Position and displacement sensing with shack-hartmann wave-front sensors

Characterizing Biphoton Spatial Wave Function Dynamics with Quantum Wavefront Sensing

With an extremely high dimensionality, the spatial degree of freedom of entangled photons is a key tool for quantum foundation and applied quantum techniques. To fully utilize the feature, the essential task is to experimentally characterize the multiphoton spatial wave function including the entangled amplitude and phase information at different evolutionary stages. However, there is no effective method to measure it. Quantum state tomography is costly, and quantum holography requires additional references. Here, we introduce quantum Shack-Hartmann wavefront sensing to perform efficient and reference-free measurement of the biphoton spatial wave function. The joint probability distribution of photon pairs at the back focal plane of a microlens array is measured and used for amplitude extraction and phase reconstruction. In the experiment, we observe that the biphoton amplitude correlation becomes weak while phase correlation shows up during free-space propagation. Our work is a crucial step in quantum physical and adaptive optics and paves the way for characterizing quantum optical fields with high-order correlations or topological patterns.

A Method Used to Improve the Dynamic Range of Shack-Hartmann Wavefront Sensor in Presence of Large Aberration

With the successful application of the Shack-Hartmann wavefront sensor in measuring aberrations of the human eye, researchers found that, when the aberration is large, the local wavefront distortion is large, and it causes the spot corresponding to the sub-aperture of the microlens to shift out of the corresponding range of the sub-aperture. However, the traditional wavefront reconstruction algorithm searches for the spot within the corresponding range of the sub-aperture of the microlens and reconstructs the wavefront according to the calculated centroid, which leads to wavefront reconstruction errors. To solve the problem of the small dynamic range of the Shack-Hartmann wavefront sensor, this paper proposes a wavefront reconstruction algorithm based on the autocorrelation method and a neural network. The autocorrelation centroid extraction method was used to calculate the centroid in the entire spot map in order to obtain a centroid map and to reconstruct the wavefront by matching the centroid with the microlens array through the neural network. This method breaks the limitation of the sub-aperture of the microlens. The experimental results show that the algorithm improves the dynamic range of the first 15 terms of the Zernike aberration reconstruction to varying degrees, ranging from 62.86% to 183.87%.

Toward practical weak measurement wavefront sensing: spatial resolution and achromatism

The weak measurement wavefront sensor detects the phase gradient of light like the Shack-Hartmann sensor does. However, the use of one thin birefringent crystal to displace light beams results in a wavelength-dependent phase difference between the two polarization components, which limits the practical application. Use of a Savart plate, which consists of two such crystals, can compensate for the phase difference and realize achromatic wavefront sensing when combined with an achromatic retarder. We discuss the spatial resolution of the sensor and experimentally reconstruct a wavefront modulated by a pattern. Then we obtain the Zernike coefficients with three different wavelengths before and after modulation. Our work makes this new wavefront sensor more applicable to actual tasks like biomedical imaging.

Detecting momentum weak value: Shack-Hartmann versus a weak measurement wavefront sensor

The task of wavefront sensing is to measure the phase of the optical field. Here, we demonstrate that the widely used Shack-Hartmann wavefront sensor detects the weak value of transverse momentum, usually achieved by the method of quantum weak measurement. We extend its input states to partially coherent states and compare it with the weak measurement wavefront sensor, which has a higher spatial resolution but a smaller dynamic range. Since weak values are commonly used in investigating fundamental quantum physics and quantum metrology, our work would find essential applications in these fields.

Centroid computation for Shack-Hartmann wavefront sensor in extreme situations based on artificial neural networks

This paper proposes a method used to calculate centroid for Shack-Hartmann wavefront sensor (SHWFS) in adaptive optics (AO) systems that suffer from strong environmental light and noise pollutions. In these extreme situations, traditional centroid calculation methods are invalid. The proposed method is based on the artificial neural networks that are designed for SHWFS, which is named SHWFS-Neural Network (SHNN). By transforming spot detection problem into a classification problem, SHNNs first find out the spot center, and then calculate centroid. In extreme low signal-noise ratio (SNR) situations with peak SNR (SNR_p) of 3, False Rate of SHNN-50 (SHNN with 50 hidden layer neurons) is 6%, and that of SHNN-900 (SHNN with 900 hidden layer neurons) is 0%, while traditional methods' best result is 26 percent. With the increase of environmental light interference's power, the False Rate of SHNN-900 remains around 0%, while traditional methods' performance decreases dramatically. In addition, experiment results of the wavefront reconstruction are presented. The proposed SHNNs achieve significantly improved performance, compared with the traditional method, the Root Mean Square (RMS) of residual decreases from 0.5349 um to 0.0383 um. This method can improve SHWFS's robustness.

Combining a Disturbance Observer with Triple-Loop Control Based on MEMS Accelerometers for Line-of-Sight Stabilization

In the CCD-based fine tracking optical system (FTOS), the whole disturbance suppression ability (DSA) is the product of the inner loop and outer position loop. Traditionally, high sampling fiber-optic gyroscopes (FOGs) are added to the platform to stabilize the line-of-sight (LOS). However, because of the FOGs’ high cost and relatively big volume relative to the back narrow space of small rotating mirrors, we attempt in this work to utilize a cheaper and smaller micro-electro-mechanical system (MEMS) accelerometer to build the inner loop, replacing the FOG. Unfortunately, since accelerometers are susceptible to the low-frequency noise, according to the classical way of using accelerometers, the crucial low-frequency DSA of the system is insufficient. To solve this problem, in this paper, we propose an approach based on MEMS accelerometers combining disturbance observer (DOB) with triple-loop control (TLC) in which the composite velocity loop is built by acceleration integration and corrected by CCD. The DOB is firstly used to reform the platform, greatly improving the medium-frequency DSA. Then the composite velocity loop exchanges a part of medium-frequency performance for the low-frequency DSA. A detailed analysis and experiments verify the proposed method has a better DSA than the traditional way and could totally substitute FOG in the LOS stabilization.

Error-Based Observer of a Charge Couple Device Tracking Loop for Fast Steering Mirror

The charge couple device (CCD) tracking loop of a fast steering mirror (FSM) is usually used to stabilize line of sight (LOS). High closed-loop bandwidth facilitates good performance. However, low-rate sample and time delay of the CCD greatly limit the high control bandwidth. This paper proposes an error-based observer (EBO) to improve the low-frequency performance of the CCD tracking system. The basic idea is by combining LOS error from the CCD and the controller output to produce the high-gain observer, forwarding into the originally closed-loop control system. This proposed EBO can improve the system both in target tracking and disturbance suppression due to LOS error from the CCD’s sensing of the two signals. From a practical engineering view, the closed-loop stability and robustness of the EBO system are investigated on the condition of gain margin and phase margin of the open-loop transfer function. Two simulations of CCD experiments are provided to verify the benefits of the proposed algorithm.

Wavefront measurement made by an off-the-shelf laser-scanning pico projector

Focal plane testing methods such as the Shack-Hartmann wavefront sensor and phase-shifting deflectometry are valuable tools for optical testing. In this study, we propose a novel wavefront slope testing method that uses a scanning galvo laser, in which a single-mode Gaussian beam scans the pupils of the tested optics in the system. In addition, the ray aberration is reconstructed by the four-step phase-shifting measurement by modulating the angular domain. The measured wavefront is verified by a Fizeau interferometer in terms of Zernike polynomials.

Reconfigurable Shack-Hartmann sensor without moving elements

We demonstrate wavefront sensing with variable measurement sensitivity and dynamic range by means of a programmable microlens array implemented onto an off-the-shelf twisted nematic liquid crystal display operating as a phase-only spatial light modulator. Electronic control of the optical power of a liquid lens inserted at the aperture stop of a telecentric relay system allows sensing reconfigurability without moving components. Results of laboratory experiments show the ability of the setup to detect both smooth and highly aberrated wavefronts with adequate sensitivity.

Error analysis of CCD-based point source centroid computation under the background light

The CCD-based point source centroid computation (PSCC) error under the background light is analyzed integrally in theory, numerical simulation and experiment. Furthermore, a comprehensive formula of the PSCC error caused by the diversified error sources is put forward. The optimum threshold to reduce the effects of all the error sources to a minimum is selected. The best threshold level is N(B) +3sigma(B), where N(B) is the average value of the error sources and sigma(B) is the mean-square value of the fluctuation of the error sources. The simulation and experiment results are in great accordance with the theoretical analysis.

Improving the system stability of a digital Shack-Hartmann wavefront sensor with a special lenslet array

There has been very limited study on the stability of a Shack-Hartmann wavefront sensor (SHWS) since its emergence in the early 1970s. In this paper, through experimental study of the system stability of a digital SHWS, a special lenslet array with long focal range is designed and implemented with a spatial light modulator to improve the system performance. Diffractive lenses with long focal length range can provide pseudo-nondiffracting beams and a long range of focusing plane. The performance and effect of the modified SHWS with this lenslet array are investigated, and the experimental results show that the system stability and measurement repeatability are not sensitive to the sensing distance and stay at an acceptable level.

High-speed Shack-Hartmann wavefront sensor design with commercial off-the-shelf optics

Several trade-offs relevant to the design of a two-dimensional high-speed Shack-Hartmann wavefront sensor are presented. Also outlined are some simple preliminary experiments that can be used to establish critical design specifications not already known. These specifications include angular uncertainty, maximum measurable wavefront tilt, and spatial resolution. A generic design procedure is then introduced to enable the adaptation of a limited selection of CCD cameras and lenslet arrays to the desired design specifications by use of commercial off-the-shelf optics. Although initially developed to aid in the design of high-speed (i.e., megahertz-frame-rate) Shack-Hartmann wavefront sensors, our method also works when used for slower CCD cameras. A design example of our procedure is provided.

Calibration of a Shack-Hartmann sensor for absolute measurements of wavefronts

We demonstrate a method with which to calibrate a Shack-Hartmann sensor for absolute wavefront measurement of collimated laser beams. Nearly perfect spherical wavefronts originating from a single-mode fiber were used as references. After the calibration, the uncertainty of the wavefront was less than lambda/100 peak to valley across a diameter of 6 mm. For example, this method allowed us to balance aberrations and prepare collimated beams with wavefronts that are plane to lambda/500 across 1 mm.

Influence of thresholding on centroid statistics: full analytical description

The centroid method is a common procedure for subpixel location that is applied to a large number of optical sensors. In practice, it is always accompanied by thresholding algorithms used to eliminate undesirable background that may decrease precision. We present a full analytical description of the interaction between centroiding and thresholding applied over an intensity distribution corrupted by additive Gaussian noise. An in depth analysis of the most outstanding statistical properties of this relation (mean and variance) is also presented by means of simulated and experimental data. This work provides fundamental concepts to the designers of sensors that are based on centroid measurements to allow them to use thresholding correctly before centroid computation.

Measuring eye aberrations with Hartmann-Shack wave-front sensors: should the irradiance distribution across the eye pupil be taken into account?

A usual approximation in Hartmann-Shack aberrometry is that the centroid displacements are proportional to the spatial averages of the wave-front slopes at the sampling subapertures. However, these spatial averages are actually weighted by the local irradiance distribution across each microlens. The irradiance across the eye pupil is not uniform in usual reflectometric aberrometers, which is due to several factors including retinal scattering and cone waveguiding directionality. It is shown that neglecting this fact in usual least-squares reconstruction procedures gives rise to a biased estimation of the aberration coefficients. The magnitude of this bias depends on the actual irradiance distribution across the eye pupil, the mode being estimated, the detailed modal composition of the aberrated wave front, and the geometry of the wave-front sampling array. Order-of-magnitude calculations suggest that this bias may well be in the range 5%-10% for relatively smooth irradiance distributions. The systematic nature of this error makes it advisable to check for its presence and, if required, to compensate for it by an adequate choice of the least-squares reconstruction matrix.

Minimum variance centroid thresholding

Image-processing thresholding algorithms are extended segmentation tools that are suitable for tracking applications. The centroid of the tracked image distribution is a good point of reference for the location of the image. We describe a new thresholding technique that is based on the estimation of the optimum threshold for achieving minimal variance in the centroid of the processed image. Experimental proofs for evaluating the technique's performance are given. The direct extension of these results to Shack-Hartmann wave-front sensors is also shown.