Series Of Optical Elements Research Articles

Simulation of digital holographic recording and reconstruction using a generalized matrix method.

In recent years, research efforts in the field of digital holography have expanded significantly, due to the ability to obtain high-resolution intensity and phase images. The information contained in these images have become of great interest to the machine learning community, with applications spanning a wide portfolio of research areas, including bioengineering. In this work, we seek to demonstrate a high-fidelity simulation of holographic recording. By accurately and numerically simulating the propagation of a coherent light source through a series of optical elements and the object itself, we accurately predict the optical interference of the object and reference wave at the recording plane, including diffraction effects, aberrations, and speckle. We show that the optical transformation that predicts the complex field at the recording plane can be generalized for arbitrary holographic recording configurations using a matrix method. In addition, we provide a detailed description of digital phase reconstruction and aberration compensation for a variety of off-axis holographic configurations. Reconstruction errors are presented for the various holographic recording geometries and complex field objects. While the primary objective of this work is not to evaluate phase reconstruction approaches, the reconstruction of simulated holograms provides validation of the generalized simulation method. The long-term goal of this work is that the generalized holographic simulation motivates the use of phase reconstruction of the simulated holograms to populate databases for training machine-learning algorithms aimed at classifying relevant objects recorded through a variety of holographic setups.

Crosstalk Noise Reduction Through Adaptive Power Control in Inter/Intra-Chip Optical Networks

In recent years, optical interconnection networks have been proposed in order to achieve the ultrahigh bandwidth and low latency requirements for inter/intra-chip communication. In these optical interconection networks, series of basic optical elements are employed. Via these series of optical elements, the intrinsic crosstalk noise is generated. With a large scale of these optical elements, the signal-to-noise ratio (SNR) of an optical interconnect can be reduced by this crosstalk noise. In this paper, we utilize the adaptive power control (APC) to enhance the SNR under the crosstalk noise constraints. APC has been known to save energy and reduce power consumption. We apply this technique in one of the inter/intra-chip optical interconnect called I2CON. A new cluster design, namely the Beam cluster, is also introduced. Results have demonstrated that the APC can help to reduce crosstalk noise, hence, the overall SNR is improved. Comparison results have also indicated the further improvement of SNR in I2CON using Beam cluster when APC is applied.

Error Analysis of Ray’s Light Path for Axis-Symmetrical Optical System by Using Skew Ray Tracing

ωThis study applies a skew ray tracing approach based on a 4×4 homogeneous coordinate transformation matrix and Snell’s law to analyze the errors of a ray’s light path as it passes through a series of optical elements for axis-symmetrical optical system. The proposed error analysis methodology considers two principal sources of light path error, namely: (1) the translational errors Δxi, Δyi and Δzi and the rotational errors Δωix, Δωiy and Δωiz, which determine the deviation of the light path at each boundary surface, and (2) the differential changes induced in the incident point position and unit directional vector of the refracted / reflected ray as a result of differential changes in the position and unit directional vector of the light source. The validity of the proposed methodology is verified by analyzing the effects of optical errors in Petzval lens.

Optimizing Methods to Recover Absolute FRET Efficiency from Immobilized Single Molecules

Microscopy-based fluorescence resonance energy transfer (FRET) experiments measure donor and acceptor intensities by isolating these signals with a series of optical elements. Because this filtering discards portions of the spectrum, the observed FRET efficiency is dependent on the set of filters in use. Similarly, observed FRET efficiency is also affected by differences in fluorophore quantum yield. Recovering the absolute FRET efficiency requires normalization for these effects to account for differences between the donor and acceptor fluorophores in their quantum yield and detection efficiency. Without this correction, FRET is consistent across multiple experiments only if the photophysical and instrument properties remain unchanged. Here we present what is, to our knowledge, the first systematic study of methods to recover the true FRET efficiency using DNA rulers with known fluorophore separations. We varied optical elements to purposefully alter observed FRET and examined protein samples to achieve quantum yields distinct from those in the DNA samples. Correction for calculated instrument transmission reduced FRET deviations, which can facilitate comparison of results from different instruments. Empirical normalization was more effective but required significant effort. Normalization based on single-molecule photobleaching was the most effective depending on how it is applied. Surprisingly, per-molecule γ-normalization reduced the peak width in the DNA FRET distribution because anomalous γ-values correspond to FRET outliers. Thus, molecule-to-molecule variation in gamma has an unrecognized effect on the FRET distribution that must be considered to extract information on sample dynamics from the distribution width.

Recovering Absolute Fret Efficiency from Single Molecules: Comparing Methods of Gamma Correction

Fluorescence resonance energy transfer is widely thought of as a “spectroscopic ruler.” Because biological processes and cellular assemblies occur on the nanometer scale, FRET is a popular tool for structural biology. In contrast to ensemble solution FRET measurements which record the entire emission spectrum, microscopy- based FRET experiments separate donor and acceptor intensity by passing the emission through a series of optical elements. Observed FRET efficiency, determined from the uncorrected donor and acceptor intensities, has been called a relative proximity ratio, which is internally consistent only if the photophysical properties and instrument remain unchanged. However, it is desirable to measure absolute distances using FRET, which requires that FRET efficiency be corrected for both instrument response and fluorophore properties. Thus, “gamma” correction adjusts for differences between the donor and acceptor dyes in their probability of photon emission upon excitation and the probability that emitted photons will be detected. Methods of gamma correction vary depending on the single molecule methodology. To test different methods for correcting FRET efficiency, we recorded smFRET distributions for protein and DNA on different instruments and with different filter sets which altered the observed FRET efficiency. Knowledge of filter set transmission allows for comparison of results between groups using different instruments. Applying empirically-derived corrections for instrument response and quantum yield was only slightly better than corrections based solely on filter set transmission data. We found that gamma correction based on single molecule photobleaching was the most effective particularly when gamma was determined for each sample or even each molecule. Variations in focus of the two colors and sub-pixel errors in image mapping affect both FRET and gamma. As such, per molecule correction affects distribution width because FRET outliers may also have anomalous gamma values.

A skew ray tracing approach for the error analysis of optical elements with spherical boundary surfaces

This study applies a skew ray tracing approach based on a 4 × 4 homogeneous coordinate transformation matrix and Snell's law to analyze the errors of a ray's light path as it passes through a series of optical elements with spherical boundary surfaces. The proposed error analysis methodology considers two principal sources of light path error, namely: (1) the translational errors ΔX i , ΔY i and ΔZ i and the rotational errors , and , which determine the deviation of the light path at each boundary surface, and (2) the differential changes induced in the incident point position and unit directional vector of the refracted/reflected ray as a result of differential changes in the position and unit directional vector of the light source. The validity of the proposed methodology is verified by analyzing the effects of optical errors in a solid glass cat's eye.