Measuring the translational and rotational velocities of particles in helical motion using structured light

Detection of a spinning object using a superimposed optical vortex array

The optical vortex (OV) carries unique orbital angular momentum (OAM) and experiences a Doppler frequency shift when backscattered from a spinning object. This rotational Doppler effect (RDE) has provided a solution for the non-contact detection of rotating motion. The reported RDE researches mainly use a single OV that generates frequency shifts proportional to its topological charge and has low robustness to light incidence. Here, we show the distinctive RDE of superimposed optical vortex array (SOVA). We analyze the holistic OAM of SOVA which is represented in terms of a superposition of azimuthal harmonics and displays a unique modal gathering effect. In the experiment of RDE, the frequency shift signals of SOVA show a precise mapping to the OAM modes and the modal gathering effect contributes to enhance the amplitude of signals, which has the potential to enhance robustness against non-coaxial incidence. This finding provides a new aspect of RDE and a pioneered example for introducing various SOVAs into rotation detection.

Rotational Doppler Effect in Vortex Light and Its Applications for Detection of the Rotational Motion

The linear Doppler effect has been widely used to detect the translational motion of objects. However, it suffers difficulties in measuring the angular motion of a rotating target. In recent years, the rotational Doppler effect based on a vortex beam has been helpful to solve the problem of rotational measurement and has attracted extensive attention in remote sensing. This paper expounds the theoretical and experimental basis of the rotational Doppler effect and briefly summarizes its development for the detection of macro and micro targets. Specifically, the properties and analysis methods of a rotational Doppler shift when the vortex beam is misaligned with the rotation axis are described in detail. In addition, the existing problems and further developments in rotation detection based on the rotational Doppler effect are discussed.

Orbital angular momentum-based dual-comb interferometer for ranging and rotation sensing

We present a dual-comb interferometer capable of measuring both the range to a target as well as the target's transverse rotation rate. Measurement of the transverse rotation of the target is achieved by preparing the probe comb with orbital angular momentum and measuring the resultant phase shift between interferograms, which arises from the rotational Doppler shift. The distance to the target is measured simultaneously by measuring the time-of-flight delay between the target and reference interferogram centerbursts. With 40 ms of averaging, we measure rotation rates up to 313 Hz with a precision reaching 1 Hz. Distances are measured with an ambiguity range of 75 cm and with a precision of 5.9 µm for rotating targets and 400 nm for a static target. This is the first dual-comb ranging system capable of measuring transverse rotation of a target. This technique has many potential terrestrial and space-based applications for lidar and remote sensing systems.

Rotational object detection at noncoaxial light incidence based on the rotational Doppler effect

The rotational Doppler effect (RDE) of optical vortex which can be used to detect the rotation speed, has become a well-known phenomenon and a hot topic of research in recent years. However, because the beam axis must be coaxial with the rotational axis of the object, it can only be used to detect cooperative targets in practical application. Here, we provide a novel approach for measuring rotational speed under light non-coaxial incidence relative to the rotating axis that uses the adjacent frequency difference of rotational Doppler shift signals. Theoretically, the rotational Doppler shift is proportional to the OAM mode of the incident beam, and the nature of the OAM carried by each photon is a discrete or quantized quantity under off-axis conditions leading to the discrete distribution of the Doppler shift signals. Experimentally, by extracting the difference between two adjacent Doppler shift signals, the rotating speed of the object can be determined. Based on our method, the rotational speed of the object can be measured precisely without the pre-known information about the position of the rotating axis. Our work supplies a significant complement to the conventional RDE theory and we believe it may promote the realistic application of the optical RDE-based metrology.

Detection of a spinning object with circular procession using an optical vortex beam

The rotational Doppler effect (RDE) provides an efficient way to measure rotational frequency using an optical vortex beam. Crucially, most research based on the RDE just involves a spinning object or a spinning object coupled with a longitudinal velocity along the beam propagation. We analyze the interaction mechanism between optical orbital angular momentum and a spinning object with circular procession and experimentally demonstrate simultaneous measurements of two rotational frequencies. This technique broadens application of the RDE in optical metrology and remote detection of targets with micro-motions.

Locating the center of rotation of a planar object using an optical vortex

The rotational Doppler effect (RDE) of optical vortex beams provides an efficient way to measure the rotational frequency of objects based on rotational Doppler frequency shifts, while the frequency shift signals display a distinct broadening effect when the vortex beam is laterally misaligned with the center of rotation of a planar object. We use a modal decomposition method to reveal the broadening effect and obtain a linear fitting equation between the quantity of signals and lateral misalignments. In an experiment of RDE, the lateral misalignment is extracted from the quantity of signal peaks. The fitting equation is proved to be precise within the uncertainty of ±0.17mm (±2.8% of the vortex beam radius), and the center of rotation is located with an error less than 3.33% of the beam radius. Our work provides a new approach to locate the center of rotation of noncooperative objects, which may be valuable in mechanical manufacturing and optical noncontact metrology.

Vectorial Doppler metrology

The Doppler effect is a universal wave phenomenon that has spurred a myriad of applications. In early manifestations, it was implemented by interference with a reference wave to infer linear velocities along the direction of motion, and more recently lateral and angular velocities using scalar phase structured light. A consequence of the scalar wave approach is that it is technically challenging to directly deduce the motion direction of moving targets. Here we overcome this challenge using vectorially structured light with spatially variant polarization, allowing the velocity and motion direction of a moving particle to be fully determined. Using what we call a vectorial Doppler effect, we conduct a proof of principle experiment and successfully measure the rotational velocity (magnitude and direction) of a moving isotropic particle. The instantaneous position of the moving particle is also tracked under the conditions of knowing its starting position and continuous tracking. Additionally, we discuss its applicability to anisotropic particle detection, and show its potential to distinguish the rotation and spin of the anisotropic particle and measure its rotational velocity and spin speed (magnitude and direction). Our demonstration opens the path to vectorial Doppler metrology for detection of universal motion vectors with vectorially structured light.

Analysis of misaligned optical rotational Doppler effect by modal decomposition

The optical rotational Doppler effect (RDE) is closely related to the unique orbital angular momentum (OAM) carried by optical vortex, whose topological charge means the mode of OAM. Compared with the coaxial incidence, the rotational Doppler frequency shift spectrum of a misaligned optical vortex (misaligned RDE) widens according to a certain law. In this paper, an OAM modal decomposition method of the misaligned optical RDE is proposed and the relative intensity of different OAM modes, namely the OAM spectrum, is derived based on an inner product computation. Analyses show that lateral displacements and angular deflections change the distribution of OAM modes relative to the rotation axis of the object. A misaligned Laguerre-Gaussian (LG) vortex can be represented as a specific combination of coaxial LG modes, and the difference between the topological charge of two adjacent modes is 1 or 2 with lateral displacements or angular deflections respectively. An experiment of misaligned optical RDE using a superimposed LG vortex is executed, and the obtained frequency shift spectrum with misaligned incidence expands into a set of discrete signals, which agrees well with the theoretical results. Moreover, we can get the rotation frequency of the object from an expanded frequency spectrum more quickly and accurately based on the difference between two adjacent signal peaks. The proposed method contributes to analyze the misaligned optical RDE comprehensively, which is significant in remote sensing and optical metrology.

Angular velocimetry for fluid flows: an optical sensor using structured light and machine learning

Most velocimetry approaches for fluid flows measure linear components of the velocity vector; yet, the angular velocity components, particularly at small scales in turbulent flows, also need to be resolved to study energy transfer and other important flow characteristics. Here, we detail an optical sensor approach to determine a component of the angular velocity vector. This approach uses beams of structured light and a machine learning-based analysis. We discuss the methodology to train the machine learning model and test it in experimentally validated simulations. This approach represents an interesting new direction for fluid flow velocimetry which may be extended to sense other flow parameters by selecting different light structures.

Direction-sensitive detection of a spinning object using dual-frequency vortex light

Rotational Doppler effect (RDE) has attracted much attention in recent years which opens new avenues to angular velocity measurement. However, most previous studies used single-frequency vortex light as the detection beam so that the rotational Doppler signal is in the low frequency domain where most of noise signals exist. In this article, we use the dual-frequency 2-fold multiplexed vortex light as the probe beam and transform the Doppler signals from the low frequency domain to the high frequency domain successfully. The results show hardly any noise compared with the measurement in the low frequency domain. More importantly, the direction of rotation can be obtained directly by comparing the modulated signal and the reference signal. Our work demonstrates a new detection method for the RDE and provides a reference for its practical application.

Observation of the rotational Doppler shift with spatially incoherent light

The rotational Doppler shift (RDS) is typically measured by illuminating a rotating target with a laser prepared in a simple, known orbital angular momentum (OAM) superposition. We establish theoretically and experimentally that detecting the rotational Doppler shift does not require the incident light to have a well-defined OAM spectrum but instead requires well-defined correlations within the OAM spectrum. We demonstrate measurement of the rotational Doppler shift using spatially incoherent light.

Detection of spinning objects at oblique light incidence using the optical rotational Doppler effect

The optical rotational Doppler effect of light beams with angular momentum has recently found applications in the remote sensing of spinning objects. However, most of the reported experimental demonstrations rely on the particular condition of normal incidence, while the general case of oblique incidence has not been addressed yet. Herein, we investigate the optical rotational Doppler effect at oblique incidence based on a local scattering model and formulate the quantitative relation between the Doppler frequency shift and the tilt angle. The analytic results indicate that even if the rotational axis of the spinning object is oriented at a specific tilt angle relative to the light propagation direction, the rotational speed can still be extracted from an asymmetrically broadened Doppler signal. The geometric mean value of the extreme frequency shift is a constant despite the variation of the incident angle. An experiment with obliquely incident and superimposed optical vortices is executed to verify our theoretical predictions, achieving a successful detection of the rotational speed at relatively large tilt angles with a relative error less than 2%. The scheme proposed in this study may be useful for practical applications of rotational Doppler effect in remote sensing and metrology.

In situ detection of a cooperative target's longitudinal and angular speed using structured light

Laser remote sensing represents a powerful tool that enables the accurate measurement of the speed of moving targets. Crucially, most sensing techniques are two-dimensional (2D) and only enable direct determination of the speed along the line of sight. Here we put forward a novel three-dimensional technique that enables the direct and simultaneous measurement of both the longitudinal and angular speed of cooperative targets. This technique is based on the use of complex vector light beams, whose polarization and spatial degree of freedom are coupled in a non-separable way. We present evidence of our technique by performing a proof-of-principle experiment.

OAM interferometry: the detection of the rotational Doppler shift

In this paper, we propose a new type of rotational Doppler shift measurement based on the OAM of light which is capable of measuring the rotation of a point source in the plane orthogonal to the observer line of sight. By analysing the correlations between OAM states of light emitted by rotating sources, the rotational Doppler shift, and hence the rate of rotation, can be measured. We demonstrate that an OAM interferometer capable of extracting the rotational Doppler shift from OAM correlations can be constructed from a standard OAM modesorter combined with a phase filter.

Direction-sensitive transverse velocity measurement by phase-modulated structured light beams

The use of structured light beams to detect the velocity of targets moving perpendicularly to the beam's propagation axis opens new avenues for remote sensing of moving objects. However, determining the direction of motion is still a challenge because detection is usually done by means of an interferometric setup, which only provides an absolute value of the frequency shift. In this Letter, we present a novel method that addresses this issue. It uses dynamic control of the phase in the transverse plane of the structured light beam so that the direction of the particles' movement can be deduced. This is done by noting the change in the magnitude of the frequency shift as the transverse phase of the structured light is moved appropriately. We demonstrate our method with rotating microparticles that are illuminated by a Laguerre-Gaussian beam with a rotating phase about its propagation axis. Our method, which only requires a dynamically configurable optical beam generator, can easily be used with other types of motion by appropriate engineering and dynamic modulation of the phase of the light beam.