidt basis, thereby verifying the conservation of OAM at the single-photon level

Fig. 12. Advanced applications of quantum OAM metrology.

a Enhanced precision in physical quantity measurements through OAM quantum states, achieving superior accuracy and sensitivity. b Quantum OAM metrology for advanced detection and imaging of living tissues. c Interaction of OAM beams with particles, enabling precise control and manipulation at microscopic scales. d Generation of high-resolution holography using entangled photon pairs, enhancing imaging techniques in terms of depth and clarity. e Utilization of the HOM effect for precise quantum state discrimination, advancing quantum computing and information processing capabilities. f Detailed study and characterization of complex quantum communication channels, which enhances the understanding of quantum information transfer mechanisms. References are given in the insets