Radial Index Research Articles

Broadband 2D n × n Vortex Arrays Generated from an Efficient Petal‐Like Raman Laser with an Astigmatic Mode Convertor

Broadband vortex arrays distributed in 2D n × n vortices are extremely needed for multiple microparticle manipulation, high‐capacity optical communication, and quantum information. Vortex arrays are usually generated with spatial light modulators, metamaterials; it is a big challenge to improve beam quality and output power. Herein, crisscross 2D n × n vortex arrays are converted from petal‐like Raman lasers with an astigmatic mode convertor. Efficient petal‐like lasers in the form of the Laguerre–Gaussian mode with zero radial index and l azimuthal index (LG0,l ) are irradiated in a Raman microchip laser (RML) by adjusting optimal beam waist and locating the position of focus spot of the annular pump beam. High‐beam‐quality LG0,9 petal‐like Raman laser oscillating at broadband wavelength (bandwidth: 16.2 nm) is generated with power of 773 mW and an efficiency of 10.6%. The conversion efficiency from petal‐like laser to crisscross vortex array is as high as 90%. The vortex array with 5 × 5 vortices operating around 1078 nm is generated with a power of 693 mW and an optical efficiency of 9.5%. Taking advantages of the broad emission spectrum of ytterbium‐doped laser materials and stimulated Raman scattering effect, RMLs are potential sources for generating flexible vortex arrays with desired 2D n × n vortices oscillating in Raman wavelengths.

Гибридные сферические микрорезонаторы с люминесцентными органическими красителями FITC и DCM

Luminescent hybrid spherical microresonators of two types consisting of monodisperse spherical silica particles with a diameter of 3.5 mcm coated with either FITC dye molecules or a 200 nm thick mesoporous silica shell containing DCM dye are fabricated. The luminescence spectra of microresonators are studied and the experimental emission spectra are simulated using the method of spherical wave transfer matrices. The ratio of intensities of emission lines into whispering gallery modes with different polarizations and the same polar and radial indices is analyzed. It is shown that the ratio depends on the orientation of the dipole moment of the radiative transition of dye molecules relative to the surface of spherical silica particles.

Hybrid spherical microresonators with luminescent organic dyes FITC and DCM

Luminescent hybrid spherical microresonators of two types consisting of monodisperse spherical silica particles with a diameter of 3.5 μm coated with either FITC dye molecules or a 200 nm thick mesoporous silica shell containing DCM dye are fabricated. The luminescence spectra of microresonators are studied and the experimental emission spectra are simulated using the method of spherical wave transfer matrices. The ratio of intensities of emission lines into whispering gallery modes with different polarizations and the same polar and radial indices is analyzed. It is shown that the ratio depends on the orientation of the dipole moment of the radiative transition of dye molecules relative to the surface of spherical silica particles. Keywords: spherical microresonator, whispering gallery modes, organic dyes, photoluminescence.

PS-BPC12-1: AGE-RELATED DIFFERENCES IN LONGITUDINAL ASSOCIATIONS BETWEEN ALCOHOL INTAKE AND ARTERIAL STIFFNESS, PRESSURE WAVE REFLECTION, AND INFLAMMATION IN MALE EMPLOYEES

Backgrounds: The effect of alcohol intake on arterial stiffness related to macro-vascular damage, pressure wave reflection related to both macro- and micro- vascular damages and inflammation have not been fully concluded. Aims: In the present longitudinal observational study, which conducted in annually repeated measurements data, mixed model analyses were applied to examine the difference of longitudinal associations of amount of alcohol intake (i.e., non, mild, moderate and heavy) with arterial stiffness, pressure wave reflection and inflammation. Methods: In 4016 middle-aged (43 ± 9 years) healthy Japanese men without cardiovascular disease (CVD) at the study baseline, alcohol intake, which obtained by questionnaire, risk factors for CVD, brachial-ankle pulse wave velocity (brachial-ankle PWV), radial augmentation index (rAI), and serum C-reactive protein levels (CRP) were measured annually during a 9-year study period. Results: In this repeated measurements data, mix model linear regression analyses demonstrated that alcohol intake had a significant longitudinal association with brachial-ankle PWV and rAI in dose-dependent manner {i.e., non, Mild (1–10 g/day), Moderate (10–30 g/day) and heavy (Over 30 g/day) ethanol intake} (Figure). When baPWV was included as a covariate, the association of alcohol intake with rAI was significant. On the other hand, the serum CRP levels were significantly lower in mild to moderate alcohol intake groups as compared to other groups (i.e., U-shaped) (Figure). Conclusion: The amount of alcohol intake may have longitudinal linear association with increased arterial stiffness and abnormal pressure wave reflection, but it may have a U-shaped relationship with inflammation reflected by serum CRP levels. Thus, the alcohol intake may longitudinally affect both macro- and micro- vascular damages in a linear dose-dependent manner without mediating inflammation.

PS-C29-8: EFFECT OF WEIGHT GAIN ON ARTERIAL STIFFNESS AND PRESSURE WAVE REFLECTION: A 9-YEAR LONGITUDINAL STUDY

Background and Aim: Obesity is a causal factor for conventional risk factors for cardiovascular disease (CVD), and these risk factors affect increased arterial stiffness and also abnormal pressure wave reflection in arterial tree. Even so, because of the potent direct influences of these risk factors on arterial stiffness and pressure wave reflection, the direct effect of obesity on these vascular abnormalities has been still controversial. Then, the present study examined the effect of weight gain on those vascular abnormalities. Methods and Results: In 4016 middle-aged (43 ± 9 years) healthy Japanese men without CVD at the study baseline, body weight, risk factors for CVD, brachial-ankle pulse wave velocity (baPWV), and radial augmentation index (rAI) were measured at the baseline and end of study period (mean duration of follow-up was 6.3 years). The study subjects were divided into 3 groups by the change of BMI during the study period. While the change of baPWV in the highest tertile range of increase in BMI (57 ± 138 cm/sec) was larger than that in the lowest tertile range of increase in BMI (46 ± 136 cm/sec)(P < 0.05), these differences were not significant after the adjustment of changes of blood pressure. In addition, the change of rAI was similar between both groups. Conclusions: Weight gain may affect increase in arterial stiffness rather than abnormal pressure wave reflection, and this effect may be mediated by increase in blood pressure related to weight gain rather than the direct effect of weight gain.

Association of Pressure Wave Reflections With Left Ventricular Mass: a Systematic Review and Meta-Analysis.

Pressure wave reflections (PWRs) within the circulation are assessed at various arterial sites by various noninvasive methods. We aimed at reviewing the conflicting data regarding the hypothesis that higher PWRs are associated with higher left ventricular mass and tested whether this association stands for all available indices of PWRs, all (proximal or distal to the heart) sites of assessment, and is modified by sex, age and heart rate. Based on a predefined protocol applying the Meta-Analysis of Observational Studies in Epidemiology (MOOSE) guidelines, we identified eligible for meta-analysis data regarding: augmentation index, augmentation pressure, backward pressure (Pb), reflection index, and their association with left ventricular mass index (19 studies, total population n=8686). We found statistically significant associations, independent from blood pressure level, for all indices of PWRs at all arterial sites (carotid augmentation index; odds ratio; standardized beta coefficient [β]: 0.14 [95% CI, 0.07% to 0.21%], per SD increase), radial augmentation index (β: 0.21; 0.11 to 0.31), central augmentation pressure (β: 0.15; 0.03 to 0.27), central Pb (β: 0.23; 0.05 to 0.42), and central reflection index (β: 0.14; 0.06 to 0.22), except for aortic augmentation index as estimated by generalized transfer functions. Meta-regression analysis showed that the association between carotid augmentation index and left ventricular mass was higher among populations with higher heart rate (P=0.036, beta: 0.017 [95% CI, 0.001 to 0.033]) and tended to be higher in middle-aged (P=0.07, beta: -0.001; -0.021 to 0.001). A clinically meaningful association between PWRs and left ventricular mass, assessed at either central or peripheral arterial sites by most available methods was shown, suggesting that PWR reduction strategies might be useful. Based on the present evidence, such trials should target middle-aged populations with high normal heart rate.

Hybrid opto-electronic deep neural network based orbital angular momentum mode recognition scheme in oceanic turbulence

Orbital angular momentum (OAM) has been widely used in underwater wireless optical communication (UWOC) systems due to the mutual orthogonality between modes. However, wavefront distortion caused by oceanic turbulence (OT) on the OAM mode seriously affects its mode recognition and communication quality. In this work, we propose a hybrid opto-electronic deep neural network (HOEDNN) based OAM mode recognition scheme. The HOEDNN model consists of a diffractive DNN (DDNN) and convolutional neural network (CNN), where the DDNN is trained to obtain the mapping between intensity patterns of a distorted OAM mode and intensity distributions without OT interference, and the CNN is used to recognize the output of the DDNN. The diffractive layers of the trained DDNN model are solidified, fabricated, and loaded into a spatial light modulator, and the results recorded by a charge-coupled device camera are processed and fed into the trained CNN model. The results show that the proposed scheme can overcome the interference of OT to OAM modes and recognize accurately azimuthal and radial indices. The OAM mode recognition scheme based on HOEDNN has potential application value in UWOC systems.

Generation of OAM-carrying space-time wave packets with time-dependent beam radii using a coherent combination of multiple LG modes on multiple frequencies.

Space-time (ST) wave packets, in which spatial and temporal characteristics are coupled, have gained attention due to their unique propagation characteristics, such as propagation invariance and tunable group velocity in addition to their potential ability to carry orbital angular momentum (OAM). Through experiment and simulation, we explore the generation of OAM-carrying ST wave packets, with the unique property of a time-dependent beam radius at various ranges of propagation distances. To achieve this, we synthesize multiple frequency comb lines, each assigned to a coherent combination of multiple Laguerre-Gaussian (LGℓ,p) modes with the same azimuthal index but different radial indices. The time-dependent interference among the spatial modes at the different frequencies leads to the generation of the desired OAM-carrying ST wave packet with dynamically varying radii. The simulation results indicate that the dynamic range of beam radius oscillations increases with the number of modes and frequency lines. The simulated ST wave packet for OAM of orders +1 or +3 has an OAM purity of >95%. In addition, we experimentally generate and measure the OAM-carrying ST wave packets with time-dependent beam radii. In the experiment, several lines of a Kerr frequency comb are spatially modulated with the superposition of multiple LG modes and combined to generate such an ST wave packet. In the experiment, ST wave packets for OAM of orders +1 or +3 have an OAM purity of >64%. In simulation and experiment, OAM purity decreases and beam radius becomes larger over the propagation.

The singularity of the partially coherent beam in biological tissue

The singularity of the partially coherent beam propagating in biological tissue has been demonstrated, mainly including the properties of the normalized intensity distribution and phase evolution. It is shown that as the propagation distance increases, the evolution of the normalized intensity distribution undergoes several different stages, as well as the transformation of phase singularities takes place. Especially, the effect of the topological charge, the radial index, beam wave length and spatial coherence length on the beam singularity is analyzed, respectively.

Rapid readout of terahertz orbital angular momentum beams using atom-based imaging.

We demonstrate the rapid readout of terahertz orbital angular momentum (OAM) beams using an atomic-vapor-based imaging technique. OAM modes with both azimuthal and radial indices are created using phase-only transmission plates. The beams undergo terahertz-to-optical conversion in an atomic vapor, before being imaged in the far field using an optical CCD camera. In addition to the spatial intensity profile, we also observe the self-interferogram of the beams by imaging through a tilted lens, allowing the sign and magnitude of the azimuthal index to be read out directly. Using this technique, we can reliably read out the OAM mode of low-intensity beams with high fidelity in 10 ms. Such a demonstration is expected to have far-reaching consequences for proposed applications of terahertz OAM beams in communications and microscopy.

Mixed circuit training acutely reduces arterial stiffness in patients with chronic stroke: a crossover randomized controlled trial.

Investigate whether a single bout of mixed circuit training (MCT) can elicit changes in arterial stiffness in patients with chronic stroke. Second, to assess the between-day reproducibility of post-MCT arterial stiffness measurements. Seven participants (58 ± 12years) performed a non-exercise control session (CTL) and two bouts of MCT on separate days in a randomized counterbalanced order. The MCT involved 3 sets of 15 repetition maximum for 10 exercises, with each set separated by 45-s of walking. Brachial-radial pulse wave velocity (br-PWV), radial artery compliance (AC) and reflection index (RI1,2) were assessed 10min before and 60min after CTL and MCT. Ambulatory arterial stiffness index (AASI) was calculated from 24-h recovery ambulatory blood pressure monitoring. Compared to CTL, after 60min of recovery from the 1st and 2nd bouts of MCT, lower values were observed for br-PWV (mean diff = -3.9 and -3.7m/s, respectively, P < 0.01; ICC2,1 = 0.75) and RI1,2 (mean diff = -16.1 and -16.0%, respectively, P < 0.05; ICC2,1 = 0.83) concomitant with higher AC (mean diff = 1.2 and 1.0 × 10-6cm5/dyna, respectively, P < 0.01; ICC2,1 = 0.40). The 24-h AASI was reduced after bouts of MCT vs. CTL (1st and 2nd bouts of MCT vs. CTL: mean diff = -0.32 and -0.29 units, respectively, P < 0.001; ICC2,1 = 0.64). A single bout of MCT reduces arterial stiffness during laboratory (60min) and ambulatory (24h) recovery phases in patients with chronic stroke with moderate-to-high reproducibility. Ensaiosclinicos.gov.br identifier RBR-5dn5zd.

Echocardiographic assessment of left ventricular radial strain to differentiate cardiac amyloidosis from Fabry disease

Abstract Background Left ventricular (LV) wall thickening is a typical echocardiographic finding in infiltrative cardiomyopathies like cardiac amyloidosis (CA) and Fabry disease (FD). The discrimination of both infiltrative diseases remains challenging by standard as well as 2D speckle tracking echocardiography (2DSTE)-based analysis of longitudinal LV strain patterns. Over the recent years, a constant development in image quality and data processing provided better possibilities to analyse layer specific myocardial deformation indices. With regards to FD, specific layer LV strain patterns may be useful to rule-in FD in patients with suspected infiltrative cardiomyopathy. Purpose The aim of the present study was to investigate differences and the diagnostic value of layer specific 2D STE-based radial LV strain indices in CA and FD. Methods Next to standard parameters of a comprehensive echocardiographic assessment (Vivid E9 or E95, GE Vingmed, Horton, Norway, with an M5S 1.5–4.5MHz transducer), we retrospectively analysed the transmural radial LV strain (GSradial), the subendocardial radial LV strain (GSendo), the subepicardial radial LV strain (GSepi), and the strain gradient (GSendo − GSepi) (EchoPAC software, GE) in FD patients and CA patient from the amyloidosis registry at our study site. A Receiver operating curve (ROC) analysis was used to assess the diagnostic value of the respective LV strain values and the layer-specific strain gradient to discriminate FD and CA. Results A total of 38 FD and 40 CA patients were included in our analyses. In patients with FD, GSepi showed a marked impairment. LV radial and layer strain were significantly reduced in CA compared to FD patients [GSradial −12.0 (−16.2 to −9.9) in CA vs. −17.7 (−20.5 to −14.6) in FD; p&amp;lt;0.001); GSendo (−20.6 (−27.0 to −15.7) in CA vs. −30.0 (−32.0 to −25.6) in FD; p&amp;lt;0.001); and GSepi (−7.4 (−8.9 to −4.8) in CA vs. −9.1 (−11.86 to −7.6) in FD; p&amp;lt;0.001)]. The gradient of GSendo and GSepi was significantly lower in patients with CA compared to FD (−14.0±5.6 in CA vs. −19.4±4.3 in FD respectively; p&amp;lt;0.001). GSendo held the highest diagnostic accuracy to discriminate CA and FD (area under the curve [AUC] 0.83, 95% confidence interval [CI] 0.73–0.92). The layer-specific strain gradient GSendo − Gsepi showed an AUC of 0.79 (CI 0.69 to 0.89). Conclusion Layer-specific strain analysis demonstrated significantly reduced strain values in CA patients compared to FD. The analysis of GSendo held a high diagnostic accuracy to discriminate FD and CA in patients. The integration of layer-specific LV strain indices into the diagnostic work-up may improve the management of patients with an unclear thick heart pathology in future. Funding Acknowledgement Type of funding sources: Private company. Main funding source(s): Alnylam Pharmaceuticals (Cambridge, MA, USA)

Age-related differences in longitudinal associations between alcohol intake and arterial stiffness, pressure wave reflection, and inflammation in male employees

Abstract Backgrounds While arterial stiffness and abnormal pressure wave reflection are independent cardiovascular risk, the difference of their association with alcohol intake have not been fully clarified. Aim This prospective observational study, which utilized repeated annual measurements performed over a 9-year period, applied mixed model analyses to examine age-related differences in longitudinal associations between alcohol intake and arterial stiffness, pressure wave reflection, and inflammation. Methods In 4016 middle-aged (43±9 years) healthy Japanese male employees, alcohol intake, brachial-ankle pulse wave velocity (baPWV), radial augmentation index (rAI), and serum C-reactive protein (CRP) levels were measured annually during a 9-year study period. Based on the questionnaire, alcohol intake was classified as non-drinker, mild-moderate drinker (ethanol 1–20 g/day) and heavy drinker (&amp;gt;20 g/day). Results The estimated marginal mean baPWV (non-drinkers = 1306 cm/s, mild-moderate drinkers = 1311 cm/s, and heavy drinkers = 1337 cm/s, P&amp;lt;0.01) and that of rAI showed significant stepped increases in an alcohol dose-dependent manner in the entire cohort, but an increase in rAI was not observed in subjects aged ≥50 years. The estimated slope of the annual increase in baPWV, but not rAI, was higher for heavy drinkers than for non-drinkers (slope difference, 2.73; P&amp;lt;0.01), especially for subjects aged &amp;lt;50 years. The estimated marginal mean of the serum CRP levels was lower for drinkers than for non-drinkers. Conclusion In middle-aged male Japanese employees, alcohol intake may attenuate inflammatory activity. While alcohol intake may exacerbate the progression of arterial stiffening in a dose-dependent manner without mediating inflammation, especially in subjects under 50 years of age, it may promote pressure wave reflection abnormalities with aging at earlier ages without further exacerbation at older ages. Funding Acknowledgement Type of funding sources: Private company. Main funding source(s): Omroncarpis

Myocardial deformation in athletes measured with feature tracking cardiovascular magnetic resonance

Abstract Background Morphological changes of the heart associated with exercise are well studied. However, changes in myocardial mechanics of athlete's heart are less understood. The aim of this study was to analyze myocardial deformation parameters in athletes and controls, using feature tracking cardiac magnetic resonance (FT-CMR). Methods In a cohort of 73 athletes who had been submitted to CMR at 1.5T and 3 T (mean age 31±12 years, 69% males), we used CMR-FT to measure longitudinal, circumferential and radial strain and strain rates of both ventricles. Left ventricle (LV) longitudinal, circumferential and radial dyssynchrony index (L-SDI, C-SDI and R-CDI, respectively) was calculated as the standard deviation of the calculated time to peak strain percentages of the cardiac cycle with segmental strain analysis. We also measured these parameters in 73 age-matched healthy subjects. Results In comparison to the control subjects, athletes revealed lower left and right ventricle global longitudinal strain (−14.24% vs. −13.31%, p=0.03, and −18.12% vs. −15.95% p=0.01, respectively) and right ventricular (RV) global radial strain (19.28 vs 15.74, p&amp;lt;0.05) – Figure 1. There were no significant differences in LV global radial and circumferential strain. LV longitudinal, radial and circumferential systolic strain rate were also lower in athletes compared to controls (−0.69 s–1 vs. −0.78 s–1, p=0.04; 1.35 s–1 vs. 1.50 s–1, p=0.03: −0.92 s–1 vs −0.98 s–1, p=0.05, respectively). Regarding LV dyssynchrony index, we found no significant difference for L-SDI (10.76% vs. 10.72%, p=0.956), but athletes group showed lower C-SDI and R-SDI values (5.99% vs 4.84%, p=0.006, and 5.53% vs 4.47%, p=0.002). Conclusion Our study revealed attenuation of biventricular strain values and lower circumferential and radial LV dyssynchrony indexes in athletes, compared with healthy controls. We hypothesize that these differences may be related with exercise physiologic cardiac adaptations. Funding Acknowledgement Type of funding sources: None.

PROJEÇÃO DA FADIGA E AS ALTERAÇÕES NEUROMUSCULARES PROVOCADAS EM DISTINTAS ATIVIDADES FÍSICAS

ABSTRACT Introduction: Athletes’ muscles can be weakened by fatigue caused by excessive activity. This limitation compromises their functional capacity and professional performance. The competition's performance correlates positively with muscular quality of function. The changes analysis caused by different athletic activities in muscle contraction by noninvasive tensiomyography reflects the functional state of the muscles. Still, no experiments are adapted to verify the fatigue risk level. Objective: Verify the possible relationship between exercise and neuromuscular fatigue using noninvasive tensiomyography. Methods: 90 athletes were randomly selected in weightlifting, badminton, and athletics sports. Maximum radial displacement, contraction, delay, duration, and relaxation time indices were collected. Muscle fatigue detection was based on the empirical mode decomposition modeling method with the Rogers sensitivity fluctuation rate. All values were collected in the rectus femoris muscle before and after the exercises. They were statistically treated and compared (P&lt;0.05). Results: All athletes showed a decline in maximum radial displacement values after exercise. It reveals that their muscles are in a considerable state of tension, especially in the track and field group (from 8.57±3.42mm to 5.43±2.14mm). However, the slightest change in delay time was observed in the weightlifting group (16.21±4.15ms initial versus 18.34±3.27ms final). Conclusion: Through tensiomyography technology, it is possible to obtain a relationship between exercise and neuromuscular fatigue, analyzing the physical activity effects in a noninvasive way. Evidence Level II; Therapeutic Studies - Investigating the result.

Laguerre-Gaussian Beams with an Increased Dark Area and Autofocusing

We introduce and investigate a novel Laguerre-Gaussian (LG) beam, different from the conventional modal LG beams, which conserve the transverse intensity structure (up to scale) on propagation. The proposed beam does not conserve its structure on free space propagation but possesses some interesting properties. This beam is Fourier-invariant, and it has an increased dark area both in the initial (waist) plane and in the far field. Thus, without changing the topological charge of the beam, varying the radial (lower) index of the associated Laguerre polynomial allows increasing or decreasing the effective diameter of the central dark spot in the intensity pattern. In addition, the beam is autofocusing, i.e., the intensity distribution at the Rayleigh distance from the waist has a shape of the light ring (at any value of the radial index) with the minimal diameter and with the maximal on-ring intensity. Such a beam can be adopted for microparticle manipulation. Increasing the dark area in the focus of a high-aperture spherical lens allows the simultaneous trapping of several absorbing microparticles into this dark area.

Effect of the Addition of Soybean Residue (Okara) on the Physicochemical, Tribological, Instrumental, and Sensory Texture Properties of Extruded Snacks.

An extrusion process was used to improve the physical and textural characteristics of an extruded snack supplemented with soybean residue (okara). An extreme vertices mixture design with a constraint for okara flour (0–50%), mung bean flour (20–70%), and rice flour (20–80%) resulted in the production of eleven formulations. The color, radial expansion index (REI), bulk density, tribological behavior, and instrumental and sensory texture of the extruded snacks were evaluated. Increasing the quantity of okara resulted in an extrudate with a darker, redder color, decreased REI, increased bulk density, and decreased crispness. The tribological pattern of the snack was determined by its dominant composition (protein, starch, or fiber) in the flour mixture, which contributed to the stability of the lubricating film under rotational shear. A principal component analysis of sensory data captured a total of 81.9% variations in the first two dimensions. Texture appeal was inversely related to tooth packing (r = −0.646, p < 0.05). The optimized formulation for texture preference had an okara content of 19%, which was 104% crispier and 168% tougher than an okara content of 40%. This by-product of soybean milk processing can thus be used to develop gluten-free snacks with desirable physical characteristics and texture.

Diffraction deep neural network based orbital angular momentum mode recognition scheme in oceanic turbulence

Orbital angular momentum (OAM) has the characteristics of mutual orthogonality between modes, and has been applied to underwater wireless optical communication (UWOC) systems to increase the channel capacity. In this work, we propose a diffractive deep neural network (DDNN) based OAM mode recognition scheme, where the DDNN is trained to capture the features of the intensity distribution of the OAM modes and output the corresponding azimuthal indices and radial indices. The results show that the proposed scheme can recognize the azimuthal indices and radial indices of the OAM modes accurately and quickly. In addition, the proposed scheme can resist weak oceanic turbulence (OT), and exhibit excellent ability to recognize OAM modes in a strong OT environment. The DDNN-based OAM mode recognition scheme has potential applications in UWOC systems.

Theoretical study on the diffraction-based generation of a 2D orthogonal lattice of optical beams: physical bases and application for a vortex beam multiplication.

A comprehensive theoretical study on the generation of a 2D orthogonal lattice of optical beams based on the near-field diffraction and Talbot effect is presented. First we investigate the near-field diffraction of an optical beam with a finite lateral extension from an infinite 2D orthogonal grating. It is shown that the resulting diffraction patterns over the Talbot planes depend on the following parameters: the period and opening ratio (OR) of the grating, wavelength and spatial spectral bandwidth of the incident beam, and the propagation distance. In terms of these parameters, we find multiplication conditions: the certain conditions under which a 2D orthogonal lattice of the Fourier transform of the incident beam is generated on the Talbot planes. Therefore, if the incident beam is Fourier-invariant and all the established multiplication conditions are fulfilled, the intensity profile of each of the individual Talbot images resembles the intensity profile of the incident beam. We consider the Laguerre-Gaussian beams having zero radial index as an important class of the vortex beams. We explicitly show that these beams are Fourier-invariant and we calculate their spatial spectral bandwidth. As a result, in the illumination of a 2D orthogonal binary grating with this kind of vortex beam, a 2D orthogonal lattice of the incident optical vortex is generated at the Talbot planes. Considering the obtained multiplication conditions, for the first time, to our knowledge, we determine a multiplication interval. This interval covers the propagation distances at which the vortex beam multiplication occurs. Moreover, we obtain the maximum possible value of the grating's OR for the realizations of the vortex multiplication. It is shown that both the multiplication interval and the maximum value of the OR depend on the topological charge (TC) of the incident beam. With the aid of some practical examples and defining a multiplication quality factor, the mentioned results are verified quantitatively. In addition to the vortex beam multiplication effect, we consider another interesting phenomenon that results from the interference of the grating's first diffraction orders. We call this phenomenon the first diffraction orders interference (FDOI) effect. We show that both the multiplication and the FDOI effects occur simultaneously but at different propagation distances. It is also shown that the multiplication and FDOI intervals separate and distance from each other by increasing the TC of the incident beam.

Characteristics of biscuits containing different proportions of whole mung bean, wheat and rice brown flours.

A simplex-centroid design was used to evaluate the effect of proportions (0 to 100%) of whole wheat flour (WWF), whole mung bean flour (WMF) and whole rice flour (BRF) on the quality of cookies savory. The dough cut in the shape of a disks (37 mm × 2 mm) showed a 13% retraction in diameter when they contained exclusively WWF, it was less intense (5%) with BRF and null (0%) with WMF. The dough expansion occurred only vertically, the thicknesses of the WWF, WMF and BRF biscuits were 5.33, 2.79 and 2.13 times greater than the initial dough height, respectively. This characteristic showed high correlations with volumetric expansion (r = 0.95), specific volume (r = 0.90), hardness (r = 0.92), fracturability (r = 0.93) and spread factor (r = -0.96). BRF increased the value of the color difference of the biscuits up to 17.70, the effect of WMF was smaller (6.51). Only the radial expansion index correlated with the trough (r = 0.76), final viscosity (r = 0.79) and setback (r = 0.77) parameters. Considering the main desirable physical characteristics in savory biscuits, the highest global desirability obtained was for the proportion of 49% WWF, 24% WMF and 27% BRF.