Large-Dynamic-Range Ocular Aberration Measurement Based on Deep Learning with a Shack-Hartmann Wavefront Sensor.

The Shack-Hartmann wavefront sensor (SHWFS) is widely utilized for ocular aberration measurement. However, large ocular aberrations caused by individual differences can easily make the spot move out of the range of the corresponding sub-aperture in SHWFS, rendering the traditional centroiding method ineffective. This study applied a novel convolutional neural network (CNN) model to wavefront sensing for large dynamic ocular aberration measurement. The simulation results demonstrate that, compared to the modal method, the dynamic range of our method for main low-order aberrations in ocular system is increased by 1.86 to 43.88 times in variety. Meanwhile, the proposed method also has the best measurement accuracy, and the statistical root mean square (RMS) of the residual wavefronts is 0.0082 ± 0.0185 λ (mean ± standard deviation). The proposed method generally has a higher accuracy while having a similar or even better dynamic range as compared to traditional large-dynamic schemes. On the other hand, compared with recently developed deep learning methods, the proposed method has a much larger dynamic range and better measurement accuracy.

Analytical calibration of slope response of Zernike modes in a Shack-Hartmann wavefront sensor based on matrix product.

The Shack-Hartmann wavefront sensor (SH-WFS) is widely used as a slope-based wavefront sensing device. The modal method is favored for wavefront reconstruction from SH-WFS output because of its excellent performance. In this case, the calibration of modal (commonly Zernike modes) slope is required in advance. Traditional numerical or symbolic integral-based methods are not satisfactory because of their low accuracy or efficiency, particularly when an extremely large number of microlenses are involved. In this Letter, a novel method based on matrix product is proposed in which two key matrix operators are utilized. The first, namely the derivative matrix operator, is used to obtain the derivative of the Zernike modes; the second, that is, the transformation matrix operator, is then used to map the Zernike derivative defined in the original, whole circular pupil into modes defined in a scaled, translated circle pupil enveloping a specific microlens. With these two operators, the evaluation of slope response of Zernike modes could be unified into a matrix-product framework, which contributes its high efficiency. Numerical simulations show the superior advantages of the proposed method in accuracy and efficiency over traditional ones.

3-Pyridylacetic-Based Lanthanide Complexes Exhibiting Magnetic Entropy Changes, Single-Molecule Magnet, and Fluorescence.

Four complexes from lanthanides, 3-pyridylacetate, and 1,10-phenanthroline, formulated as [Ln2(3-PAA)2(µ-Cl)2(phen)4](ClO4)2 [Ln = Gd(1), Dy(2), Eu(3), Tb(4), 3-PAA = 3-pyridylacetic acid, phen = 1,10-phenanthroline], were obtained. The four compounds were characterized by IR spectra, thermogravimetric analyses, powder X-ray diffraction, and single-crystal X-ray diffraction. Compounds 1-4 are isomorphous, and they have a dinuclear structure. Magnetic studies reveal that 1 shows the magnetocaloric effect with -ΔS m max = 19.03 J kg-1 K-1 at 2 K for ΔH = 5 T, and 2 displays a field-induced single-molecule magnet with U eff = 19.02 K. The photoluminescent spectra of 3 and 4 exhibit strong characteristic emission, which demonstrate that the ligand-to-EuIII/TbIII energy transfer is efficient.

Method for optimizing the capture range of the dispersed fringe sensor.

The dispersed fringe sensor (DFS) is a phasing sensor based on the principle of white-light double-slit interferometry. We theoretically and experimentally analyze characteristics of the capture range of the DFS, propose a mathematic description of the capture range of the DFS, and put forward a simple but practical strategy to maximize the capture range of the DFS in our project. Finally, the experimental demonstration verifies the validity of the mathematic description of the capture range of the DFS and the strategy for optimizing the capture range.

Unified analytical method for Zernike coefficient transformation of scaled, rotated, and translated pupils based on Shack's vector multiplication.

Zernike polynomials play an essential role in characterizing and analyzing wavefront aberrations. Transformation of weighted coefficients for Zernike modes is required when pupil scaling, rotation, and/or translation exist. Here, a novel method based on Shack's vector multiplication is first proposed to derive the transformation relation. The derived modes resulting from pupil scaling, rotation, and/or translation for each individual mode are easily indicated via this method; thus, the effect of each kind of pupil change could be studied qualitatively and quantitatively. Its remarkable computational efficiency against the direct integral is demonstrated by simulation. The method introduced here provides a generalized methodology to analyze the relationship between weighted coefficients for different description basis sets.

Optical phasing method based on scanning white-light interferometry for multi-aperture optical telescopes.

A novel, to the best of our knowledge, sensing approach based on scanning white-light interferometry (SWLI) is proposed to detect piston errors of the multi-aperture optical telescope. The scanning white-light interferometer is composed of a Mach-Zehnder interferometer (MZI) and an optical path modulator (OPM). A lenslet array is used to image the interferometric wavefront between the reference and the other individual apertures. The piston errors can be estimated from these SWLI signals focused by the lenslet array. The measurement range of the proposed method depends on the modulation range of the OPM and can reach millimeter order, and its accuracy is better than a 1/20 wavelength. In addition, the proposed method's amplitude-splitting interferometry of the MZI makes it fit for a multi-aperture optical telescope. We demonstrate a proof of concept and validate the feasibility of our proposed phasing method.

Phase diversity method based on an improved particle swarm algorithm used in co-phasing error detection.

The phase diversity (PD) algorithm is an image-based co-phasing error detection method for segmented mirror synthetic aperture optical systems. Particle swarm optimization (PSO) is suitable for PD for its fast convergence speed and simple structure. However, with the increase of the numbers of subapertures, optimization of cost function formed by the PD algorithm becomes a high-dimension non-linear optimization problem, which would lead PSO to result in a premature solution. Regarding the problem above, this paper presented a modified PSO in the PD algorithm to co-phase the segmented primary mirror, which overcame drawbacks of the traditional PSO, such as premature convergence and deactivation of particles, and enhanced the dig ability of the algorithm. Vast simulation results show that the modified PSO in the PD algorithm can effectively restore the segmented primary mirror, reducing the peak-to-valley (PV) value to 0.0012λ and the root mean square error to 0.0007λ, and raising the Strehl ratio to over 0.999. A comparison was also conducted to show that the modified PSO has advantages over two existing algorithms in higher accuracy and faster convergence speed.

Modulation-nonmodulation pyramid wavefront sensor with direct gradient reconstruction algorithm on the closed-loop adaptive optics system.

A modulation-nonmodulation pyramid wavefront sensor with direct gradient reconstruction algorithm using on the adaptive optics is reported in this paper. This means that the interaction matrix of the system is obtained by using a modulated pyramid and the closed-loop control process is performed with a nonmodulated pyramid. The theoretical basis and simulation analysis of the direct gradient reconstruction algorithm are described in detail, and laboratory results show that the pyramid wavefront sensor based on this algorithm can work as expected in a closed-loop adaptive optics system.

Dispersed-fringe-accumulation-based left-subtract-right method for fine co-phasing of a dispersed fringe sensor.

In this paper, a dispersed-fringe-accumulation (DFA)-based left-subtract-right (LSR) piston estimation method (DFA-LSR), in which the dispersed fringe image is accumulated in the dispersed direction, and then the LSR method is used to estimate the piston error, is proposed for dispersed fringe sensors (DFS) in the fine co-phasing stage. The DFS is usually used to detect the piston errors (optical path difference) between different segmented mirrors or synthetic aperture telescopes. The DFA-LSR makes up for the shortcomings of the main peak position (MPP) method, which suffers from the constant offset in the pixel counts. The analysis and experiment results show that the proposed method can keep relatively better performance even at the condition of poor signal-to-noise ratio, compared with the MPP method in fine co-phasing stage.

Laboratory demonstrations on a pyramid wavefront sensor without modulation for closed-loop adaptive optics system.

The feasibility and performance of the pyramid wavefront sensor without modulation used in closed-loop adaptive optics system is investigated in this paper. The theory concepts and some simulation results are given to describe the detection trend and the linearity range of such a sensor with the aim to better understand its properties, and then a laboratory setup of the adaptive optics system based on this sensor and the liquid-crystal spatial light modulator is built. The correction results for the individual Zernike aberrations and the Kolmogorov phase screens are presented to demonstrate that the pyramid wavefront sensor without modulation can work as expected for closed-loop adaptive optics system.

Comparison between non-modulation four-sided and two-sided pyramid wavefront sensor.

Based on the diffraction theory the paper analyzes non-modulation Pyramid wavefront sensor (PWFS, namely, four-sided pyramid) and two-sided pyramid wavefront sensor (TSPWFS), and expresses the detected signals as a function of the measured wavefront. The expressions of the detected signals show that non-modulation PWFS and TSPWFS hold the same properties of both slope and direct phase sensors. We compare both sensors working in slope and phase sensing by theory and numerical simulations. The results demonstrate that the performance of TSPWFS excels that of PWFS. Additionally, the influence of interference between adjacent pupils is discussed.

Picometer displacement sensing using the ultrahigh-order modes in a submillimeter scale optical waveguide.

An improved scheme for displacement measurement using the ultrahigh-order guided modes in a symmetrical metal-cladding optical waveguide is proposed. Based on this idea together with the lock-in amplification technique, a sensor with a stable displacement resolution of 3.3 pm is experimentally demonstrated without any complicated servo system.