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We report the experimental demonstration of an optical differentiation wavefront sensor (ODWS) based on binary pixelated linear and nonlinear amplitude filtering in the far-field. We trained and tested a convolutional neural network that reconstructs the spatial phase map from nonlinear-filter-based ODWS data for which an analytic reconstruction algorithm is not available. It shows accurate zonal retrieval over different magnitudes of wavefronts and on randomly shaped wavefronts. This work paves the way for the implementation of simultaneously sensitive, high dynamic range, and high-resolution wavefront sensing.

 

We present a new, to the best of our knowledge, experimental method for assessing sub-micron level subsurface damage (SSD) on optical glass. The method correlates surface characteristics such as the fracture toughness and Young’s modulus via nanoindentation with the penetration depth into the tested surfaces at different overall penetration depths, as revealed by magnetorheological finishing spotting techniques. Our results on ground surfaces suggest that low surface roughness does not necessarily imply the absence of SSD. We also compared SSD on surfaces processed by deterministic microgrinding and femtosecond (fs) laser polishing. The fs-laser polished surfaces revealed no detectable SSD, thus establishing the feasibility of fs-laser polishing for precision optical manufacturing.

 

We demonstrate simultaneous figuring and surface finishing of glass using a femtosecond laser. For the first time, to the best of our knowledge, we have achieved deterministic material removal with nanometer precision and maintained sub-nanometer surface roughness without inducing any mid-spatial-frequency errors to the initial surface. A dynamic pulse propagation model is established to predict the interaction process, including plasma generation and surface temperature. The interactive modeling and the experiments enable the selection of a set of laser parameters to achieve controllable optical figuring and finishing. This demonstration shows the potential for using femtosecond lasers for advanced freeform optic forming, finishing, and reduction of detrimental mid-spatial-frequency errors, and laser-ablation-based patterning used for fabrication of integrated photonics and lasers.

 

An important problem across multiple disciplines is to infer and understand meaningful latent variables. One strategy commonly used is to model the measured variables in terms of the latent variables under suitable assumptions on the connectivity from the latents to the measured (known as measurement model). Furthermore, it might be even more interesting to discover the causal relations among the latent variables (known as structural model). Recently, some methods have been proposed to estimate the structural model by assuming that the noise terms in the measured and latent variables are non-Gaussian. However, they are not suitable when some of the noise terms become Gaussian. To bridge this gap, we investigate the problem of identification of the structural model with arbitrary noise distributions. We provide necessary and sufficient condition under which the structural model is identifiable: it is identifiable iff for each pair of adjacent latent variables Lx, Ly, (1) at least one of Lx and Ly has non-Gaussian noise, or (2) at least one of them has a non-Gaussian ancestor and is not d-separated from the non-Gaussian component of this ancestor by the common causes of Lx and Ly. This identifiability result relaxes the non-Gaussianity requirements to only a (hopefully small) subset of variables, and accordingly elegantly extends the application scope of the structural model. Based on the above identifiability result, we further propose a practical algorithm to learn the structural model. We verify the correctness of the identifiability result and the effectiveness of the proposed method through empirical studies. 

We report an Optical Differentiation Wavefront Sensor based on a telephoto lens system and binary pixelated filters. It provides a five-fold reduction in the system length compared to a 4fsystem with identical effective focal length. Measurements of phase plates with this system are compared to measurements performed with a commercial low-coherence interferometer. The telephoto-lens-based system can measure wavefronts with accuracy better thanλ/10 Root Mean Squared (RMS) atλ=633 nm. Experimental investigation shows that the system has a high tolerance to components alignment errors.

 

Identification of causal direction between a causal-effect pair from observed data has recently attracted much attention. Various methods based on functional causal models have been proposed to solve this problem, by assuming the causal process satisfies some (structural) constraints and showing that the reverse direction violates such constraints. The nonlinear additive noise model has been demonstrated to be effective for this purpose, but the model class is not transitive--even if each direct causal relation follows this model, indirect causal influences, which result from omitted intermediate causal variables and are frequently encountered in practice, do not necessarily follow the model constraints; as a consequence, the nonlinear additive noise model may fail to correctly discover causal direction. In this work, we propose a cascade nonlinear additive noise model to represent such causal influences--each direct causal relation follows the nonlinear additive noise model but we observe only the initial cause and final effect. We further propose a method to estimate the model, including the unmeasured intermediate variables, from data, under the variational auto-encoder framework. Our theoretical results show that with our model, causal direction is identifiable under suitable technical conditions on the data generation process. Simulation results illustrate the power of the proposed method in identifying indirect causal relations across various settings, and experimental results on real data suggest that the proposed model and method greatly extend the applicability of causal discovery based on functional causal models in nonlinear cases.

 

Domain adaptation is an important but challenging task. Most of the existing domain adaptation methods struggle to extract the domain-invariant representation on the feature space with entangling domain information and semantic information. Different from previous efforts on the entangled feature space, we aim to extract the domain invariant semantic information in the latent disentangled semantic representation (DSR) of the data. In DSR, we assume the data generation process is controlled by two independent sets of variables, i.e., the semantic latent variables and the domain latent variables. Under the above assumption, we employ a variational auto-encoder to reconstruct the semantic latent variables and domain latent variables behind the data. We further devise a dual adversarial network to disentangle these two sets of reconstructed latent variables. The disentangled semantic latent variables are finally adapted across the domains. Experimental studies testify that our model yields state-of-the-art performance on several domain adaptation benchmark datasets.