Static Aberrations Research Articles

利用相位差异技术校准非共光路静态像差

利用相位差异技术校准非共光路静态像差

Estimation and Compensation of aberrations in Spatial Light Modulators

The spatial light modulator (SLM) Holoeye LC-R720 is based on LCoS (Liquid Crystal on Silicon) technology. Due to the induced curvatures on the silicon plate by the production process, there are static aberrations in the wave-fronts modified by the SLM. In order to calculate the aberrated wave-front we used phase-shifting interferometry, an optimization algorithm for far field propagation, and the geometric characterization of the focal spot along the caustic. Zernike polynomials were used for expanding and comparing the wave-fronts. The aberration compensation was carried out by displaying the conjugated transmittance on the SLM. The complexity of the experimental setup and the requirements of the digital processing of each estimation method were comparatively analyzed.

Diffraction theory analysis and numerical simulation of non-modulation two-sided pyramid wavefront sensor

Two-sided pyramid wavefront sensor (TSPWFS) is a kind of wavefront sensor with high spatial resolution and light energy utilization. To deeply study the principle of wavefront reconstruction of this wavefront sensor using wave optics theory, this paper deduces the diffraction theory of non-modulation TSPWFS and gives the analytic solution of linear reconstruction matrix for wavefront reconstruction. With numerical simulation the optimal distance between adjacent pupil image centers was determined. Also, wavefront reconstruction and closed-loop correction of static aberrations by using non-modulation TSPWFS as a wavefront sensor were simulated. The results show that non-modulation TSPWFS has three main advantages. i.e., it does not require measuring the response matrix in real optical setup, and can correct the optical systemic aberration, and can achieve stable closed-loop correction result. Additionally, non-modulation TSPWFS can be applied to a real adaptive optics system to detect wavefront.

Model-based aberration correction in a closed-loop wavefront-sensor-less adaptive optics system

In many scientific and medical applications, such as laser systems and microscopes, wavefront-sensor-less (WFSless) adaptive optics (AO) systems are used to improve the laser beam quality or the image resolution by correcting the wavefront aberration in the optical path. The lack of direct wavefront measurement in WFSless AO systems imposes a challenge to achieve efficient aberration correction. This paper presents an aberration correction approach for WFSlss AO systems based on the model of the WFSless AO system and a small number of intensity measurements, where the model is identified from the input-output data of the WFSless AO system by black-box identification. This approach is validated in an experimental setup with 20 static aberrations having Kolmogorov spatial distributions. By correcting N=9 Zernike modes (N is the number of aberration modes), an intensity improvement from 49% of the maximum value to 89% has been achieved in average based on N+5=14 intensity measurements. With the worst initial intensity, an improvement from 17% of the maximum value to 86% has been achieved based on N+4=13 intensity measurements.

Analytical expression of long-exposure adaptive-optics-corrected coronagraphic image First application to exoplanet detection

In this paper we derive an analytical model of a long-exposure star image for an adaptive-optics(AO)-corrected coronagraphic imaging system. This expression accounts for static aberrations upstream and downstream of the coronagraphic mask as well as turbulence residuals. It is based on the perfect coronagraph model. The analytical model is validated by means of simulations using the design and parameters of the SPHERE instrument. The analytical model is also compared to a simulated four-quadrant phase-mask coronagraph. Then, its sensitivity to a miscalibration of structure function and upstream static aberrations is studied, and the impact on exoplanet detectability is quantified. Last, a first inversion method is presented for a simulation case using a single monochromatic image with no reference. The obtained result shows a planet detectability increase by two orders of magnitude with respect to the raw image. This analytical model presents numerous potential applications in coronographic imaging, such as exoplanet direct detection, and circumstellar disk observation.

Shack — Hartmann wavefront sensor for measuring the parameters of high-power pulsed solid-state lasers

The wavefront of the radiation of two types from high-power solid-state (Ti:sapphire and Nd:glass) lasers is experimentally studied. The measurements are performed using a Shack — Hartmann wavefront sensor. The technical and functional potential of this sensor in measuring laser-based schemes is demonstrated. The results of measuring both static and dynamic wavefront aberrations are discussed. The estimated dynamics of defocus aberration is in agreement with the experimental data.

High precision Zernike modal gray map reconstruction for liquid crystal corrector

This paper proposes a new Zernike modal gray map reconstruction algorithm used in the nematic liquid crystal adaptive optics system. Firstly, the new modal algorithm is described. Secondly, a single loop correction experiment was conducted, and it showed that the modal method has a higher precision in gray map reconstruction than the widely used slope method. Finally, the contrast close-loop correction experiment was conducted to correct static aberration in the laboratory. The experimental results showed that the average peak to valley (PV) and root mean square (RMS) of the wavefront corrected by mode method were reduced from 2.501λ (λ = 633 nm) and 0.610λ to 0.0334λ and 0.00845λ, respectively. The corrected PV and RMS were much smaller than those of 0.173λ and 0.048λ by slope method. The Strehl ratio and modulation transfer function of the system corrected by mode method were much closer to diffraction limit than with slope method. These results indicate that the mode method can take good advantage of the large number of pixels of the liquid crystal corrector to realize high correction precision.

A “virtual-interferometer” technique for surface metrology

We demonstrate a novel technique for performing aberration-corrected surface metrology within existing wavefront-feedback systems. Our technique uses several phase measurements to calculate phase differences that directly reveal the surface gradients of an object under test, due to orthogonal displacements of that object between measurements. We then apply a least-squares algorithm for surface reconstruction using the gradient information. This approach also removes static system aberrations, providing an absolute measurement of the surface profile. To date, we have profiled a number of test optics with 20- to 40-nm RMS error, where the accuracy is determined by the amount of angular crosstalk over the system aperture.

Beam wavefront control of a thermal inertia laser for inertial confinement fusion application

A novel scheme to correct aberration of each beam from the front-end to the target point in a thermal inertia laser (TIL) is presented. Each beam contains a deformable mirror (DM) with an aperture of 70 mm x 70 mm at the injection of the main amplifier and a Hartman-Shack (HS) sensor in a parameter diagnostic unit (PDU). A temporary HS sensor for measuring the static aberration of each beam with 1 Hz source is placed at the target point. The sensor will be removed from the target point during the main single shot, so we transfer the results measured at the target point to the sensors in the PDU. Dynamic aberration can also be measured by the HS sensor in the PDU during the single shot. In this way, we need not calibrate the aberration of the PDU, and aberration of each beam can be corrected by the DM with the HS sensor in the PDU. We demonstrate that with this scheme the divergence angle of the TIL pulses can be improved from 100 to less than 60 murad with a focal length of 2200 mm and beam size of 290 mm x 290 mm, which meets the requirement of a TIL.

Optimal method for exoplanet detection by angular differential imaging

We propose a novel method for the efficient direct detection of exoplanets from the ground using angular differential imaging. The method combines images appropriately, then uses the combined images jointly in a maximum-likelihood framework to estimate the position and intensity of potential planets orbiting the observed star. It takes into account the mixture of photon and detector noises and a positivity constraint on the planet's intensity. A reasonable detection criterion is also proposed based on the computation of the noise propagation from the images to the estimated intensity of the potential planet. The implementation of this method is tested on simulated data that take into account static aberrations before and after the coronagraph, residual turbulence after adaptive optics correction, and noise.

The contribution of the fixational eye movements to the variability of the measured ocular aberration

The purpose of this work is to analyze the contribution of eye movements to the variability of the Zernike coefficients as determined with a Hartmann-Shack aberrometer. In order to isolate this effect we considered static aberrations tied to the eye pupil. We used several eye movements of different magnitude, both synthetic and corresponding to actual series recorded in our laboratory with different subjects. Our results show the relevance of the modal coupling induced by the estimation process and the benefit of correcting eye movements in order to get a better estimate of the ocular aberrations. They also show that eye movements during aberrometric measurements are an important source of apparent wavefront variability.

Conformal optical design with combination of static and dynamic aberration corrections

Conformal domes that are shaped to meet aerodynamic requirements can increase range and speed for the host platform. Because these domes typically deviate greatly from spherical surface descriptions, a variety of aberrations are induced which vary with the field-of-regard (FOR) angle. A system for correcting optical aberrations created by a conformal dome has an outer surface and an inner surface. Optimizing the inner surface is regard as static aberration correction. A deformable mirror is placed at the position of the secondary mirror in the two-mirror all reflective imaging system, which is the dynamic aberration correction. An ellipsoidal MgF2 conformal dome with a fineness ratio of 1.0 is designed as an example. The FOR angle is 0°− 30°, and the design wavelength is 4 μm. After the optimization at 7 zoom positions by using the design tools Code V, the root-mean-square (RMS) spot size is reduced to approximately 0.99 to 1.48 times the diffraction limit. The design results show that the performances of the conformal optical systems can be greatly improved by the combination of the static correction and the dynamic correction.

Performance test and closed-loop correction experiment of a 20-element bimorph deformable mirror

Performances of a 20-element bimorph deformable mirror are measured and a closed-loop adaptive optics system, which consists of the bimorph mirror and a Shack-Hartmann wave-front sensor with 13×13 sub-aperture array, is established to test the mirror’s capability of correcting static aberrations. Experimental results show that, the mean displacement response to voltage of discrete actuators is 0.57 μm/100 V and that of defocus electrode is 1.09 μm/100 V. The hysteresis of actuator is limited to ten percents of the maximal displacement. With the ambient temperature increasing from 13℃ to 25℃, the P-V of defocus of the mirror surface is enlarged by 1.37 μm and the P-V of other distortions, such as astigmatism, coma and spherical aberration, is enlarged by 0.15 μm. The frequency response of the bimorph mirror is about 4 kHz. When the closed-loop control is on, intensity distributions at the image plane of distorted wave-fronts are effectively improved. The Strehl ratios increase from 0.02 to 0.95, and 0.03 to 0.54， respectively.

On-Line Long-Exposure Phase Diversity: a Powerful Tool for Sensing Quasi-Static Aberrations of Extreme Adaptive Optics Imaging Systems

The phase diversity technique is a useful tool to measure and pre-compensate for quasi-static aberrations, in particular non-common path aberrations, in an adaptive optics corrected imaging system. In this paper, we propose and validate by simulations an extension of the phase diversity technique that uses long exposure adaptive optics corrected images for sensing quasi-static aberrations during the scientific observation, in particular for high-contrast imaging. The principle of the method is that, for a sufficiently long exposure time, the residual turbulence is averaged into a convolutive component of the image and that phase diversity estimates the sole static aberrations of interest. The advantages of such a procedure, compared to the processing of shortexposure image pairs, are that the separation between static aberrations and turbulence-induced ones is performed by the long-exposure itself and not numerically, that only one image pair must be processed, that the estimation benefits from the high SNR of long-exposure images, and that only the static aberrations of interest are to be estimated. Long-exposure phase diversity can also be used as a phasing sensor for a segmented aperture telescope. Thus, it may be particularly useful for future planet finder projects such as EPICS on the European ELT.

Fainter and closer: finding planets by symmetry breaking

Imaging of planets is very difficult, due to the glare from their nearby, much brighter suns. Static and slowly-evolving aberrations are the limiting factors, even after application of adaptive optics. The residual speckle pattern is highly symmetrical due to diffraction from the telescope's aperture. We suggest to break this symmetry and thus to locate planets hidden beneath it. An eccentric pupil mask is rotated to modulate the residual light pattern not removed by other means. This modulation is then exploited to reveal the planet's constant signal. In well-corrected ground-based observations we can reach planets six stellar magnitudes fainter than their sun, and only 2-3 times the diffraction limit from it. At ten times the diffraction limit, we detect planets 16 magnitudes fainter. The stellar background drops by five magnitudes.

Efficient aberrations pre-compensation and wavefront correction with a deformable mirror in the middle of a petawatt-class CPA laser system

AbstractIn this paper, we describe the experimental validation of the technique of correction of wavefront aberration in the middle of the laser amplifying chain. This technique allows the correction of the aberrations from the first part of the laser system, and the pre-compensation of the aberrations built in the second part. This approach will allow an effective aberration management in the laser chain, to protect the optical surfaces and optimize performances, and is the only possible approach for multi-petawatt laser system from the technical and economical point of view. This approach is now possible after the introduction of new deformable mirrors with lower static aberrations and higher dynamic than the standard devices.

Correcting Highly Aberrated Eyes Using Large-stroke Adaptive Optics

To investigate the optical performance of a large-stroke deformable mirror in correcting large aberrations in highly aberrated eyes. A large-stroke deformable mirror (Mirao 52D; Imagine Eyes) and a Shack-Hartmann wavefront sensor were used in an adaptive optics system. Closed-loop correction of the static aberrations of a phase plate designed for an advanced keratoconic eye was performed for a 6-mm pupil. The same adaptive optics system was also used to correct the aberrations in one eye each of two moderate keratoconic and three normal human eyes for a 6-mm pupil. With closed-loop correction of the phase plate, the total root-mean-square (RMS) over a 6-mm pupil was reduced from 3.54 to 0.04 microm in 30 to 40 iterations, corresponding to 3 to 4 seconds. Adaptive optics closed-loop correction reduced an average total RMS of 1.73+/-0.998 to 0.10+/-0.017 microm (higher order RMS of 0.39+/-0.124 to 0.06+/-0.004 microm) in the three normal eyes and 2.73+/-1.754 to 0.10+/-0.001 microm (higher order RMS of 1.82+/-1.058 to 0.05+/-0.017 microm) in the two keratoconic eyes. Aberrations in both normal and highly aberrated eyes were successfully corrected using the large-stroke deformable mirror to provide almost perfect optical quality. This mirror can be a powerful tool to assess the limit of visual performance achievable after correcting the aberrations, especially in eyes with abnormal corneal profiles.

Phase retrieval from speckle images

In ground-based astronomy, the inverse problem of phase retrieval from speckle images is a means to calibrate static aberrations for correction by active optics. It can also be used to sense turbulent wavefronts. However, the number of local minima drastically increases with the turbulence strength, mainly because of phase wrapping ambiguities. Multifocal phase diversity has been considered to overcome some ambiguities of the phase retrieval problem. We propose an effective algorithm for phase retrieval from a single focused image. Our algorithm makes use of a global optimization strategy and an automatically tuned smoothness prior to overcome local minima and phase degeneracies. We push the limit of D/r(0)=4 achieved by Irwan and Lane [J. Opt. Soc. Am. A.15, 2302 (1998)] up to D/r(0)=11, which is a major improvement owing to the drastic increase in the problem complexity. We estimate the performances of our approach from consistent simulations for different turbulence strengths and noise levels (down to 1500 photons per image). We also investigate the benefit of temporal correlation.

Calibration and precompensation of noncommon path aberrations for extreme adaptive optics

Noncommon path aberrations (NCPAs) are one of the main limitations of an extreme adaptive optics (AO) system. NCPAs prevent extreme AO systems from achieving their ultimate performance. These static aberrations are unseen by the wavefront sensor and therefore are not corrected in closed loop. We present experimental results validating what we believe to be new procedures of measurement and precompensation of the NCPAs on the AO bench at ONERA (Office National d'Etudes et de Recherches Aérospatiales). The measurement procedure is based on refined algorithms of phase diversity. The precompensation procedure makes use of a pseudo-closed-loop scheme to overcome the AO wavefront-sensor-model uncertainties. Strehl ratio obtained in the images reaches 98.7% at 632.8 nm. This result allows us to be confident of achieving the challenging performance required for direct observation of extrasolar planets.

First On‐Sky High‐Contrast Imaging with an Apodizing Phase Plate

We present the first astronomical observations obtained with an apodizing phase plate (APP). The plate is designed to suppress the stellar diffraction pattern by 5 mag from 2 - 9λ/D over a 180° region. Stellar images were obtained in the M' band (λc = 4.85 μm) at the MMTO 6.5 m telescope, with adaptive wave-front correction made with a deformable secondary mirror designed for low thermal background observations. The measured point-spread function (PSF) shows a halo intensity of 0.1% of the stellar peak at 2λ/D (0.36''), tapering off as r-5/3 out to radius 9λ/D. Such a profile is consistent with residual errors predicted for servo lag in the AO system. We project a 5 σ contrast limit, set by residual atmospheric fluctuations, of 10.2 mag at 0.36'' separation for a 1 hr exposure. This can be realized if static and quasi-static aberrations are removed by differential imaging, and is close to the sensitivity level set by thermal background photon noise for target stars with M' > 3. The advantage of using the phase plate is the removal of speckle noise caused by the residuals in the diffraction pattern that remain after PSF subtraction. The APP gives higher sensitivity over the range (2-5) λ/D than direct imaging techniques.