Fast, intelligent and high-precision adaptive null interferometry for optical freeform surfaces by backpropagation.

In the past 10 years, adaptive wavefront interferometry (AWI) has been employed for measuring freeform surface profiles. However, existing AWI techniques relying on stepwise and model-free stochastic optimizations have resulted in inefficient tests. To address these issues, deterministic adaptive wavefront interferometry (DAWI) is firstly introduced in this paper based on backpropagation (BP), which employs a loss function to simultaneously reconstruct and sparsify initial incomplete interferometric fringes until they are nulled. Each iteration of BP requires two phase shifts. Through simulations, we have verified that freeform wavefront error with a peak-to-valley (PV) of up to 168 λ can be fully compensated in tens of iterations using a 1024 × 1024 pixel area of a liquid-crystal spatial light modulator. In experiments, we accomplished a null test of a freeform surface with 80% missing interference fringes in 39 iterations, resulting in a surface profile error PV of 66.22 λ and measurement error better than λ/4. The DAWI has at least 20 times fewer iterations in fringe reconstruction than the 3-step AWI methods, and nearly an order of magnitude fewer iterations in the whole process, paving the way for significantly enhanced efficiency, generality and precision in freeform surface adaptive interferometry.

Theoretical studies on the electronic structures and photoelectron spectra of tri-rhenium oxide clusters: Re3O(n)(-) and Re3O(n) (n=1-6).

Density functional theory (DFT) calculations are performed to study the structural and electronic properties of tri-rhenium oxide clusters Re3On(-/0) (n=1-6). Generalized Koopmans' theorem is applied to predict the vertical detachment energies (VDEs) and simulate the photoelectron spectra (PES). Theoretical calculations at the B3LYP level are carried out to search for the global minima for both the anions and the neutrals. For the anions, the first two O atoms prefer the same corner position of a Re3 triangle. Whereas, Re3O3(-) possesses a C2v symmetry with one bridging and two terminal O atoms. The next three O atoms (n=4-6) are adding sequentially on the basis of Re3O3(-) motif, i.e., adding one terminal O atom for Re3O4(-), one terminal and one bridging O atoms for Re3O5(-), and one terminal and two bridging O atoms for Re3O6(-), respectively. Their corresponding neutral species are similar to the anions in geometry except Re3O4 and Re3O5. Molecular orbital analyses are employed to investigate the chemical bonding and structural evolution in these tri-rhenium oxide clusters.