Effects Of Partial Coherence Research Articles

Wave Optical Modeling of the SEM Column From Source to Specimen.

Probe formation in scanning electron microscope (SEM) is often reduced to objective lens action modeling based on a point-spread function or Fourier transforms. In this study, we present the first complete wave optical modeling of the whole SEM column based on plane-by-plane propagation of the electron beam wavefunction without simplifying the optical system. We identify the challenges in plane-by-plane beam propagation and show how sampling limitations produce aliased results. Through a careful selection and combination of propagators, we have developed a general wave optical propagation method that is able to overcome the aliasing problem to achieve the appropriate probe widths. Using a two-step propagator, we show that it is possible to model the electron beam distribution throughout the column from the virtual source plane to the specimen plane. We also show that our results from the wave optical simulations are consistent with the geometrical theory of probe formation. Finally, as a direct application of this method, we demonstrated that the combined effect of aberrations in the condenser lens and the probe forming objective lens cannot be accurately represented using only the objective lens. Designing beam shaping experiments and studying the effect of partial coherence can be some novel applications.

Signal to Noise in Low-Dose Ptychography: The Effect of Imaging Parameters and Partial Coherence

Signal to Noise in Low-Dose Ptychography: The Effect of Imaging Parameters and Partial Coherence

Effect of partial coherence on signal-to-noise ratio performance of free space optical communication system in weak turbulence

The effect of source coherence on the average signal-to-noise ratio SNR performance of free space optical communication (FSOC) systems operating in weak atmospheric turbulence is investigated with the help of the extended Huygens–Fresnel​ principle. For an FSOC system that uses a partially coherent laser source, first, the received power at the finite-sized receiver aperture is derived. Then, the power scintillation index is evaluated that reflects the aperture averaging. Using these derived optical entities, the variations of SNR are examined versus parameters such as the degree of source coherence, wavelength, link distance, source size, structure constant of atmosphere and the receiver aperture radius. Obtained results show that a decrease in the degree of source coherence has a positive effect on SNR.

Effect of Partial Coherence on Signal-to-Noise Ratio Performance of Free Space Optical Communication System in Weak Turbulence

Effect of Partial Coherence on Signal-to-Noise Ratio Performance of Free Space Optical Communication System in Weak Turbulence

Experimental demonstration of superresolution of partially coherent light sources using parity sorting.

Analyses based on quantum metrology have shown that the ability to localize the positions of two incoherent point sources can be significantly enhanced over direct imaging through the use of mode sorting. Here we theoretically and experimentally investigate the effect of partial coherence on the sub-diffraction limit localization of two sources based on parity sorting. With the prior information of a negative and real-valued degree of coherence, higher Fisher information is obtained than that for the incoherent case. Our results pave the way to clarifying the role of coherence in quantum-limited metrology.

A wave optics model for the effect of partial coherence on coherent diffractive imaging

With the development of fourth-generation synchrotron sources, coherent diffractive imaging (CDI) will be a mainstream method for 3D structure determination at nanometre resolution. The partial coherence of incident X-rays plays a critical role in the reconstructed image quality. Here a wave optics model is proposed to analyze the effect of partial coherence on CDI for an actual beamline layout, based on the finite size of the source and the influence of the optics on the wavefront. Based on this model, the light field distribution at any plane, the coherence between any two points on this plane and CDI experiments can be simulated. The plane-wave CDI simulation result also shows that in order to reconstruct good image quality of complex samples the visibility of the interference fringes of any two points in the horizontal and vertical directions of the incident light field at the sample needs to be higher than 0.95.

Light source optimization for partially coherent holographic displays with consideration of speckle contrast, resolution, and depth of field

Speckle reduction is an important topic in holographic displays as speckles not only reduce signal-to-noise ratio but also possess an eye-safety issue. Despite thorough exploration of speckle reduction methods using partially coherent light sources, the trade-off involved by the partial coherence has not been thoroughly discussed. Here, we introduce theoretical models that quantify the effects of partial coherence on the resolution and the speckle contrast. The theoretical models allow us to find an optimal light source that maximizes the speckle reduction while minimizing the decline of the other terms. We implement benchtop prototypes of partially coherent holographic displays using the optimal light source, and verify the theoretical models via simulation and experiment. We also present a criterion to evaluate the depth of field in partially coherent holographic displays. We conclude with a discussion about approximations and limitations inherent in the theoretical models.

Effects of source spatial partial coherence on intensity statistics of optical beams in mono-static turbulent channels.

We investigate, via both experimental measurements and wave-optics computer simulations, the statistical characteristics of the fluctuating intensity, such as the average intensity, the beam wander and the scintillation index, of the Gaussian Schell-model (GSM) beams on passing through double-pass, monostatic turbulence channels with either a retro-reflector (RR) or a flat mirror (FM). Our experimental results reveal that the enhanced backscatter (EBS) gradually weakens as the spatial coherence of the GSM source decreases, and eventually disappears for the sufficiently low source spatial coherence states. The r.m.s beam wander remains practically invariant with the variation of the source coherence width in the range from 0.2 to 6.0 mm both in the case of the RR and the FM, which formed the RR case being much smaller. In addition, it is found that the long-term scintillation index of the untracked beam with the RR is smaller than that with the FM, while the situation is reversed for the short-term scintillation index of the tracked beam. In both cases, the scintillation index decreases as the spatial coherence of the GSM source decreases. The obtained computer simulation results agree reasonably well with the experimental results. In addition, the effects of spatial coherence on statistical characteristics of the GSM beams along a 1 km propagation distance through the double-pass monostatic turbulence are also investigated using wave-optics simulation. We also carry out evaluation and comparison of the intensity probability density functions for the RR and FM cases and for various source coherence states that are of utmost importance for free-space optical communications in retro-reflection modulation regime. In addition, our findings will be beneficial for the development of remote sensing and directed energy laser applications in the presence of air turbulence.

Analysis of the caustics of partially coherently combined truncated Gaussian beams.

A theoretical model of the caustics of partially coherently combined beams (CBCs) was derived to model CBCs in the case of truncated Gaussian beams. The model enables the analysis of different lattice structures and partial coherence effects, including incoherent beam combining. The impacts of the coherence state, geometry of the array and truncation losses were analyzed. An optimal truncation level of about 6% was found and a maximum CBC efficiency of 62% was determined for this CBC system. With an increase in the beam numbers in the lattice, the relative caustics length decreases, which is consistent with the general rules of diffraction theory.

Effect of Partial Spatial Coherence on Image Sharpness

Effect of Partial Spatial Coherence on Image Sharpness

Effect of partial coherence on dimensional measurement sensitivity for DUV scatterfield imaging microscopy.

Optical scatterfield imaging microscopy technique which has the capability of controlling scattered fields in the imaging mode is useful for quantitative nanoscale dimensional metrology that yields precise characterization of nanoscale features for semiconductor device manufacturing process control. To increase the sensitivity in the metrology using this method, it is required to optimize illumination and collection optics that enhance scatterfield signals from the nanoscale targets. Partial coherence of the optical imaging system is used not only for enhancing image quality in the traditional microscopy or lithography but also for increasing the sensitivity of the scatterfield imaging microscopy. This paper presents an empirical investigation of the effect of partial coherence on measurement sensitivity using a deep ultraviolet scatterfield imaging microscope platform that uses a 193 nm excimer laser as a source and a conjugate back focal plane as a unit for controlling partial coherence. Dimensional measurement sensitivity is assessed through analyzing scatterfield images measured at the edge area of periodic multiline structures with nominal linewidths ranging 44-80 nm on a Molybdenum Silicide (MoSi) photomask. Intensities scattered from the targets under the illuminations with various partial coherence factors and two orthogonal polarizations are assessed with respect to sensitivity coefficient. The optimization of partial coherence factor for the target dimension is discussed through the sensitivity coefficient maps.

Strategies for the characterization of partially coherent ultrashort pulses with dispersion scan

Established characterization methods for repetitive pulse trains tend to fail in the presence of degraded coherence properties. Partial coherence is present in several pulse generation schemes but is not yet properly addressed in many pulse characterization techniques. Full coherence is a common assumption in most techniques, and failing to detect and account for it can lead to erroneous measurements that can be easily overlooked. While some techniques can indicate the presence of a coherence degradation, no method is known that can simultaneously retrieve the enveloping pulse width as well as the coherence time within a pulse train. Here we propose different pertinent strategies to deal with partially coherent ultrashort pulses measured using dispersion scan. The effect of partial coherence in dispersion scan is first investigated, and the three strategies, namely fidelity measurement, mixed-states reconstruction, and self-calibrating dispersion scan, are subsequently demonstrated and compared. The demonstrated retrieval algorithms can be readily adapted to existing dispersion scan hardware. Therefore, this study leads the way toward a more holistic approach to pulse characterization, dealing with fewer assumptions on the pulse trains and resulting in more accurate measurements.

Effect of beam profile and partial coherence on coherent beam combining performance

A numerical model of a coherent beam composed of a two-dimensional array of laser beams was developed; the model enables analysis of random phase mismatch in the combined system, as well as analysis of the influence of atmospheric turbulence. The negative impact of the beam profile, filling factor, and average inter-beam coherence was analyzed. This analysis reveals parametric ranges in which performance metrics decrease by less than 20% of their peak values. Ensuring partial coherence was the most challenging task.

Beam drift and partial probe coherence effects in EUV reflective-mode coherent diffractive imaging

While the industrial implementation of extreme ultraviolet lithography for upcoming technology nodes is becoming ever more realistic, a number of challenges have yet to be overcome. Among them is the need for actinic mask inspection. We report on reflective-mode lensless imaging of a patterned multi-layer mask sample at extreme ultraviolet wavelength that provides a finely structured defect map of the sample under test. Here, we present the imaging results obtained using ptychography in reflection mode at 6° angle of incidence from the surface normal and 13.5 nm wavelength. Moreover, an extended version of the difference map algorithm is employed that substantially enhances the reconstruction quality by taking into account both long and short-term variations of the incident illumination.

Analytical transmission cross-coefficients for pink beam X-ray microscopy based on compound refractive lenses

Analytical expressions for the transmission cross-coefficients for x-ray microscopes based on compound refractive lenses are derived based on Gaussian approximations of the source shape and energy spectrum. The effects of partial coherence, defocus, beam convergence, as well as lateral and longitudinal chromatic aberrations are accounted for and discussed. Taking the incoherent limit of the transmission cross-coefficients, a compact analytical expression for the modulation transfer function of the system is obtained, and the resulting point, line and edge spread functions are presented. Finally, analytical expressions for optimal numerical aperture, coherence ratio, and bandwidth are given.

Resolution modeling of dispersive imaging spectrometers

This paper presents best practices for modeling the resolution of dispersive imaging spectrometers. The differences between sampling, width, and resolution are discussed. It is proposed that the spectral imaging community adopt a standard definition for resolution as the full-width at half maximum of the total line spread function. Resolution should be computed for each of the spectral, cross-scan spatial, and along-scan spatial/temporal dimensions separately. A physical optics resolution model is presented that incorporates the effects of slit diffraction and partial coherence, the result of which is a narrower slit image width and reduced radiometric throughput.

Modal approach for partially coherent diffractive imaging with simultaneous sample and coherence recovery.

We demonstrate a modal approach to simultaneous recovery of a sample transmission function and coherence properties of an illuminating X-ray beam that works from a single measurement. The approach based on coherence diffractive imaging, does not depend on a particular model for the coherence function. This single shot imaging method separates the effects of partial coherence in the illuminating beam from the sample, allowing the recovery of high quality sample information.

Impact of partial coherence on the apparent optical transfer function derived from the response to amplitude edges.

We present an investigation of the impact of partial coherence on optical imaging systems with the focus on whole slide imaging (WSI) systems for digital pathology. The investigation is based on the analysis of the edge response of the optical system, which gives rise to an apparent optical transfer function (OTF) that can be linked to two elementary complex functions Q and U. The function Q is directly related to the transmission cross coefficient (TCC) and can be identified with the performance function first introduced by Kintner and Sillitto. The function U depends on the TCC in a more involved way. When there are no aberrations the Q-function corresponds to the real part of the apparent OTF and the U function to the imaginary part of the apparent OTF. Close to the incoherent limit the effect of the U function is a mere shift of the edge compared to the fully incoherent case. We propose a new expression for the dependence of the depth of focus (DOF) on spatial frequency and on the partial coherence factor σ, and validate it by simulation. Partial coherence effects are investigated experimentally on a WSI system with a compact LED-based Köhler illumination unit with variable condenser NA. This unit incorporates a top hat diffuser for providing a reasonably uniform illumination field, with variations below 10% across the imaged field of view. The measurements of the apparent through-focus OTF derived from edges on a custom resolution chart for different σ were substantially in agreement with the simulations. Finding an optimal value for σ is not straightforward as lateral resolution and the level of edge ringing improve with increasing σ, whereas edge contrast and DOF improve with decreasing σ. We assess that the trade-off for the particular application of WSI systems for digital pathology is optimized for a σ value in the range of 0.55-0.75.

Effect of partial coherence on diffraction intensity of a Gaussian Schell-model beam using two-level atomic grating

The role of spatial coherence on diffraction intensity is investigated for a partially coherent incident Gaussian Schell-model beam which is diffracted from a two-level atomic grating. It is shown that the performance of the atomic grating is greatly influenced by the spectral coherence width of the partially coherent fields. It is observed that relatively large intensity of the diffracted light can be obtained via spatial coherence, beam width, interaction length, and mode index of partially coherent incident light. The scheme provides possibilities for the potential applications of atomic grating in lensless imaging using the partially coherent light field.

Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating.

A procedure for a technique to measure the transverse coherence of synchrotron radiation X-ray sources using a single phase grating interferometer is reported. The measurements were demonstrated at the 1-BM bending magnet beamline of the Advanced Photon Source (APS) at Argonne National Laboratory (ANL). By using a 2-D checkerboard π/2 phase-shift grating, transverse coherence lengths were obtained along the vertical and horizontal directions as well as along the 45° and 135° directions to the horizontal direction. Following the technical details specified in this paper, interferograms were measured at different positions downstream of the phase grating along the beam propagation direction. Visibility values of each interferogram were extracted from analyzing harmonic peaks in its Fourier Transformed image. Consequently, the coherence length along each direction can be extracted from the evolution of visibility as a function of the grating-to-detector distance. The simultaneous measurement of coherence lengths in four directions helped identify the elliptical shape of the coherence area of the Gaussian-shaped X-ray source. The reported technique for multiple-direction coherence characterization is important for selecting the appropriate sample size and orientation as well as for correcting the partial coherence effects in coherence scattering experiments. This technique can also be applied for assessing coherence preserving capabilities of X-ray optics.