Full-field-of-view aberration correction for large arrays of focused beams

TL;DR

The paper tackles the challenge of generating large, diffraction-limited arrays of focal spots over a wide field by correcting field-dependent aberrations across the full optical field. It introduces a CWGS algorithm that integrates a low-order parametric aberration model, based on modified Seidel coefficients and Zernike polynomials, with a practical measurement protocol to determine those coefficients. Demonstrated on an aspherical lens using a phase-only SLM, the method extends the aberration-free field from ~50 μm to ~500 μm and enables up to 5194 corrected spots with high Strehl ratios. The approach yields uniform, high-quality spot arrays and enables robust bottle-beam configurations, offering significant utility for optical tweezers, neutral-atom quantum processors, and advanced imaging/microscopy techniques.

Abstract

We propose and implement an aberration correction method for the creation of extended arrays of spots well beyond the isoplanatic region of any optical system. The method relies on an extensive calibration of aberrations in terms of Zernike polynomials over the full accessible field of an optical system. We introduce a modified Gerchberg-Saxton algorithm for generating holographic phase masks creating fully corrected arbitrary arrays of spots. By applying the method to an aspherical lens, and using a liquid-crystal spatial light modulator (SLM), we increase the aberration-free field of view from 50 to 500 $μ$m, only limited by the largest diffraction angles accessible to the SLM. This opens new perspectives for the generation of large arrays of optical tweezers, especially for neutral atom based quantum processors and simulators.

Figures (6)

• Figure 1: Experimental setup. A collimated input laser beam is diffracted using the SLM. We form the image of the SLM on the back focal plane of the convergent optical system of interest $\bf L$ (focal distance $f$) by using an afocal telescope in the 4f configuration. A blade $\bf B$ removes the zero-order reflection. An array of spots is formed in the focal plane of $\bf L$. We test the quality of this array by imaging with a camera using an aberration-free optical system $\bf I$noauthor_see_nodate.
• Figure 2: Spatial dependance of the aberrations. (a) First-order coma. The blue line highlights the linear dependance of $\theta_C({\bm r}))$ as a function of $|\bm r|$. Panel (b) corresponds to astigmatism and (c) to curvature. The points are measurement results, while the shaded surfaces correspond to the fits. The drop lines are the residuals of the fits. The paraboloids corresponding to astigmatism and curvature are centered at positions $(-2\mu\text{m},-3\mu\text{m})$ and $(7\mu\text{m},-18\mu\text{m})$, respectively. These values are small compared to the dimension of the corrected field. The larger values obtained for the field curvature can be explained by a small tilt between the focal plane of the aspherical lens and the the plane of the camera sensor.
• Figure 3: Images of two 34$\times$34 arrays without [WGS, panels (a-d)] and with field aberration correction [CWGS, panels (e-h)]. The six right panels are zooms onto regions of interest defined by colored squares on the corresponding left panel. Intensities are normalized to the maximum intensity of the central spot highlighted by a circle on panel (c) and (g). The insets are cross-sections along the $x$ direction of the intensity profile of the spots highlighted by a black circle in each panel. Cross-sections are centered to contain the highest-intensity pixel of the selected spot.
• Figure 4: Performance of the aberration correction procedure. (a) Spatial variation of the larger waist of spots, determined by Gaussian fits before (left) and after (center) applying field correction. In both cases, the global correction mask $\phi_0$ corrects aberrations on the optical axis. Right panel: histogram of larger-waist distribution before (blue) and after correction (green). The vertical dotted line corresponds to the expected diffraction-limited waist. (b-d) Similar representations of the ellipticity (b), of the orientation of the major axis of spots (c) and of the Strehl ratio of the spots (d). For the two left panels of (c) we represent the orientation of the major axis of ellipses relative to the $x$ axis. The right panel of (c) represents the histogram of the orientation of the major axis of ellipses relative to a radial axis.
• Figure 5: Performance of the aberration correction as a function of the field size for a number of spots ranging from 121 to 5184. Lines connecting data points are a guide to the eyes. For each number of spots the smallest array corresponds to $d=5\,\mu$m. For the largest number of spots $d$ ranges from 5 to 7 $\mu$m. (a), (b) and (c) present the variation of the average value of the Strehl ratio $\bar{S}$, maximum waist $\bar{w}_{\mathrm{max}}$ and background intensity $\bar{I}_{\mathrm{back}}$ respectively. The latter is normalized to the maximum intensity of the central spot highlighted by a circle on fig. \ref{['Fig2']}(g). A red dotted line connects the datapoints with $d=5\,\mu$m.