Tolerance of optical interconnections to misalignment

The fundamental reasons that determine the tolerance of free-space optical interconnect systems to misalignment are considered. By evaluation of the overlap of single-mode optical beams in the presence of misalignment it possible to determine an optimum beam configuration. It is shown that for any level of misalignment there is an optimum beam diameter that maximizes the coupling of light through the system. Many interconnect systems are not single mode throughout, so the analysis is extended to cover multimode systems. It is shown that, in principle, any level of misalignment can be accommodated by use of multimode beams, although at the cost of reduced channel density. It is shown that the presence of misalignment will mean that the number of channels that can be supported by an interconnect reduces with the length of the interconnect. As possible candidates for passively aligned systems, three example optical systems are analyzed by use of the methods developed.     

Wavefront sensor architectures fully embedded in an image sensor

Several architectures of wavefront sensors have been developed since the rise of adaptive optics. In all cases, optical elements are placed in front of image sensors. This makes the sensor quite bulky, expensive, and sensitive to optical misalignment. I propose two novel architectures fully embedded in the image sensor that require no additional optical element. The sensor can be placed directly in the beam to analyze, leading to small, easy to use, and cost-efficient systems. The two architectures are described before testing by simulation of their ability to sense the wavefront distortion and their sensitivity to signal-to-noise ratio.     

Intrinsic aberrations due to Mie scattering in particle holography

Holography of small particles is a newly revived topic because of its importance in holographic particle image velocimetry (HPIV). However, the property of particle images formed through holography remains largely unexplored. This fact undermines the measurement reliability of HPIV techniques and has become one of the obstacles in the full deployment of HPIV. We study the intrinsic aberrations in the holographic particle image introduced by particle light scattering and investigate how accurately holography can deliver information about the particles that are being imaged. Consistent with our experimental observations, simulations based on Mie scattering theory show that even with a perfect hologram the reconstructed particle images demonstrate complex three-dimensional morphologies and bodily shifts. These characteristics, manifested as image aberrations, result from uneven scattering amplitude and phase distributions across the finite aperture of the hologram. Such aberrations degrade the signal-to-noise ratio in the reconstructed image as well as introducing systematic errors in detected particle image positions. We examine the effect of these aberrations on HPIV measurements.     

Simple integration technique to realize parallel optical interconnects: implementation of a pluggable two-dimensional optical data link

An assembly technique is presented to realize pluggable or fully integrated optoelectronic systems based on image relays. A method to visually align and assemble optoelectronic chips or fiber bundles to half of a relay is explained. To validate this technique, two-dimensional arrays of vertical-cavity surface-emitting lasers and photodetectors and a fiber image guide have been integrated to gradient index lenses with simple optomechanical parts. Although the connection of these modules was realized with +/-0.5 mm lateral tolerances, parallel optical interconnects were successfully achieved at 10 MHz. The lateral misalignment between chips was on average 20 microm and at worst 60 microm.     

Intrinsic speckle noise in off-axis particle holography

In holographic imaging of particle fields, the interference among coherent wave fronts associated with particle scattering gives rise to intrinsic speckle noise, which sets a fundamental limit on the amount of information that particle holography can deliver. It has been established that the intrinsic speckle noise is especially severe in in-line holography because of superposition of virtual image waves, the direct transmitted wave, and the real image. However, at sufficiently high particle number densities, such as those typical in holographic particle image velocimetry (HPIV) applications, intrinsic speckle noise also arises in off-axis particle holography from self-interference among wave fronts that form the real image of particles. To overcome the latter problem we have constructed a mathematical model that relates the first- and second-order statistical properties of the intrinsic speckle noise to relevant holographic system parameters. Consistent with our experimental data, the model provides a direct estimate of the information capacity of particle holography. We show that the noise-limited information capacity can be expressed as the product of particle number density and the extent of the particle field along the optical axis. A large angular aperture of the hologram contributes directly to achievement of high information capacity. We also show that filtering in either digital or optical form is generally ineffective in removing the intrinsic speckle noise from the particle image as a result of the similar spectral properties of the two. These findings emphasize the importance of angular aperture in designing holographic particle imaging systems.     

Four-dimensional dynamic flow measurement by holographic particle image velocimetry

The ultimate goal of holographic particle image velocimetry (HPIV) is to provide space- and time-resolved measurement of complex flows. Recent new understanding of holographic imaging of small particles, pertaining to intrinsic aberration and noise in particular, has enabled us to elucidate fundamental issues in HPIV and implement a new HPIV system. This system is based on our previously reported off-axis HPIV setup, but the design is optimized by incorporating our new insights of holographic particle imaging characteristics. Furthermore, the new system benefits from advanced data processing algorithms and distributed parallel computing technology. Because of its robustness and efficiency, for the first time to our knowledge, the goal of both temporally and spatially resolved flow measurements becomes tangible. We demonstrate its temporal measurement capability by a series of phase-locked dynamic measurements of instantaneous three-dimensional, three-component velocity fields in a highly three-dimensional vortical flow-the flow past a tab.     

Design and characterization of a microchannel optical interconnect for optical backplanes

The design, modeling, and experimental characterization of a microchannel-based free-space optical interconnect is described. The microchannel interconnect was used to implement a representative portion of an optical backplane that was based on field-effect transistor, self-electro-optic device smart-pixel transceivers. Telecentric relays were used to form the optical interconnect, and two modes based on two different optical window clusterings were implemented. The optical system design, including the optical geometry for different degrees of clustering of windows supported by a lenslet relay and the image mapping associated with a free-space optical system, is described. A comparison of the optical beam properties at the device planes, including the spot size and power uniformity of the spot array, as well as the effects of clipping and misalignment for the different operating modes, is presented. In addition, the effects of beam clipping and misalignment for the different operating modes is presented. We show that microchannel free-space optical interconnects based on a window-clustering scheme significantly increase the connection density. A connection density of 2222 connections/cm(2) was achieved for this prototype system with 2 x 2 window clustering.     

Misalignment correction for optical interconnects using vertical cavity semiconductor optical amplifiers

In board-to-board optical interconnects, the misalignment between the board and the backplane connections can cause both optical loss and interchannel cross talk. A vertical cavity semiconductor optical amplifier (VCSOA) is proposed to correct optical misalignment in an optical connector between the board and the backplane. Angular or lateral misalignment can be corrected with the designed module. The correction ability is determined by the acceptance angle of the VCSOA, which was characterized to be 9.4 degrees full angle at a 3 dB gain drop for a 30 microW optical signal at 1 GHz. The lateral misalignment correction ability is 0.16f, where f is the focal length of the mini lens to converge the input light onto the VCSOA.     

Noise-equivalent change in radiance for misalignment noise in a double-sided interferogram

Engineers designing optical alignment servo systems for Michelson interferometers and Fourier-transform infrared spectrometers need to predict the amount of noise expected from the small and randomly varying amounts of misalignment that occur as the servo attempts to maintain alignment while taking data. A formula is derived for the noise-equivalent change in radiance due to this effect and the formula's accuracy is demonstrated by comparison of its predictions to the errors found in simulated interferometer measurements contaminated by misalignment noise.     

一种振动失调反射光学系统模拟计算的实验分析方法

在光学元件动力学计算模型和光线传输失调模型建立的基础上,形成了一种振动失调反射光学系统的模拟计算方法。分别通过模态实验和振动台实验对系统模型进行验证和修正。实验和模拟的结果对比表明:修正后元件动力学模型的模态参数计算结果和实验结果偏差在5%以内,修正后振动失调反射光学系统模拟计算结果与振动台测试结果偏差在17%以内,得到了可靠的振动失调反射光学系统模拟计算方法,为光学系统的抗振性能分析和减振分析奠定理论基础。     

Angular sensitivities of volume gratings for substrate-mode optical interconnects

The angular sensitivities of slanted volume gratings (VGs) illuminated by three-dimensional (3-D) converging-diverging spherical Gaussian beams for substrate-mode optical interconnects in microelectronics are analyzed by application of 3-D finite-beam rigorous coupled-wave analysis. Angular misalignments about the z, y, and x axes that correspond to yaw, pitch, and roll misalignments resulting from manufacturing tolerances of chips are investigated. Two cases of linear polarization of the central beam of the Gaussian are considered: E perpendicular K and H perpendicular K, where K is the grating vector. From worst-case manufacturing tolerances, the ranges of yaw, pitch, and roll misalignment angles are alpha = +/-1.17 degrees, beta= +/-3.04 degrees, and gamma = +/-3.04 degrees, respectively. Based on these ranges of misalignment angles, the decreases of diffraction efficiencies for slanted VGs that are due to both the yaw and the roll misalignments are relatively small. However, the efficiency of substrate-mode optical interconnects achieved by slanted VGs could be reduced by 61.04% for E perpendicular K polarization and by 58.63% for H perpendicular K polarization because of the pitch misalignment. Thus the performance of a VG optical interconnect is most sensitive to pitch misalignment.     

Effect of encoder--decoder mismatch due to wavelength and time misalignments on the performance of two-dimensional wavelength--time optical code-division multiple access systems

We examine the effects of encoder and decoder mismatch due to wavelength and time chip misalignments on the bit-error rate (BER) performance of two-dimensional (2D) wavelength--time optical code-division multiple access systems. We investigate several instances of misalignment in the desired user encoder and decoder as well as in the interfering user encoders. Our simulation methodology can be used to analyze any type of 2D wavelength--time code family as well as probability distribution for misalignment. For illustration purposes, we consider codes generated by use of the depth-first search algorithm and a Gaussian distribution for the misalignment. Our simulation results show that, in the case of a misalignment in either wavelength or time chip, the variance of the distribution for the misalignment must be below 0.01 for the corresponding degradation in the BER system's performance to be less than 1 order of magnitude compared with that when there is no mismatch between the encoders and decoders. The tolerances become even more strict when misalignments in both wavelength and time chips are considered. Furthermore, our results show that the effect of misalignment in wavelength (time chips) is the same regardless of the number of wavelengths (time chips) used in the codes.     

Design of lenses with curved Petzval image surfaces

Abstract

Design strategies have been devoted to simplify and miniaturize optical systems. In this paper, by constraining image surface to coincide with the Petzval surface, we achieve a compact f/2.8 lens system design with a curved Petzval image surface. Arc distortion is proposed to accurately measure the distortion relative to a curved image surface. The optical performance of our curved image surface lens is analysed and compared. Results show that modulation transfer function (MTF) of our curved Petzval design over 69% at 100 cycles/mm for entire fields is achievable with 100-mm effective focal length, 40º full field of view, >92.4% edge relative illumination, <0.5% arc distortion. Comparisons with a traditional lens with a planar image plane demonstrate that a curved Petzval image surface is an excellent strategy to simplify and miniaturize optical systems, compensate field curvature and benefit astigmatism correction, increase off-axis illumination and improve MTF. Furthermore, the lens with a curved Petzval image surface has a more uniform optical power distribution and greater degree of lens symmetry.     

Changes in the polarization and coherence of a random electromagnetic beam propagating through a misaligned optical system

On the basis of the generalized diffraction integral formula for misaligned optical systems in the spatial domain, an analytical propagation expression for the elements of the cross-spectral density matrix of a random electromagnetic beam passing through a misaligned optical system is derived. Some analyses are illustrated by numerical examples relating to changes in the spectral degree of polarization and in the spectral degree of coherence of an electromagnetic Gaussian-Schell-model beam propagating through such an optical system. We find that the degree of polarization in the neighboring areas of the focal plane is oscillating, and the effect of misalignment on coherence is not so evident as that on polarization.     

The effect of misalignment errors in optical elements of VUV polarimeter

We have designed a Vacuum Ultra Violet polarimeter for Indian Synchrotron Radiation Source Indus-1. This polarimeter will be installed on a toroidal grating monochromator-based beamline. Polarimeter consists of four-mirror phase retarder and three-mirror linear polarizer. Three-mirror linear polarizer has glancing angles of incidence 23°, 46° and 23°, working in 200–1100 Å wavelength region, with linear polarizence greater than 90%. Detailed ray-tracing analysis was carried out to find the effect of various misalignment errors in each of the optical element of the polarimeter. It is found that misalignment errors in optical element of the polarimeter affect only the beam spot position and do not affect the spot size, polarization state and photon flux of outgoing beam, substantially. Accuracies in the linear and angular positions of optical elements in phase retarder and linear polarizer must be very precise to perform ellipsometric experiments. Tolerance limit for various misalignment errors has been obtained. Required accuracy in angular position around X-axis is more than that required in angular position around Z-axis.     

High-speed path-length scanning with a multiple-pass cavity delay line

Techniques for high-speed delay scanning are important for low-coherence interferometry, optical coherence tomography, pump probe measurements, and other applications. We demonstrate a novel scanning delay line using a multiple-pass cavity. Differential delays are accumulated with each pass so that millimeter delays can be generated with tens of micrometer mirror displacements. With special design criteria, misalignment sensitivity can be dramatically reduced. The system is demonstrated to scan 6 m/s at 2-kHz repetition rates. Real-time optical coherence tomography imaging with 500 pixel images at four frames/s is performed. Using a Cr:forsterite laser source, we obtained axial image resolutions of 6 microm with 92-dB sensitivity.     

Optical encryption system that uses phase conjugation in a photorefractive crystal

We implement an optical encryption system based on double-random phase encoding of the data at the input and the Fourier planes. In our method we decrypt the image by generating a conjugate of the encrypted image through phase conjugation in a photorefractive crystal. The use of phase conjugation results in near-diffraction-limited imaging. Also, the key that is used during encryption can also be used for decrypting the data, thereby alleviating the need for using a conjugate of the key. The effect of a finite space-bandwidth product of the random phase mask on the encryption system's performance is discussed. A theoretical analysis is given of the sensitivity of the system to misalignment errors of a Fourier plane random phase mask.     

Accurate pixel-to-pixel correspondence adjustment in a digital micromirror device camera by using the phase-shifting moiré method

A camera based on the digital micromirror device (DMD) technology has been previously developed. In this optical system, the correspondence of each mirror of the DMD to each pixel of the CCD cannot readily be done since the pixel sizes of the DMD and the CCD are very small. An accurate pixel-to-pixel correspondence adjustment in the DMD camera by means of the phase-shifting moiré method is proposed. To perform high accurate adjustment of the optical system, the phase distribution of a moiré fringe pattern is analyzed when the CCD pixels and the DMD mirrors have a mismatch and/or misalignment with each other. This technique does not need a complicated setting or complex image processing to generate the moiré fringe pattern, and it needs only one captured image. In the adjustment experiment, the proposed method provided very accurate adjustment whose error was less than 1/25 pixel. An experiment of phase analysis to demonstrate the usefulness was performed.     

A novel image analysis procedure for measuring fibre misalignment in unidirectional fibre composites

A novel image analysis procedure named Fourier transform misalignment analysis (FTMA) for measuring fibre misalignment in unidirectional fibre composites is presented. Existing methods are briefly illustrated and evaluated. The FTMA-method is presented, describing the specimen preparation and elaborating how the image analysis algorithm uses Fourier transformation and a least squares method to compute single fibre orientations. On the basis of parameter investigations the robustness of the FTMA-method is investigated. Software generated micrographs with known fibre misalignment are used to determine the precision of the method. The precision is used, along with computation time and memory usage, to benchmark the FTMA-method against the existing multiple field image analysis (MFIA) method. It is found that the FTMA-method is at least as accurate as existing methods. Furthermore, the FTMA-method is much faster than the existing methods, completing a typical analysis in approximately 1 min. Overall, it is concluded that the FTMA-method is a robust, precise and time efficient tool for determining fibre misalignment in unidirectional fibre composites, offering a higher degree of detail than the existing MFIA-method.     

Image fiber optic space-CDMA parallel transmission experiment using 8 x 8 VCSEL/PD arrays

We experimentally demonstrate space-code-division multiple access (space-CDMA) based twodimensional (2-D) parallel optical interconnections by using image fibers and 8 x 8 vertical-cavity surface-emitting laser (VCSEL)/photo diode (PD) arrays. Two spatially encoded four-bit (2 x 2) parallel optical signals were emitted fiom 2-D VCSEL arrays and transmitted through image fibers. The encoded signals were multiplexed by an image-fiber coupler and detected by a 2-D PD array on the receiver side. The receiver recovered the intended parallel signal by decoding the signal. The transmission speed was 64 Mbps/ch (total throughput: 512 Mbps). Bit-error-rate (BER) measurement with a laterally misaligned PD array showed the array had a misalignment tolerance of 25 microm for a BER performance of 10(-9).