Expansion of the Laser Beam Wavefront in Terms of Zernike Polynomials in the Problem of Turbulence Testing

The results of a study of the wavefront distortions of laser radiation caused by artificial turbulence obtained in laboratory conditions using a fan heater are presented. Decomposition of the wavefront in terms of Zernike polynomials is a standard procedure that traditionally is used to investigate the set of existing aberrations. In addition, the spectral analysis of the wavefront dynamics makes it possible to estimate the fraction of the energy distributed between different Zernike modes. It is shown that the fraction of energy related to the low-order polynomials is higher compared to the high-order polynomials. Also, one of the consequences of Taylor’s hypothesis is confirmed—low-order aberrations are slower compared to the higher-order ones.

Is Aberrometric Analysis Based on Zernike Modes That May Not be Correct?

Context: Aberrometric analysis of the wavefront in patients with refractive disorders is performed using the Zernike pyramid mode and based on that, a treatment plan is determined however, it is not clear what Zernike modes are derived from mathematical analysis, exactly how much they correspond to the clinical facts this article discusses ways to study this issue. Evidence Acquisition: One of the methods for studying optical systems is the aberrometry of wavefront. the wavefront is a two-dimensional surface perpendicular to a bunch of parallel light rays, that all these rays have the same phase on this surface (because light emits sinusoidally and therefore has multiple identical phases) whenever these rays pass through a refractive surface, it is also called the reference level this refractive index will be ideal if the homogeneity of these rays is maintained and the rays of this bunch of light will be able to focus at one point, but if the by passing light through the refractive surface the wavefront will be disturbed and the lights on this surface have different phases than the reference surface then it is said there is a discrepancy or deviation between the reference surface and the wavefront. Therefore, aberration is the creation of the distance of the wavefront in a certain phase from the refractive surface or reference surface. When we say refractive surface, we do not mean a specific place like the cornea because other than the cornea other factors such as crystalline lens, vitreous, retin even tear layer they are involved in creating aberrations, but usually the pupil range is considered as the reference surface. Results: Modes z-13 and z13 of the fourth order and modes z04 and z-24, z24 from the fifth order and modes z-15, z15 of six order and modes z06, z-26, z26 of seventh order they are not pure and mathematically they have some lower order which may cause in analysis aberrometry disruption as a result, the relevant orders have a little more or less value. Conclusions: There are no strong clinical reasons for Zernike modes to be a fully accurate description of aberromerty, so clinicians should consider other clinical data and findings in their interpretation. Some modes of high-order Zernike have sentences of low-order This can cause abnormal analysis.

Defocused Image Deep Learning Designed for Wavefront Reconstruction in Tomographic Pupil Image Sensors

Mathematical modelling methods have several limitations when addressing complex physics whose calculations require considerable amount of time. This is the case of adaptive optics, a series of techniques used to process and improve the resolution of astronomical images acquired from ground-based telescopes due to the aberrations introduced by the atmosphere. Usually, with adaptive optics the wavefront is measured with sensors and then reconstructed and corrected by means of a deformable mirror. An improvement in the reconstruction of the wavefront is presented in this work, using convolutional neural networks (CNN) for data obtained from the Tomographic Pupil Image Wavefront Sensor (TPI-WFS). The TPI-WFS is a modified curvature sensor, designed for measuring atmospheric turbulences with defocused wavefront images. CNNs are well-known techniques for its capacity to model and predict complex systems. The results obtained from the presented reconstructor, named Convolutional Neural Networks in Defocused Pupil Images (CRONOS), are compared with the results of Wave-Front Reconstruction (WFR) software, initially developed for the TPI-WFS measurements, based on the least-squares fit. The performance of both reconstruction techniques is tested for 153 Zernike modes and with simulated noise. In general, CRONOS showed better performance than the reconstruction from WFR in most of the turbulent profiles, with significant improvements found for the most turbulent profiles; overall, obtaining around 7% of improvements in wavefront restoration, and 18% of improvements in Strehl.

An Automatic Optimized Method for a Digital Optical Phase Conjugation System in Focusing through Scattering Media

In this paper, a reliable automatic optimized method for a digital optical phase conjugation (DOPC) system based on a multipopulation genetic algorithm (MPGA) is proposed for improving the compensation quality of DOPC. The practical implementation and compensation quality of DOPC in focusing through scattering media are greatly limited by imperfect pixel alignment, optical aberration, and mechanical error in the DOPC system. For comprehensively solving the above problems, the concept of global optimization is introduced by Zernike polynomials (Zernike modes) to characterize overall imperfections, and MPGA is used to search for the most optimal Zernike coefficient and compensate for the overall imperfections of the DOPC system. The significant optimization ability of the proposed method is verified in DOPC-related experiments for focusing through scattering media. The peak-to-background ratio (PBR) of the OPC focus increases 174 times that of the initial OPC focus. Furthermore, we evaluated the optimization results of the proposed method with a fitness function of intensity fitness and correlation coefficient fitness in MPGA. The results show that the optimized capability is excellent and more efficiently used than the correlation coefficient fitness function in the Zernike modes.

Leveraging the orthogonality of Zernike modes for robust free-space optical communication

Free-space optical communication systems exploit the properties of light beams to transfer information through a free-space link. Indeed such systems provide an exciting alternative for communication. Here we introduce information transfer through free-space using a laser beam having its phase encoded with multiple orthogonal aberration modes. We use Zernike polynomials, which form a complete basis set, to represent the aberration modes. The user information is converted to co-efficients of the Zernike modes which are summed digitally to obtain the resultant phase profile. A single phase modulating device then reads the resultant phase to shape the wavefront of the beam to be transmitted. The receiving station estimates the co-efficients of all modes in the beam from a single measurement of a wavefront sensor, to retrieve the user information. We demonstrate data transfer using multiple modes, each with multiple strengths, and external perturbation compensation using the completeness property of the modes.

Compensating atmospheric turbulence with CNNs for defocused pupil image wavefront sensors

Adaptive optics are techniques used for processing the spatial resolution of astronomical images taken from large ground-based telescopes. In this work, computational results are presented for a modified curvature sensor, the tomographic pupil image wavefront sensor (TPI-WFS), which measures the turbulence of the atmosphere, expressed in terms of an expansion over Zernike polynomials. Convolutional neural networks (CNN) are presented as an alternative to the TPI-WFS reconstruction. This technique is a machine learning model of the family of artificial neural networks, which are widely known for its performance as modeling and prediction technique in complex systems. Results obtained from the reconstruction of the networks are compared with the TPI-WFS reconstruction by estimating errors and optical measurements (root mean square error, mean structural similarity and Strehl ratio). The reconstructed wavefronts from both techniques are compared for wavefronts of 153 Zernike modes. For this case, a detailed comparison and grid search to find the most suitable neural network is performed, searching between multi-layer perceptron, CNN and recurrent networks topologies. In general, the best network was a CNN trained for TPI-WFS reconstruction, achieving better performance than the reconstruction software from TPI-WFS in most of the turbulent profiles, but the most significant improvements were found for higher turbulent profiles that have the lowest r0 values.

Focal-plane wavefront sensing with the vector-Apodizing Phase Plate

Context. One of the key limitations of the direct imaging of exoplanets at small angular separations are quasi-static speckles that originate from evolving non-common path aberrations (NCPA) in the optical train downstream of the instrument’s main wavefront sensor split-off. Aims. In this article we show that the vector-Apodizing Phase Plate (vAPP) coronagraph can be designed such that the coronagraphic point spread functions (PSFs) can act as wavefront sensors to measure and correct the (quasi-)static aberrations without dedicated wavefront sensing holograms or modulation by the deformable mirror. The absolute wavefront retrieval is performed with a non-linear algorithm. Methods. The focal-plane wavefront sensing (FPWFS) performance of the vAPP and the algorithm are evaluated via numerical simulations to test various photon and read noise levels, the sensitivity to the 100 lowest Zernike modes, and the maximum wavefront error (WFE) that can be accurately estimated in one iteration. We apply these methods to the vAPP within SCExAO, first with the internal source and subsequently on-sky. Results. In idealized simulations we show that for 107 photons the root mean square (rms) WFE can be reduced to ∼λ/1000, which is 1 nm rms in the context of the SCExAO system. We find that the maximum WFE that can be corrected in one iteration is ∼λ/8 rms or ∼200 nm rms (SCExAO). Furthermore, we demonstrate the SCExAO vAPP capabilities by measuring and controlling the 30 lowest Zernike modes with the internal source and on-sky. On-sky, we report a raw contrast improvement of a factor ∼2 between 2 and 4 λ/D after five iterations of closed-loop correction. When artificially introducing 150 nm rms WFE, the algorithm corrects it within five iterations of closed-loop operation. Conclusions. FPWFS with the vAPP coronagraphic PSFs is a powerful technique since it integrates coronagraphy and wavefront sensing, eliminating the need for additional probes and thus resulting in a 100% science duty cycle and maximum throughput for the target.