Phase retrieval (PR) is widely applied in wavefront sensing for adaptive optics, diagnosing the aberrations, and wavefront measurement of optics elements. A single lens is often used in PR models to achieve better transmission of optical radiation thereby avoiding loss of high frequency information. In this paper, the sampling requirement of PR wavefront measurement model based on numerical Fourier optical theory is analyzed clearly. First, combined with the Fresnel diffraction theory, the diffraction field of the wavefront after passing through the lens is established. Next, according to the Nyquist sampling theorem, the sampling requirements for the phase factor of wavefront spatial frequency are deduced. Further, according to the relationship between the pixel size of CCD and the sampling pitch of pupil surface, the constraints and applicable range of PR model based on various diffraction transform are discussed quantitatively. The numerical simulations are carried out to verify the effectiveness of PR model based on the GS algorithm within the analyzed diffraction constraints, which shows that the recovery accuracy of the PR model can reach 0.0025 λ. The established sampling strategy and the constraint theory in this paper would provide a theoretical guidance for full-band wavefront measurement of the PR technology.
As a computational imaging method, phase retrieval has wide applications in image reconstruction, wavefront detection, image encryption, etc. It is an image-based wavefront sensing technique and compared with some other traditional measurement methods such as interferometry, phase retrieval has the advantages of easy operation, high accuracy and strong adaptability to the environment. Conventional phase retrieval algorithms, such as the Gerchberg–Saxton (GS) algorithm, retrieve wavefront by iterative calculation. But limited by finite information of the captured diffractive light filed, the calculation process is easy to fall into local minimum value and stagnation occurs in practical, making it unable to converge to the right wavefront. In this paper, in order to improve this phenomenon, a phase retrieval method combined with the zone plate is proposed in this paper. In this method, zone plates are added into the traditional iterative phase retrieval algorithm to modulate the incident wavefront and combined with the multi-focus property, it can collect more effective information about the wavefront in a single optical intensity distribution image and realize a better wavefront reconstruction result. Simulation results indicate that by taking zone plates into calculation, more effective reconstruction results can be acquired. On the one hand, the recovery residual is smaller compared with conventional lens. On the other, although all of these methods reach to a stagnation, zone-plate-based methods are more efficient to get a better result.
In the Multi-intensities phase retrieval processing, the measurement uncertainty of the defocus distance undermines its measurement accuracy. In this paper, using a general phase retrieval experimental arrangement, we propose an adaptive autofocusing nonlinear optimization phase retrieval algorithm based on the extended Nijboer-Zernike (ENZ) theory. This method concurrently accomplishes correction of defocusing position error and the wavefront measurement requiring without additional facility. The numerical experiments show that the proposed method accuracy searching for the optimal defocusing position is superior to 10 μm among different measurement planes. The numerical experiments show that the wavefront measurement accuracy with the proposed method is superior to λ/100 , RMSE.
In recent years, with the development of new materials, transparent objects are playing an increasingly important role in many fields, from industrial manufacturing to military technology. However, transparent objects sensing still remains a challenging problem in the area of computational imaging and optical engineering. As an indispensable part of 3-D modeling, transparent object sensing is a long-standing research topic, which aims to reconstruct the surface shape of a given transparent object using various kinds of measurement methods. In this paper, we put forward a new method for the sensing of such objects. Specifically, we focus on the sensing of thin transparent objects, including thin films and various kinds of nano-materials. The proposed method consists of two main steps. Firstly, we use a deep convolutional neural network to predict the original distribution of the objects from its recorded intensity pattern. Secondly, the predicted results are used as initial estimates, and the iterative projection phase retrieval algorithm is performed with the enhanced priors to obtain finer reconstruction results. The numerical experiment results turned out that, with the two steps, our method is able to reconstruct the surface shape of a given thin transparent object with a high speed and simple experimental setup. Moreover, the proposed method shows a new path of transparent object sensing with the combination of state-of-art deep learning technique and conventional computational imaging algorithm. It indicates that, following the same framework, the performance of such method can be significantly improved with more advanced hardware and software implementation.
It is necessary to fit the discrete sampling value of the optical element surface obtained by measuring equipment, because the results of fitting are useful for manufacturing and optical design. The commonly used fitting methods are X-Y polynomial approximation, Zernike polynomial approximation and radial basis function (RBF) approximation. Compared with others, radial basis function is more suitable to fit the complex optical surface. However, the further improvement of fitting accuracy and cost are limited by the fixed shape parameter of the classic RBF approximation. In this paper, we propose the sparse radial basis function approximation with spatially variable shape parameters to fit discretely sampled optical surfaces. Our main purpose is to improve fitting accuracy and to reduce computational cost. Then, we analyze the impact of the spatial distribution of RBF nodes on fitting. Finally, we compare the accuracy and cost between the classic RBF approximation and the sparse RBF approximation with spatially variable shape parameters by fitting various complex surface.
During the fabricating procedure of optical elements, computer-controlled tools will introduce some periodic structured errors, named mid-spatial frequency errors, which may scatter the laser beams, create filamentous spots or even damage the optical components in Inertial Confinement Fusion (ICF) high power laser system. Transverse translation diverse phase retrieval (TTDPR) is an ingenious phase retrieval method for measuring aspheric and freeform surfaces. In this paper, we explore the measurement of optical elements with mid-spatial frequency errors by using TTDPR. First, we briefly introduce the features of mid-spatial frequency errors and establish the relation between mid-spatial frequency errors and diffraction pattern. Second, with the knowledge of the mid-spatial frequency error, we analyze the feasibility of optical elements with mid-spatial frequency error measurement by using TTDPR. In order to improve the convergence and measurement accuracy of phase retrieval algorithm, initial inputs are optimized for the following iterative phase retrieval algorithm. Results indicate that a 50% higher reconstruction accuracy can be achieved, when the initial input is the ideal lens to recover the phase of lens with mid-spatial frequency errors. For TTDPR, sub-aperture illuminated with overlapping part among adjacent sub-apertures will improve accuracy of iterative phase algorithm than never overlapped sub-aperture, while it encumbers the efficiency of iterative phase retrieval algorithm. Based on the characteristics of the particular optical surfaces, the influence of major parameter of sub-aperture including the size of sub-aperture and the overlapped proportion among adjacent sub-aperture to accuracy and efficiency of TTDPR are also discussed.
In inertial confinement fusion high energy system, the mid-spatial frequency (MSF) errors of optical elements induced by computer numerical control tools lead to damage to the optical system. Based on the characteristics of the mid-spatial frequency errors, it is measured by using phase retrieval technology. Compared with conventional measurement methods such as interferometry, MSF errors can be measured by phase retrieval without complex measurement systems and large aperture optical elements with MSF errors can be measured via phase retrieval in theory. In this paper, we compare multiple phase retrieval algorithms that are used to measure optical element with MSF errors and explore approaches to improve the quality of results. First, we briefly introduce the feature of MSF errors and the relation between the wavefront of optical element with MSF errors and its diffraction pattern. Second, multiple phase retrieval algorithms including error-reduction (ER) algorithm, hybrid input-output (HIO) algorithm and oversampling smoothness (OSS) algorithm are adapted for the measurement of MSF errors. According to the bandwidth and structure characteristics of MSF errors, the convergence speed and the accuracy of above algorithms are discussed and compared. Then, according to the characteristics of different algorithms, different retrieved wavefront phase via using these algorithms are integrated to improve the accuracy of results. Last, based on the feature of MSF errors, the priori knowledge of algorithms is also discussed to further gear up the convergence speed and the accuracy of algorithms.
The ripple errors of the lens lead to optical damage in high energy laser system. The analysis of sidelobe on the focal plane, caused by ripple error, provides a reference to evaluate the error and the imaging quality. In this paper, we analyze the diffraction characteristics of sidelobe of optical elements with ripple errors. First, we analyze the characteristics of ripple error and build relationship between ripple error and sidelobe. The sidelobe results from the diffraction of ripple errors. The ripple error tends to be periodic due to fabrication method on the optical surface. The simulated experiments are carried out based on angular spectrum method by characterizing ripple error as rotationally symmetric periodic structures. The influence of two major parameter of ripple including spatial frequency and peak-to-valley value to sidelobe is discussed. The results indicate that spatial frequency and peak-to-valley value both impact sidelobe at the image plane. The peak-tovalley value is the major factor to affect the energy proportion of the sidelobe. The spatial frequency is the major factor to affect the distribution of the sidelobe at the image plane.
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