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J. Eur. Opt. Society-Rapid Publ. 21, 17( 2025)
Figure 8. Example measurements of the beam shaping results with an LCoS-SLM. Left: The LCoS-SLM is modelled as an ideal phase mask but effects like pixel crosstalk lead to deviations in the displayed phase mask with a corresponding deterioration in the final intensity distribution. Right: Pixel crosstalk, astigmatism and a partial reflection at the cover glass of the LCoS-SLM are considered with a DNN and compensated for in the calculation of the phase mask. conjugate to that focal plane. While this simplifies the implementation and calculation of the wave-optical propagation between phase mask and target plane, it often leads to suboptimal choices of optical systems for a given beam shaping task.
The iterative wave-optical propagation algorithm( IWPA) is an adaptation of the IFTA that keeps the iterative structure of the IFTA but simulates the( inverse) waveoptical propagation of light through an arbitrary optical system. One advantage of the IWPA is the possibility to freely position the target plane for laser beam shaping, thus eliminating the restriction to the focal plane of a focusing lens imposed by the IFTA. We also demonstrate the use of the IWPA for laser beam shaping with subsequent amplification based on the ability of the IWPA to consider non-linear effects in the optical system. Additionally, we present an approach to calculate phase masks that minimize the deviation from a target temperature distribution in a work piece by coupling the IWPA with a solver for the inverse heat conduction problem.
Diffractive neural networks are a physical representation of artificial neural networks and enable the use of established machine-learning approaches for high fidelity laser beam shaping. DNNs enable to design an optical system with two or more phase masks for full amplitude and phase control of the laser beam. This allows for the direct optimization of 3D light fields and for phase mask design that is robust against changes of the input beam or misalignments in the optical system. DNNs also enable phase mask design that compensates for properties of the chosen beam shaping element like pixel crosstalk in liquid crystal on silicon spatial light modulators.
When selecting a suitable optical system and a phase retrieval algorithm for a specific beam shaping task, all alternatives should therefore be considered and weighed against each other. IFTA-based approaches offer relatively easy integration combined with strict limitations regarding the optical system and often limited achievable quality of the beam shaping results. Approaches like the here presented IWPA and DNN require additional effort in their implementation compared to an IFTA, but offer a higher flexibility in terms of suitable optical systems and often enable a higher fidelity in the achievable beam shaping results.
Funding
The presented work was funded by the Deutsche Forschungsgemeinschaft( DFG, German Research Foundation) – LO 640 / 20-1, 387868000, and EXC-2023 Internet of Production- 390621612. Oskar Hofmann was part of the Max Planck School of Photonics supported by BMBF, Max Planck Society, and Fraunhofer Society. This research was completed within the European Union project METAMORPHA. The METAMORPHA project has received funding from Horizon Europe, the European Union’ s Framework Programme for Research and Innovation, under grant agreement 101057457. Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union. The European Union cannot be held responsible for them.
Conflicts of interest The authors have nothing to disclose.
Data availability statement
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Author contribution statement
Conceptualization, O. H.; Methodology, O. H., P. B., R. K., A. B. and C. H.; Software, O. H., P. B., R. K., and A. B.; Validation, O. H., P. B. and R. K.; Formal Analysis, O. H., P. B., R. K., A. B. and C. H.; Investigation, O. H., P. B. and R. K.; Resources, A. B. and C. H.; Data Curation, O. H., P. B. and R. K.; Writing – Original Draft Preparation, O. H.; Writing – Review & Editing, P. B., R. K., A. B. and C. H.; Visualization, O. H. and P. B.; Supervision, O. H., A. B. and C. H.; Project Administration, O. H., A. B. and C. H.; Funding Acquisition, O. H., A. B. and C. H.