Electronic imaging using a logarithmic asphere

Geometric-phase-based axicon lens for computational achromatic imaging

Conventional optical imaging systems usually utilize several lenses within a precise assembly to eliminate chromatic aberration, which increases the difficulty of system integration. In recent years, with the rapid development of metasurfaces and liquid crystals (LCs), planar optical elements provide feasible solutions to realize flexible light manipulation and lightweight systems. However, there also exists chromatic aberration, which can be corrected but at the cost of a complex device design. Here, a geometric-phase-based axicon lens is utilized to correct chromatic aberration across a broadband wavelength with the assistance of a post-process algorithm. The axicon lens is fabricated through arranging orientations of liquid-crystal molecules with a standard photoalignment technique, and it produces an approximately invariant point spread function (PSF) at several discrete wavelengths, which is used as the prior information to extract the object in the blurred image. In the experiment, the reconstruction quality is significantly improved after the post-process algorithm. We expect our work to provide further development to reduce the dispersion with both the device design and the computational image technique.

Single-shot optical surface profiling using extended depth of field 3D microscopy

The measurement of three-dimensional samples at high speed is essential for many applications, either due to the requirement for measuring samples that change fast over time, or due to the requirement of reducing the scanning time, and therefore inspection cost, in industrial environments. Conventionally, the measurement of surface topographies at high resolution typically requires an axial scanning of the sample. We report the implementation of a technique able to reconstruct surface topographies at high resolution, only from the acquisition of a single camera shot, dropping the need to perform an axial scan. A system prototype is reported and assessed as an ultra-fast optical surface profiler. We propose robust calibration and operation methods and algorithms to reconstruct surface topographies of optically-rough samples, and compare the experimental results with a reference confocal optical profiler.

Refractive Bi-Conic Axicon (Volcone) for Polarization Conversion of Monochromatic Radiation

A new element is proposed for producing an azimuthally polarized beam with a vortex phase dependence. The element is formed by two conical surfaces in such a way that the optical element resembles a mountain with a crater on top, like a volcano (volcanic cone is volcone). The element in the form of a refractive bi-conic axicon is fabricated by diamond turning, in which an internal conical cavity is made. Polarization conversion in this optical element occurs on the inner surface due to the refraction of beams at the Brewster angle. The outer surface is used to collimate the converted beam, which significantly distinguishes the proposed element from previously proposed approaches. The paper describes a method for calculating the path of beams through a refractive bi-conic axicon, taking into account phase and polarization conversions. In the case of incident circularly polarized radiation, azimuthally polarized ring-shape beam radiation is generated at the output. The proposed element is experimentally made of polymethyl methacrylate on a CNC milling machine. The experiment demonstrates the effectiveness of the proposed element.

Freeform optics for variable extended depth of field imaging

Imaging depth of field is shallow in applications with high magnification and high numerical aperture, such as microscopy, resulting in images with in- and out-of-focus regions. Therefore, methods to extend depth of field are of particular interest. Researchers have previously shown the advantages of using freeform components to extend depth of field, with each optical system requiring a specially designed phase plate. In this paper we present a method to enable extended depth-of-field imaging for a range of numerical apertures using freeform phase plates to create variable cubic wavefronts. The concept is similar to an Alvarez lens which creates variable spherical wavefronts through the relative translation of two transmissive elements with XY polynomial surfaces. We discuss design and optimization methods to enable extended depth of field for lenses with different numerical aperture values by considering through-focus variation of the point spread function and compare on- and off-axis performance through multiple metrics.

Modern Types of Axicons: New Functions and Applications

Axicon is a versatile optical element for forming a zero-order Bessel beam, including high-power laser radiation schemes. Nevertheless, it has drawbacks such as the produced beam's parameters being dependent on a particular element, the output beam's intensity distribution being dependent on the quality of element manufacturing, and uneven axial intensity distribution. To address these issues, extensive research has been undertaken to develop nondiffracting beams using a variety of advanced techniques. We looked at four different and special approaches for creating nondiffracting beams in this article. Diffractive axicons, meta-axicons-flat optics, spatial light modulators, and photonic integrated circuit-based axicons are among these approaches. Lately, there has been noteworthy curiosity in reducing the thickness and weight of axicons by exploiting diffraction. Meta-axicons, which are ultrathin flat optical elements made up of metasurfaces built up of arrays of subwavelength optical antennas, are one way to address such needs. In addition, when compared to their traditional refractive and diffractive equivalents, meta-axicons have a number of distinguishing advantages, including aberration correction, active tunability, and semi-transparency. This paper is not intended to be a critique of any method. We have outlined the most recent advancements in this field and let readers determine which approach best meets their needs based on the ease of fabrication and utilization. Moreover, one section is devoted to applications of axicons utilized as sensors of optical properties of devices and elements as well as singular beams states and wavefront features.

Optical volumetric projection with large NA objectives for fast high-resolution 3D imaging of neural signals

One critical challenge in studying neural circuits of freely behaving model organisms is to record neural signals distributed within the whole brain, yet simultaneously maintaining cellular resolution. However, due to the dense packing of neuron cells in animal brains, high numerical aperture (NA) objectives are often required to differentiate neighboring neurons with the consequent need for axial scanning for whole brain imaging. Extending the depth of focus (EDoF) will be beneficial for fast 3D imaging of those neurons. However, current EDoF-enabled microscopes are primarily based on objectives with small NAs (≤0.3 ) such that the paraxial approximation can be applied. In this paper, we started from a nonparaxial approximation of the defocus aberration and derived a new phase mask that was appropriate for large NA microscopic systems. We validated the performance experimentally with a spatial light modulator (SLM) to create the designed phase mask. The performance was tested on different samples such as multilayered fluorescence beads and thick brain tissues, as well as with different objectives. Results confirmed that our design has extended the depth of focus about 10 fold and the image quality is much higher than those based on the most common EDoF method, the cubic phase method, popularly used to generate Airy beams. Meanwhile, our phase mask is rotationally symmetric and easy to fabricate. We fabricated one such phase plate and tested it on the pan-neuronal labeled Caenorhabditis elegans (C.elegans). The imaging performance demonstrated that we can capture all neurons in the whole brain with one snapshot and with cellular resolution, while the imaging speed is increased about 3 fold compared to the system using SLM. Thus we have shown that our method can not only provide the required imaging speed and resolution for studying neural activities in model animals, but also can be implemented as a low-cost, add-on module that can immediately augment existing fluorescence microscopes with only minor system modifications, and yielding substantially higher photon efficiency than SLM-based methods.

Refractive twisted microaxicons

Complex-shaped light fields with specially designed intensity, phase, and polarization distributions are highly demanded for various applications including optical tweezers, laser material processing, and lithography. Here, we propose a novel (to the best of our knowledge) optical element formed by the twisting of a conic surface, a twisted microaxicon, allowing us to controllably generate high-quality spiral-shaped intensity patterns. Performance of the proposed element was analyzed both analytically and numerically using ray approximation and the rigorous finite difference time domain (FDTD) solution of Maxwell's equation. The main geometric parameters, an apex cone angle and a degree of twisting, were considered to control and optimize the generated spiral-shaped intensity patterns. The three-dimensional structure of such a microaxicon cannot be described by an unambiguous height function; therefore, it has no diffraction analogue in the form of a thin optical element. Such an element can be produced via direct laser ablation of transparent targets with structured laser beams or direct laser writing via two-photon photopolymerization and can be used in various micro- and nano-optical applications.

Metasurface lens with angular modulation for extended depth of focus imaging

The depth of focus (DOF) indicates the tolerance of the imaging displacement. The axial long-focal-depth is significant in practical applications, including optical imaging and communication. The importance of extending the DOF is rapidly growing with the advance of metasurface lenses. Angular modulation, as a promising way to extend the DOF, offers an additional degree of freedom to improve the imaging quality. Here we theoretically and experimentally demonstrate an angular modulated metasurface lens for extended DOF imaging by means of applying the geometrical phase. Unlike previous studies of the geometrical phase, which is sensitive to the polarity of circular polarization incidence, the polarity of circular polarization independence and broadband characteristic of angular modulation yield the potential of robust and efficient extension of the DOF imaging, thus providing novel opportunities for highly integrated optical circuits.

Experimental demonstration of wave-front coded imaging with a very low response of the modulation transfer function at the Nyquist frequency

Wave-front coding (WFC) is a well-known technique that can be used to extend the depth of field (DOF) of incoherent imaging systems. The phase masks make the optical transfer function drop significantly, and digital restoration must be used to obtain a clear image with a largely extended DOF. According to the existing literature, in order to obtain satisfactory restoration results, the optical modulation transfer function (MTF) at the Nyquist frequency is required to be bigger than 0.1, which has already become a popularly accepted design constraint. However, according to our experimental research reported in this paper, this requirement is overly strict. By assembling one already fabricated WFC lens and another camera having physically higher resolution, the MTF of the newly assembled WFC system used in the experimentation has quite a low response at its Nyquist frequency. The experimental results demonstrate that when the optical MTF value at the Nyquist frequency reaches the minimum value of about 0.05, visually satisfactory restoration results can still be obtained as long as the MTF is optimized to be highly insensitive to defocus and the corresponding SNR of the coded intermediate images goes beyond 20 dB at the same time. The experimental results indicate that the overly strict constraint could be alleviated while designing a WFC system.

Improved vector-extrapolation-based Richardson-Lucy algorithm used for wavefront coded imaging

The Richardson-Lucy (RL) algorithm is a well-known nonlinear restoration method and has been widely applied in the fields of astronomical image restoration, microscopic image restoration, and so on because of its capability of generating high-quality restoration results and potential in realizing super-resolution. However, when being applied to restore the wavefront coded blurry images, the classical RL algorithm converges very slowly and has to be iterated many times before obtaining a satisfactory result, which severely prohibits its real-time application. Vector-extrapolation-based RL algorithm was invented to solve this problem, but the noise amplification increases fast, and additional post-processing is needed to further improve the signal-to-noise ratio. Therefore, in this paper, an improved RL algorithm is proposed by introducing an exponential modified correction term into the framework of the original vector-extrapolation-based RL algorithm. It not only results in a bigger iteration step, which ensures a faster convergence can be obtained, but also the noise amplification is effectively prohibited. Besides that, we design a structure-similarity-index-metric-based stopping criterion, based on which the optimum number of iterations for each color channel is obtained. Experimental results reveal that the total iterations decreases approximately 78.9%, and the restored images demonstrate a superior visual quality without denoising additionally.

Propagation of a Bessel-Gaussian beam in a gradient-index medium

Based on the ABCD matrix method and Collins diffraction integral formula, analytical expression for Bessel-Gaussian beam propagation in a gradient-index medium is derived. The propagation trajectory, intensity, and phase distributions of the zeroth-order, second-order, and superposition cases are numerically investigated. The effect of beam waist radius w₀ on the properties of beam propagation in a gradient-index medium is discussed in detail. The result shows that the beam is focused at z/L=N/2 (N=0,1,2,…) and propagates periodically in the medium. Evolution of the vortical structure of the superposed Bessel-Gaussian beam is investigated, showing that the superposed beam forms new singularities, and the rotation of the beam occurs mainly near the singularities.

Extending depth of field for hybrid imaging systems via the use of both dark and dot point spread functions

In this paper, we propose one method based on the use of both dark and dot point spread functions (PSFs) to extend depth of field in hybrid imaging systems. Two different phase modulations of two phase masks are used to generate both dark and dot PSFs. The quartic phase mask (QPM) is used to generate the dot PSF. A combined phase mask between the QPM and the angle for generating the dark PSF is investigated. The simulation images show that the proposed method can produce superior imaging performance of hybrid imaging systems in extending the depth of field.

Assessment of imaging with extended depth-of-field by means of the light sword lens in terms of visual acuity scale

We present outcomes of an imaging experiment using the refractive light sword lens (LSL) as a contact lens in an optical system that serves as a simplified model of the presbyopic eye. The results show that the LSL produces significant improvements in visual acuity of the simplified presbyopic eye model over a wide range of defocus. Therefore, this element can be an interesting alternative for the multifocal contact and intraocular lenses currently used in ophthalmology. The second part of the article discusses possible modifications of the LSL profile in order to render it more suitable for fabrication and ophthalmological applications.

A compact Airy beam light sheet microscope with a tilted cylindrical lens

Light-sheet imaging is rapidly gaining importance for imaging intact biological specimens. Many of the latest innovations rely on the propagation-invariant Bessel or Airy beams to form an extended light sheet to provide high resolution across a large field of view. Shaping light to realize propagation-invariant beams often relies on complex programming of spatial light modulators or specialized, custom made, optical elements. Here we present a straightforward and low-cost modification to the traditional light-sheet setup, based on the open-access light-sheet microscope OpenSPIM, to achieve Airy light-sheet illumination. This brings wide field single-photon light-sheet imaging to a broader range of endusers. Fluorescent microspheres embedded in agarose and a zebrafish larva were imaged to demonstrate how such a microscope can have a minimal footprint and cost without compromising on imaging quality.

Extended depth of field using a liquid crystal annular spatial light modulator

A detailed investigation is presented on the tunable extended depth of field (EDOF) method, proposed recently by Klapp et al. [Opt. Lett.39, 1414 (2014)]. This method is based on temporal multiplexing of phase masks, using an annular liquid crystal spatial light modulator possessing a small number of rings. Examples of 3D simulations used to determine the phase profiles in the pupil plane are presented, as well as more detailed experimental results. Both the experimental and numerical results include comprehensive analysis of contrast dependence on both the spatial spectrum of the object and the amount of defocus. In addition, for the first time, we present the EDOF order inversion in the experimental and simulated data. The results show a profound performance of the proposed system and method.

Tunable extended depth of field using a liquid crystal annular spatial filter

A tunable extended depth of field (EDOF) imaging is presented using temporal multiplexing and a low-cost eight-ring, annular liquid crystal spatial light modulator. By changing between different phase profiles in the pupil plane of a lens we perform several levels of EDOF. Using these levels as a "database" it is shown by temporal multiplexing how to decompose tunable levels of EDOF.

Instantaneous three-dimensional sensing using spatial light modulator illumination with extended depth of field imaging

Imaging three-dimensional structures represents a major challenge for conventional microscopies. Here we describe a Spatial Light Modulator (SLM) microscope that can simultaneously address and image multiple targets in three dimensions. A wavefront coding element and computational image processing enables extended depth-of-field imaging. High-resolution, multi-site three-dimensional targeting and sensing is demonstrated in both transparent and scattering media over a depth range of 300-1,000 microns.

Holistic optical-digital hybrid-imaging design: wide-field reflective imaging

Reflective imaging systems are typically limited to small field angles in order to avoid overly large obscurations or off-axis aberrations. Reflective optics are often preferred in astronomy due to the associated lower weight and cost, as well as the absence of chromatic aberrations. Although these advantages are compelling, off-axis aberrations typically limit the field of view to a few degrees, while many imaging applications require a considerably larger useful field of view. A hybrid optical-digital design could alleviate the issues associated with wide-field reflective optics by exploiting the larger design freedom inherent in such systems. In this paper we demonstrate how a holistic design approach can enable reflective imaging systems with a consistently sharp image across a wide field of view.

Logarithmic axicon characterized by scanning optical probe system

A scanning optical probe system is proposed to measure a logarithmic axicon (LA) with subwavelength resolution. Multiple plane intensity profiles measured by a fiber probe are interpreted by solving an optimization problem to get the phase retardation function (PRF) of the LA. Experimental results show that this approach can accurately obtain the PRF with which the optical path difference of the generated quasi-nondiffracting beam in the propagation is calculated.

When does computational imaging improve performance?

A number of computational imaging techniques are introduced to improve image quality by increasing light throughput. These techniques use optical coding to measure a stronger signal level. However, the performance of these techniques is limited by the decoding step, which amplifies noise. Although it is well understood that optical coding can increase performance at low light levels, little is known about the quantitative performance advantage of computational imaging in general settings. In this paper, we derive the performance bounds for various computational imaging techniques. We then discuss the implications of these bounds for several real-world scenarios (e.g., illumination conditions, scene properties, and sensor noise characteristics). Our results show that computational imaging techniques do not provide a significant performance advantage when imaging with illumination that is brighter than typical daylight. These results can be readily used by practitioners to design the most suitable imaging systems given the application at hand.

Optimized annular phase masks to extend depth of field

A radially symmetric phase mask composed of several annular zones with equal area (called APM) was designed based on the incoherent imaging theory from Fourier Optics. The phase of any ring equals minus of the phase function caused by certain defocus. Another circularly symmetric phase mask similar to the APM (called MQPM) was proposed, except for the different phase function deriving from the quartic phase mask (QPM). For MQPM, there are two differences from an existing phase mask: the selection of the phase parameters and the method to divide the phase mask. An optimization model was developed to obtain optimized parameters of the phase masks. Numerical evaluations show that both APM and MQPM are less insensitive to defocus than QPM, and the defocused optical transfer functions with two phase masks are symmetric about the in-focus plane in the axial direction.

Three-dimensional locating of paraxial point source with axicon

This Letter presents a theoretical and experimental study of an axicon illuminated by an off-axis paraxial point source. The Fresnel diffraction integral is applied to show that a paraxial point source produces a Bessel beam. A simple analytical relationship is demonstrated between the location of the point source and the spatial frequency and the center of the resulting Bessel beam in the image plane of a camera. Finally, experimental verification is given by translating a point source of light along the optical axis of an axicon and comparing the resulting predicted and recorded beam intensity profiles. The resulting images are then analyzed to predict the location of the point source with excellent accuracy.

Experimental evidence of the theoretical spatial frequency response of cubic phase mask wavefront coding imaging systems

The optical transfer function of a cubic phase mask wavefront coding imaging system is experimentally measured across the entire range of defocus values encompassing the system's functional limits. The results are compared against mathematical expressions describing the spatial frequency response of these computational imagers. Experimental data shows that the observed modulation and phase transfer functions, available spatial frequency bandwidth and design range of this imaging system strongly agree with previously published mathematical analyses. An imaging system characterization application is also presented wherein it is shown that the phase transfer function is more robust than the modulation transfer function in estimating the strength of the cubic phase mask.

Imaging properties of the light sword optical element used as a contact lens in a presbyopic eye model

The paper analyzes the imaging properties of the light sword optical element (LSOE) applied as a contact lens to the presbyopic human eye. We performed our studies with a human eye model based on the Gullstrand parameterization. In order to quantify the discussion concerning imaging with extended depth of focus, we introduced quantitative parameters characterizing output images of optotypes obtained in numerical simulations. The quality of the images formed by the LSOE were compared with those created by a presbyopic human eye, reading glasses and a quartic inverse axicon. Then we complemented the numerical results by an experiment where a 3D scene was imaged by means of the refractive LSOE correcting an artificial eye based on the Gullstrand model. According to performed simulations and experiments the LSOE exhibits abilities for presbyopia correction in a wide range of functional vision distances.

Coding for compressive focal tomography

We consider the capabilities and limits of strategies for single-aperture three-dimensional and extended depth of field optical imaging. We show that reduced spatial resolution is implicit in forward models for light field sampling and that reduced modulation transfer efficiency is intrinsic to pupil coding. We propose a novel strategy based on image space modulation and show that this strategy can be sensitive to high-resolution spatial features across an extended focal volume.

Strehl ratios characterizing optical elements designed for presbyopia compensation

We present results of numerical analysis of the Strehl ratio characteristics for the light sword optical element (LSOE). For comparison there were analyzed other optical imaging elements proposed for compensation of presbyopia such as the bifocal lens, the trifocal lens, the stenopeic contact lens, and elements with extended depth of focus (EDOF), such as the logarithmic and quartic axicons. The simulations were based on a human eye's model being a simplified version of the Gullstrand model. The results obtained allow to state that the LSOE exhibits much more uniform characteristics of the Strehl ratio comparing with other known hitherto elements and therefore it could be a promising aid to compensate for the insufficient accommodation range of the human eye.

Airy beams: a geometric optics perspective

Theoretically formulated in the 1970s within the context of nonrelativistic quantum mechanics, Airy beams have been experimentally realized for the first time only recently, paving the way to innovative optical techniques. While their remarkable features, a non-diffracting property and a transverse shift of the intensity maximum during propagation, are currently theoretically described from the wave optics viewpoint, here their exact relation to rays and geometric wavefront aberrations is revealed using a wavefront family that includes two-dimensional Airy beams. Several members of this family are computationally and experimentally implemented here. The lateral shift of Airy beams during propagation is presented in the context of the three-dimensional caustic representation. This new description allows re-emphasizing the use of "Airy-like" beams in computational imaging for depth of focus extension.

Iterative aperture mask design in phase space using a rank constraint

We present an iterative camera aperture design procedure, which determines an optimal mask pattern based on a sparse set of desired intensity distributions at different focal depths. This iterative method uses the ambiguity function as a tool to shape the camera's response to defocus, and shares conceptual similarities with phase retrieval procedures. An analysis of algorithm convergence is presented, and experimental examples are shown to demonstrate the flexibility of the design process. This algorithm potentially ties together previous disjointed PSF design approaches under a common framework, and offers new insights for the creation of future application-specific imaging systems.

Characterization of a refractive logarithmic axicon

We show that it is feasible to design and manufacture a refractive logarithmic axicon that generates a quasi-diffraction-free/Bessel beam with nearly constant beam size and intensity over a predetermined range. The novel optical element was characterized with both coherent and incoherent light, and good correspondence with the predicted behavior of the intensity distribution and spot size was found. The energy flow was also found to be nearly constant over most of the designed range. Logarithmic axicons may find applications in situations where large depth of field and uniform axial intensity/energy distributions are important.

Novel approach for extending the depth of field of Barcode decoders by using RGB channels of information

A specially designed phase mask embedded in the lens assembly of an imaging system is shown to provide different response in the three major color bands, R, G and B of a detector array. Each channel provides optimal performance for different depth of field regions, such that the three channels jointly provide an imaging system with wide depth of field. The approach is useful in particular for Barcode imagers.

Optimized logarithmic phase masks used to generate defocus invariant modulation transfer function for wavefront coding system

In a previous Letter [Opt. Lett. 33, 1171 (2008)], we proposed an improved logarithmic phase mask by making modifications to the original one designed by Sherif. However, further studies in another paper [Appl. Opt. 49, 229 (2010)] show that even when the Sherif mask and the improved one are optimized, their corresponding defocused modulation transfer functions (MTFs) are still not stable with respect to focus errors. So, by further modifying their phase profiles, we design another two logarithmic phase masks that exhibit more stable defocused MTF. However, with the defocus-induced phase effect considered, we find that the performance of the two masks proposed in this Letter is better than the Sherif mask, but worse than our previously proposed phase mask, according to the Hilbert space angle.

Pupil coding masks for imaging polychromatic scenes with high resolution and extended depth of field

An algorithm for the design of imaging systems with circular symmetry that exhibit high resolution as well as extended depth of field for polychromatic incoherent illumination is presented. The approach provides a significant improvement over a publication [1] where the design was carried for a single wavelength. The approach is based on searching for a binary phase pupil mask that provides imaging with the highest cut-off spatial frequency, while assuring a desired contrast value over a given depth of field. Simulations followed by experimental results are provided.

Experimental demonstration of continuously variable optical encoding in a hybrid imaging system

We demonstrate an experimental method to obtain a continuously variable hybrid imaging system that uses two generalized cubic phase masks, to enable real-time optimization of the trade between extended depth-of-field and noise gain. We obtain point-spread functions as a function of the rotation angle and show an example of optimization based on recovered image quality.

Fidelity optimization for aberration-tolerant hybrid imaging systems

Several phase-modulation functions have been reported to decrease the aberration variance of the modulation-transfer-function (MTF) in aberration-tolerant hybrid imaging systems. The choice of this phase-modulation function is crucial for optimization of the overall system performance. To prevent a significant loss in signal-to-noise ratio, it is common to enforce restorability constraints on the MTF, requiring trade of aberration-tolerance and noise-gain. Instead of optimizing specific MTF characteristics, we directly minimize the expected imaging-error of the joint design. This method is used to compare commonly used phase-modulation functions: the antisymmetric generalized cubic polynomial and fourth-degree rotational symmetric phase-modulation. The analysis shows how optimal imaging performance is obtained using moderate phase-modulation, and more importantly, the relative merits of the above functions.

Extending the depth of focus for enhanced three-dimensional imaging and profilometry: an overview

We overview the benefits that extended depth of focus technology may provide for three-dimensional imaging and profilometry. The approaches for which the extended depth of focus benefits are being examined include stereoscopy, light coherence, pattern projection, scanning line, speckles projection, and projection of axially varied shapes.

Infrared imaging with a wavefront-coded singlet lens

We describe the use of wavefront coding for the mitigation of optical aberrations in a thermal imaging system. Diffraction-limited imaging is demonstrated with a simple singlet which enables an approximate halving in length and mass of the optical system compared to an equivalent two-element lens.

Incoherently combining logarithmic aspheric lenses for extended depth of field

We describe a method for combining concentric logarithmic aspheric lenses in order to obtain an extended depth of field. Substantial improvement in extending the depth of field is obtained by carefully controlling the optical path difference among the concentric lenses so that their outputs combine incoherently. The system is analyzed through diffraction theory and the point spread function is shown to be highly invariant over a long range of object distances. After testing the image performance on a three-dimensional scene, we found that the incoherently combined logarithmic aspheres can provide a high-quality image over an axial distance corresponding to a defocus of +/- 14(lambda/4). Studies of the images of two-point objects are presented to illustrate the resolution of these lenses.

Optimized circularly symmetric phase mask to extend the depth of focus

We propose a novel design method for a circularly symmetric phase mask to extend the depth of focus. Using the free-form rational function as the solution space, we optimize the profile of the phase mask by analysis of the axial intensity distribution, which can be calculated efficiently by employing the fast Fourier transform algorithm. Numerical comparisons prove the resulting rational phase mask's superiority to the existing quartic phase mask in intensity distribution and imaging performance.

Extended depth of focus contact lenses for presbyopia

The purpose of this Letter is to design, develop, fabricate, and test in clinical trials a new (to our knowledge) type of contact lenses that provides simultaneous near and distance focused vision for presbyopic subjects, including those with up to 2.00 diopters (D) of regular/irregular astigmatism, as an alternative to multifocal contact lenses. The purpose is obtained by generating an optical pattern on the front surface of contact lenses, capable of extending the depth of focus of lenses by 3.00 D with high visual contrast. The pattern was fabricated on top of contact lenses and tested by the use of an eye simulation as well as in clinical trials. Use of the extended depth of focus contact lens enabled patients to achieve good visual acuity and contrast sensitivity for both distance and near vision without compromising the energy distribution or the visual fields.

Improvement of matrix condition of Hybrid, space variant optics by the means of parallel optics design

The problem of image restoration of space variant blur is common and important. One of the most useful descriptions of this problem is in its algebraic form I=H*O, where O is the object represented as a column vector, I is the blur image represented as a column vector and H is the PSF matrix that represents the optical system. When inverting the problem to restore the geometric object from the blurred image and the known system matrix, restoration is limited in speed and quality by the system condition. Current optical design methods focus on image quality, therefore if additional image processing is needed the matrix condition is taken "as is". In this paper we would like to present a new optical approach which aims to improve the system condition by proper optical design. In this new method we use Singular Value Decomposition (SVD) to define the weak parts of the matrix condition. We design a second optical system based on those weak SVD parts and then we add the second system parallel to the first one. The original and second systems together work as an improved parallel optics system. Following that, we present a method for designing such a "parallel filter" for systems with a spread SVD pattern. Finally we present a study case in which by using our new method we improve a space variant image system with an initial condition number of 8.76e4, down to a condition number of 2.29e3. We use matrix inversion to simulate image restoration. Results show that the new parallel optics immunity to Additive White Gaussian Noise (AWGN) is much better then that of the original simple lens. Comparing the original and the parallel optics systems, the parallel optics system crosses the MSEIF=0 [db] limit in SNR value which is more than 50db lower then the SNR value in the case of the original simple lens. The new parallel optics system performance is also compared to another method based on the MTF approach.

Miniaturization of zoom lenses with a single moving element

We present an analysis of single-moving-element zoom lenses in the thin-lens limit and show how the length of these zoom lenses is determined by the zoom-factor, sensor-dimension and the depth-of-focus. By decreasing the sensor size and extending the depth-of-focus, the lengths of these zoom lenses can be reduced significantly. As an example we present a ray-traced design of a miniaturized single-moving-element zoom lens with a 2.3 x zoom-factor and show how the exploitation of modern miniaturized detector array combined with wavefront coding enables a reduction in length of almost three orders-of-magnitude to 10mm.

Ultrathin four-reflection imager

We present the design and experimental demonstration of an ultrathin four-reflection imager. The F/1.15 prototype imager achieves a focal length of 18.6 mm in a track length of just 5.5 mm, providing a 17 degrees field of view over 1.92 megapixels of a color image sensor with 3 microm pixels. We also present the design and experimental results of pupil-phase encoding and postprocessing, which were applied to extend the depth of field and compensate a small amount of axial chromatic aberration present in the four-reflection imager prototype.

An optimal binary amplitude-phase mask for hybrid imaging systems that exhibit high resolution and extended depth of field

The design of a circularly symmetric hybrid imaging system that exhibits high resolution as well as extended depth of field is presented. The design, which assumes spatially incoherent illumination, searches for an optimal "binary amplitude and phase" pupil mask, which for a certain desired depth of field, provides the largest spatial frequency band that assures a certain desired contrast value. The captured images are electronically processed by an off-line Wiener filter, to finally obtain high quality output images. Simulations as well as experimental results are provided.

Imaging with extended focal depth by means of the refractive light sword optical element

The paper presents first experiments with a refractive light sword optical element (LSOE). A refractive version of the LSOE was prepared in photoresist by gray scale photolithography. Then we examined chromatic aberrations of the produced element and compared them with those corresponding to two different lenses. For this purpose we performed two experiments, the first one where white light illumination was used and the latter one by the help of monochromatic illumination with three different wavelengths. The obtained results lead to the conclusion that the refractive LSOE does not exhibit significant chromatic aberrations and can be successfully used for imaging with extended depth of focus in polychromatic illumination.

Conjugate phase plate use in analysis of the frequency response of imaging systems designed for extended depth of field

We unveil a relationship between generating a point spread function with a pair of conjugate phase elements and visualizing the modulation transfer function (MTF) of a single phase element for a variable focus error, at a tunable spatial frequency. We show that the defocused MTF of a pair of conjugate phase elements can be expressed as the modulus of the second order ambiguity function of a single phase element. Finally, we propose a tunable wavefront coding technique with a pair of quartic (4th power) conjugate phase elements.

Polynomial phase masks for extending the depth of field of a microscope

A polynomial phase mask is designed and fabricated for enhancing the depth of field of a microscope by more than tenfold. A generic polynomial of degree 31 that consists of 16 odd power terms is optimized by simulated annealing with a realistic average modulation transfer function (MTF) iteratively set as the target MTF. Optical experimental results are shown.

Lens axicons in oblique illumination

Lens axicons, i.e., lenses or lens systems designed to work like axicons, can be a simple and inexpensive way of generating the characteristic axicon focal line. In the design of most lens axicons, only on-axis properties have been considered. We present the design of a lens axicon with improved off-axis characteristics. It is constructed from a singlet lens but with a double-pass feature that allows for a line of uniform width and a stop positioned to minimize aberrations. We perform off-axis analysis and experiments for this system and for another lens axicon, one designed for its on-axis characteristics. We conclude that the off-axis performance of the double-pass axicon is better than both that of an ordinary cone axicon and that of the other lens axicon.

Frequency analysis of the wavefront-coding odd-symmetric quadratic phase mask

A mathematical analysis of the frequency response of the wavefront-coding odd-symmetric quadratic phase mask is presented. An exact solution for the optical transfer function of a wavefront-coding imager using this type of mask is derived from first principles, whose result applies over all misfocus values. The misfocus-dependent spatial filtering property of this imager is described. The available spatial frequency bandwidth for a given misfocus condition is quantified. A special imaging condition that yields an increased dynamic range is identified.

Radial mask for imaging systems that exhibit high resolution and extended depths of field

A novel algorithm for the design of an imaging system that exhibits high resolution as well as extended depth of field is presented. This novel approach searches for an optimal pupil mask that minimizes the value of the mean-square error when performed over the intensity rather than in the field distribution of the acquired image. The captured images in such system do not require any postprocessing, and thus utilization of such a system is simplified. Simulations as well as experimental results are provided.