Technique for enhancing the accuracy of the Rayleigh-Sommerfeld convolutional diffraction through the utilization of independent spatial sampling.

The Rayleigh-Sommerfeld diffraction integral (RSD) is a rigorous solution that precisely satisfies both Maxwell's equations and Helmholtz's equations. It seamlessly integrates Huygens' principle, providing an accurate description of the coherent light propagation within the entire diffraction field. Therefore, the rapid and precise computation of the RSD is crucial for light transport simulation and optical technology applications based on it. However, the current FFT-based Rayleigh-Sommerfeld integral convolution algorithm (CRSD) exhibits poor performance in the near field, thereby limiting its applicability and impeding further development across various fields. The present study proposes, to our knowledge, a novel approach to enhance the accuracy of the Rayleigh-Sommerfeld convolution algorithm by employing independent sampling techniques in both spatial and frequency domains. The crux of this methodology involves segregating the spatial and frequency domains, followed by autonomous sampling within each domain. The proposed method significantly enhances the accuracy of RSD during the short distance while ensuring computational efficiency.

Technique for enhancing the accuracy of the Rayleigh-Sommerfeld convolutional diffraction through the utilization of independent spatial sampling: publisher's note.

This publisher's note contains a correction to Opt. Lett.49, 1385 (2024)10.1364/OL.509688.

Generation controllable optical chain using an optical pen.

An aperiodic snake-like optical chain has been proposed and generated by using an optical pen technique, whose numbers and positions of focal points are controllable. Moreover, by introducing a fan phase together with a twisted phase into the optical pen technique, a self-rotation optical chain can be obtained; meanwhile, it transforms the bright optical chain into a twisted optical chain with a rotating hollow region in a three-dimensional (3D) space. The properties of the rotatable focal points and the variable diameters of cross-sectional intensities during the propagation of the optical chain are demonstrated in the experimental results. Consequently, this research framework can be applied in the techniques such as deep multiplexing and rotation angle multiplexing while also enabling the realization of multiple capture sites and more intricate manipulations.

Full-angle single-shot quantitative phase imaging based on Kramers-Kronig relations.

As a non-interference and non-iterative method, annular-illumination quantitative phase imaging based on Kramers-Kronig relations (AIKK) can realize phase measurement with full-angle resolution enhancement under multiple exposures. In order to completely record the object spectrum with a single shot, we proposed a colorful complementary illumination method in the recording process. The angle of this illumination mode is not symmetrical with each other, so the spectrum between the three channels can complement each other to avoid spectrum loss caused by spectrum conjugation. Meanwhile, the three spectral segments of full-angle information spectrum respectively carried by three wavelengths can be recorded. Additionally, the numerical filter is applied to correct the overlapped spectrum in the reconstruction process. Simulation and experimental results show that this method can achieve high spatiotemporal resolution quantitative phase measurement.

Generation of a modulated versatile spiral beam with varying intensity distribution along the propagation.

A new type of versatile spiral beam (VSB) is generated based on the competition mechanism between the self-focusing property of ring Airy beam and metalens phase distribution, which exhibits twisted properties and optical bottle structure along the propagation direction. The number of spiral lobes, rotation direction, shape and magnification times on the cross section of the proposed beam can be customized by flexibly tuning diffraction distance, topological charge and constant parameter. Therefore, the VSB can be viewed as tunable three-dimensional (3D) spiral beam, and our scheme has the superiority with more diverse and tunable intensity distribution. The properties of intensity distribution variation depended on the propagation distance and topological charge are demonstrated convincingly by employing the Poynting vector intuitive presentation the energy flow. The VSBs with the aid of above-mentioned properties are beneficial for guiding microparticles along the designed spiral path and capturing multiple microparticles into the closed dark regions. Finally, the modulated spiral beams are implemented as tool for particle manipulation in the three dimensional space to demonstrate the advantages of the modulated spiral beam and we can observe the stable trapping of the particles.

Single-shot resolution-enhancement quantitative phase imaging based on Kramers-Kronig relations.

A single-shot quantitative phase imaging (QPI) method with improved resolution based on Kramers-Kronig relations is proposed. Two pairs of in-line holograms containing the high-frequency information in the x and y directions are recorded by a polarization camera in a single exposure, which makes the recording setup compact. The deduced Kramers-Kronig relations based on multiplexing polarization can successfully separate recorded amplitude and phase information. The experimental results demonstrate that the resolution can be doubled by using the proposed method. This technique is expected to be used in the fields of biomedicine and surface inspection.

Vortex array generation based on quasi-Talbot effects.

A lens-less method for generating vortex arrays with tunable parameters is proposed based on quasi-Talbot effects. By illuminating a two-dimensional periodic sinusoidal grating with a vortex beam carrying a fourth-order cross-phase, the continuous vortex array structure can be generated in the Fresnel diffraction region. Due to the shaping effect of the fourth-order cross-phase on the vortex beam, by changing the constant parameter of the fourth-order cross-phase, it is possible to shape the generation of optical vortex arrays at different positions. This will somewhat broaden the flexibility of the lens-free optical vortex array in terms of generation position. In addition, the generation of polygonal optical vortex arrays is achieved by higher-order cross-phases of different orders. This technique has potential applications in various fields such as optical tweezers, multi-particle screening, microscopic manipulation, etc.

Multiple-dimensional multiplexed holography based on modulated chiro-optical fields.

Orbital angular momentum (OAM) multiplexing technology has been developed in the optical information encryption fields. Here, the modulated chiro-optical OAM (MC-OAM) holography is proposed to further improve information security capacity, which integrates the OAM multiplexing technology with the chiro phase modulation. The orthogonality of the axicon parameter, chiro coefficient and rotation angle modulating the chiro phase distributions are analyzed, respectively, which demonstrate their potential usages as extra degrees of freedom besides the topological charge (TC). Those three parameters combining TC serve as four optical keys, which provides a four-dimensional spatial multiplexing method for information security. Furthermore, we have demonstrated that TC minimum interval of the fractional MC-OAM reaches 0.01. The experimental and simulation results exhibit the essential properties in selectivity and multiplexing of MC-OAM holography. This method can significantly increase the holographic information capacity and safety and inspire widespread applications, such as display, information security and communication.

Residue calibrated least-squares unwrapping algorithm for noisy and steep phase maps.

This work proposes a robust unwrapping algorithm for noisy and steep phase maps based on the residue calibrated least-squares method. The proposed algorithm calculates and calibrates the residues in the derivative maps to get a noise-free Poisson equation. Moreover, it compensates for the residuals between the wrapped and unwrapped phase maps iteratively to eliminate approximation errors and the smoothing effect of the least-squares method. The robustness and efficiency of the proposed algorithm are validated by unwrapping simulated and experimentally wrapped phase maps. Compared with the other three typical algorithms, the proposed algorithm has the most effective performance in noisy and steep phase unwrapping, providing a reliable alternative for practical applications.

Problems on polarization aberrations in large aperture dynamic interferometry based on the polarization phase shifting technique.

The polarization based phase shifting method is an effective way for dynamic measurements. However, when this technique is applied to the measurements of large optics, the interferometric results are easily limited by the birefringence of large optics. The birefringence changes the polarization states of reference light and test light, and brings constant polarization aberrations into the measurement results independent of the phase shifting procedure. In this article, the detailed theoretical analysis on the mechanism of polarization aberration is presented. Afterwards, we propose a new interferometric method to determine the birefringence effects by measuring the transmitted wavefronts of the large optics, which are considered as birefringent samples. Theoretical analysis shows that the polarization error in the linearly polarized system can be corrected by two independent measurements with orthogonal polarization states. The phase retardance can be obtained from the wavefront difference of the transmitted wavefronts when switching the polarization states of the incident lights. The birefringence distribution obtained is used to calibrate the polarization aberrations in the measurement result of a homemade large aperture measurement platform and the correction result is compared with the result via the wavelength tuning phase shifting method. The elimination of the polarization aberrations can be observed in the final results.

Phase unwrapping algorithm for a segmented phase based on iterative pseudo-phase inpainting.

Segmented phase unwrapping is an intractable problem in the phase-shifting technique. To solve the problem, this Letter presents an iterative pseudo-phase inpainting algorithm (IPPI). By means of image inpainting, the IPPI can be used to realize the pseudo-phases connecting each other among these phase islands. The error points in the pseudo-phases can be reduced by iterations of phase inpainting with the assistance of the reference pseudo-phase obtained by introducing the numerical carrier frequency and using the 2D Fourier transform. Compared with other methods, the proposed algorithm does not have to do any processing on the effective area of the wrapped phase, which ensures the authenticity of the result. The simulated and experimental verifications show that the proposed method not only possesses high precision, but also can be applied to a segmented phase with severe noise.

DL-SI-DHM: a deep network generating the high-resolution phase and amplitude images from wide-field images.

Structured illumination digital holographic microscopy (SI-DHM) is a high-resolution, label-free technique enabling us to image unstained biological samples. SI-DHM has high requirements on the stability of the experimental setup and needs long exposure time. Furthermore, image synthesizing and phase correcting in the reconstruction process are both challenging tasks. We propose a deep-learning-based method called DL-SI-DHM to improve the recording, the reconstruction efficiency and the accuracy of SI-DHM and to provide high-resolution phase imaging. In the training process, high-resolution amplitude and phase images obtained by phase-shifting SI-DHM together with wide-field amplitudes are used as inputs of DL-SI-DHM. The well-trained network can reconstruct both the high-resolution amplitude and phase images from a single wide-field amplitude image. Compared with the traditional SI-DHM, this method significantly shortens the recording time and simplifies the reconstruction process and complex phase correction, and frequency synthesizing are not required anymore. By comparsion, with other learning-based reconstruction schemes, the proposed network has better response to high frequencies. The possibility of using the proposed method for the investigation of different biological samples has been experimentally verified, and the low-noise characteristics were also proved.

Auto-focusing and quantitative phase imaging using deep learning for the incoherent illumination microscopy system.

It is well known that the quantitative phase information which is vital in the biomedical study is hard to be directly obtained with bright-field microscopy under incoherent illumination. In addition, it is impossible to maintain the living sample in focus over long-term observation. Therefore, both the autofocusing and quantitative phase imaging techniques have to be solved in microscopy simultaneously. Here, we propose a lightweight deep learning-based framework, which is constructed by residual structure and is constrained by a novel loss function model, to realize both autofocusing and quantitative phase imaging. It outputs the corresponding in-focus amplitude and phase information at high speed (10fps) from a single-shot out-of-focus bright-field image. The training data were captured with a designed system under a hybrid incoherent and coherent illumination system. The experimental results verify that the focused and quantitative phase images of non-biological samples and biological samples can be reconstructed by using the framework. It provides a versatile quantitative technique for continuous monitoring of living cells in long-term and label-free imaging by using a traditional incoherent illumination microscopy system.

Optical scanning Fourier ptychographic microscopy.

We propose a lower-cost and practical active scanning optical scanning Fourier ptychographic microscopy (OSFPM). Featured is a simple setup of Galvo mirrors capable of scanning large-sized objects. The active scanning laser beam is projected onto the sample in a circular pattern to form multiple lower-resolution images. With multiple lower-resolution images, a higher-resolution image is subsequently reconstructed. The OSFPM is able to more precisely control the overlap of the incident light illumination as compared to that in conventional LED-based or other laser-based scanning FPM systems. The proposed microscope is also suitable for applications where a larger size of the object needs to be imaged with efficient illumination.

High-efficiency full-surface defects detection for an ICF capsule based on a null interferometric microscope.

Laser inertial confinement fusion (ICF) triggers a nuclear fusion reaction via the evenly compressed capsule containing deuterium tritium fuel with a high-power laser. However, isolated defects on the surface of the capsules reduce the probability of ignition. In this paper, we present a full-surface defects detection method based on a null interferometric microscope (NIM) to achieve high-precision, high-efficiency, and full-surface defects detection on ICF capsules. A dynamic phase-shifting module is applied to the NIM to achieve a single-shot measurement in a single subaperture. With the capsule controlling system, the capsule is rotated and scanned along a planned lattice to get all subapertures measured. The eccentricity error can be measured from wavefront aberrations and compensated online to guarantee the measurement accuracy during the scanning process. After the scanning process, all of the surface defects are identified on the full-surface map. Theories and experimental results indicate that for the capsule with 875-µm-diameter, the lateral resolution could reach 0.7 µm and the measurement time is less than 1 h. The number of sampling points can reach about 50 million. To the best of our knowledge, our proposed system is the first to achieve full-surface defects detection of ICF capsules with such high efficiency and high resolution at the same time.

Numerical dark-field imaging using deep-learning.

Dark-field microscopy is a powerful technique for enhancing the imaging resolution and contrast of small unstained samples. In this study, we report a method based on end-to-end convolutional neural network to reconstruct high-resolution dark-field images from low-resolution bright-field images. The relation between bright- and dark-field which was difficult to deduce theoretically can be obtained by training the corresponding network. The training data, namely the matched bright- and dark-field images of the same object view, are simultaneously obtained by a special designed multiplexed image system. Since the image registration work which is the key step in data preparation is not needed, the manual error can be largely avoided. After training, a high-resolution numerical dark-field image is generated from a conventional bright-field image as the input of this network. We validated the method by the resolution test target and quantitative analysis of the reconstructed numerical dark-field images of biological tissues. The experimental results show that the proposed learning-based method can realize the conversion from bright-field image to dark-field image, so that can efficiently achieve high-resolution numerical dark-field imaging. The proposed network is universal for different kinds of samples. In addition, we also verify that the proposed method has good anti-noise performance and is not affected by the unstable factors caused by experiment setup.

Modelling and correction for polarization errors of a 600†mm aperture dynamic Fizeau interferometer.

The polarization errors of large aperture dynamic interferometers based on the polarization phase shifting method are mainly coming from the effects of imperfect polarized elements and birefringence of large elements. Using the Lissajous ellipse fitting algorithm to correct the influence of the polarized device can effectively eliminate single and double frequency print through errors. We develop a wave plate model for analyzing the birefringence effect, and on this basis, we establish the relationship between the calculated phase and the ideal phase distribution. Experiments are carried out on a 600mm aperture Fizeau interferometer and then compared with the result acquired through the wavelength tuning method. The difference between PV is only 0.002λ.

A flexible numerical calculation method of angular spectrum based on matrix product.

Fast Fourier transform (FFT) is the most commonly used mathematical method in numerical calculation, and the FFT-based angular spectrum method (ASM) is also used widely in diffraction calculation. However, the frequency and spatial sampling rules in FFT limit the effective propagation distance and the observation window range of ASM. A novel method for calculating the angular spectrum based on the matrix product is proposed in this Letter. This method realizes the fast calculation of discrete Fourier transform (DFT) based on the matrix product, in which the sampling matrix is orthogonally decomposed into two vectors. Instead of FFT, angular spectrum diffraction calculation is carried out based on the matrix product, which is named the matrix product ASM. The method in this Letter uses a simple mathematical transformation to achieve maximum compression of the sampling interval in the frequency domain, which significantly increases the effective propagation distance of the angular spectrum. Additionally, the size of the observation window can be enlarged to obtain a wider calculation range by changing the spatial sampling of the output plane.

High-contrast anisotropic edge enhancement free of shadow effect.

We propose a Bessel-like composite vortex filter to perform high-contrast and power-controlled anisotropic edge enhancement with shadow-effect-free and low background noise. The background noise, which is commonly found and strongly decreases the filtered image quality in previous anisotropic vortex filters, is effectively reduced by suppressing the side lobes of the system point spread function, thereby increasing the image edge contrast to 0.98. The shadow effect is totally eliminated by keeping the radial symmetry of the filtering process, which makes edges sharper and improves image resolution. By introducing a weighting factor between two opposite vortex filter components, the power of edge enhancement becomes controllable. Numerical simulations and experimental results prove that the proposed filter achieves higher-contrast edge enhancement for both phase-contrast and amplitude-contrast objects.

Accurate phase-shift estimation for fringe-pattern profilometry.

Fringe-pattern profilometry (FPP) has been widely used for phase reconstruction. It involves the use of phase shifting for phase retrieval. Phase-shift errors can affect the accuracy of phase reconstruction, and limited studies have been dedicated to studying phase-shift errors due to experimental, human, or environmental factors. We propose a simple and yet accurate phase-shift estimation method. Our study shows that the method is able to accurately estimate the actual phase shifts used in the FPP technique. The proposed method can find its applications in FPP and other phase shifting-based three-dimensional imaging techniques.