Gaussian Intensity Distribution Research Articles

Ramp Distribution-Based Contrast Enhancement Techniques and Over-Contrast Measure

Our approach to contrast enhancement (CE) of images is based on natural scene statistics (NSS). We show, in this paper, that the average intensity distribution of natural images can be linearly approximated to the ramp distribution in an ordered histogram domain as the contrast increases. Based on this finding, we propose ramp distribution-based global and local CE algorithms. The ramp distribution-based slant thresholding (RDST) algorithm is proposed as a global CE method which uses slant thresholding in an ordered histogram domain to yield a contrast-enhanced image. Also, the ramp distribution-based adaptive slant thresholding (RDAST) algorithm is proposed as a local CE method. It adaptively adjusts a slant angle of the ramp distribution in each block to suppress noise amplification in uniform regions and maximizes contrast in non-uniform regions. The RDAST also employs a scaled global modified histogram to minimize sensitivity to block size changes. Moreover, we propose a metric to measure the amount of over-contrast in an image to evaluate all CE algorithms more correctly. The experimental results show that the proposed algorithms have better or competitive performance as well as computational efficiency.

Novel method to design laser beam shaping lenses using PSO techniques

To design beam shaping lenses converting the light from Gaussian intensity distribution into flat-top profile, a new method—particle swarm optimization (PSO) algorithm—was employed. The theoretical values of ray intersections at the output plane are precisely calculated by the energy conservation when a Gaussian beam is converted to a flat-top one, and these values are then used as target values in the optimization process. Real values of ray intersections are obtained from the ray tracing. The absolute values of the differences between real and theoretical values are used to construct the merit function of a shaping lens system, which are also used as the fitness function values for the PSO. By the manipulation of minimizing the fitness function, refractive two-element beam shapers and a refractive single-element beam shaper have been designed. The analyses for the design results demonstrated the feasibility and validity of the PSO method in the design of laser beam shaping lenses.

Evolution properties of the radially polarized multi-Gaussian Schell-model beam in uniaxial crystals.

The evolution properties of the normalized intensity distribution, the spectral degree of coherence (SDOC), and the spectral degree of polarization (SDOP) of the radially polarized multi-Gaussian Schell-model (MGSM) beam in uniaxial crystals are illustrated. Numerical results show that the intensity distribution of the radially polarized MGSM beam gradually evolves from a doughnut shape into an elliptical symmetric flattop shape and retains its elliptical flattop shape on further propagation in anisotropic crystals. The evolution behavior of the SDOC and SDOP for the radially polarized MGSM beam is quite different from that of the linearly polarized one. In addition, the influences of the spatial coherence length δ0, beam index M, and the ratio of the extraordinary refractive index to the ordinary refractive index ne/no of the uniaxial crystals on the evolution properties of the normalized intensity distribution, the SDOC, and the SDOP of the radially polarized MGSM beam are discussed in detail.

Elemental imaging (LA-ICP-MS) of zebrafish embryos to study the toxicokinetics of the acetylcholinesterase inhibitor naled

The zebrafish embryo is an important model in ecotoxicology but the spatial distribution of chemicals and the relation to observed effects is not well understood. Quantitative imaging can help to gain insights into the distribution of chemicals in the zebrafish embryo. Laser ablation inductively coupled plasma-mass spectrometry (LA-ICP-MS) is used to quantify the uptake and the uptake kinetics of the bromine (Br) containing organophosphate naled (Dibrom®, dimethyl-1,2-dibromo-2,2-dichloroethylphosphate) and its distribution in zebrafish embryos using Br as the marker element. During exposure, the Br amounts increase in the embryos parallel to the irreversible inhibition of the acetylcholinesterase (AChE). The final amount of Br in the embryo (545 pmol/embryo) corresponds to a 280-fold enrichment of naled from the exposure solution. However, LC-MS/MS analyses showed that the internal concentration of naled remained below the LOD (7.8 fmol/embryo); also the concentration of its known transformation product dichlorvos remained low (0.85 to 2.8 pmol/embryo). These findings indicate the high reactivity and high transformation rate of naled to other products than dichlorvos. 12C normalized intensity distributions of Br in the zebrafish embryo showed an enrichment of Br in its head region. Kernel density estimates of the LA-ICP-MS data were calculated and outline the high reproducibility between replicated and the shift in the Br distribution during exposure. The Br enrichment indicates a preferential debromination or direct covalent reaction of naled with AChE in this region.Graphical abstractᅟ

Simulation and experimental study on developed profiles in the positive polymer resist PMMA

Theoretical and experimental study on developed profiles in the positive tone PMMA (polymethyl-methacrylate) resist and e-beam lithography process parameters was performed. E-beam lithography control system Elphy Quantum (Raith) installed on Scanning Electron Microscope Quanta FEG (FEI) with a field emission cathode and Gaussian intensity distribution has been used for the conducted experiments. Simulation results obtained by different models concerning the geometry of the developed resist profiles in PMMA were compared and verified with experimental data for improvement characterization of PMMA resist. The estimated models presented are useful for prediction and optimization of the developed resist profiles at electron beam lithography.

Propagation of hollow vortex Gaussian beams in a strongly nonlocal nonlinear media

An analytical expression of a hollow vortex Gaussian beam is derived in a strongly nonlocal nonlinear media. The analytical expressions of the beam width, the curvature radius, the kurtosis parameter, and the orbital angular momentum density for the hollow vortex Gaussian beam have been also derived. The normalized intensity, the beam width, the curvature radius, the kurtosis parameter, and the orbital angular momentum density versus the axial propagation distance are all periodic, and the period is the same. Their periodic behaviors are also demonstrated. When the parameter η is used to describe the strength of the nonlocality, the periodic behaviors of the normalized intensity distribution, the beam width, the curvature radius in the strongly nonlocal nonlinear media of η = 0.5 are opposite to those in the strongly nonlocal nonlinear media of η = 1.0, respectively. When η reaches a critical value, the normalized intensity distribution, the beam width, and the curvature radius keep unvaried upon propagation. The periodic evolution of the kurtosis parameter is independent of the parameter η. The magnitude of the orbital angular momentum density is inversely proportional to the beam width, while the corresponding distribution area is proportional to the beam width. The periodic evolutions of the hollow vortex Gaussian beam in the strongly nonlocal nonlinear media are well exhibited, and have promising application in optical switch and optical micromanipulation.

Theoretical modeling of photo-induced lens formation in a polymerizable matrix containing quantum dots

We present a theoretical model describing the dynamic modulation of the refractive index of quantum dots (QDs) containing a photopolymerizable mixture under spatially non-uniform illumination. The case of a laser beam with Gaussian spatial intensity distribution is used to model the process of non-uniform polymerization, followed by the processes of diffusion of monomers, polymers, and QDs. This results in the creation of a lens-like refractive index transversal distribution. The contribution of QDs is taken into account by using the conservation of the sum of volume fractions of polymers, monomers, and QDs. Dynamic variations of different parameters influencing the lens formation and the focal length of the lens are obtained. In particular, it is shown how the change of time of irradiation varies the profile of the refractive index and, hence, controls the focal length of the lens.

The properties of anomalous hollow beam propagating in the slant atmosphere

The equations of anomalous hollow beam (AHB) in slant atmosphere have been derived, and the average intensity distributions have been illustrated and analyzed using numerical examples. The results shown that the AHB propagating in slant atmosphere will lose the initial dark hollow with a solid core profile and evolve into Gaussian beam as the propagation distance increases. The results also shown the AHB propagating in slant atmosphere with larger strength (larger C0 or small zenith angle α) will lose the initial beam profile faster at the same propagation distance L.

Calibration and testing of a Raman hyperspectral imaging system to reveal powdered food adulteration.

The potential adulteration of foodstuffs has led to increasing concern regarding food safety and security, in particular for powdered food products where cheap ground materials or hazardous chemicals can be added to increase the quantity of powder or to obtain the desired aesthetic quality. Due to the resulting potential health threat to consumers, the development of a fast, label-free, and non-invasive technique for the detection of adulteration over a wide range of food products is necessary. We therefore report the development of a rapid Raman hyperspectral imaging technique for the detection of food adulteration and for authenticity analysis. The Raman hyperspectral imaging system comprises of a custom designed laser illumination system, sensing module, and a software interface. Laser illumination system generates a 785 nm laser line of high power, and the Gaussian like intensity distribution of laser beam is shaped by incorporating an engineered diffuser. The sensing module utilize Rayleigh filters, imaging spectrometer, and detector for collection of the Raman scattering signals along the laser line. A custom-built software to acquire Raman hyperspectral images which also facilitate the real time visualization of Raman chemical images of scanned samples. The developed system was employed for the simultaneous detection of Sudan dye and Congo red dye adulteration in paprika powder, and benzoyl peroxide and alloxan monohydrate adulteration in wheat flour at six different concentrations (w/w) from 0.05 to 1%. The collected Raman imaging data of the adulterated samples were analyzed to visualize and detect the adulterant concentrations by generating a binary image for each individual adulterant material. The results obtained based on the Raman chemical images of adulterants showed a strong correlation (R>0.98) between added and pixel based calculated concentration of adulterant materials. This developed Raman imaging system thus, can be considered as a powerful analytical technique for the quality and authenticity analysis of food products.

A reference-defining criterion for light focusing through scattering media based on circular Gaussian distribution of speckle background intensity

This paper investigates the reference-defining-criterion problem in the field of light focusing through scattering media. In many analogous light focusing experiments, the enhancement values differ greatly from each other. By analyzing the focusing picture after optimizations, we concluded that the discrepancy in enhancement originates from the unclear definition of reference boundary. By averaging multiple speckle backgrounds, we found that the intensity of speckle background obeys circular Gaussian distribution. Based on the intensity statistics and Gaussian-function fitting to the speckle background, we proposed a clear reference-defining criterion– 1/e2 criterion. With this reference-defining criterion, we have carried out light focusing experiments with the speckle backgrounds possessing different shape and size. The enhancements obtained from the repetitive experiments for both weakly scattering medium and strongly scattering medium were all in the reasonable range, demonstrating its validity and universality. This criterion will provide a comparison standard for light focusing experiments in wavefront-shaping field.

Compact diffractive optics for THz imaging

We present a compact diffractive silicon-based multilevel phase Fresnel lens (MPFL) with up to 50 mm in diameter and a numerical aperture up to 0.86 designed and fabricated for compact terahertz (THz) imaging systems. The laser direct writing technology based on a picosecond laser was used to fabricate diffractive optics on silicon with a different number of phase quantization levels P reaching an almost kinoform spherical surface needed for efficient THz beam focusing. Focusing performance was investigated by measuring Gaussian beam intensity distribution in the focal plane and along the optical axis of the lens. The beam waist and the focal depth for each MPFL were evaluated. The influence of the phase quantization number on the focused beam amplitude was estimated, and the power transmission efficiency reaching more than 90% was revealed. The THz imaging of less than 1 mm using a robust 50 mm diameter multilevel THz lens was achieved and demonstrated at 580 GHz frequency.

Fractional Fourier transform of double-half inverse Gaussian hollow beams

In this paper, we study an appropriate mathematical model of dark-hollow beam by concerning double-half inverse Gaussian hollow (DHIGH) beams passing through fractional Fourier transform (FRFT) optical systems. Based on Collins integral formula and using the expression of the hard-edged aperture function into a finite sum of complex Gaussian functions, analytical expressions for the propagation properties of DHIGH beams through the FRFT optical systems without and with apertures have been derived in detail. Some numerical simulations are given to illustrate the normalized intensity distribution of DHIGH beams in a FRFT system by studying the important factors of both incident beams order and the FRFT order. Our results obtained by using an approximate analytical formula, are in a good agreement with those obtained by using numerical integral method. The results show that the FRFT optical system is a convenient way for DHIGH beams shaping.

A Particle Strength Exchange Method for Metal Removal in Laser Drilling

A meshfree Particle Strength Exchange (PSE) method is developed for metal removal in a simplified laser drilling problem. To this end, the problem of transient state heat transfer is solved by exerting a static laser beam with a Gaussian intensity distribution, as the external heat source. The proposed PSE scheme is a fully Lagrangian approach, which is straightforward to implement as compared to alternative meshfree methods currently adopted in the state of the art. The performance of the PSE method in solving the heat transfer problem at hand is assessed through a case-study on single-pulse laser heating of a metal workpiece. The simulation results are finally verified against both numerical and experimental data available in the literature, demonstrating the suitability of the proposed approach in addressing the thermal issues of complex manufacturing processes.

Study on the Mainardi beam through the fractional Fourier transforms system

In this paper, we introduced the Mainardi beam and indicated its attributes under the Fractional Fourier transform for power variations of Fractional Fourier transform. The results represent that the behavior of the Mainardi beam is similar to that of the Airy beam. The obtained formula is a very powerful tool to describe propagation of a Mainardi beam through the FFT and the FrFT systems. An analytical expression of the Mainardi beam passing through an Fractional Fourier transform system presented. The influences of the Fractional Fourier transform, rational order of the Mittag-Leffler function (Fourier transform of the Mainardi function) on the normalized intensity distribution and characteristics of the Mainardi beam in the Fractional Fourier transform system examined. Power of the Fractional Fourier transform (p) and rational order of the Mittag-Leffler function (q) control characteristics of the Mainardi beam such as effective beam size, number, width, height, and orientation of the beam spot.

X-ray beam-shaping via deformable mirrors: surface profile and point spread function computation for Gaussian beams using physical optics.

X-ray mirrors with high focusing performances are commonly used in different sectors of science, such as X-ray astronomy, medical imaging and synchrotron/free-electron laser beamlines. While deformations of the mirror profile may cause degradation of the focus sharpness, a deliberate deformation of the mirror can be made to endow the focus with a desired size and distribution, via piezo actuators. The resulting profile can be characterized with suitable metrology tools and correlated with the expected optical quality via a wavefront propagation code or, sometimes, predicted using geometric optics. In the latter case and for the special class of profile deformations with monotonically increasing derivative, i.e. concave upwards, the point spread function (PSF) can even be predicted analytically. Moreover, under these assumptions, the relation can also be reversed: from the desired PSF the required profile deformation can be computed analytically, avoiding the use of trial-and-error search codes. However, the computation has been so far limited to geometric optics, which entailed some limitations: for example, mirror diffraction effects and the size of the coherent X-ray source were not considered. In this paper, the beam-shaping formalism in the framework of physical optics is reviewed, in the limit of small light wavelengths and in the case of Gaussian intensity wavefronts. Some examples of shaped profiles are also shown, aiming at turning a Gaussian intensity distribution into a top-hat one, and checks of the shaping performances computing the at-wavelength PSF by means of the WISE code are made.

Filamentation and supercontinuum emission with flattened femtosecond laser beam by use of microlens array in fused silica

The high power supercontinuum from femtosecond filamentation has attracted great attention for recent years due to its various applications. In our previous researches, we have used microlens array to obtain filament-array in fused silica and to generate the high spectral power supercontinuum. To further improve the ability to generate the high power supercontinuum by using microlens array, in this work we adopt flattened femtosecond laser beam with a flat-top energy distribution to generate filament-array in fused silica and supercontinuum. By using a laser beam shaping system consisting of aspherical lenses, the Gaussian intensity distribution of initial femtosecond laser beam is converted into a flat-top distribution. The flattened laser beam is focused by a microlens array into a fused silica block, and consequently a filament array is formed in the block. Our experimental results show that compared with the filaments formed by a Gaussian laser beam, the filaments formed by the flattened beam have a uniform distribution and almost the same onset due to the initial uniform energy distribution across the section of the laser beam. Furthermore, the spectral stability of supercontinuum emission is used to evaluate the damage of the fused silica block. It is demonstrated that the flattened beam with a pulse energy of 1.9 mJ does not induce permanent damage to the fused silica block, while the Gaussian beam with a relatively low pulse energy of 1.46 mJ leads to the damage to the block. Therefore, a higher incident laser pulse energy is allowed in the case of flattened laser beam, and consequently stronger supercontinuum generation than in the case of the Gaussian laser beam can be expected. In our experiments, the relative spectral intensity of flattened beam generated supercontinuum in the visible range is about twice higher than that for the Gaussian beam case. The conversion efficiencies of the supercontinuum for the two kinds of laser beams are further analyzed. The conversion efficiencies are 49% and 55% for the cases of Gaussian and flattened beams respectively. In this work, we demonstrate the formation of filament array with uniform distribution in fused silica, and, as a proof of principle, we also demonstrate the high power supercontinuum generation with high conversion efficiency from the filamentation, by using flattened femtosecond laser beam as the incident laser and microlens array as the focusing element. This approach provides a way to obtain a high power femtosecond supercontinuum source which is of great importance in many applications such as some absorption spectroscopies based on coherent supercontinuum light.

Axial multi-particle trapping and real-time direct observation

The optical tweezers with the special advantages of non-mechanical contact and the accurate measurement of positions of particles, are a powerful manipulating tool in numerous applications such as in colloidal physics and life science. However, the standard optical tweezers system uses a single objective lens for both trapping and imaging. As a result, the trapping and imaging regions are confined to the volume near the focal plane of the objective lens, making it difficult to track the trapped particles arranged in the axial direction. Therefore, multiple trapping along axial direction remains a challenge. The three-dimensional imaging technology can realize the monitoring of the axial plane, but neither the laser scanning microscopy nor the wide-field imaging technology can meet the requirement of the real-time imaging. To address this issue, we propose a modified axial-plane Gerchberg-Saxton (GS) iterative algorithm based on the Fourier transform in the axial plane. Compared with the direct algorithm such as the Fresnel lens method, the modified axial-plane GS iterative algorithm has a higher modulation efficiency, and the generated axial distribution has a sharper intensity. In theory, the traps generated each have an ideal Gaussian intensity distribution independently, which is proved by the simulation of reconstructed field. With such an iterative algorithm, we can directly create multiple point-trap array arranged along the axial direction. We also develop an axial-imaging scheme. In this scheme, the particles are trapped and a right-angled silver-coated 45 reflector is used to realize axial-plane imaging. The scheme is verified by imaging silica particles in an axial plane and a lateral plane simultaneously. Furthermore, we combine the axial-plane imaging technique with holographic optical tweezers, and demonstrate the simultaneous optical trapping in 22 trap array and the monitoring of multiple silica particles in the axial plane. The trap stiffness of traps array in axial plane is calibrated by measuring the Brownian motion of the trapped particles in the axial trap array with digital video microscopy. The proposed technique provides a new perspective for optical micromanipulation, and enriches the functionality of optical micromanipulation technology, and thus it will have many applications in biological and physical research.

Laser inscription of pseudorandom structures for microphotonic diffuser applications.

Optical diffusers provide a solution for a variety of applications requiring a Gaussian intensity distribution including imaging systems, biomedical optics, and aerospace. Advances in laser ablation processes have allowed the rapid production of efficient optical diffusers. Here, we demonstrate a novel technique to fabricate high-quality glass optical diffusers with cost-efficiency using a continuous CO2 laser. Surface relief pseudorandom microstructures were patterned on both sides of the glass substrates. A numerical simulation of the temperature distribution showed that the CO2 laser drills a 137 μm hole in the glass for every 2 ms of processing time. FFT simulation was utilized to design predictable optical diffusers. The pseudorandom microstructures were characterized by optical microscopy, Raman spectroscopy, and angle-resolved spectroscopy to assess their chemical properties, optical scattering, transmittance, and polarization response. Increasing laser exposure and the number of diffusing surfaces enhanced the diffusion and homogenized the incident light. The recorded speckle pattern showed high contrast with sharp bright spot free diffusion in the far field view range (250 mm). A model of glass surface peeling was also developed to prevent its occurrence during the fabrication process. The demonstrated method provides an economical approach in fabricating optical glass diffusers in a controlled and predictable manner. The produced optical diffusers have application in fibre optics, LED systems, and spotlights.

Impact of mismatched and misaligned laser light sheet profiles on PIV performance

The effect of mismatched or misaligned laser light sheet profiles on the quality of particle image velocimetry (PIV) results is considered in this study. Light sheet profiles with differing widths, shapes, or alignment can reduce the correlation between PIV images and increase experimental errors. Systematic PIV simulations isolate these behaviours to assess the sensitivity and implications of light sheet mismatch on measurements. The simulations in this work use flow fields from a turbulent boundary layer; however, the behaviours and impacts of laser profile mismatch are highly relevant to any fluid flow or PIV application. Experimental measurements from a turbulent boundary layer facility are incorporated, as well as additional simulations matched to experimental image characteristics, to validate the synthetic image analysis. Experimental laser profiles are captured using a modular laser profiling camera, designed to quantify the distribution of laser light sheet intensities and inform any corrective adjustments to an experimental configuration. Results suggest that an offset of just 1.35 standard deviations in the Gaussian light sheet intensity distributions can cause a 40% reduction in the average correlation coefficient and a 45% increase in spurious vectors. Errors in measured flow statistics are also amplified when two successive laser profiles are no longer well matched in alignment or intensity distribution. Consequently, an awareness of how laser light sheet overlap influences PIV results can guide faster setup of an experiment, as well as achieve superior experimental measurements.

Phonon transport in a curved aluminum thin film due to laser short pulse irradiation

Laser short-pulse heating of a curved aluminum thin film is investigated. The Boltzmann transport equation is incorporated to formulate the heating situation. A Gaussian laser intensity distribution is considered along the film arc and time exponentially decaying of pulse intensity is incorporated in the analysis. The governing equations of energy transport in the electron and lattice sub-systems are coupled through the electron-phonon coupling parameter. To quantify the phonon intensity distribution in the thin film, equivalent equilibrium temperature is introduced, which is associated with the average energy of all phonons around a local point when the phonon energies are redistributed adiabatically to an equilibrium state. It is found the numerical simulations that electron temperature follows similar trend to the spatial distribution of the laser pulse intensity at the film edge. Temporal variation of electron temperature does not follow the laser pulse intensity distribution. The rise of temperature in the electron sub-system is fast while it remains slow in the lattice sub-system.