Phase unwrapping algorithm based on phase diversity wavefront reconstruction and virtual Hartmann-Shack technology.

Phase unwrapping (PU) algorithms play a crucial role in various phase measurement techniques. Traditional algorithms cannot work well in strong noise environments, which makes it very difficult to obtain the accurate absolute phase from the noisy wrapped phase. In this Letter, we introduce a novel, to the best of our knowledge, phase unwrapping algorithm named PD-VHS. This algorithm innovatively employs point spread function (PSF) filtering to eliminate noise from the wrapped phase. Furthermore, it combines a phase diversity (PD) wavefront reconstruction technology with a virtual Hartmann-Shack (VHS) technology for phase reconstruction and phase unwrapping of the filtered PSFs. In simulations, hundreds of random noise wrapped phases, containing the first 45 Zernike polynomials (excluding piston and the two tilt terms) and the wavefront RMS = 0.5λ and 1λ, are used to compare the classical quality-map guided algorithm, the VHS algorithm with decent noise immunity, with our PD-VHS algorithm. When signal-to-noise ratio (SNR) drops to just 2 dB, the mean root mean square errors (RMSEs) of the residual wavefront between the unwrapped result and the absolute phase of the quality-map guided algorithm and the VHS algorithm are up to 3.99λ, 0.44λ, 4.29λ, and 0.85λ, respectively; however, our algorithm RMSEs are low: 0.11λ and 0.17λ. Simulation results demonstrated that the PD-VHS algorithm significantly outperforms the quality-map guided algorithm and the VHS algorithm under large-scale noise conditions.

Ocular aberration measurement with and without an aperture stop using a Shack-Hartmann wavefront sensor.

Pupil size is an important parameter since it governs the magnitude of ocular aberrations. The pupil size of a human eye has significant individual differences and varies with light level and accommodation. In order to accurately measure ocular aberrations under different pupil sizes using a Shack-Hartmann wavefront sensor (SHWFS), two types of relationship matrices R (1) and R (2) were proposed, which corresponded to wavefront reconstruction with and without an aperture stop, respectively. The numerical and experimental results indicated that matrix R (2) can significantly improve the accuracy of wavefront restoration when the incident beam size is inconsistent with the wavefront reconstruction aperture. Meanwhile, the impact of the aperture stop on the reconstruction accuracy will become smaller and smaller as the ratio ρ of the outer area to the detection aperture decreases. This study not only can be used for accurately measuring ocular aberrations under different pupil sizes, but also for other variable aperture aberrations measurement in other applications.

Enhanced-resolution Shack-Hartmann wavefront sensing for extended objects.

Adaptive optics systems for large-aperture solar telescopes, especially multiconjugate adaptive optics systems, suffer from a fundamental trade-off between wavefront sampling rate and sub-aperture resolution. We introduce an enhanced-resolution Shack-Hartmann wavefront sensing method that decouples sub-aperture resolution from the desired wavefront sampling rate. We experimentally verified the validity of this method. Results show that by synthesizing multiple low-spatial samplings, this method is capable to sense higher-frequency aberrations beyond any low-spatial sampling involved in the synthesis, and it allows higher sub-aperture resolution and higher operating bandwidths, which can better fulfill the needs of solar adaptive optics.

Full-Stokes Retrieving and Configuration Optimization in a Time-Integration Imaging Polarimeter.

A time-integration imaging polarimeter with continuous rotating retarder is presented, and its full-Stokes retrieving and configuration optimization are also demonstrated. The mathematical expression between the full-Stokes vector and the time-integration light intensities is derived. As a result, the state of polarization of incident light can be retrieved by only one matrix calculation. However, the modulation matrix deviates from the initial well-conditioned status due to time integration. Thus, we re-optimize the nominal angles for the special retardance of 132° and 90° with an exposure angle of 30°, which results in a reduction of 31.8% and 16.8% of condition numbers comparing to the original configuration, respectively. We also give global optimization results under different exposure angles and retardance of retarder; as a result, the 137.7° of retardance achieves a minimal condition number of 2.0, which indicates a well-conditioned polarimeter configuration. Besides, the frame-by-frame algorithm ensures the dynamic performance of the presented polarimeter. For a general brushless DC motor with a rotating speed of over 2000 rounds per minute, the speed of polarization imaging will achieve up to 270 frames per second. High precision and excellent dynamic performance, together with features of compactness, simplicity, and low cost, may give this traditional imaging polarimeter new life and attractive prospects.

Polarization imaging based on time-integration by a continuous rotating polarizer.

Polarimeter by rotating polarizer is one of the well-known and classic division of time polarimeter (DoTP). It is generally acknowledged that this kind of polarimeter is time consuming for each measurement although it has simple, accurate and compact performances. In this paper we present a time-integration polarimeter by using a continuous rotating polarizer. The basic principle and the corresponding mathematical expressions are derived. Numeric analysis and experiments are also made in this paper. Experimental results validate the precision and feasibility of the proposed imaging polarization and state of polarization retrieve theory. The frame-frequency of polarization image is 80fps which is limited mainly by the speed of the photodetector in our experiments, and its maximum frame-frequency can achieve over 270fps in theory for some special applications. That may give this kind of classic polarimeter new attractive prospects and life.

Compact single-shot radial shearing interferometer with random phase shift.

We propose a compact phase-shifting radial shearing interferometer based on a pixelated micro-retarder array (MRA). The MRA is made of a thin birefringence plate, and is composed of identical units that have pixels of four different thicknesses. We demonstrate that pixelated phase delay between two shearing beams can be introduced by applying the fast axis of birefringence plate in the horizontal or vertical orientation. We also present an approach to extract the wavefront under test with random phase shift, which dramatically reduces the machining difficulty of the MRA. The feasibility and accuracy of the proposed method are further validated through our numerical analysis. With the advantages of vibration immunity, simultaneous phase stepping, and broad spectral range, the presented interferometer is expected to be of potential use in a variety of applications, such as the detection of moving objects and dynamic processes.

[The Aberration Corrected Grating Spectrometer Based on Adaptive Optics].

To study the thermodynamics properties of the solar atmosphere with different height distribution, the imaging grating spectrometer with excellent image quality is one of the important tools to achieve this goal. However, the atmosphere turbulence can not be avoided for the imaging grating spectrometer installed in the ground-based solar telescope, and the imaging properties of the grating spectrometer will influenced by the wavefront aberration generalized by the atmosphere turbulence and the wavefront aberration generalized by the optical system adjusting errors and the optical element manufacturing errors. The atmospheric turbulence can be effectively compensated by the Adaptive Optics. To correct the wavefront aberrations of the optical system, a correction method based on Adaptive Optics is proposed, and the experiment validation is carried out to verify the feasibility of the method. The results demonstrate that the correction method proposed can effectively correct the wavefront aberration generalized by the atmosphere turbulence and the optical system aberration. The RMS value is roughly equal to 0.025λ after the Adaptive Optics correction. Besides, it has the virtue of lower the requirement of optical system adjusting errors and optical elements manufacturing errors.

Quantitative evaluation on internal seeing induced by heat-stop of solar telescope.

heat-stop is one of the essential thermal control devices of solar telescope. The internal seeing induced by its temperature rise will degrade the imaging quality significantly. For quantitative evaluation on internal seeing, an integrated analysis method based on computational fluid dynamics and geometric optics is proposed in this paper. Firstly, the temperature field of the heat-affected zone induced by heat-stop temperature rise is obtained by the method of computational fluid dynamics calculation. Secondly, the temperature field is transformed to refractive index field by corresponding equations. Thirdly, the wavefront aberration induced by internal seeing is calculated by geometric optics based on optical integration in the refractive index field. This integrated method is applied in the heat-stop of the Chinese Large Solar Telescope to quantitatively evaluate its internal seeing. The analytical results show that the maximum acceptable temperature rise of heat-stop is up to 5 Kelvins above the ambient air at any telescope pointing directions under the condition that the root-mean-square of wavefront aberration induced by internal seeing is less than 25nm. Furthermore, it is found that the magnitude of wavefront aberration gradually increases with the increase of heat-stop temperature rise for a certain telescope pointing direction. Meanwhile, with the variation of telescope pointing varying from the horizontal to the vertical direction, the magnitude of wavefront aberration decreases at first and then increases for the same heat-stop temperature rise.

Heat-stop structure design with high cooling efficiency for large ground-based solar telescope.

A heat-stop is one of the most important thermal control devices for a large ground-based solar telescope. For controlling the internal seeing effect, the temperature difference between the heat-stop and the ambient environment needs to be reduced, and a heat-stop with high cooling efficiency is required. In this paper, a novel design concept for the heat-stop, in which a multichannel loop cooling system is utilized to obtain higher cooling efficiency, is proposed. To validate the design, we analyze and compare the cooling efficiency for the multichannel and existing single-channel loop cooling system under the same conditions. Comparative results show that the new design obviously enhances the cooling efficiency of the heat-stop, and the novel design based on the multichannel loop cooling system is obviously better than the existing design by increasing the thermal transfer coefficient.

Experimental study of a modified phase diversity with a diffraction grating.

The measurement ability of the conventional Phase diversity wavefront sensor (C-PD WFS) is limited by the accuracy and dynamic range of CCD cameras. In this letter, a modified Phase diversity wavefront sensor based on a diffraction grating (G-PD WFS) is proposed. We build a corresponding experimental setup to compare the measurement accuracy of the G-PD WFS and the C-GPDWFS under the same experimental conditions. The experimental results show that the measurement ability of G-PD WFS is improved obviously, especially for the wavefront aberration with larger amplitude.

Modal wavefront reconstruction for radial shearing interferometer with lateral shear.

In a radial shearing interferometer, a portion of the test beam is magnified and used as the reference for the tested wavefront. However, the reference portion is always off center (lateral shear), which complicates the wavefront reconstruction. A modal method for solving this problem is presented here. This method uses orthogonal Zernike polynomials and its matrix formalism to calculate the Zernike coefficient of the wavefront under test. This approach has easier implementation, is better filtering, and has a more adaptive practical situation. The corresponding mathematical formula is deduced, and a computer simulation is also made to verify operation of the algorithm. The result of simulation analysis shows that the proposed method is correct and accurate.

A single-shot common-path phase-stepping radial shearing interferometer for wavefront measurements.

A single-shot common-path phase-stepping radial shearing interferometer (RSI) is proposed for wavefront measurements. In the proposed RSI, three quarter-wave plates are used as phase shifters to produce four spatially separated phase-stepping fringe patterns that are recorded simultaneously by a single CCD camera. The proposed RSI can measure the wavefront under test in real-time, and it is also insensitive to environmental vibration due to its common-path structure. Experimentally the proposed RSI is applied to detect the distorted wavefronts generated by a liquid crystal spatial light modulator. The measured aberrations are in good agreement with that obtained with (by) a Hartmann-Shack wavefront sensor, indicating that the proposed RSI is a useful tool for wavefront measurements.