Effect of Variable Apodization Functions on the Image Quality of Optical System

The relationship between image quality and piston errors of synthetical aperture optical imaging system has been studied. An active segmented cophasing imaging system and its Zemax simulation model were set up. Diversity piston errors were introduced and the corresponding MTF were calculated with the Zemax simulation model. Simulation experiments have been carried out with the cophasing imaging system, and the results are coincident with the simulated results. The results show that image quality changes with the increase of the piston error periodically if the piston error is smaller than the coherent length of the light source, and the image quality becomes the worst if the piston error is an odd multiple of π.

Light scattering from residual manufacturing errors of optical surfaces has a large impact on the image quality of optical systems. Classical ray-based methods to simulate surface scattering in optical systems depend on statistical models of surface errors and neglect the wave properties of light, which prohibit the integration of statistical surface error models with beam propagation methods. Additionally, the impact of multiple scattering from different frequency components of surface errors cannot be easily modelled by existing methods. Here we analyze the impact of different frequency components of surface errors induced by diamond-turned surface grinding on image quality, and we propose a Wigner function-based approach in which light is modelled as partially coherent. In this unified model, by selecting the proper definition of light coherence, we can combine the statistical and deterministic models of surface errors, enabling efficient, simultaneous simulation of multiple scattering from high- and mid-spatial frequency (HSF and MSF, respectively) surface errors, as well as the interference and edge diffraction of light.

On the basis of optical correlation detection, photoelectric hybrid joint transform correlator(JTC) is widely used in military, aviation and intelligentization, etc. It has the advantages of great flexibility and high precision of recognition. However, the optical system which is in front of joint transform correlator(JTC) is applied to receive the infrared radiation of the target. It also has a certain influence on JTC’s detecting precision and tracking ability. Dual band infrared imaging system can receive different wave band of infrared radiation. Therefore, the image quality of optical system plays an important role in the joint transform correlator(JTC). According to the requirements of the joint transform correlator (JTC), the processes of optical design including the allocation of parameters and the selection of initial structure are presented. The infrared dual band coaxial telephoto system is designed for target detection. The system which is composed of four lenses can image in both 3μm~5μm and 8μm~12μm wavebands. The focal length is 200 mm and the relative aperture is 1:3. The system has the characteristics of small volume and compact structure. The optical system image quality is evaluated with ZEMAX optical design software. The results have shown that MTFs of the system are 0.62 and 0.35 for both wavebands respectively at 17lp/mm of spatial frequency which are closed to the diffraction limited curve. The relative aperture, field of view, and focal length are same for both spectral regions. The system meets the requirements of technical specification and improves the ability of JTC in target tracking and recognition.

It is now well known that a modification of the diffraction-limited point-spread function is possible by using various types of amplitude apodization filter. A comparative study of the performance of optical systems apodized with a few commonly used amplitude filters has been made. The comparison has been made from the considerations of the diffracted field characteristics, namely, point-spread function, encircled energy factor, Strehl ratio, second-order moment, mean apodization ratio, two-point resolution, etc. The imaging characteristics of extended objects, both periodic and nonperiodic in various conditions of coherence, have also been compared with special reference to optical transfer function, generalized frequency response function, image contrast, etc. Attempts have been made to correlate the functional form of the pupil function to the performance of the apodized optical system in terms of the various diffracted fields and the imaging characteristic parameters considered. Finally, experimental methods to fabricate a few of these filters for superresolution, image processing, etc. are described.

To realize direct image of faint object which is in the close proximity of very bright object could be technologically feasible by introducing asymmetric apodization. The point spread function (PSF) of an optical system with asymmetric apodization has been found to possess a so‐called good side and a bad side. The good‐side has decreased side lobes whereas the bad‐side shows increased side lobes. This has been observed when the aperture is divided into three parts viz. two semi‐circular edge rings and a central region with an apodizer. The asymmetry in the PSF has been found to increase with the width of the edge rings and is seen to decrease with the increased apodization of the central region.

A computational camera uses a combination of optics and processing to produce images that cannot be captured with traditional cameras. Over the last decade, a range of computational cameras have been proposed, which use various optics designs to encode and use computation to decode useful visual information. What is often missing, however, is the quantitative analysis of the relation between camera design and the captured visual information, and little systematic work has been done to evaluate and optimize these computational camera designs. While the optics of computational cameras may be quite complicated, many of them can be effectively characterized by their point spread functions (PSFs): the intensity distribution on an image sensor as a response to a point light source in a scene. This thesis explores the techniques to characterize, evaluate and optimize computational cameras via PSF engineering for computer vision tasks, including image recovery, 3D reconstruction, and image refocusing. I first explore PSF engineering techniques to recover image details from blurry images. Image blur is a problem commonly seen in photography due to a number of reasons, including defocus, lens aberration, diffraction, atmospheric turbulence, object motion, and etc. Image blur is often formulated as a convolution of the latent blur-free image and a PSF, and deconvolution (or deblurring) techniques have to be used to recover image details from a blurry region. Here, I propose a comprehensive framework of PSF evaluation for the purpose of image deblurring, in which the effects of image noise, deblurring algorithm, and the structure of natural images are all taken into account. In defocus blur, the shape of defocus PSF is largely determined by the aperture pattern of the camera lens. By using an evaluation criterion derived from the comprehensive framework, I optimize the aperture pattern to preserve many more image details when defocus occurs. Both through simulations and experiments, I demonstrate the significant improvement gained by using optimized aperture patterns. While defocus blur causes a loss in image detail, it also encodes depth information of scenes in images. A typical depth from defocus (DFD) technique computes depth from two or more images that are captured with circular aperture lenses of different focus settings. Circular apertures produce circular defocus PSFs. In this thesis, I show that the use of a circular aperture severely restricts the accuracy of DFD, and propose a comprehensive framework of PSF evaluation for depth recovery. With this framework, we can derive a criterion for evaluating a pair of apertures with respect to the precision of depth recovery. This criterion is optimized using a genetic algorithm and gradient descent search to arrive at a pair of high resolution apertures. The two coded apertures are found to complement each other in the scene frequencies they preserve. With this property it becomes possible to not only recover depth with greater fidelity but also to obtain a high quality all-focused image from the two defocused images. While depth recovery can significantly benefit from optimized aperture patterns, its overall performance is rigidly limited by the lens aperture's physical size. To transcend this limitation, I propose a novel depth recovery technique using an optical diffuser - referred to as depth from diffusion (DFDiff). I show that DFDiff is analogous to conventional DFD, in which the scatter angle of the diffuser determines the system's effective aperture. High precision depth estimation can be achieved by choosing a proper diffuser and no longer requires the large lenses that DFD requires. Even a consumer camera with a low-end small lens can be used to do high-precision depth estimation when coupled with an optical diffuser. In my detailed analysis of the image formation properties of a DFDiff system, I show a number of examples demonstrating greater precision in depth estimation when using DFDiff. While the finite depth of field (DOF) of a lens camera leads to defocus blur, it also produces artistic visual experience. Many of today's displays are interactive in nature, which opens up a possibility for new kind of visual representations. Users could, for example, interactively refocus images to different depths, so that they can experience the artistic narrow DOF images while simultaneously making available the image detail for the entire image. To enable image refocusing, one typical approach is to capture the entire light field. But this method has the drawback of a significant sacrifice in spatial resolution due to the dimensionality gap: the captured information (light field) is 4D, while the required information (focal stack) is only 3D.In this thesis, I present an imaging system that directly captures focal stacks by a sweeping focal plane. First, I describe how to synchronize focus sweeping with image capturing so that the summed DOF of a focal stack efficiently covers the entire depth range. Then, I take a customized algorithm to enable a seamless refocusing experience, even in textureless regions or with moving objects. Prototype cameras are presented to capture real space-time focal stacks. There is also an interactive refocusing viewer available online at www.focalsweep.com.

Abstract. One-dimensional modulation transfer function (1-D MTF) has been generally calculated to evaluatethe image quality of optical imaging systems, such as the horizontal MTF and vertical MTF. These MTFs can bemeasured by the use of some mature ways. However, the information of 1-D MTF for performance evaluationmay not enough for the systems handling two-dimensional (2-D) targets of high resolution, thus discussing 2-DMTF will be necessary. We investigate the measurement method for the 1-D and 2-D MTF of optical imagingsystems based on the random target method, and the characteristics of 2-D MTF and 1-D MTF in terms of MTFvalues and cutoff frequency are also noted. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 UnportedLicense. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI. [DOI: 10.1117/1.OE.53.10.104105] Keywords: image quality evaluation; modulation transfer function; random image; liquid-crystal display; fast Fourier transform; powerspectral density.Paper 140973 received Jun. 18, 2014; revised manuscript received Sep. 16, 2014; accepted for publication Sep. 26, 2014; publishedonline Oct. 30, 2014.

Taking a certain type of photoelectric system of armored vehicle as an example, the influence of angular vibration on the optical system image quality is analyzed. Firstly, the paper introduces the characteristics of photovoltaic system and the basic theory of imaging; Then it uses the ZEMAX to build optical system model; finally, it simulates the MTF and Spot Diagram as the change of lens angular. By making quantitative analysis of the photoelectric system influence on imaging quality of lens deflection angular, we get the relationship between geometry maximum radius and mean root square radius with the lens deflection angular, and evaluate the effects of angular vibration on image quality synthetically, which has important reference value to the design of photoelectric system.

A recent study of the influence of the Goos-Hänchen shift on the imaging properties of planar optical systems is commented on. It is shown that the model chosen for a description of the Goos-Hänchen shift must be modified considerably and that there is one more shift in total reflection that will also influence the imaging quality.

The design of optical systems not only considers the imaging performance but also the manufacturing difficulty and feasibility of the system. In practice, errors in the manufacturing process of glass materials and deviations in glass material parameters introduced in complex environments can both lead to degradation in the imaging quality of optical systems. Optical systems that are sensitive to glass material errors face increased manufacturing difficulty and reduced stability. This paper, based on geometrical optics theory, establishes an evaluation function for refractive index error sensitivity and analyzes its relationship with optical parameters and glass materials. It proposes a design method to reduce the refractive index sensitivity of optical systems. Through simulation verification and analysis using examples, the validity of the desensitization design method is confirmed.

Adaptive optics (AO) enhances astronomical images by correcting perturbations in the optical system, resulting in complex point spread function (PSF) shapes, which provide critical information for optical design, calibration, and diagnostics. This paper presents a parametric model for an AO-corrected long-exposure PSF that adapts to complex shapes and various seeing conditions. A complementary estimation method is also introduced, addressing the inverse problem of estimating the atmospheric PSF or power spectral density (PSD) from observed PSF data. The model, based on Gaussian sum approximation (GSA), was tested using simulated PSF data from the OOMAO toolbox for Fried parameter (r0) values ranging from 0.10 to 0.20 m and on-sky data from the Very Large Telescope’s MUSE instrument. Two approaches were analyzed: (i) direct PSF estimation using GSA, and (ii) PSF estimation derived from atmospheric PSD estimation. Both methods were evaluated using root mean square error (RMSE). While approach (i) provided the best performance, approach (ii) produced more accurate atmospheric PSF estimates compared to the Moffat approximation and the Fetick method. Additionally, approach (ii) enabled the estimation of key physical parameters, such as the Fried parameter (r0) and residual AO variance ($\sigma _{AO}^2$). The proposed methods effectively estimate atmospheric PSF and PSD, even for complex PSF shapes influenced by spiders, central obstructions, or static aberrations.

Distinguishing whether a signal corresponds to a single source or a limited number of highly overlapping point spread functions (PSFs) is a ubiquitous problem across all imaging scales, whether detecting receptor-ligand interactions in cells or detecting binary stars. Super-resolution imaging based upon compressed sensing exploits the relative sparseness of the point sources to successfully resolve sources which may be separated by much less than the Rayleigh criterion. However, as a solution to an underdetermined system of linear equations, compressive sensing requires the imposition of constraints which may not always be valid. One typical constraint is that the PSF is known. However, the PSF of the actual optical system may reflect aberrations not present in the theoretical ideal optical system. Even when the optics are well characterized, the actual PSF may reflect factors such as non-uniform emission of the point source (e.g. fluorophore dipole emission). As such, the actual PSF may differ from the PSF used as a constraint. Similarly, multiple different regularization constraints have been suggested including the l1-norm, l0-norm, and generalized Gaussian Markov random fields (GGMRFs), each of which imposes a different constraint. Other important factors include the signal-to-noise ratio of the point sources and whether the point sources vary in intensity. In this work, we explore how these factors influence super-resolution image recovery robustness, determining the sensitivity and specificity. As a result, we determine an approach that is more robust to the types of PSF errors present in actual optical systems.

We show the feasibility of two new programmable diffractive optical elements (DOE). On one hand, we demonstrate the realization of programmable apodizers. With the term apodizer we refer to non-uniform amplitude filters used to modify the point-spread function (PSF) of an optical system. On the other hand, we show the simultaneous realization of a Fresnel lens and an amplitude filter in a single DOE: the programmable amplitude apodized Fresnel lens (PAAFL). Two different modulation regimes are required to generate these DOEs: amplitude-only regime for the programmable apodizer and phase-only regime for the PAAFL. We show that a twisted-nematic liquid crystal spatial light modulator (TN-LCSLM) inserted between two wave plates and two polarizers is able to provide both modulation regimes. Different types of amplitude filters, such as axial hyperresolving, transverse apodizing and transverse hyperresolving have been implemented both as programmable apodizers and as PAAFLs. We provide experimental results for the performance of the two new DOEs. The agreement with the numerical results is excellent, thus demonstrating the feasibility of our proposal.

The Point Spread Function (PSF) or star test is one of the main criteria to be considered in the quality of the image formed by a telescope. In a real system the distribution of irradiance in the image of a point source is given by the PSF, a function which is highly sensitive to aberrations. The PSF of a telescope may be determined by measuring the intensity distribution in the image of a star. Alternatively, if we already know the aberrations present in the optical system, then we may use diffraction theory to calculate the function. In this paper we propose a method for determining the wavefront aberrations from the PSF, using Genetic Algorithms to perform an optimization process starting from the PSF instead of the more traditional method of adjusting an aberration polynomial. We show that this method of phase recuperation is immune to noise-induced errors arising during image aquisition and registration. Some practical results are shown.

We analyzed the point spread function (PSF) of the typical 4f optical image processing system by use of a spatially variable half-wave plate as the spatial filter and found that the PSF is an elementary vector beam. Theoretical analysis and real experiments show that the optical system can be used for a radially symmetric Hilbert transform that permits two-dimensional edge enhancement as the spiral phase plate. This kind of radial Hilbert transform is useful for image processing because it can enhance the edges of an input image selectively by exerting a polarization analyzer before the output plane. The optical system also can be used for generation of vector beams with arbitrary array and shape in real time conveniently.