Asymmetric apodization in confocal scanning systems

A new class of superresolution pairs of pupil filters for three-dimensional, two-pupil confocal imaging is proposed. A distinctive feature of these filters is the asymmetry of their impulse response. For synthesizing the amplitude transmittance of such filters the Fourier transform properties of Hermitian functions are employed. It is shown that, with simple phase-only filters that belong to the class in question, either axial or unidirectional lateral superresolution is achieved.     

Design of three-dimensional superresolution filters and limits of axial optical superresolution

Theories to design a three-dimensional superresolution filter (TDSF) for confocal microscopy are proposed that can obtain a globally optimal solution through linear programming. The designed TDSF is proved to be a phase-only element introducing a phase delay of 0 or pi. Five design examples of the TDSF are presented to demonstrate the validity of these theories, Regardless of transverse superresolution, a curve of Seu(Ga+/-) defined as the maximum value of Strehl ratio S under the axial resolving power of Ga+/- is calculated to set the fundamental limits of axial optical superresolution. Finally, what is to our knowledge a novel analytic expression of Seu(Ga+/-) is deduced.     

Precise analysis of combination homogeneous-inhomogeneous-material superresolution filters with double-tunable modes

By using a Jones matrix, the precise expression for the pupil function of a two-adjustable-mode superresolving filter, a combination of a radial birefringent plate and a glass annular plate, is obtained. This filter can provide superresolution in both radial and axial adjustment operations, which can supplement each other in setting accuracy and superresolution range in practical use. As an adjustable filter, it is less dependent on wavelength. With the relative radius of the inner plate set to be epsilon=0.52 and the rotating angle set to be 45 degrees , this type of filter can achieve better superresolution performance than the continuous-phase filters reported in Opt. Lett.28, 607 (2003).     

Comparison of superresolution effects with annular phase and amplitude filters

The characteristics of annular amplitude and phase filters are compared. The behavior of two-zone phase and amplitude filters as the inner zone is increased is studied in detail. Numerical simulations show that a phase filter can achieve a superresolution effect, a circular Dammann effect, and flat-topped intensity for different applications, whereas a two-zone amplitude filter can generate only a superresolution effect. The experimental results show that both amplitude and phase filters can achieve superresolution. Generally, a phase superresolution filter is recommended for its higher efficiency and its special diffraction patterns that are impossible to achieve with an amplitude filter.     

Transverse or axial superresolution with radial birefringent filter

The superresolution technique is well known for its ability to compress the central diffraction spot to a size that is smaller than the Airy diffraction spot. The radial birefringent filter, which consists of two parallel polarizers and a rotationally symmetric birefringent element, is introduced into the superresolution technology, and the pupil function of it is deduced. It is shown that such a filter can be adapted either for transverse superresolution or for axial superresolution simply by changing the angle between either of the two polarizers and the radial birefringent element. At the same time the superresolution parameters are discussed. The filter is relatively simple in construction as it requires no phase changes, and low-cost replication is possible.     

Axial superresolution of two-photon microfabrication

An axial superresolution diffraction theory is developed in a two-photon microfabrication system. This method can improve the axial superresolution of the two-photon microfabrication system. A theoretical analysis of the photosensitive resin is discussed based on the exciting power and the concentration of free radical theory. Simulated results of the two-photon microfabrication verify the method and show that it can provide insight into the microfabrication system.     

基于遗传算法的超分辨多元环形滤光片设计

本文研究利用光学超分辨技术提高光盘存储密度.给出了一种可以达到衍射超分辨力的多元环形滤光片的设计结果.介绍了该多元环形滤光片的理论设计方法.之后用遗传算法设计了多组多元环形滤光片的结构参数,模拟结果显示设计的环形滤光片能使横向的半峰全宽半径值减小30%,达到提高信息存储密度的目的.另一方面该环形滤光片能使焦深不变或变长,减小了在记录过程中因为光盘的微小波动而引起的记录信息的错误率.     

Continuous radial superresolution filters with large focal depth

A new set of continuous superresolution filters is proposed which exhibits a radial superresolution performance with an extended depth of focus in an optical system by properly choosing the design parameters. Numerical simulation results of the performance parameters of the superresolution gain, the radial central core size, the Strehl ratio, the side-lobe factor and the depth of focus with different design parameters for the optimized patterns are displayed. We also give a design example for this kind of filter characterized by a birefringent element inserted between two parallel polarizers. This kind of filter would be useful in fields such as optical data storage systems.     

Superresolution along extended depth of focus with binary-phase filters for the Gaussian beam

In the paraxial Debye regime, simple and power-efficient pupil filters are designed to break the diffraction limit along a large depth of focus (DOF) for the Gaussian beam. Dependences of the superresolution factor, DOF gain, Strehl ratio, sidelobe strength, and axial intensity nonuniformity on the Gaussian profile in the pupil plane are characterized using the numerical method. Optimal filter designs are proposed for either high-resolution or ultra-large-DOF applications followed by experimental verifications.     

Small-kernel superresolution methods for microscanning imaging systems

Two computationally efficient methods for superresolution reconstruction and restoration of microscanning imaging systems are presented. Microscanning creates multiple low-resolution images with slightly different sample-scene phase shifts. The digital processing methods developed here combine the low-resolution images to produce an image with higher pixel resolution (i.e., superresolution) and higher fidelity. The methods implement reconstruction to increase resolution and restoration to improve fidelity in one-pass convolution with a small kernel. One method uses a small-kernel Wiener filter and the other method uses a parametric cubic convolution filter. Both methods are based on an end-to-end, continuous-discrete-continuous microscanning imaging system model. Because the filters are constrained to small spatial kernels they can be efficiently applied by convolution and are amenable to adaptive processing and to parallel processing. Experimental results with simulated imaging and with real microscanned images indicate that the small-kernel methods efficiently and effectively increase resolution and fidelity.     

A Magnifying Glass for Virtual Imaging of Subwavelength Resolution by Transformation Optics

Traditional magnifying glasses can give magnified virtual images with diffraction‐limited resolution, that is, detailed information is lost. Here, a novel magnifying glass by transformation optics, referred to as a “superresolution magnifying glass” (SMG) is designed, which can produce magnified virtual images with a predetermined magnification factor and resolve subwavelength details (i.e., light sources with subwavelength distances can be resolved). Based on theoretical calculations and reductions, a metallic plate structure to produce the reduced SMG in microwave frequencies, which gives good performance verified by both numerical simulations and experimental results, is proposed and realized. The function of SMG is to create a superresolution virtual image, unlike traditional superresolution imaging devices that create real images. The proposed SMG will create a new branch of superresolution imaging technology.     

Convex objective function-based design method developed for minimizing side lobe

The existence of multiple local solutions makes it very difficult to search for filter parameters to achieve a desired side lobe level during the design of superresolution pupil filters. To deal with the difficult issue of side lobe control in the designing process, a convex objective function-based design method is developed through phase rotation and variable replacement to transform the complicated solving process with multiextreme subintervals into a simple optimization process with a convex interval. A group of constant annular complex superresolving filters are designed using the developed method. The comparison of the superresolving filters designed in this way with the well-known continuous phase filter and 3-zone multiphase diffractive superresolution filters proves the validity of the developed method.     

Focal shift and extended focal depth with tunable pupil filter

Extended focal depth and focal shift are very important in microscopy, imaging and optical storage systems, and have attracted much attention in recent years. In order to obtain the extended focal depth and focal shift, a new kind of tunable pupil filter is proposed in this article. It consists of one half-wave plate between two quarter-wave plates, and the half-wave plate is made up of two zones that can rotate with respect to each other. By analyzing the intensity distribution in the focal region of the optical system with such a device, it reveals that focal shift can be realized by rotating any zone of the half-wave plate. When the phase difference of the two zones is π, the extended focal depth and transverse superresolution can be obtained at the same time. Therefore, it may be feasible to use such a tunable pupil filter in optical systems that need focal shift and extended focal depth.     

Design of adjustable superresolving filters based on birefringent crystals

A two-mode adjustable superresolving filter based on a birefringent filter is proposed. This kind of filter has superresolution in two modes of adjustment. One is rotation of the binary pupil filter on the optical axis of the system and the other is the tilt of the filter away from the pupil plane on axis parallel or perpendicular to the optical axis of the crystal. The filters act as complex amplitude filters in the former mode, and as pure phase filters in the latter. By analyzing two superresolving parameters, we obtain the optimal design parameters that ensure a large field of view, a large superresolving range, and a high setting accuracy. This kind of filter can provide more flexibility in practical applications.     

High focal depth with a pure-phase apodizer

High-density optical data storage requires high-numerical-aperture (NA) lenses and short wavelengths. But, with increasing NA and decreasing wavelength, the depth of focus (DOF) decreases rapidly. We propose to use pure-phase superresolution apodizers to optimize the axial intensity distribution and extend the DOF of an optical pickup. With this kind of apodizer, the expected DOF can be 2-4.88 times greater than that of the original system, and the spot size will be smaller than that of the original system.     

Improved superresolution in coherent optical systems

Objects that temporally vary slowly can be superresolved by the use of two synchronized moving masks such as pinholes or gratings. This approach to superresolution allows one to exceed Abbe's limit of resolution. Moreover, under coherent illumination, superresolution requires a certain approximation based on the time averaging of intensity rather than of field distribution. When extensive digital postprocessing can be incorporated into the optical system, a detector array and some postprocessing algorithms can replace the grating that is responsible for information decoding. In this way, no approximation is needed and the synchronization that is necessary when two gratings are used is simplified. Furthermore, we present two novel approaches for overcoming distortions when extensive digital postprocessing cannot be incorporated into the optical system. In the first approach, one of the gratings, in the input or at the output plane, is shifted at half the velocity of the other. In the second approach, various spectral regions are transmitted through the system's aperture to facilitate postprocessing. Experimental results are provided to demonstrate the properties of the proposed methods.     

Nonlinear optical hit-miss transform for detection

Morphological processing involves nonlinear low-level image-processing operations that can be realized on optical processors. Amodified version of the hit-miss morphological transform is described for object detection. Simulation results and optical laboratory realizations are presented. Some of the simple filters required can be realized as ternary-phase-amplitude optical filters.     

Axial and Extra-axial Responses in Aberrated Optical Systems with Apodizers. Optimization of the Strehl Ratio

Abstract

The effect of non-uniform transmission filters on the axial and extra-axial responses of aberrated optical systems is studied. The axial Strehl ratio (SR) is increased by varying the filter transmission function and the extra-axial SR by shifting the filter position along the axis of the optical system. It is shown that a filter which optimizes the axial SR can also improve the extra-axial SR. There are some positions of the filter for which the total results are improved. These positions are explained from the lack of radial symmetry of the wave aberration. The filters which improve the SR are also studied in terms of energy transmission.     

Motion-free superresolution and the role of relative blur

Motion-free superresolution refers to the process of generating a high-resolution image from a set of defocused and downsampled observations blurred to different extents. We first examine the theory of motion-free superresolution and derive analytical expressions in the discrete Fourier transform domain for obtaining a superresolved image from its blurred and downsampled versions. The analysis leads to the construction of an appropriate system matrix whose inverse yields the desired reconstruction filters. Next, we address the effect of relative blurring among the defocused observations on the quality of the reconstructed image. To get a quantitative perspective of this effect, we derive the Cramér-Rao lower bound (CRLB) for the covariance of the error in the estimate of the superresolved image. The CRLB depends on the system matrix, and the condition number of this matrix is studied as a function of the blur kernels. It is shown that the stability of the problem and the estimate of the superresolved image become better as the relative blur increases. Adding more observations without enriching the blur span does not improve the quality of reconstruction. Several simulation results are given for the purpose of validation.     

Two-dimensional superresolution optical system for temporally restricted objects

Objects that vary slowly over time may be superresolved by use of moving gratings. A system of this kind was proposed three decades ago. However, such a system creates some distortion of the spectral response of the resolved objects, and it achieves superresolution in only one dimension. We propose an enhanced method based on Dammann gratings instead of regular gratings for achieving two-dimensional superresolution. The modified approach achieves results with undistorted output and relatively high light efficiency, and it is effective for both coherent and incoherent illumination. Preliminary results demonstrate the feasibility of the new approach.