Phase retrieval (PR) technology can reconstruct the complex amplitude information of the entrance pupil surface from the captured defocus intensity images, and has been successfully applied in many scientific fields such as astronomical observation, biomedical imaging and digital signal restoration. For low numerical aperture (NA) optical systems, the point spread function (PSF) can be calculated using the Fresnel diffraction propagation theory based on Fourier transform, ignoring the polarization field of the light field. However, for high-NA systems, the focal spot not only includes the transverse component, but also the longitudinal component accounts for a proportion that cannot be ignored, thus necessitating a vector model when calculating the PSF in the non-paraxial region. In this paper, the vector diffraction calculation model with arbitrary defocus distance based on the extended Nijboer-Zernike (ENZ) theory is established, which can characterize the light field components in three directions under the Cartesian coordinate system. What’s more, a modified Gauss-Newton theory is innovatively applied to the axial phase difference PR model. Compared with the traditional first-order algorithm, the second-order algorithm can reduce the number of iterations. In addition, so as to verify the effectiveness of the proposed method, numerical simulations matching the physical model are carried out, the results show that the proposed method can accurately reconstruction the wavefront with high robustness. In conclusion, the established vector PR model in this paper would provide a creatively guidance for wavefront measurement of high-NA optical systems that is significant in the fields of semiconductor lithography, micro imaging and micro manipulation.
White Light Scanning Interferometry (WLSI) is a mature and key method of non-contact three-dimensional (3D) morphometry. However, bat-wing is an inherent problem with WLSI, introducing systematic errors to the measurement results. In this paper, we proposed a filtering algorithm based on the convolutional neural networks (CNN) to solve the problem. A 450 nm standard step is tested to verify the effectiveness of the algorithm. The results show that the method can effectively suppress the batwing effect.
Infrared imaging system is widely used in unmanned aerial vehicle (UAV) detection because of the advantage of precise monitoring and anti-interference. However, it is difficult to simultaneously achieve large field of view (FOV) and light weight. In this paper, we propose a compact infrared panoramic annular lens (PAL) system with a large FOV and a three-piece simple structure, which contains three standard spherical lenses and has a FOV of (30°~100°) ×360°, total length of 51.6 mm, maximum diameter of 72 mm, focal length of 2.2 mm, and F number of three. The modulation transfer function of the system is higher than 0.7 at the Nyquist frequency, and F-theta distortion is controlled to less than 2%, which can meet the requirements of UAV detection. In addition, we use optical compensation method to achieve athermalized design in the range of -40°C~+80°C. The system possesses low sensitivity in tolerance, therefore we design a straight-tube mechanical structure for the system to simplify the assembly process and ensure the assembly precision at the same time. The PAL system we proposed is easy to be carried by UAVs due to its features of large FOV and lightweight, which can achieve accurate detection, large-scale monitoring, target recognition and tracking in harsh environments. It has important application value in military, security monitoring, machine vision and other fields.
With the advancement of aerospace technology, space debris generated by the collision and shedding of failed spacecraft is increasing, which threatens the safe operation of spacecraft in orbit seriously, and arouses people's attention to the detection of space debris. To achieve high-performance detection in dark environments, we propose a large relative aperture space-based detection optical system, which has a field of view of 16°, focal length of 182mm, F number of 1.52, and a working wavelength of 450~850nm. The system contains total 11 lenses, making the imaging performance more sensitive to temperature, therefore, we carry out thermal analysis for the system and use optical compensation method to achieve athermalized design. Finally, the system can work in the range of -10°C~+30°C, and the variation of the radius of the spot diagram with temperature is less than 3μm. In addition, we control the influence of stray light in the design process in order to observe bright and dark targets simultaneously. The numerical simulation results demonstrate that the veiling glare index of the system is 2.9%, which meets the requirement of dark object observation. The proposed optical system with large relative aperture and excellent imaging quality could be applied to accurate detection of space debris.
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.
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