Aperture Length Research Articles

Influence of atmospheric turbulence on temporal coherence characteristics of received optical field

In the process of laser propagation in atmosphere, its coherence characteristics are reduced by turbulence, which further affects the efficiency and performance of coherent detection process. In this paper, atmospheric coherence time is defined to describe the fluctuation speed of laser field after atmospheric transmission. The relative size of atmospheric coherence time and coherence process duration time determines the performance of coherent detection process. According to the infinitely long phase screen technology, we simulate laser atmospheric transmission, and systematically study the influences of atmospheric parameters, transceiver parameters and wavelength on atmospheric coherence time. It is found that the atmospheric coherence time is positively correlated with wavelength, receiving aperture and atmospheric coherence length, and inversely proportional to wind speed, which shows that the atmospheric coherence time can be effectively improved by improving the optical design and changing the laser band, thus effectively reducing the disturbance caused by turbulence and improving the stability of the received light field. The atmospheric coherence time defined in this paper is an important parameter to measure the influence of turbulence on coherent detection. This study can provide a powerful reference for evaluating the influence of atmosphere on coherent detection process.

Assessment of the phenotypic diversity of wild cherry (Prunus avium L.) populations and halfsib lines by multivariate statistical analyses

Abstract Wild cherry (Prunus avium L.) is a multi-purpose tree species with great ecological and economic importance for European forestry. Evaluating this species phenotypic diversity and quantitative traits characterization is of great importance to define its genetic resources conservation and breeding strategies. In this work, variations of physiological, biochemical, anatomical and morphological traits of one-year-old wild cherry seedlings were evaluated within and among populations to distinguish and characterize their phenotypic portfolio. We observed significant differences at the intra- and inter-population levels considering both biochemical and physiological leaf traits, whereas differences in morphological and anatomical traits were found to be significant only among half-sib lines within populations (i.e. intra-population level). With a multivariate approach, we explored the inter-population specificity and found out that the tiered approach spanning from organ morphology, across physiological scale, to the biochemical level gave out enough power to discriminate between different populations, and their acquisition and resource-use strategies. Moreover, stepwise discriminative analysis showed that radical scavenger capacity against 2,2’-azino-bis(3-ethylbenzothiazoline- 6-sulfonic acid) (ABTS•+) and water-use efficiency contributed to discrimination of studied populations to the largest extend. Lastly, our study highlights the robustness of certain functional traits, such as ABTS•+, water-use efficiency, net photosynthesis, total flavonoid content, width of stomata guard cell, and stomatal aperture length, which could be considered as a proxy to discriminate between wild cherry populations and assess phenotypic diversity.

Resolution Enhancement for Large-Scale Real Beam Mapping Based on Adaptive Low-Rank Approximation

Recently, a variety of super-resolution (SR) methods have been devoted to enhancing the angular resolution of real beam mapping (RBM) imagery in modern microwave remote sensing applications. When addressing large-scale datasets, however, they suffer from notably high computational complexity due to high-dimensional matrix inversion, multiplication, or singular value decomposition (SVD). To overcome this limitation, this article presents a low-complexity SR strategy based on adaptive low-rank approximation (LRA). Our underlying idea is first to construct a random matrix sketching to sample the raw echo measurements and restore the surface map of reflectivity in a low-dimensional linear space. The resulting low-complexity strategy enables substantial computational complexity reduction for a group of SR methods, at the cost of introducing a manually adjusted LRA parameter. Using the Fourier transform-based antenna analysis method, we further reveal that the LRA parameter that ensures support resolution improvement can be determined by a closed-form function of the aperture length, the wavelength, and the field of view, allowing for adaptively and efficiently selecting the optimal LRA parameter that well balances the tradeoff between LRA error and computational efficiency. We use both simulated and real datasets to demonstrate that the proposed LRA-based SR strategy can provide significant speedup without performance loss.

In vitro germination, storage and microscopic studies of pollen grains of four Ocimum species

In the present investigation, pollen morphology and viability of four Ocimum L. species viz. O. sanctum (CIM-Angana), O. basilicum (CIM-Saumya), O. gratissimum, and O. kilimandscharicum were studied. Morphological characters were observed using scanning electron and light microscopy. Pollen of all the four studied Ocimum species have hexacolpate apertures with varied aperture length and width. The exine ornamentation was reticulate and bi-reticulate. O. basilicum has large size (53.9 µm) pollen grains and rest three have medium sized pollen. The viability of pollen was assessed through staining dyes such as 2,5-diphenyl tetrazolium bromide (MTT) and 2,3,5-triphenyl tetrazolium chloride (TTC) and in vitro pollen germination method. O. basilicum possessed maximum viability (92.4%) whereas least viability was found in O. sanctum (38.2%). The maximum pollen germination percentage and tube growth were observed in the semisolid medium gelled with phytagel supplemented with 15% sucrose, 15% PEG, 6.4 mM boric acid and 7.3 mM calcium nitrate. O. basilicum showed the highest germination percentage (90.3%) followed by O. kilimandscharicum (57.1%), O. gratissimum (42.5%) and O. sanctum (25.5%). Pollen of the four Ocimum species were stored at different temperatures viz. 37 °C, + 4 °C, 0 °C, − 20 °C, and − 80 °C for 75 days. The highest pollen germinability of all the four Ocimum species was observed at − 20 °C. This study can be helpful in taxonomic identification of Ocimum species and further utilized in conservation and improvement of different Ocimum species by cross-hybridization breeding programmes.

Spontaneous Emission Enhancement by a Rectangular-Aperture Optical Nanoantenna: An Intuitive Semi-Analytical Model of Surface Plasmon Polaritons

The spontaneous-emission enhancement effect of a single metallic rectangular-aperture optical nanoantenna on a SiO2 substrate was investigated theoretically. By considering the excitation and multiple scattering of surface plasmon polaritons (SPPs) in the aperture, an intuitive and comprehensive SPP model was established. The model can comprehensively predict the total spontaneous emission rate, the radiative emission rate and the angular distribution of the far-field emission of a point source in the aperture. Two phase-matching conditions are derived from the model for predicting the resonance and show that the spontaneous-emission enhancement by the antenna comes from the Fabry–Perot resonance of the SPP in the aperture. In addition, when scanning the position of the point source and the aperture length, the SPP model does not need to repeatedly solve the Maxwell’s equations, which shows a superior computational efficiency compared to the full-wave numerical method.

Modeling evaluation on solid-liquid mixing characteristics in a dislocated guide impeller stirred tank

Abstract The solid-liquid mixing characteristics in a stirred tank with pitched blade impellers, dislocated impellers, and dislocated guide impellers were investigated through using CFD simulation. The effects of impeller speed, impeller type, aperture ratio, aperture length, solid particle diameter and initial solid holdup on the homogeneity degree in the solid-liquid mixing process were investigated. As expected, the solid particle suspension quality was increased with an increase in impeller speed. The dislocated impeller could reduce the accumulation of solid particles and improve the cloud height compared with pitched blade impeller under the same power consumption. The dislocated guide impeller could enhance the solid particles suspension quality on the basis of dislocated impeller, and the optimum aperture ratio and aperture length of dislocated guide impeller were 12.25% and 7 mm, respectively, in the solid-liquid mixing process. Smaller solid particle diameter and lower initial solid holdup led to higher homogeneity degree of solid-liquid mixing system. The dislocated guide impeller could increase solid particle integrated velocity and enhance turbulent intensity of solid-liquid two-phase compared with pitched blade impeller and dislocated impeller under the same power consumption.

Insight into the cellular and physiological regulatory modulations of Class-I TCP9 to enhance drought and salinity stress tolerance in cowpea.

The Teosinte branched 1/Cycloidea/Proliferating cell factor (TCP) transcription factors are potent growth and developmental regulators in plants, also responsive to various hormonal and environmental stimuli. In this study, we primarily focused on the functional role of TCP9, a nuclear-localised Class-I TCP transcription factor in a drought and heat-tolerant legume crop, cowpea (Vigna unguiculata). Under drought stress, a higher protein expression level of TCP9 was observed in the leaves of the drought-tolerant cowpea cultivar Pusa Komal as compared to the drought-sensitive cultivar TVu-7778. Further, overexpression of VuTCP9 resulted in reduced cell and stomata size, aperture length and width while cell and overall stomatal density in the 35S::VuTCP9 transgenic cowpea lines increased. Phenotypic alterations, such as reduced leaf size and vigour, altered seed coats displaying extension pattern similar to the 'Watson pattern' and delayed senescence were prominent in the transgenic lines. Under normal conditions, the gas exchange and fluorescence measurements indicated reduction in transpiration rate (E), stomatal conductance (gs ) and photosynthetic efficiency (Φ PSII). However, water usage efficiency (WUE) remained unaltered in the transgenic lines as compared to the wild-type (WT) plants. Furthermore, the transgenic lines displayed higher tolerance to oxidative, drought and salinity stress, maintained relatively higher relative water content and lower occurrence of H2 O2 , as compared to the WT plants. Genes related to the jasmonic acid biosynthesis, stomatal development and abiotic stress responsiveness, such as TTG1, NAC25, SPCH and GRP1, increased and LOX2 decreased significantly in the transgenic lines.

Investigation on the Optical Design and Performance of a Single-Axis-Tracking Solar Parabolic trough Collector with a Secondary Reflector

The design of solar concentrating collectors for the effective utilization of solar energy is a challenging condition due to tracking errors leading to different divergences of the solar incidence angle. To enhance the optical performance of solar parabolic trough collectors (SPTC) under a diverged solar incidence angle, an additional compound parabolic concentrator (CPC) is introduced as a secondary reflector. SPTC with CPC is designed and modeled for a single axis-tracking concentrating collector based on the local ambient conditions. In this work, the optical performance of the novel SPTC system with and without a secondary reflector is investigated using MATLAB and TRACEPRO software simulations for various tracking errors. The significance parameters such as the solar incidence angle, aperture length, receiver tube diameter, rim angle, concentration ratio, solar radiation, and absorbed flux are analyzed. The simulation results show that the rate of the absorbed flux on the receiver tube is significantly improved by providing the secondary reflector, which enhances the optical efficiency of the collector. It is found that the optical efficiency of the SPTC with a secondary reflector is 20% higher than the conventional collector system for a solar incidence angle of 2°. This work can effectively direct the choice of optimal secondary reflectors for SPTC under different design and operating conditions.

Field nonuniformity of limited-aperture planar SAWs and its implications for designing SSAW acoustofluidics

Acoustofluidics operating at high frequencies usually use surface acoustic waves (SAWs), and those emitted by limited-aperture planar interdigital transducers (IDTs) are prevalent. In such devices, field nonuniformity along the lateral direction is observed by many, but there lacks a study to quantitatively clarifying this effect. Here, by modeling IDTs using dirac-type transfer functions, we examine how field nonuniformity changes at varied aperture length, axial distance, and number of finger pairs of the IDTs. For standing SAW (SSAW) devices, field predictions from numerical analysis are validated through experimental measurements employing laser vibrometry. Finally, particle acoustophoresis is carried out in three SSAW devices, while the results provide some useful implications for future device designs.

Orbital-angular-momentum-based super-resolution ISAR imaging for maneuvering targets: Modeling and performance analysis

Vortex electromagnetic (EM) waves carrying orbital angular momentum (OAM) wave, whose infinitely helical wavefront and orthogonal eigenvalues of unique physical properties introduce additional rotational degrees of freedom, which has demonstrated superior performance in target detection and azimuthal imaging. In order to enhance the imaging performance for maneuvering targets, this paper offers a solution to develop the vortex inverse synthetic aperture radar (ISAR) technique based on OAM beams design. Firstly, by the space geometry of radar and maneuvering targets, the vortex echo signal model is derived, and the characteristics are analyzed as well. Secondly, pre-processing approach is developed for initial phase compensation by the design of the transmitted OAM beams. Thirdly, the imaging method, based on fractional Fourier transform (FrFT) and Doppler centroid tracking (DCT), is proposed to achieve high-precision range compression and motion compensation to accomplish the range alignment while removing the phases caused by residual azimuth displacements. Finally, after the slow-time pulse compression, the time-invariant Doppler shift is generated, and the well-focused ISAR image can be obtained. The simulation results demonstrate that the proposed vortex ISAR imaging can achieve a higher azimuth resolution than the conventional planar EM ISAR paradigm with the same synthetic aperture length. This discovery provides an approach for OAM-based microwave imaging in a rather efficient manner, which has no harsh requirements for complicated and heavily computational post-processing.

Rock joint detection from borehole imaging logs based on grey-level co-occurrence matrix and Canny edge detector

Rock joints play an important role in characterizing the rock mass quality for geomechanical design and stability analysis. An approach was developed to detect and characterize rock joints from images collected by a borehole imaging system. A grey-level co-occurrence matrix was employed to locate the joint regions, allowing more focused and effective detection processing, followed by extractions of the upper and lower edges of rock joints using the Canny algorithm. Four basic geometric parameters of rock joints (orientation, depth, aperture and core length) were determined based on the fitting of sinusoids to joint edges. Furthermore, the joint density was determined based on the geometric parameters. To calibrate the proposed approach, a borehole on the site of the planned Rumei hydropower station at Lantsang River was selected as a case study. Orientation of rock joints with gentle dip angles, which was determined from borehole imaging logs, corresponded to the measurements in three horizontal tunnels. Additionally, both joint density and pressure-wave velocity revealed that jointed rock mass was observed at depths from 100 to 120 m, and intact rock mass was present at depths of 150–170 m, indicating the good performance of the proposed method.

Volk eye check ocular measurement device for objective periorbital measurements: A prospective study.

Volk Eye Check (VEC) is a portable digital ocular measurement device that automatically captures clinical photographs with facial measurements in real time (Volk Optical Inc), claiming to reduce measurement errors. The accuracy and repeatability of this ocular measurement device in the periorbital region has not been reported. To report the reproducibility and repeatability of periocular biometric measurements using Volk Eye Check Ocular measurement device. Prospective, single blind, comparative study. Two experts performed digital photography of 100 volunteers using the standard photography technique using Oculoplasty module of the Volk Eye Check ocular measurement device. Each expert photographed the volunteer twice, to obtain two sets of automated printouts of 13 periorbital biometrics that were measured automatically by the ocular measurement device. Bland Altman plot and multiple comparisons of means from linear mixed-effects model fit by REML using simultaneous contrasts with p values reported by Bonferroni method were used as statistical tests to analyze following parameters: MRD1 (margin reflex distance-1), MRD2 (margin reflex distance-2), PFH (palpebral fissure height), HVID (horizontal visible iris diameter), ALL (aperture length at lateral limbus), and ALM (aperture length at medial limbus). The mean inter-observer difference in measurement (mm) was as follows: MRD1 (0.04), MRD2 (0.02), HVID (0.01), PFH (0.03), ALL (0.05), ALM (0.08). The mean intra-observer difference in measurement (mm) was as follows: MRD1 (0.02), MRD2 (0.09), HVID (0.0), PFH (0.09), ALL (0.06), ALM (0.05). Periorbital biometric measurements using Volk Eye Check ocular measurement devices are highly reproducible and repeatable. The oculoplasty module of Volk Eye Check ocular measurement device can provide reliable periorbital measurements for routine clinical use and for objective clinical studies.

Description of a new species of giant guitarfish, Glaucostegus younholeei sp. nov. (Rhinopristiformes: Glaucostegidae) from the northern Bay of Bengal, Bangladesh.

A new species of giant guitarfish, Glaucostegus younholeei sp. nov., is described from 13 specimens, 730933 mm total length, collected from fish landing center of Bangladesh Fisheries Development Corporation in Cox's Bazar district of Bangladesh. The new species is distinguished from congeners in having the following combination of characters: Body brownish or greyish in color with a narrowly wedge-shaped disc, and long narrow bluntly pointed snout (angle 3140°), and broad oblique nostrils with the narrow anterior opening. Nostrils about half of the mouth width, subequal (0.981.33) to internasal width; ~5557 nasal lamellae; anterior nasal flaps slightly penetrating into internasal space, their interspace 2.20 2.61 in length of the posterior nasal aperture. Orbit very small in adults, diameter 8.1911.62 in preorbital length, 2.252.69 in interorbital space. Rostral ridges almost joined along their entire length; margin of cranium sharply demarcated before eyes. Spiracular folds very short and widely separated. Skin rough, densely covered with small denticles, more coarsely granular on the dorsal surface than ventrally, enlarged between orbits and in a distinct band between nape and first dorsal fin. Tail relatively longer, length 1.151.48 in disc length; dorsal fins narrowly spaced, interspace 1.322.11 in base length of the first dorsal fin. Clasper length in adult male 4.375.70 in total length. Phylogenetic analysis of DNA barcode sequences also shows the clear divergence of Glaucostegus younholeei from other congeneric species obtained from GenBank. A key is provided to the 8 known members including new species of the genus Glaucostegus.

A joint sparse recovery algorithm for coprime adjacent array synthetic aperture radar 3D sparse imaging

ABSTRACT In the linear array synthetic aperture radar (LASAR) three-dimensional (3D) imaging, the spacing between adjacent elements in the uniform linear array (ULA) must satisfy the Nyquist sampling theorem to avoid the grating lobes, which makes the number of elements in the ULA very large. To reduce the elements in the ULA, the coprime adjacent array (CAA) with the same aperture length as the ULA is used when conducting LASAR 3D sparse imaging by compressed sensing (CS) algorithms. However, due to the increased autocorrelation coefficient of the measurement matrix, there exists grating lobes interference in the CAA-SAR imaging results. To solve this problem, we propose a joint sparse recovery (JSR) algorithm for CAA-SAR 3D sparse imaging. Firstly, we conduct sparse imaging on the CAA and its two subarrays, respectively. Secondly, the imaging results of the CAA and its two subarrays are performed image segmentation by the OTSU algorithm to extract their target-areas’ imaging results. Finally, we perform the image fusion by the wavelet transform on the target-areas’ imaging results to obtain the final imaging results. Both simulation and experimental results indicate that the imaging quality and computational efficiency of the JSR algorithm are higher than the random sampling array (RSA) and CAA under the same number of array elements. Besides, under the same aperture length, the JSR algorithm improves the computational efficiency than the ULA without imaging-quality loss.

Shell morphometric ratios as a tool for taxonomic determination in gastropods: a case study inNerita(Gastropoda, Neritidae)

AbstractIn the study, we compare the shell shape morphometrics in four species of neritid gastropods (Nerita fulgurans,Nerita tessellata,Nerita pelorontaandNerita versicolor), collected in Accra Beach (Barbados Island). We tested the hypothesis that the morphometric ratios can be used as a tool in the taxonomic determination among these four species of neritids. For this we determine the morphometric ratios from the external (length, height, width) and internal (shell aperture length, shell aperture width) measures. A principal component analysis (PCA) was used to determine which ratios were significant, and subsequently the proposed hypothesis was tested using the Kruskal–Wallis test. The morphometric ratios AW/H and AL/L were decisive in distinguishing the four species of neritids studied. In this study, the hypothesis of the efficacy of the use of shell morphometric ratios as an instrument in taxonomic studies was corroborated for the four species. Due to its low cost, this methodology can be applied in the recognition of species that have lost their external characteristics such as operculum, spire or colour and also in the identification of fossil specimens.

Design of Star Sensor Optical Lens with Large Aperture and Long Focal Length

Design of Star Sensor Optical Lens with Large Aperture and Long Focal Length

Temporal morphometric analyses of Pila globosa in India for its use in aquaculture and food industry

BackgroundAlthough the apple snail Pila globosa is used as indicator species for human consumption locally and as fish feed, research on it in general is very scanty. It is used in food industry, in aquaculture as fish bait and used as food in many regions of India and many other countries, but research on it has been started in the 1970s. Only 40 articles are available on this organism in PubMed indicating an urgent need of basic research on it especially work on its spatiotemporal morphometry Therefore, sampling of P. globosa was done from different parts of India in different seasons (summer, winter and rainy), and different morphometric studies were performed on this organism to draw baseline information. Analysis was conducted to study morphometry, the relationship between shell length and the weight and relative condition factor of Indian apple snail Pila globosa collected from five zones (east, west, north, south and centre) of India during 2018–2019 year.ResultsThe shell length (SL) (46.5 ± 13.33), shell width (SW) (40.22±11.5 mm), spire length (SPL) (2.99±0.15 mm), base length (BL) (12.53±2.94 mm), aperture length (AL) (21.95±4.36 mm), aperture width (AW) (2.74±0.47 mm) and shell weight (WT) (31.08±13.76 g) were observed to be varied among the individual sampled across India. Different relationships for SL/SW (Log SW=0.9889 Log SL + 0.9444), SL/SPL (Log SPL = 0.1452 Log SL+0.3815), SL/BL (Log BL=0.7789 Log SL+0.5814), SL/AL (Log AL= 0.6518 Log SL+0.9111) and SL/AW (Log AW=0.4475 Log SL+0.1422) were observed by considering shell length as basic index. The relationship between shell length and shell weight was found to be Log WT=2.0263 Log SL+0.1098. The relative condition factor revealed uninterrupted and good environmental condition observed for apple snails. A negative allometric growth pattern was observed from the length–weight relationship.ConclusionThe environments of apple snail in India are not contaminated, and the results can be used as baseline data in aquaculture for model analysis and can be used as a reference for drawing relationship among different morphometric indices of P. globosa in India, as there is no such information available on it. The data can also be used for mass scale production of P. globosa for consumption by human and use in aquatic industries as fish feed.

Analysis of shielding effectiveness by optimizing aperture dimensions of a rectangular enclosure with genetic algorithm

Electromagnetic compatibility (EMC) has now become a substantial challenge more than any other time sincethe number of electric vehicles (EV) increased rapidly. The electric driving system in an EV consists of power electroniccomponents supplied by high voltage battery source. They are both source and victim of potential electromagneticinterference (EMI) since fast switching process occurs inside them. Electromagnetic shielding provides a significantprotection against EMI for any electrical and electronic components inside the vehicle. In this paper, analysis of shieldingeffectiveness (SE) by optimizing aperture dimensions of a rectangular enclosure is investigated. Realistic dimensions of theshielding enclosure of an inverter component are employed. An optimization methodology based on genetic algorithm(GA) is carried out and applied to an SE analytical model. It is aimed to keep the total aperture area as large aspossible inside a particular dimension range while improving SE of the enclosure compared with the reference level.Obtained optimization results are presented by indicating optimum aperture length and width which satisfy both EMCand dimension requirements. Finally, it is concluded that through the optimization methodology designed in this study,the SE of the enclosure is raised from a poor level to an average one while providing larger aperture area.

Developing Upscaling Approach for Swarming Hydraulic Fractures Observed at Hydraulic Fracturing Test Site through Multiscale Simulations

Summary This work aims to address a challenge posed by recent observations of tightly spaced hydraulic fractures in core samples from the hydraulic fracturing test site (HFTS) in the Middle Wolfcamp Formation. Many fractures in retrieved cores have subfoot spacing, which is at odds with conventional models in which usually one hydraulic fracture is initiated per cluster. Models assuming a single fracture at each cluster, although a common practice, often predict excessive fracture propagation that is inconsistent with microseismic observation. Here, we aim to develop a numerical approach to effectively account for densely spaced hydraulic fractures in field-scale simulations. Because it is impractical to explicitly model all aforementioned fractures, we develop a new upscaling law that enables existing simulation tools to predict reservoir response to fracture swarms. The upscaling law is derived based on an energy equivalence argument and validated through multiscale simulations using a high-fidelity code, GEOS. The swarming fractures are first modeled with a spacing that is much smaller than the cluster spacing; these fractures are then approximated by an upscaled, single fracture based on the proposed upscaling law. The upscaled fracture is shown to successfully match the energy input rate and produce the total fracture aperture and average propagation length of the explicitly simulated swarm. Afterward, the upscaling approach is further implemented in 3D field-scale simulations and validated against the HFTS microseismic data of a horizontal well. Our results show that hydraulic fracture swarming can significantly affect fracture propagation behaviors compared with the propagation of single fractures as assumed by conventional modeling approaches. Under the considered situations, the conventional treatment yields fast propagation speed that far exceeds that indicated by the microseismic data. We also illustrate that this discrepancy can be reduced readily through the implementation of the upscaling law. Our results demonstrate the importance of accounting for the fracture swarming effect in field-scale simulations and the efficacy of this approach to enable realistic predictions of reservoir responses to fracture swarms, without the need to model tightly spaced fractures individually.

Determining the Minimum Scan Step of an Electronically Scanned Antenna

Introduction. Electronically scanned antennas (ESA) appeared about a century ago. Although the methods of their design and production have been sufficiently studied, some individual parameters are yet to be revealed. One of such parameters is the minimum step of movement, along with a related parameter – the accuracy of beam alignment in a given direction. From the electrodynamic problem of radiation, it is obvious that the step is associated with the number of radiators and the accuracy of phase adjustment in analogue phase shifters, or with the quantization step in the case of using phase shifters with a discrete step.Aim. To discover a connection between the design parameters of ESA and the step of beam steering; to investigate the dependence between the step and the parameters of the phase shifter and types of beam forming phased array circuits; to create a mathematical apparatus for calculating the minimum step of beam movement for the sum and difference radiation patterns.Materials and methods. Analytical relations were determined for calculating the step depending on the geometric dimensions and location of the radiators. A software application was developed for calculating radiation patterns. A software and hardware complex was designed for beam control of an experimental C-band ESA.Results. A method was developed for calculating the minimum step of ESA scanning. Mathematical relations for calculating the minimum step and accuracy of the ESA beam setting were obtained. A comparison of the experimental and theoretical data on the minimum step of movement of the sum and difference beams of a C-band ESA with the ratio D/λ=10 in the X coordinate and D/λ=5 in the Y coordinate showed good agreement.Conclusion. The created mathematical apparatus makes it possible to calculate the minimum step of electron beam scanning with sufficient accuracy. The experimentally measured steps of the beam movement for an array of 144 elements confirmed the obtained analytical relationships. In an ESA with a small number of elements (N < 10), the minimum step of movement can be variable. The theoretically achievable minimum step of beam movement is determined by the phase shift of the least significant bit of the phase shifter and the electrical length of the antenna aperture.