Adaptive In-Situ Aberration Correction Using Orbital Dynamics of Trapped Microparticles in LG Beams

High-resolution optical microscopy and optical tweezers have transformed how we explore the microscopic world and enabled unprecedented wealth of knowledge into everything from cellular systems to colloidal particles. At the heart of these tools is our ability to finely control and focus beams of light through intricate optical setups, often involving high-numerical-aperture objective lenses. But even the most precisely manufactured lenses aren’t perfect. They inevitably introduce small optical aberrations that can compromise image clarity and reduce the effectiveness of optical traps. These imperfections may arise from minor flaws in lens fabrication, misalignments during assembly, or mismatches in refractive indices along the light path. For systems operating at sub-micrometer precision, such aberrations, though small, can be surprisingly impactful—and correcting them remains a stubborn challenge in optical engineering. Conventional strategies for addressing this issue typically rely on far-field wavefront sensing tools, such as Shack-Hartmann sensors or interferometric techniques. While these approaches can be effective under many conditions, they start to falter when applied to high-NA systems where the vector nature of light becomes significant. The problem becomes even more pronounced when working with structured light fields like Laguerre-Gaussian (LG) beams, which carry orbital angular momentum. These beams, with their signature “donut-shaped” intensity profile, are widely used for rotating microscopic particles or performing high-precision manipulations. However, they’re also highly susceptible to wavefront distortions—aberrations can easily warp their structure and undermine their functionality.

To address these shortcomings, new research paper published in Optics Express and conducted by Mr. Tomoko Otsu-Hyodo, Mr. Yoshiyuki Ohtake and Dr. Taro Ando from the Hamamatsu Photonics K.K. in Japan, explored a new path and instead of relying solely on traditional sensing methods or indirect reconstructions of the wavefront, they focused on something more immediate and intuitive: the physical behavior of matter under light. Specifically, they proposed that by observing the motion of a single colloidal microsphere—trapped and rotated by an LG beam—they could infer the presence and nature of optical aberrations in real time. If the beam’s wavefront were pristine, the particle should exhibit smooth, circular motion. Any asymmetry or irregularity in its orbit would signal a deviation in the optical field.

The researchers hypothesized that when a tiny bead is trapped and rotated by LG beam, the exact shape of its orbit would be highly sensitive to any distortions in the light field. To explore this, they built a holographic optical tweezers system integrated into a conventional inverted microscope. Using a continuous-wave laser at 1064 nm, they generated LG beams with an azimuthal order of l=2. This choice struck a careful balance: low enough to be responsive to minor aberrations, but stable enough to maintain a clean, circular orbit. A spatial light modulator (SLM) played a key role in the setup, simultaneously sculpting the LG beam and encoding phase corrections needed to fine-tune the wavefront. Into this carefully engineered beam path, the team introduced polystyrene spheres with a radius of 0.2 microns. These were suspended in ultra-pure water inside a flow cell made of two glass coverslips, separated by a spacer. Once inside the beam, the spheres began to revolve under the influence of the beam’s optical torque in midwater, forming visible circular paths—or at least they should have, if the optics were perfect.
What they observed aligned perfectly with their intuition. If the beam was free from aberrations, the trapped particle followed a near-perfect circular trajectory, however, when wavefront errors were present, the orbit deformed. It became elliptical or showed irregular angular speeds. The authors used high-speed imaging at over 6,000 frames per second to track the motion of the sphere in great detail. From these recordings, they calculated two key metrics: orbit ellipticity (to capture deviations from circularity) and angular position variance (which measured how consistently the particle moved around the beam’s center). To correct the beam, they applied an optimization algorithm built around Zernike polynomials—a mathematical tool commonly used to model and correct optical aberrations. They focused on 16 specific Zernike terms, intentionally excluding piston, tilt, and spherical aberrations since these would either shift the beam or fall outside the sensitivity of their method. Through a simple yet effective linear search, they scanned for the set of coefficients that would minimize the cost function, based on the shape and symmetry of the particle’s orbit. While this process involved several iterations and took time to converge, it proved surprisingly precise. In some cases, the corrections they achieved addressed aberrations as subtle as 0.01λ—distortions so fine that traditional optical techniques would have trouble even detecting them. Moreover, the authors applied the new method across several objective lenses that were supposedly identical with each carrying the same product code. Surprisingly, they found no two lenses behaved the same and indeed each one had its own unique pattern of aberrations, like a fingerprint. Not only could the researchers enhance the beam quality for each lens, but they could also use the correction profiles to distinguish one lens from another. This finding suggests that small variations in manufacturing—often considered negligible—can translate into real differences in optical performance. Thanks to their approach, these differences are now both measurable and correctable. Furthermore, the research team evaluated the broader applicability of their method to different types of lenses and found that plan-fluorite objectives, they consistently observed marked improvements in angular uniformity. Even when the ellipticity remained relatively unchanged, the circular symmetry and steadiness of the particle’s motion improved noticeably. When they turned to achromatic lenses—known to suffer from more pronounced aberrations—the results were even more dramatic. The angular variance dropped effectively leveling the playing field between these lower-cost lenses and their more corrected counterparts.

Perhaps the most compelling aspect of this work was the method’s ability to detect and correct higher-order aberrations—such as trefoil, tetrafoil, and even pentafoil components. These types of aberrations are often overlooked or left uncorrected by conventional systems, which tend to focus on more dominant, lower-order terms. Yet, through the subtle nuances in the particle’s orbital behavior, the team could tease out these complex distortions and account for them during correction. When they compared their results to measurements taken using a Shack-Hartmann wavefront sensor placed at the objective lens’s entrance pupil, they found that their particle-based method offered a richer and more detailed picture of the focal region’s optical field.

Now, from a practical point of view, the impact of this method is significant. In setups using high-resolution optical tweezers, even a tiny distortion in the beam can mess with how well particles are held in place or how forces are applied. What this approach offers is a way to fix those problems in real time, right there in the experiment, without needing to take apart the equipment or bolt on any extra wavefront sensors. It is simple, flexible, and it works across a variety of lenses and sample types. This is not just about fixing tweezers, either. Structured light, like LG beams, plays a role in all sorts of areas—quantum optics, high-speed communications, cutting-edge microscopy. But these beams are touchy. Small aberrations can break their symmetry or mess up their focus. What the researchers have done here helps keep those beams clean and sharp right where it matters most. Additionally, there is also something forward-thinking in the way they have managed to highlight subtle differences between lenses that are supposed to be identical. Turns out, no two lenses are exactly the same. By creating a kind of optical fingerprint for each one, the method opens the door to tuning each lens individually. That is a big deal for experiments where you need everything to be just right, like in super-resolution imaging or precise laser writing.