This article presents a high-precision algorithm for extracting laser centroids using a four-quadrant detector (4QD), specifically designed for situations where laser position shifts happen on the nanoscale. The algorithm uses an iterative method to create a functional relationship between position changes and the differential output signals from the 4QD. We have validated the algorithm through simulations and experimental tests.
Wavefront aberration is a crucial metric for evaluating the imaging quality of an optical system and enhancing the accuracy of wavefront detection is of significant importance. Noise is a critical factor that affects detection accuracy. Simulating and suppressing noise can help explore the theoretical limit of wavefront detection and improve the actual measurement accuracy. We develop a comprehensive noise model where the input is a simulated, noise-free image in units of photons, and the output is a noisy digital signal. The model considers external disturbance noise, speckle noise, and camera noise. Speckle noise is selectively added based on the light source’s coherence. Camera noise is modeled using real camera parameters and includes photon shot noise, dark shot noise, readout noise, and quantization noise. Additionally, a noise suppression algorithm based on frame averaging is designed. We introduce the concept of a noise suppression factor, calculate this factor based on the noise characteristics and system properties, and apply it to the frame-averaged noisy image on a pixel-by-pixel basis, achieving effective noise reduction. Using the established noise model, we calculate the theoretical peak-to-valley (PV) and root mean square (RMS) limit determined by noise for two typical high-precision wavefront aberration detection systems: the Ronchi lateral shearing interferometry (LSI) system and the phase-diverse phase retrieval (PDPR) system. With our proposed noise suppression algorithm, the theoretical RMS limit can be reduced to 10% of the previous value, demonstrating its effectiveness in noise suppression. Our model provides a definitive standard for the theoretical accuracy limit of optical metrology, guiding the selection of hardware and the design of wavefront detection algorithms for subsequent research.
Current mainstream phase retrieval research is only applicable to monochromatic light wavelengths and relies on experimental devices such as narrowband filters. Especially when there is high noise or frequent reflections in the system, narrowband wavelengths may cause poor signal-to-noise ratio and unexpected artifacts, thereby reducing measurement accuracy. Therefore, phase retrieval with broadband sources has received widespread attention. In this paper, we proposed a fast broadband phase retrieval model based on Zernike coefficient matrix. Firstly, a coefficient matrix was established to represent the relationship between various Zernike coefficients at different wavelengths. In addition, we have utilized time division multiplexing technology to achieve a diffraction free iterative process, greatly improving computational efficiency. The numerical simulations are carried out to verify the effectiveness of broadband phase retrieval model.
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.
The grating lateral-shear interferometry has a wide range of applications in wavefront sensing. The lateral-shear interferometer based on Ronchi grating can be applied for high-precision wavefront aberration detection of lithography projection lenses, which is one of the critical issues to overcome lithography challenges. The conventional Ronchi shearing interferometer object grating consists of two sets of one-dimensional Ronchi grating lines perpendicular to each other in order to obtain wavefront information in two directions, namely X and Y. During the experiment, one set is moved into the optical path for phase shifting and measurement, then the other set of grating lines is repeatedly operated. To reduce the complexity of experimental operations, this paper proposes a lateral-shear interference system based on double checkerboard gratings. The object grating and image grating are both set as checkerboard grating, and the rotation angle of the checkerboard grating varies according to the optical system's shear rate, allowing each phase shift to obtain wavefront information in X and Y directions. Multiple uniform phase shifts are performed to extract ± 1 order diffraction wavefronts of X and Y directions. The shear wavefront of the optical system to be measured is calculated from the four-wave interference light field, then the original wavefront can be restored by differential Zernike. Through theoretical analysis and simulation, this double checkerboard system can achieve wave aberration measurement with the same accuracy as traditional Ronchi interferometers, improving the real-time performance of projection lenses wave aberration measurement, and providing more possibilities for subsequent structural improvements of Ronchi lateral-shear interferometer.
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.
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.
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