Correcting astigmatism and ellipticity in Gaussian beams using a cylindrical lens pair with tunable focal lengths
Bibliographic record
Abstract
Correcting astigmatism and ellipticity in laser beams is critical for improving performance in many applications like microscopy, atomic physics, quantum information processing, and advanced manufacturing. Passive correction methods based on cylindrical lens telescopes require choosing lenses with precise focal lengths, effectively limiting the range of tunability when using standard catalog optics. Active solutions based on diffractive optical elements can achieve superior performance and dynamic response, but they are bulky, expensive, and suffer from finite diffraction efficiency and added complexity. Here, we introduce a simple method to convert astigmatic elliptical beams into circular Gaussian beams without astigmatism. Our method comprises three cylindrical lenses. The first lens focuses the beam along its major axis to create a plane where the intensity profile is radially symmetric. The second and third lenses are placed one behind the other in that plane at a relative angle, acting as a biaxial lens pair with tunable focal lengths. By adjusting the relative angle of the lenses, the two separate beam waists of the astigmatic beam can be overlapped, resulting in a circular Gaussian beam without astigmatism. We theoretically validate our method, numerically quantify its robustness to experimental imperfections, and experimentally demonstrate its ability to circularize the output beam of a commercial laser source. Compared to SLM-based approaches, our design is significantly more compact and cost-effective, with component prices comparable to standard lenses and dimensions suitable for integration into tabletop optical paths. Its performance is ultimately limited by the validity of the paraxial approximation (breaking down for beam sizes comparable to the wavelength), the finite inter-lens distance between the second and third lenses, and the inability of cylindrical lenses to address higher-order aberrations. Its simple and compact design makes it well-suited for both laboratory and industrial optical systems.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".