Towards efficient structure prediction and pre-compensation in multi-photon lithography

Microscale 3D printing technologies have been of increasing interest in industry and research for several years. Unfortunately, the fabricated structures always deviate from the respective expectations, often caused by the physico-chemical properties during and after the printing process. Here, we show first steps towards a simple, fast and easy to implement algorithm to predict the final structure topography for multi-photon lithography - also known as Direct Laser Writing (DLW). The three main steps of DLW, (i) exposure of a photo resin, (ii) cross-linking of the resin, and (iii) subsequent shrinkage are approximated by mathematical operations, showing promising results in coincidence with experimental observations. E.g., the root-mean-square error (rmse) between the unmodified 3D print of a radial-symmetrically chirped topography and our predicted topography is only 0.46 $\mu$m, whereas the rmse between this 3D print and its target is 1.49 $\mu$m. Thus, our robust predictions can be used prior to the printing process to minimize undesired deviations between the target structure and the final 3D printed structure. Using a Downhill-Simplex algorithm for identifying the optimal prediction parameters, we were able to reduce the rmse from 4.04 $\mu$m to 0.33 $\mu$m by only two correction loops in our best-case scenario (rmse = 0.72 $\mu$m after one loop). Consequently, this approach can eliminate the need for many structural optimization loops to produce highly conformal and high quality micro structures in the future.