Joint digital-optical design of superresolution multiframe imaging systems

Typical electro-optic imaging systems produce image aliasing artifacts. Superresolution algorithms process multiple aliased images to yield a single high-resolution image. We design imaging systems by jointly optimizing the optics and postprocessing to maximize such multiframe imaging performance. We describe efficient software methods that can be used to perform joint design by use of commercially available lens design software.     

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.     

Integral imaging using phase-only LCoS spatial light modulators as Fresnel lenslet arrays

We present a digital integral imaging system. A Fresnel lenslet array pattern is written on a phase-only LCoS spatial light modulator device (SLM) to replace the regular analog lenslet array in a conventional integral imaging system. We theoretically analyze the capture part of the proposed system based on Fresnel wave propagation formulation. Because of pixelation and quantization of the lenslet array pattern, higher diffraction orders and multiple focal points emerge. Because of the multiple focal planes introduced by the discrete lenslets, multiple image planes are observed. The use of discrete lenslet arrays also causes some other artifacts on the recorded elemental images. The results reduce to those available in the literature when the effects introduced by the discrete nature of the lenslets are omitted. We performed simulations of the capture part. It is possible to obtain the elemental images with an acceptable visual quality. We also constructed an optical integral imaging system with both capture and display parts using the proposed discrete Fresnel lenslet array written on a SLM. Optical results when self-luminous objects, such as an LED array, are used indicate that the proposed system yields satisfactory results.     

Aberration-free superresolution imaging via binary speckle pattern encoding and processing

We present an approach that provides superresolution beyond the classical limit as well as image restoration in the presence of aberrations; in particular, the ability to obtain superresolution while extending the depth of field (DOF) simultaneously is tested experimentally. It is based on an approach, recently proposed, shown to increase the resolution significantly for in-focus images by speckle encoding and decoding. In our approach, an object multiplied by a fine binary speckle pattern may be located anywhere along an extended DOF region. Since the exact magnification is not known in the presence of defocus aberration, the acquired low-resolution image is electronically processed via a parallel-branch decoding scheme, where in each branch the image is multiplied by the same high-resolution synchronized time-varying binary speckle but with different magnification. Finally, a hard-decision algorithm chooses the branch that provides the highest-resolution output image, thus achieving insensitivity to aberrations as well as DOF variations. Simulation as well as experimental results are presented, exhibiting significant resolution improvement factors.     

Characteristics of infrared imaging systems that benefit from superresolution reconstruction

There have been numerous applications of superresolution reconstruction algorithms to improve the range performance of infrared imagers. These studies show there can be a dramatic improvement in range performance when superresolution algorithms are applied to undersampled imager outputs. These occur when the imager is moving relative to the target, which creates different spatial samplings of the field of view for each frame. The degree of performance benefit is dependent on the relative sizes of the detector/spacing and the optical blur spot in focal plane space. The minimum blur spot size achievable on the focal plane is dependent on the system F/number. Hence, we provide a range of these sensor characteristics, for which there is a benefit from superresolution reconstruction algorithms. Additionally, we quantify the potential performance improvements associated with these algorithms. We also provide three infrared sensor examples to show the range of improvements associated with provided guidelines.     

Improvement of viewing angle in integral imaging by use of moving lenslet arrays with low fill factor

Lenslet arrays with a low fill factor can improve the viewing angle in integral imaging. However, the viewing resolution is degraded by low fill-factor lenslets because the spatial sampling rate of the ray information is reduced. We show that both the viewing resolution and the viewing angle of integral imaging can be improved by adopting a moving array-lenslet technique.     

Characterization of excimer lasers for application to lenslet array homogenizers

We investigate the best method of characterizing high-divergence lasers, such as excimer lasers, to suppress fine-scale intensity nonuniformity that is due to coherence effects of lenslet homogenizers. We show by a detailed analysis of the lenslet homogenizer that, for highest accuracy, a direct measurement of the value of the autocorrelation function should be made at the separation p of the lenslet elements, identified as the critical spatial period. We show that the commonly used characterization of lasers by the 1/e(2) width of the angular divergence is not the most accurate test and may overstate or understate the effectiveness of a given laser.     

Design and processing of high-density single-mode fiber arrays for imaging and parallel interferometer applications

The design and fabrication procedures for implementing a high-density (16-microm center spacing) single-mode fiber (SMF) array are described. The specific application for this array is a parallel optical coherence tomography system for endoscopic imaging. We obtained fiber elements by etching standard single-mode SMF-28 fibers to a diameter of 14-15 microm. We equalized 1-m lengths of fiber to within 1 mm by using a fiber interferometer setup, and we describe a method for packaging arrays with as many as 100 fibers.     

Generalized Wigner function for the analysis of superresolution systems

The generalized Wigner function is able to represent light distributions that contain spatial and temporal information. The use of such a generalized Wigner distribution function for analysis and understanding of temporally restricted superresolving systems is demonstrated. These systems gain spatial resolution by conversion of the temporal degrees of freedom to spatial degrees of freedom.     

Pseudorandom phase masks for superresolution imaging from subpixel shifting

We present a method for overcoming the pixel-limited resolution of digital imagers. Our method combines optical point-spread function engineering with subpixel image shifting. We place an optimized pseudorandom phase mask in the aperture stop of a conventional imager and demonstrate the improved performance that can be achieved by combining multiple subpixel shifted images. Simulation results show that the pseudorandom phase-enhanced lens (PRPEL) imager achieves as much as 50% resolution improvement over a conventional multiframe imager. The PRPEL imager also enhances reconstruction root-mean-squared error by as much as 20%. We present experimental results that validate the predicted PRPEL imager performance.     

Calculation of the average lenslet shape and aberrations of microlens arrays from their far-field intensity distribution

We present a method to obtain the average lenslet shape of microlens arrays and especially their aberrations from the far-field intensity distribution of the whole array. The method is based on the phase-retrieval algorithm introduced by Gerchberg and Saxton [Optik (Stuttgart) 35, 237 (1972)]. We show how to overcome the crucial point of this algorithm, that is finding suitable start parameters to end up with correct results. The procedure is successfully applied to a cylindrical microlens array produced by reflow technique and the result is compared with surface profilometric measurements. The technique is applicable for lenslets having small numerical apertures and fill factors near unity.     

Analysis of diffracted image patterns from volume holographic imaging systems and applications to image processing

Diffracted image patterns from volume holograms that are used in volume holographic imaging systems (VHISs) are investigated. It is shown that, in VHISs, prior information about the shape and spectral properties of the diffracted patterns is important not only to determine the curvature and field of view of the image, but also for image registration and noise removal. A new methodology to study numerically and analytically the dependence of VHIS diffraction patterns with the hologram construction parameters and the readout wavelength is described. Modeling and experimental results demonstrate that, in most cases, VHIS diffracted shapes can be accurately represented by hyperbolas.     

Microlens arrays for integral imaging system

When designing a system capable of capturing and displaying 3D moving images in real time by the integral imaging (II) method, one challenge is to eliminate pseudoscopic images. To overcome this problem, we propose a simple system with an array of three convex lenses. First, the lateral magnification of the elemental optics and the expansion of an elemental image is described by geometrical optics, confirming that the elemental optics satisfies the conditions under which pseudoscopic images can be avoided. In using the II method, adjacent elemental images must not overlap, a condition also satisfied by the proposed optical system. Next, an experiment carried out to acquire and display 3D images is described. The real-time system we have constructed comprises an elemental optics array with 54 H x 59 V elements, a CCD camera to capture a group of elemental images created by the lens array, and a liquid crystal panel to display these images. The results of the experiment confirm that the system produces orthoscopic images in real time, and thus is effective for real-time application of the II method.     

Forward-viewing CMUT arrays for medical imaging

This paper reports the design and testing of forward-viewing annular arrays fabricated using capacitive micromachined ultrasonic transducer (CMUT) technology. Recent research studies have shown that CMUTs have broad frequency bandwidth and high-transduction efficiency. One- and two-dimensional CMUT arrays of various sizes already have been fabricated, and their viability for medical imaging applications has been demonstrated. We fabricated 64-element, forward-viewing annular arrays using the standard CMUT fabrication process and carried out experiments to measure the operating frequency, bandwidth, and transmit/receive efficiency of the array elements. The annular array elements, designed for imaging applications in the 20 MHz range, had a resonance frequency of 13.5 MHz in air. The immersion pulse-echo data collected from a plane reflector showed that the devices operate in the 5-26 MHz range with a fractional bandwidth of 135%. The output pressure at the surface of the transducer was measured to be 24 kPa/V. These values translate into a dynamic range of 131.5 dB for 1-V excitation in 1-Hz bandwidth with a commercial low noise receiving circuitry. The designed, forward-viewing annular CMUT array is suitable for mounting on the front surface of a cylindrical catheter probe and can provide Doppler information for measurement of blood flow and guiding information for navigation through blood vessels in intravascular ultrasound imaging.     

DNA-templated protein arrays for single-molecule imaging

Single-particle electron cryomicroscopy permits structural characterization of noncrystalline protein samples, but throughput is limited by problems associated with sample preparation and image processing. Three-dimensional density maps are reconstructed from high resolution but noisy images of individual molecules. We show that self-assembled DNA nanoaffinity templates can create dense, nonoverlapping arrays of protein molecules, greatly facilitating data collection. We demonstrate this technique using a G-protein-coupled membrane receptor, a soluble G-protein, and a signaling complex of both molecules.     

Theories for the design of diffractive superresolution elements and limits of optical superresolution

We suggest using the theory of linear programming to design diffractive superresolution elements if the upper bound of the intensity distribution on the input plane is restricted, and using variation theory of functional or wide-sense eigenvalue theory of matrix if the upper bound of the radiation flux through the input plane is restricted. Globally optimal solutions can be obtained by each of these theories. Several rules of the structure and the superresolution performance of diffractive superresolution elements are provided, which verify the validity of these theories and set some limits of optical superresolution.     

Photorefractive processing for large adaptive phased arrays

An adaptive null-steering phased-array optical processor that utilizes a photorefractive crystal to time integrate the adaptive weights and null out correlated jammers is described. This is a beam-steering processor in which the temporal waveform of the desired signal is known but the look direction is not. The processor computes the angle(s) of arrival of the desired signal and steers the array to look in that direction while rotating the nulls of the antenna pattern toward any narrow-band jammers that may be present. We have experimentally demonstrated a simplified version of this adaptive phased-array-radar processor that nulls out the narrow-band jammers by using feedback-correlation detection. In this processor it is assumed that we know a priori only that the signal is broadband and the jammers are narrow band. These are examples of a class of optical processors that use the angular selectivity of volume holograms to form the nulls and look directions in an adaptive phased-array-radar pattern and thereby to harness the computational abilities of three-dimensional parallelism in the volume of photorefractive crystals. The development of this processing in volume holographic system has led to a new algorithm for phased-array-radar processing that uses fewer tapped-delay lines than does the classic time-domain beam former. The optical implementation of the new algorithm has the further advantage of utilization of a single photorefractive crystal to implement as many as a million adaptive weights, allowing the radar system to scale to large size with no increase in processing hardware.     

Synthetic phased arrays for intraluminal imaging of coronaryarteries

A 64-element, high efficiency, ceramic piezoelectric array transducer operating at 20 MHz has been constructed for ultrasonic intraluminal imaging. The array is mounted on the surface of a 1.2 mm diameter catheter appropriate for coronary artery applications. Integrated into the catheter tip is a custom analog chip set permitting complete data capture from the array. That is, on each firing any combination of array elements can be selected independently as transmitter or receiver. Using data acquired in this way, a complete phased array aperture (i.e., independent transmit and receive apertures) can be synthesized. Reconstruction hardware based on a custom application specific integrated circuit (ASIC) has been designed and built to produce real-time images. Beam forming coefficients are derived using an optimal filtering approach accounting for the circular geometry of the array. Simulated and measured beam patterns for this system are compared. In addition, images of coronary anatomy acquired with the real-time system are displayed demonstrating the marked image quality improvement compared to previous synthetic aperture intraluminal systems     

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.