High Space-bandwidth Product Research Articles

Fourier ptychography for high space-bandwidth product microscopy

Abstract Fourier ptychography is a novel imaging technique with high space-bandwidth product (SBP) on the scale of gigapixel, and has been successfully applied for high-resolution and large field-of-view (FOV) microscopy, termed Fourier ptychographic microscopy (FPM). FPM utilizes a low-numerical-aperture objective lens to capture multiple large FOV but low-resolution images under angularly varying illumination, and uses phase-retrieval algorithms to reconstruct the sample’s high-resolution amplitude and phase information. FPM is advantageous over conventional high SBP microscopy techniques in many aspects, including no mechanical scanning, computational acquisition of both amplitude and phase, extended depth of focus, long working distance, and high compatibility with current microscopes. In this paper, we review FPM with its principles, multiple techniques to improve its performance, and its various applications and extensions.

Multi-region phase calibration of liquid crystal SLM for holographic display.

The liquid crystal spatial light modulator (SLM) is able to provide flexible wavefront control, whereas the initial phase and its response distortions will heavily influence the modulation accuracy. The currently existing calibration methods are tedious and time consuming. A novel multi-region calibration method for minimizing those distortions is proposed. The entire panel is divided into several local regions based on the similarity of phase response characteristic. The nonlinear phase response and static phase distortion of each local region are calibrated in the iterative division procedure. The calibration method is theoretically analyzed and experimentally verified. For the Jasper 4K SLM panel, when five local regions are built, the root mean error of linear phase shifts is reduced to 0.1rad and the compensation accuracy of the static phase distortion reaches 0.24 wavelength. The calibrated SLM is applied for the color holographic display and the results show that the reconstructed image quality is improved significantly. The proposed method is simpler and faster because of the reasonable regional division and lower calibration complexity. It could be used for the calibration of various phase only or complex modulators with high space bandwidth product in the future.

Motion-corrected Fourier ptychography.

Fourier ptychography (FP) is a recently proposed computational imaging technique for high space-bandwidth product imaging. In real setups such as endoscope and transmission electron microscope, the common sample motion largely degrades the FP reconstruction and limits its practicability. In this paper, we propose a novel FP reconstruction method to efficiently correct for unknown sample motion. Specifically, we adaptively update the sample's Fourier spectrum from low spatial-frequency regions towards high spatial-frequency ones, with an additional motion recovery and phase-offset compensation procedure for each sub-spectrum. Benefiting from the phase retrieval redundancy theory, the required large overlap between adjacent sub-spectra offers an accurate guide for successful motion recovery. Experimental results on both simulated data and real captured data show that the proposed method can correct for unknown sample motion with its standard deviation being up to 10% of the field-of-view scale. We have released our source code for non-commercial use, and it may find wide applications in related FP platforms such as endoscopy and transmission electron microscopy.

Holographic display system for dynamic synthesis of 3D light fields with increased space bandwidth product.

We present a new method for the generation of a dynamic wave field with high space bandwidth product (SBP). The dynamic wave field is generated from several wave fields diffracted by a display which comprises multiple spatial light modulators (SLMs) each having a comparably low SBP. In contrast to similar approaches in stereoscopy, we describe how the independently generated wave fields can be coherently superposed. A major benefit of the scheme is that the display system may be extended to provide an even larger display. A compact experimental configuration which is composed of four phase-only SLMs to realize the coherent combination of independent wave fields is presented. Effects of important technical parameters of the display system on the wave field generated across the observation plane are investigated. These effects include, e.g., the tilt of the individual SLM and the gap between the active areas of multiple SLMs. As an example of application, holographic reconstruction of a 3D object with parallax effects is demonstrated.

Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient.

Fourier ptychographic microscopy (FPM) is a novel computational coherent imaging technique for high space-bandwidth product imaging. Mathematically, Fourier ptychographic (FP) reconstruction can be implemented as a phase retrieval optimization process, in which we only obtain low resolution intensity images corresponding to the sub-bands of the sample’s high resolution (HR) spatial spectrum, and aim to retrieve the complex HR spectrum. In real setups, the measurements always suffer from various degenerations such as Gaussian noise, Poisson noise, speckle noise and pupil location error, which would largely degrade the reconstruction. To efficiently address these degenerations, we propose a novel FP reconstruction method under a gradient descent optimization framework in this paper. The technique utilizes Poisson maximum likelihood for better signal modeling, and truncated Wirtinger gradient for effective error removal. Results on both simulated data and real data captured using our laser-illuminated FPM setup show that the proposed method outperforms other state-of-the-art algorithms. Also, we have released our source code for non-commercial use.

Design of micro-optics array to realize two dimensional perfect shuffle transform

Two-dimensional (2D) perfect shuffle transform (PST) plays an important role in optical communication and optical information processing due to very high space-bandwidth product (SBWP) and spatial degrees of freedom. The planar-array of micro-blazed grating has been proposed to realize 2D PST based on its interesting properties such as high diffraction efficiency, small size, high degree of integration, and easy to fabricate. 2D PST could be realized in free space through controling the etching direction and the period of micro-blazed grating, which results in signal beams can reach the desired spatial position. Unlike the conventional method depending on the operation of dividing, magnification, interlacing, and superimposing, this approach, which mainly relies on the diffractive properties of signal beams and the distribution of light intensity, presents a single diffractive element to perform 2D PST. Thus, this approach has the advantages of high energy efficiency, high feasibility, compact in structure, and easy to integrate. The theoretical analyses and the experimental results show that it should be helpful in optical interconnection network, especially, in PS omega network.

Data-Processing Strategies for Crossed-Strip Gamma-Ray Detectors.

Crossed-strip gamma-ray detectors are an attractive option for small-animal SPECT imagers due to their high space-bandwidth product. In systems with independent triggering of the two sides of the detector, advanced data-processing techniques are required to accurately determine gamma-ray interaction locations and energy deposition. Optimal detector operation further relies on rigorous detector characterization in order to achieve detector triggering uniformity and best timing resolution and to permit position and energy estimation with maximum-likelihood methods. We describe algorithms and methods developed for calibrating and characterizing a recently fabricated system based on 1024-strips-per-side 1-mm-thick silicon detectors.

Wave-front sensing with a sampling field sensor

We present a new type of optical wave-front sensor: the sampling field sensor (SFS). The SFS attempts to solve the problem of real-time optical phase detection. It has a high space-bandwidth product and can be made compact and vibration insensitive. We describe a particular implementation of this sensor and compare it, through numerical simulations, with a more mature technique based on the Shack-Hartmann wave-front sensor. We also present experimental results for SFS phase estimation. Finally, we discuss the advantages and drawbacks of this SFS implementation and suggest alternative implementations.

Two-step digit-set-restricted modified signed-digit addition–subtraction algorithm and its optoelectronic implementation

A novel, to our knowledge, two-step digit-set-restricted modified signed-digit (MSD) addition-subtraction algorithm is proposed. With the introduction of the reference digits, the operand words are mapped into an intermediate carry word with all digits restricted to the set {1, 0} and an intermediate sum word with all digits restricted to the set {0, 1}, which can be summed to form the final result without carry generation. The operation can be performed in parallel by use of binary logic. An optical system that utilizes an electron-trapping device is suggested for accomplishing the required binary logic operations. By programming of the illumination of data arrays, any complex logic operations of multiple variables can be realized without additional temporal latency of the intermediate results. This technique has a high space-bandwidth product and signal-to-noise ratio. The main structure can be stacked to construct a compact optoelectronic MSD adder-subtracter.

Efficient detour-phase encoding of one-dimensional multilevel phase diffractive elements

We show that detour-phase encoding with a multilevel blaze structure as a carrier grating is especially suited to the implementation of diffractive elements with relatively high complexity in one axis. For our proposal the carrier grating is aligned perpendicularly to this axis. In this way the element can be encoded with a high space-bandwidth product and a high phase resolution by use of a moderate carrier frequency. Moreover, this frequency can be adjusted to isolate the reconstructed field from the noise resulting from high diffraction orders of the carrier grating or caused by etching errors during fabrication.

Hybrid color holograms

The familiar optically recorded rainbow hologram is frequently used to produce color holograms. It is simple to compute the corresponding synthetic hologram structures, which would require no recording process and would be capable of displaying virtual three-dimensional objects. It is difficult, however, to materialize the computed structures because of the high space-bandwidth product required. To find a way around this problem we used a set of three computer-generated holograms as master holograms for an optical recording process in which each master hologram contains information about a different color. This reduces the space-bandwidth product requirements for the synthetic structures to convenient values.

Dynamic holographic interconnects that use ferroelectric liquid-crystal spatial light modulators

<p>Dynamic interconnect holograms are designed by the use of a simulated annealing algorithm and written to a 128 × 128 pixel ferroelectric spatial light modulator that is used in a binary-phase mode. Dynamic holograms are used to implement a 2 × 2 crossbar with single-mode fiber inputs and outputs, which function with as high as 27 dB of isolation between output ports. The principle is extended to two-dimensional interconnection holograms, and arbitrary fan-out to as high as 64 points is demonstrated with good performance.</p><p>Images of interconnection holograms are transferred from the spatial light modulator to an optically addressed spatial light modulator that is used in a binary-phase mode. The addition of a fixed array generator computer-generated hologram permits replication of the hologram image, thus creating a larger hologram with a high space-bandwidth product on the optically addressed spatial light modulator.</p><p>Results of a preliminary experiment are presented.</p>

Application of an optically addressed spatial light modulator to real-time speckle photography

The application of a bistable, binary, amorphous silicon ferroelectric liquid crystal optically addressed spatial light modulator to speckle photography is described. The system presented has a higher space-bandwidth product than a television system and can operate at greater than 500 Hz frame rates. The output is also amenable to further optical processing. The spatial light modulator is characterised for sensitivity, contrast ratio and resolution and speckle correlation fringes from a moving object are successfully obtained. Measurement of displacements in the range 20 μm to 70 μm with an rms error of 3 μm is demonstrated and the suitability of these devices to practical optical metrology is discussed.

Telecentric Scanner For 3-D Sensing

Triangulation systems that are based on the simultaneous deflection of the illuminating and observing light beam are able to scan large object fields fast and with high space-bandwidth product. On the other hand, in nontelecentric systems, the direction of illumination and observation vary along the scan path, and the shape of an object is usually determined with respect to a circular reference shape. We describe a telecentric system with variable reference shape, stationary measuring geometry over the whole field, and expanded depth of field.

Cosinusoidal transforms in white light

Theory and techniques of white light interferometry have been studied to devise an optoelectronic hybrid for diffraction pattern sampling. For an incoherently illuminated input scene, we obtain an output intensity that is the 2-D spatial cosine transform of the input plus a bias term. The bias can be subtracted electronically to within shot noise fluctuation limitations. The optical system consists of a double-imaging interferometer with a beam-splitter cube and crossed right-angle-prism reflectors followed by an achromatic-optical-transform lens pair. A photodiode array is placed in the optical transform plane, and this is coupled to a digital computer for further signal processing. Theoretical results are presented for the synthesis of the cosinusoidal transform configuration. From Fresnel-zone theory, a general form is derived for the impulse response of a cascade of ideal thin lenses, and this is used to design Fourier transform achromats that are well suited to this application. Experiments are presented showing cosine transforms for rough objects and for objects in reflection using illumination of negligible spatial coherence at the object. Excellent sensitivity is obtained with the bias subtraction, and a high space–bandwidth product is attained for the system.