Engineering Commons^™

Experimental And Modelling Of Lightning Damage To Carbon Fibre-Reinforced Composites Under Swept Stroke, Chengzhao Kuang, Kunkun Fu, Juhyeong Lee, Huixin Zhu, Qizhen Shi, Xiaoyu Cui

Mechanical and Aerospace Engineering Faculty Publications

Lightning swept stroke creates multiple lightning attachments along an aircraft in flight. This introduces distinct structural damage compared to that from a single-point lightning current injection test in laboratory. This study presents both experimental and numerical studies on lightning damage in carbon fibre-reinforced polymer (CFRP) composites under swept stroke. Coupled electrical–thermal finite element (FE) models were proposed to predict lightning damage to CFRP composites under single-point current injection and swept stroke, respectively. A lightning swept stroke testing method was proposed by embedding a copper wire inside the composites to simulate multiple lightning attachments on the composites. The FE-predicted damage from …

Dynamics And Scaling Of Particle Streaks In High-Reynolds-Number Turbulent Boundary Layers, Tim Berk, Filippo Coletti

Mechanical and Aerospace Engineering Faculty Publications

Inertial particles in wall-bounded turbulence are known to form streaks, but experimental evidence and predictive understanding of this phenomenon is lacking, especially in regimes relevant to atmospheric flows. We carry out wind tunnel measurements to investigate this process, characterizing the transport of microscopic particles suspended in turbulent boundary layers. The friction Reynolds number Re_𝜏 = O(10⁴) allows for significant scale separation and the emergence of large-scale motions, while the range of viscous Stokes number St⁺ = 18–870 is relevant to the transport of dust and fine sand in the atmospheric surface layer. We …

Towards A Virtual Test Framework To Predict Residual Compressive Strength After Lightning Strikes, Scott L.J. Millen, Xiaodong Xu, Juhyeong Lee, Suparno Mukhopadhyay, Michael R. Wisnom, Adrian Murphy

Mechanical and Aerospace Engineering Faculty Publications

A novel integrated modelling framework is proposed as a set of coupled virtual tests to predict the residual compressive strength of carbon/epoxy composites after a lightning strike. Sequentially-coupled thermal-electric and thermo-mechanical models were combined with Compression After Lightning Strike (CAL) analyses, considering both thermal and mechanical lightning strike damage. The predicted lightning damage was validated using experimental images and X-ray Computed Tomography. Delamination and ply degradation information were mapped to a compression model, with a maximum stress criterion, using python scripts. Experimental data, in which artificial lightning strike and compression testing were performed, was used to assess the predictive capabilities …

On Quantifying Uncertainty In Lightning Strike Damage Of Composite Laminates: A Hybrid Stochastic Framework Of Coupled Transient Thermal-Electrical Simulations, R. S. Chahar, J. Lee, T. Mukhopadhyay

Mechanical and Aerospace Engineering Faculty Publications

Lightning strike damage can severely affect the thermo-mechanical performance of composite laminates. It is essential to quantify the effect of lightning strikes considering the inevitable influence of material and geometric uncertainties for ensuring the operational safety of aircraft. This paper presents an efficient support vector machine (SVM)-based surrogate approach coupled with computationally intensive transient thermal-electrical finite element simulations to quantify the uncertainty in lightning strike damage. The uncertainty in epoxy matrix thermal damage and electrical responses of unprotected carbon/epoxy composite laminates is probabilistically quantified considering the stochasticity in temperature-dependent multi-physical material properties and ply orientations. Further, the SVM models are …

Bending Performance And Failure Mechanisms Of Hybrid And Regular Sandwich Composite Structures With 3d Printed Corrugated Cores, S.Z.H. Shah, Khurram Altaf, Juhyeong Lee, Tahir Sharif, Rizwan Saeed Choudhry, S. M. Hussain

Mechanical and Aerospace Engineering Faculty Publications

The effect of core geometry and hybridization on the bending performance and failure mechanisms of carbon fibre-reinforced polymer (CFRP) and glass fibre-reinforced polymer (GFRP) corrugated sandwich composite structures (SCS) were experimentally investigated using a three-point bend test. The CFRP and GFRP corrugated cores and facesheets were produced using Fused Filament Fabrication (FFF) and vacuum-assisted infusion processes, respectively. Three types of corrugated SCSs were built: SCSs with different core geometries (circular, square, trapezoidal, sinusoidal, and triangular), hybrid SCSs with different CFRP and GFRP cores and facesheets, and fully 3D-printed CFRP and GFRP SCSs. The corrugated SCS with square core geometry outperformed …

Model-Assisted Online Optimization Of Gain-Scheduled Pid Control Using Nsga-Ii Iterative Genetic Algorithm, Shen Qu, Tianyi He, Guoming Zhu

Mechanical and Aerospace Engineering Faculty Publications

In the practical control of nonlinear valve systems, PID control, as a model-free method, continues to play a crucial role thanks to its simple structure and performance-oriented tuning process. To improve the control performance, advanced gain-scheduling methods are used to schedule the PID control gains based on the operating conditions and/or tracking error. However, determining the scheduled gain is a major challenge, as PID control gains need to be determined at each operating condition. In this paper, a model-assisted online optimization method is proposed based on the modified Non-Dominated Sorting Genetic Algorithms-II (NSGA-II) to obtain the optimal gain-scheduled PID controller. …

A Geometrical, Reachable Set Approach For Constrained Pursuit–Evasion Games With Multiple Pursuers And Evaders, Olli Jansson, Matthew W. Harris

Mechanical and Aerospace Engineering Faculty Publications

This paper presents a solution strategy for deterministic time-optimal pursuit–evasion games with linear state constraints, convex control constraints, and linear dynamics that is consistent with linearized relative orbital motion models such as the Clohessy–Wiltshire equations and relative orbital elements. The strategy first generates polytopic inner approximations of the players’ reachable sets by solving a sequence of convex programs. A bisection method then computes the optimal termination time, which is the least time at which a set containment condition is satisfied. The pursuit–evasion games considered are games with (1) a single pursuer and single evader, (2) multiple pursuers and a single …

Multiscale Damage Modelling Of Notched And Un-Notched 3d Woven Composites With Randomly Distributed Manufacturing Defects, S.Z.H. Shah, Juhyeong Lee, P.S.M. Megat-Yusoff, Syed Zahid Hussain, T. Sharif, R.S. Choudhry

Mechanical and Aerospace Engineering Faculty Publications

This work proposes a stochastic multiscale computational framework for damage modelling in 3D woven composite laminates, by considering the random distribution of manufacturing-induced imperfections. The proposed method is demonstrated to be accurate, while being simple to implement and requiring modest computational resources. In this approach, a limited number of cross-sectional views obtained from micro-computed tomography (µCT) are used to obtain the stochastic distribution of two key manufacturing-induced defects, namely waviness and voids. This distribution is fed into a multiscale progressive damage model to predict the damage response of three-dimensional (3D) orthogonal woven composites. The accuracy of the proposed model was …

Microscale Modelling Of Lightning Damage In Fibre-Reinforced Composites, Scott L. J. Millen, Juhyeong Lee

Mechanical and Aerospace Engineering Faculty Publications

In this work, three-dimensional (3D) finite element simulations were undertaken to study the effects of lightning strikes on the microscale behaviour of continuous fibre-reinforced composite materials and to predict and understand complex lightning damage mechanisms. This approach is different from the conventional mesoscale or macroscale level of analysis, that predicts the overall lightning damage in composite laminates, thus providing better understanding of lightning-induced thermo-mechanical damage at a fundamental level. Micromechanical representative volume element (RVE) models of a UD composite laminate were created with circular carbon fibres randomly distributed in an epoxy matrix. The effects of various grounding conditions (one-, two-, …

Developing Test Methods For Compression After Lightning Strikes, Xiaodong Xu, Scott L. J. Millen, Juhyeong Lee, Gasser Abdelal, Daniel Mitchard, Michael R. Wisnom, Adrian Murphy

Mechanical and Aerospace Engineering Faculty Publications

Research into residual strength after lightning strike is increasing within the literature. However, standard test methods for measuring residual compressive strength after lightning strikes do not exist. For the first time, a systematic experimental study is undertaken to evaluate modifications necessary to standard Compression After Impact (CAI) specimen geometry and test jig design to induce specimen failure at the lightning damage region. Four laboratory generated lightning strike currents with peak amplitudes ranging from 25 to 100 kA have been studied. Test set-up modifications were made considering the scale of the lightning damage and its potential proximity to specimen edges. Specimen …

Optimal Spacecraft Guidance, Matthew W. Harris, M. Benjamin Rose

Mechanical and Aerospace Engineering Faculty Publications

This book is designed for a one-semester course at Utah State University titled MAE 6570 Optimal Spacecraft Guidance. The class meets for 75 minutes, twice per week, for 14 weeks. There are no prerequisites other than graduate standing in engineering. Proficiency in calculus, differential equations, linear algebra, and computer programming is required. Students find that previous experience in space dynamics, linear multivariable control, or optimal control is helpful.

The goal of the book and course is for students to develop fundamental skills needed to do professional work in the area of spacecraft guidance. After working through the book, students should …

Multiple Discharges Before Leader Inception In Long Air Gaps Under Positive Switching Impulses, Xiangen Zhao, Juhyeong Lee, Gang Liu, Lei Jia, Yang Liu, Junjia He, Yaping Du

Mechanical and Aerospace Engineering Faculty Publications

There are multiple corona bursts before leader inception when the rising rate of the applied voltage or electric field is not sufficiently high enough in long positive sparks. In existing studies, no attention has been paid to whether these corona bursts occur in the same location, and they are mostly considered directly as belonging to the same discharge. However, this paper presents that in a typical rod-plate long air gap, the multiple corona bursts before leader inception are distributed in at least two different locations, and the highest probability of three discharges occurs. Also, the discharge occurs with the highest …

Design Of Composite Double-Slab Radar Absorbing Structures Using Forward, Inverse, And Tandem Neural Networks, Devin Nielsen, Juhyeong Lee, Young-Woo Nam

Mechanical and Aerospace Engineering Faculty Publications

The survivability and mission of a military aircraft is often designed with minimum radar cross section (RCS) to ensure its long-term operation and maintainability. To reduce aircraft’s RCS, a specially formulated Radar Absorbing Structures (RAS) is primarily applied to its external skins. A Ni-coated glass/epoxy composite is a recent RAS material system designed for decreasing the RCS for the X-band (8.2 – 12.4 GHz), while maintaining efficient and reliable structural performance to function as the skin of an aircraft. Experimentally measured and computationally predicted radar responses (i.e., return loss responses in specific frequency ranges) of multi-layered RASs are expensive and …

Hyper-Velocity Impact Performance Of Foldcore Sandwich Composites, Nathan Hoch, Chase Mortensen, Juhyeong Lee, Khari Harrison, Kalyan Raj Kota, Thomas Lacy

Mechanical and Aerospace Engineering Faculty Publications

A foldcore is a novel core made from a flat sheet of any material folded into a desired pattern. A foldcore sandwich composite (FSC) provides highly tailorable structural performance over conventional sandwich composites made with honeycomb or synthetic polymer foam cores. Foldcore design can be optimized to accommodate complex shapes and unit cell geometries suitable for protective shielding structures

This work aims to characterize hypervelocity impact (> 2000 m/s, HVI) response and corresponding damage morphologies of carbon fiber reinforced polymer (CFRP) FSCs. A series of normal (0° impact angle) and oblique (45° impact angle) HVI (~3km/s nominal projectile velocity) impact …

Predicting Stochastic Lightning Mechanical Damage Effects On Carbon Fiber Reinforced Polymer Matrix Composites, Juhyeong Lee, Syed Zulfiqar Hussain Shah

Mechanical and Aerospace Engineering Faculty Publications

Three stochastic air blast models are developed with spatially varying elastic properties and failure strengths for predicting lightning mechanical damage to AS4/3506 carbon/epoxy composites subjected to < 100 kA peak currents: (1) the conventional weapon effects program (CWP) model, (2) the coupled eulerianlagrangian (CEL) model, and (3) the smoothed-particle hydrodynamics (SPH) model. This work is an extension of our previous studies [1–4] that used deterministic air blast models for lightning mechanical damage prediction. Stochastic variations in composite material properties were generated using the Box-Muller transformation algorithm with the mean (i.e., room temperature experimental data) and their standard deviations (i.e., 10% of the mean herein as reference). The predicted dynamic responses and corresponding damage initiation prediction for composites under equivalent air blast loading were comparable for the deterministic and stochastic models. Overall, the domains with displacement, von-Mises stress, and damage initiation contours predicted in the stochastic models were somewhat sporadic and asymmetric along the fiber’s local orientation and varied intermittently. This suggests the significance of local property variations in lightning mechanical damage prediction. Thus, stochastic air blast models may provide a more accurate lightning mechanical damage approximation than traditional (deterministic) air blast models. All stochastic models proposed in this work demonstrated satisfactory accuracy compared to the baseline models, but required substantial computational time due to the random material model generation/assignment process, which needs to be optimized in future work.

Identifying Fibre Orientations For Fracture Process Zone Characterization In Scaled Centre-Notched Quasi-Isotropic Carbon/Epoxy Laminates With A Convolutional Neural Network, Xiaodong Xu, Aser Abbas, Juhyeong Lee

Mechanical and Aerospace Engineering Faculty Publications

This paper presents a novel X-ray Computed Tomography (CT) image analysis method to characterize the Fracture Process Zone (FPZ) in scaled centre-notched quasi-isotropic carbon/epoxy laminates. A total of 61 CT images of a small specimen were used to fine-tune a pre-trained Convolutional Neural Network (CNN) (i.e., VGG16) to classify fibre orientations. The proposed CNN model achieves a 100% accuracy when tested on the CT images of the same scale as the training set. However, the accuracy drops to a maximum of 84% when tested on unlabelled images of the specimens having larger scales potentially due to their lower resolutions. Another …

Schlieren Techniques For Observations Of Long Positive Sparks: Review And Application, Junjia He, Xiankang Wang, Xiangen Zhao, Juhyeong Lee, Yaping Du, Xiaopeng Liu, Quan Gan, Yang Liu, Yuqin Liao

Mechanical and Aerospace Engineering Faculty Publications

Understanding the mechanism of positive leader discharge is important in lightning protection engineering and the external insulation design in high voltage power transmission systems. During the propagation of a positive leader, some processes without light-emitting, for example, the insulation recovery process after the breakdown, cannot be observed by optical photography techniques. With the combination of the digital high-speed imaging system, the conventional Schlieren techniques offer new vistas in the long air gap discharge observation. The important features of high spatial resolution, high sensitivity, and easy arrangement make Schlieren techniques powerful and effective tools for characterising the discharge processes without light-emitting. …

A Review Of Avian-Inspired Morphing For Uav Flight Control, Christina Harvey, Lawren L. Gamble, Christian R. Bolander, Douglas F. Hunsaker, James J. Joo, Daniel J. Inman

Mechanical and Aerospace Engineering Faculty Publications

The impressive maneuverability demonstrated by birds has so far eluded comparably sized uncrewed aerial vehicles (UAVs). Modern studies have shown that birds’ ability to change the shape of their wings and tail in flight, known as morphing, allows birds to actively control their longitudinal and lateral flight characteristics. These advances in our understanding of avian flight paired with advances in UAV manufacturing capabilities and applications has, in part, led to a growing field of researchers studying and developing avian-inspired morphing aircraft. Because avian-inspired morphing bridges at least two distinct fields (biology and engineering), it becomes challenging to compare and contrast …

Attainable Moment Set And Actuation Time Of A Bio-Inspired Rotating Empennage, Christian R. Bolander, Douglas F. Hunsaker, David Myszka, James J. Joo

Mechanical and Aerospace Engineering Faculty Publications

Future tactical aircraft will likely demonstrate improvements in efficiency, weight, and control by implementing bio-inspired control systems. This work analyzes a novel control system for a fighter aircraft inspired by the function of – and the degrees of freedom available in – a bird’s tail. The control system is introduced to an existing fighter aircraft design by removing the vertical tail and allowing the horizontal tail surfaces to rotate about the roll axis. Using a low-fidelity aerodynamic model, an analysis on the available controlling moments and actuation speeds of the baseline aircraft is compared to that of the bio-inspired rotating …

Stochastic Lightning Damage Prediction Of Carbon/Epoxy Composites With Material Uncertainties, S.Z.H. Shah, Juhyeong Lee

Mechanical and Aerospace Engineering Faculty Publications

This study presents a novel stochastic modeling framework predicting lightning thermal damage in carbon/epoxy composites. The stochastic lightning damage model (SLDM) was developed with random distributions of composite’s electrical conductivity and void. The Box-Muller transformation was applied to generate random in-plane and through-thickness electrical conductivities with Gaussian distributions. The SLDM suggested that the predicted lightning thermal damage to carbon/epoxy composites increased slightly with the use of stochastic electrical conductivity, but the presence of voids did not significantly affect the damage development. The predicted size and shape of lightning thermal damage agreed fairly well with experimental results. In addition, the proposed …

Thermal Barrier Coating For Carbon Fiber-Reinforced Composite Materials, Heejin Kim, Jungwon Kim, Juhyeong Lee, Min Wook Lee

Mechanical and Aerospace Engineering Faculty Publications

Carbon fiber-reinforced plastic (CFRP) composites are widely employed in lightweight and high performance applications including supercars, aero-vehicles, and space components. However, although carbon fibers are thermally stable, the low thermal endurance of the matrix materials remains a critical problem in terms of the performance of the material. In this study, we proposed a new, Al₂O₃-based thermal barrier coating (TBC) for the CFRP composites. The TBC comprised α-phase Al₂O₃ particles with a mean diameter of 9.27 μm. The strong adhesion between the TBC and the CFRP substrate was evaluated using a three point bending …

Lightning Arc Channel Effects On Surface Damage Development On A Prseus Composite Panel: An Experimental Study, Dounia Boushab, Pedram Gharghabi, Juhyeong Lee, Thomas E. Lacy Jr., Charles U. Pittman Jr., Michael S. Mazzola, Alexander Velicki

Mechanical and Aerospace Engineering Faculty Publications

Composite aircraft structures are vulnerable to lightning strike damage due to their relatively low electrical and thermal conductivities. A preceding work has investigated the lightning damage resistance of a carbon-epoxy Pultruded Rod Stitched Efficient Unitized Structure (PRSEUS) panel. The damage includes intense local damage (i.e., matrix decomposition/sublimation, fiber rupture, delamination) accompanied by widespread surface damage (i.e., distributed fiber rupture and tow splitting) further from the lightning attachment point. This study focuses on investigating the cause of the widespread surface damage. Two possible driving mechanisms are explored: i) magnetically-induced currents and ii) lightning arc-root/channel expansion. …

Modeling And Simulation Of A Supercritical Co2-Liquid Sodium Compact Heat Exchanger For Sodium Fast Reactors, Hailei Wang, Sean M. Kissick

Mechanical and Aerospace Engineering Faculty Publications

The study focuses on modeling and simulations of sodium-sCO2 intermediary compact heat exchangers for sodium-cooled fast reactors (SFR). A simplified 1-D analytical model was developed in companion with a 3-D CFD model. Using classic heat transfer correlations for Nusselt number, some simulation results using the 1-D model have achieved reasonable match with the CFD simulation results for longer channels (i.e., 40 cm and 80 cm). However, for short channel (10 cm) when axial conduction within the sodium fluid is significant, the 1-D model significantly over-predicted the heat transfer effectiveness. By incorporating the temperature-jump model, the 1-D model can extend its …

Change Of Exposure Time Mid-Test In High Temperature Dic Measurement, Thinh Quang Thai, Adam J. Smith, Robert J. Rowley, Paul R. Gradl, Ryan B. Berke

Mechanical and Aerospace Engineering Faculty Publications

Performing digital image correlation (DIC) at extreme temperatures has been greatly challenging due to the radiation which saturates the camera sensor. At such high temperatures, the light intensity emitted from an object is occasionally so powerful that the acquired images are overwhelmingly saturated. This induces data loss, potentially ruining the test, thus requiring the user to restart the test. For this reason, selection of an appropriate camera sensitivity plays a crucial role prior to beginning the test. Exposure time is a factor contributing to camera sensitivity and it is the easiest setting to manipulate during the test since it introduces …

Nytrox As “Drop-In” Replacement For Gaseous Oxygen In Smallsat Hybrid Propulsion Systems, Stephen A. Whitmore

Mechanical and Aerospace Engineering Faculty Publications

A medical grade nitrous oxide (N₂O) and gaseous oxygen (GOX) “Nytrox” blend is investigated as a volumetrically-efficient replacement for GOX in SmallSat-scale hybrid propulsion systems. Combined with 3-D printed acrylonitrile butadiene styrene (ABS), the propellants represent a significantly safer, but superior performing, alternative to environmentally-unsustainable spacecraft propellants like hydrazine. In a manner analogous to the creation of soda-water using dissolved carbon dioxide, Nytrox is created by bubbling GOX under pressure into N₂O until the solution reaches saturation. Oxygen in the ullage dilutes N₂O vapor and increases the required decomposition energy barrier by several orders …

Proper Orthogonal Decomposition And Recurrence Map For The Identification Of Spatial–Temporal Patterns In A Low-Re Wake Downstream Of Two Cylinders, Meihua Zhang, Zhongquan Charlie Zheng, Huixuan Wu

Mechanical and Aerospace Engineering Faculty Publications

Flow decomposition methods provide systematic ways to extract the flow modes, which can be regarded as the spatial distribution of a coherent structure. They have been successfully used in the study of wake, boundary layer, and mixing. However, real flow structures also possess complex temporal patterns that can hardly be captured using the spatial modes obtained in the decomposition. In order to analyze the temporal variation of coherent structures in a complex flow field, this paper studies the recurrence in phase space to identify the pattern and classify the evolution of the flow modes. The recurrence pattern depends on the …

Experimental Characterization Of Thermal-Hydraulic Performance Of A Microchannel Heat Exchanger For Waste Heat Recovery, James Yih, Hailei Wang

Mechanical and Aerospace Engineering Faculty Publications

Given size and performance advantages, microchannel heat exchangers are becoming increasingly important for various energy recovery and conversion processes. In this study, detailed experimental measurements were conducted to characterize flow and heat transfer performance of a microchannel heat recovery unit (HRU) manufactured using standard photochemical etching and diffusion bonding processes. According to the global flow and temperature measurement, the HRU has delivered the predicted thermal performance under various oil and air flow rates. As expected, the heat transfer effectiveness varies between 88% and 98% for a given air and oil flow rates while it increases with air inlet temperature due …

Gelatine Cavity Dynamics Of High-Speed Sphere Impact, Akihito Kiyama, Mohammad M. Mansoor, Nathan B. Spiers, Yoshiyuki Tagawa, Tadd T. Truscott

Mechanical and Aerospace Engineering Faculty Publications

We investigate the impact and penetration of a solid sphere passing through gelatine at various impact speeds up to 143.2 m s^-1 Tests were performed with several concentrations of gelatine. Impacts for low elastic Froude number Fr_e a ratio between inertia and gelatine elasticity, resulted in rebound. Higher Fr_e values resulted in penetration, forming cavities with prominent surface textures. The overall shape of the cavities resembles those observed in water-entry experiments, yet they appear in a different order with respect to increasing inertia: rebound, quasi-seal, deep-seal, shallow-seal and surface-seal. Remarkably, similar to the We – Bo phase …

How Vision Governs The Collective Behaviour Of Dense Cycling Pelotons, J. Belden, Mohammad M. Mansoor, A. Hellum, S. R. Rahman, A. Meyer, C. Pease, J. Pacheco, S. Koziol, Tadd T. Truscott

Mechanical and Aerospace Engineering Faculty Publications

In densely packed groups demonstrating collective behaviour, such as bird flocks, fish schools or packs of bicycle racers (cycling pelotons), information propagates over a network, with individuals sensing and reacting to stimuli over relatively short space and time scales. What remains elusive is a robust, mechanistic understanding of how sensory system properties affect interactions, information propagation and emergent behaviour. Here, we show through direct observation how the spatio-temporal limits of the human visual sensory system govern local interactions and set the network structure in large, dense collections of cyclists. We found that cyclists align in patterns within a ± 30° …

A High Magnification Uv Lens For High Temperature Optical Strain Measurements, Robert S. Hansen, Trevor J. Bird, Ren Voie, Katharine Z. Burn, Ryan B. Berke

Mechanical and Aerospace Engineering Faculty Publications

Digital Image Correlation (DIC) measures full-field strains by tracking displacements of a specimen using images taken before and after deformation. At high temperatures, materials emit light in the form of blackbody radiation, which can interfere with DIC images. To screen out that light, DIC has been recently adapted by using ultraviolet (UV) range cameras, lenses, and filters. Before now, UV-DIC had been demonstrated at the centimeter scale using commercially available UV lenses and filters. Commercial high-magnification lenses using visible light have also been used for DIC. However, there is currently no commercially available high-magnification lens that will allow images to …