Inferring the solution space of microscope objective lenses using deep learning.

Lens design extrapolation (LDE) is a data-driven approach to optical design that aims to generate new optical systems inspired by reference designs. Here, we build on a deep learning-enabled LDE framework with the aim of generating a significant variety of microscope objective lenses (MOLs) that are similar in structure to the reference MOLs, but with varied sequences-defined as a particular arrangement of glass elements, air gaps, and aperture stop placement. We first formulate LDE as a one-to-many problem-specifically, generating varied lenses for any set of specifications and lens sequence. Next, by quantifying the structure of a MOL from the slopes of its marginal ray, we improve the training objective to capture the structures of the reference MOLs (e.g., Double-Gauss, Lister, retrofocus, etc.). From only 34 reference MOLs, we generate designs across 7432 lens sequences and show that the inferred designs accurately capture the structural diversity and performance of the dataset. Our contribution answers two current challenges of the LDE framework: incorporating a meaningful one-to-many mapping, and successfully extrapolating to lens sequences unseen in the dataset-a problem much harder than the one of extrapolating to new specifications.

Deep learning-enabled framework for automatic lens design starting point generation.

We present a simple, highly modular deep neural network (DNN) framework to address the problem of automatically inferring lens design starting points tailored to the desired specifications. In contrast to previous work, our model can handle various and complex lens structures suitable for real-world problems such as Cooke Triplets or Double Gauss lenses. Our successfully trained dynamic model can infer lens designs with realistic glass materials whose optical performance compares favorably to reference designs from the literature on 80 different lens structures. Using our trained model as a backbone, we make available to the community a web application that outputs a selection of varied, high-quality starting points directly from the desired specifications, which we believe will complement any lens designer's toolbox.

Extrapolating from lens design databases using deep learning.

We propose for the first time a deep learning approach in assisting lens designers to find a lens design starting point. Using machine learning, lens design databases can be expanded in a continuous way to produce high-quality starting points from various optical specifications. A deep neural network (DNN) is trained to reproduce known forms of design (supervised training) and to jointly optimize the optical performance (unsupervised training) for generalization. In this work, the DNN infers high-performance cemented and air-spaced doublets that are tailored to diverse desired specifications after being fed with reference designs from the literature. The framework can be extended to lens systems with more optical surfaces.

System matrix computation vs storage on GPU: A comparative study in cone beam CT.

PURPOSE: Iterative reconstruction algorithms in computed tomography (CT) require a fast method for computing the intersection distances between the trajectories of photons and the object, also called ray tracing or system matrix computation. This work focused on the thin-ray model is aimed at comparing different system matrix handling strategies using graphical processing units (GPUs). METHODS: In this work, the system matrix is modeled by thin rays intersecting a regular grid of box-shaped voxels, known to be an accurate representation of the forward projection operator in CT. However, an uncompressed system matrix exceeds the random access memory (RAM) capacities of typical computers by one order of magnitude or more. Considering the RAM limitations of GPU hardware, several system matrix handling methods were compared: full storage of a compressed system matrix, on-the-fly computation of its coefficients, and partial storage of the system matrix with partial on-the-fly computation. These methods were tested on geometries mimicking a cone beam CT (CBCT) acquisition of a human head. Execution times of three routines of interest were compared: forward projection, backprojection, and ordered-subsets convex (OSC) iteration. RESULTS: A fully stored system matrix yielded the shortest backprojection and OSC iteration times, with a 1.52× acceleration for OSC when compared to the on-the-fly approach. Nevertheless, the maximum problem size was bound by the available GPU RAM and geometrical symmetries. On-the-fly coefficient computation did not require symmetries and was shown to be the fastest for forward projection. It also offered reasonable execution times of about 176.4 ms per view per OSC iteration for a detector of 512 × 448 pixels and a volume of 3843 voxels, using commodity GPU hardware. Partial system matrix storage has shown a performance similar to the on-the-fly approach, while still relying on symmetries. CONCLUSION: Partial system matrix storage was shown to yield the lowest relative performance. On-the-fly ray tracing was shown to be the most flexible method, yielding reasonable execution times. A fully stored system matrix allowed for the lowest backprojection and OSC iteration times and may be of interest for certain performance-oriented applications.