Surface Ablation Research Articles

Ultrafast laser-induced simultaneous carbonization and texturization of titanium alloy surface and its tribological properties

Due to the poor tribological properties, the applications of titanium alloy are restricted. Both laser texturing and surface coating are effective methods to enhance the tribological properties of titanium alloy surfaces. Hence, this study proposed a new ultrafast laser-induced simultaneous carbonization and texturization of titanium alloy surfaces to improve its tribological properties by modifying titanium alloy’s surface composition and micro-nanostructures in one step. A polymer film (polyimide, PI) was selected as the carbon source preplaced on the titanium alloy (Ti-6Al-4 V, TC4) surface. On the one hand, under ultrafast laser (picosecond 355 nm laser) irradiation, the laser-induced photothermal effect led to the carbonization of the polymer film and the formation of the pyrolytic carbon coating on the titanium alloy surface. Pyrolytic carbon also reacted with titanium alloy to form titanium carbides. On the other hand, ultrafast lasers also led to the melting and ablation of the titanium alloy surface, creating micro-nanostructures with interlocking micro-holes and micro-bumps. The coefficient of friction (COF) and wear rate of the titanium alloy surfaces were significantly reduced due to the synergistic effects of carbon coating and micro-nanostructures. It showed great significance in improving the tribological properties and the surface treatment of metallic materials.

Deriving iceberg ablation rates using an on-iceberg autonomous phase-sensitive radar (ApRES)

Abstract The increase in iceberg discharge into the polar oceans highlights the importance of understanding how quickly icebergs are deteriorating and where the resulting freshwater injection is occurring. Recent advances in quantifying iceberg deterioration through combinations of modeling, remote sensing and direct in situ measurements have successfully calculated overall ablation rates, and surface and sidewall ablation; however, in situ measurements of basal melt rates have been difficult to obtain. Radar has successfully measured iceberg thickness, but repeat measurements, which would capture a change in iceberg thickness with time, have not yet been collected. Here we test the applicability of using an on-iceberg autonomous phase-sensitive radar (ApRES) to quantify basal ablation rates of a large (~800 m long) non-tabular Arctic iceberg during an intensive 2019 summer field campaign in Sermilik Fjord, southeast Greenland. We find that ApRES can be used to measure basal ablation even over a short deployment period (10 d), and also provide a lower bound on sidewall melt. This study fills a critical gap in iceberg research and pushes the limits of field instrumentation.

Review of high-precision femtosecond laser materials processing for fabricating microstructures: Effects of laser parameters on processing quality, ablation efficiency, and microhole shape

Femtosecond lasers are promising tools for achieving high-precision processing of thin materials without causing any thermal surface damage and bulk distortion. However, thermal damage can occur even with ultrashort laser pulses. This is because of high electron penetration depth and heat accumulation at high fluence and high repetition rate. Nanoparticle redeposition can be dramatically altered with variation in repetition rate. The symmetry of microholes and ablation efficiency vary with laser polarization. The laser wavelength affects the ablation efficiency and surface roughness. Therefore, understanding these laser–matter interactions that depend on the laser parameters is essential for high-precision laser processing. This article reviews laser–matter interactions in the 64FeNi alloy, as well as analytical models for designing the desired hole size and taper angles. This can help establish strategies for creating various high-precision microstructures using femtosecond lasers.

Ice Sheet Mass Changes over Antarctica Based on GRACE Data

Assessing changes of the mass balance in the Antarctic ice sheet in the context of global warming is a key focus in polar study. This study analyzed the spatiotemporal variation in the Antarctic ice sheet’s mass balance, both as a whole and by individual basins, from 2003 to 2016 and from 2018 to 2022 using GRACE RL06 data published by the Center for Space Research (CSR) and ERA-5 meteorological data. It explored the lagged relationships between mass balance and precipitation, net surface solar radiation, and temperature, and applied the random forest method to examine the relative contributions of these factors to the ice sheet’s mass balance within a nonlinear framework. The results showed that the mass loss rates of the Antarctic ice sheet during the study periods were −123.3 ± 6.2 Gt/a and −24.8 ± 52.1 Gt/a. The region with the greatest mass loss was the Amundsen Sea in West Antarctica (−488.8 ± 5.3 Gt/a and −447.9 ± 14.7 Gt/a), while Queen Maud Land experienced the most significant mass accumulation (44.9 ± 1.0 Gt/a and 30.0 ± 3.2 Gt/a). The main factors contributing to surface ablation of the Antarctic ice sheet are rising temperatures and increased surface net solar radiation, each showing a lag effect of 1 month and 2 months, respectively. Precipitation also affects the loss of the ice sheet to some extent. Over time, the contribution of precipitation to the changes in the ice sheet’s mass balance increases.

Thermal reaction based mesoscale ablation model for phase degradation and pyrolysis of needle-punched composite

Needle-punched composites are highly valued for their exceptional resistance to interlaminar properties, ablation, and design flexibility, making them increasingly popular in aerospace thermal protection systems. This work investigates the mesoscale structural characteristics and thermophysical properties of needle-punched composites in ablation process. Oxyacetylene ablation experiments were carried out at different temperatures, and a mesoscopic needle-punched structure model was established based on the results of CT characterization. Further, Abaqus custom subroutine was used to reveal the ablation evolution mechanism of carbon fiber reinforced phenolic resin-based needle-punched composites. The results show that, at mesoscopic scale, the acicular fiber bundle perpendicular to the ablative surface accelerates the heat conduction to the interior of the material and promotes the thermal damage and performance degradation of the composite.

Transient behavior of ablation and swelling for C/C composite and HfC-coated C/C composite in an arc-heated wind tunnel

This study investigated and modeled the transient behavior of surface recession, defined as the difference between ablative length and swelling length, for thermal protection materials within a high-enthalpy flow. Needle punch carbon-carbon (NPCC) and hafnium carbide coated carbon-carbon (HfC-coated NPCC) were exposed to high-enthalpy flow with a heat flux of 7.67 MW/m2 generated by an arc-heated facility. The NPCC and the HfC-coated NPCC represent an ablative surface and a non-ablative surface, respectively. Surface recession histories were estimated through an image analysis and visualizations monitored by a high-speed camera. Moreover, measured data including surface temperature histories, mass loss, and total length were presented. We proposed the models for the transient recession on the ablative surface and the non-ablative surface considering the ablation and the swelling. The ablative length was calculated using non-dimensional parameter B′, which computes ablation rates under equilibrium air conditions. While B’ modeling accurately predicted the ablation rates, it could not reflect the swelling phenomenon during an initial heating phase. The swelling was modeled with consideration of the thermal expansion. Specifically, the effect of increased porosity near the ablative surface was incorporated into the thermal expansion coefficient. The model developed in this study well agreed with the experimental data.

Comparative study of plasma, laser, and flame induced activation of HDPE liner surfaces of type 4 hydrogen vessels

ABSTRACT In our study, we compare the surface modifications of coarse HDPE surface induced by atmospheric air plasma, CO2 laser, and flame treatments. An order of WCA decrease of air plasma>flame>CO2 laser methods was detected. The improvement in adhesion strength measured 5 days after the activations followed the same trend. FT-IR and EDS proved that different oxygen compounds were formed after treatments, resulting in increased polar component of the total surface energy. Flame activation showed a saturation character regarding the O-moiety. Hydrophobic recovery showed a linear behavior, with a larger decreasing slope for the polar component than the total surface energy. Plasma treatments induced higher recovery rate; however, restore was not complete here either. The effects of the different CO2 irradiation intensities were nonlinear; SEM and roughness measurements revealed surface ablation or structure formation on the different samples, while after plasma and flame treatment a hilly microtexture appeared. With different mechanisms and intensities, all the tested methods are suitable for increasing the adhesion strength on HDPE surfaces.

Surface energy balance closure over melting snow and ice from in situ measurements on the Greenland ice sheet

Abstract Accurately quantifying all the components of the surface energy balance (SEB) is a prerequisite for the reliable estimation of surface melt and the surface mass balance over ice and snow. This study quantifies the SEB closure by comparing the energy available for surface melt, determined from continuous measurements of radiative fluxes and turbulent heat fluxes, to the surface ablation measured on the Greenland ice sheet between 2003 and 2023. We find that the measured daily energy available for surface melt exceeds the observed surface melt by on average 18 ± 30 W m−2 for snow and 12 ± 54 W m−2 for ice conditions (mean ± SD), which corresponds to 46 and 10% of the average energy available for surface melt, respectively. When the surface is not melting, the daily SEB is on average closed within 5 W m−2. Based on the inter-comparison of different ablation sensors and radiometers installed on different stations, and on the evaluation of modelled turbulent heat fluxes, we conclude that measurement uncertainties prevent a better daily to sub-daily SEB closure. These results highlight the need and challenges in obtaining accurate long-term in situ SEB observations for the proper evaluation of climate models and for the validation of remote sensing products.

Deriving seasonal and annual surface mass balance for debris-covered glaciers from flow-corrected satellite stereo DEM time series

Abstract Glaciers in High-Mountain Asia are experiencing varying rates and patterns of mass loss due to a complex interplay between glacier surface processes, local conditions and climate forcing. Spatially distributed surface mass balance (SMB) estimates can provide valuable insight into these drivers, but observations are currently limited in both space and time. We used very-high-resolution optical stereo images acquired by commercial satellites to prepare time series of digital elevation models (DEMs), and derived contemporaneous surface velocity and elevation change products for six debris-covered glaciers in Nepal. We developed new methods to produce flow-corrected Lagrangian SMB maps to isolate local surface ablation signals with enough detail to study individual ice cliffs. Our results show reduced ablation under thick debris cover and enhanced ablation over ice cliffs. Ablating ice cliffs were responsible for $10\!-\!38\%$ of the total ablation over debris-covered areas, even though they covered $\leq \!11\%$ of the total area. Seasonal SMB products reveal the timing and patterns of summer accumulation and ablation, underscoring the importance of snow avalanches for low-elevation debris-covered glaciers in the region. Our approach can be applied to other glaciers with repeat high-resolution DEM coverage and extended for regional analyses of SMB on seasonal to interannual timescales.

Side and front fast imaging of solid and liquid fed ablative pulsed plasma thruster’s discharge

Ultra-fast camera imaging is used to capture temporal evolution of the plasma discharge in an ablative Pulsed Plasma Thruster (PPT) fueled with solid polytetrafluoroethylene (PTFE) and liquid perfluoropolyether (PFPE), with the goal of comparing the mechanism of the expelled mass acceleration and getting insight into the physics of the processes involved in the discharge maintenance and impulse bit production. The fast photos are taken from two viewpoints (non-simultaneously), directing camera parallel (side view) and perpendicular (front view) to the ablative surface of the propellants, and are correlated with the relevant phases of the discharge current. Side view images reveal the presence of two distinct exhaust fractions, velocities of which differ by an order of magnitude. The speed of the faster fraction is comparable with the median of the ionized particles velocity expelled by the thruster. The vividness of the slow propagating component of the ablated mass, which mostly corresponds to neutral particles (based on velocity estimation) and lower mass bit of PFPE shots hint towards better propellant utilization by a liquid-fed PPT. Front view images confirm stable localization of PFPE discharge, forced by design of the propellant supplying plenum, whereas PTFE discharge is characterized by irregular path that covers an area of the propellant surface in random. The last half-period of the discharge is accompanied by vortices near the cathode spots. They are supposedly formed by evaporated electrode’s material and their trajectories imply further recombination in collisions with the electrodes, making this part of evaporated copper undetectable for charged particles diagnostics.

CFRTP single-lap adhesive bonding and its mechanical performance enhanced by laser surface treatment: Finite element simulation and experimental validation

The outstanding mechanical properties of carbon fiber reinforced thermoplastic polymer (CFRTP) have led to its widespread application in many industrial sectors. In response to the engineering challenge of repairing large non-critical CFRTP structural components in situ, an infrared fiber laser surface cleaning technology is proposed to treat the bonding interface and enhance the tensile strength of polypropylene (PP)-based CFRTP single-lap bonded joints. Specifically, through single-factor and orthogonal experiments, the impact of different process parameters on the properties of the bonded joints was identified first. Then, online temperature monitoring was performed to elucidate the laser treatment mechanism of the CFRTP sample interface. Surface morphology of the laser-treated samples further indicates that when the temperature of the sample surface surpasses the resin decomposition temperature with extended holding time, the resin could be removed from the surface more thoroughly. Additionally, a novel three-dimensional woven finite element (FE) model, accounting for anisotropic heat transfer, was established to predict the surface temperature and cleaning quality of CFRTP. The FE model incorporates the anisotropic heat transfer characteristics of carbon fibers, thus accurately simulating the heat transfer behaviors between carbon fibers and the resin matrix. The laser ablation mechanism is elucidated by examining the surface ablation morphologies and peak surface temperatures. A comparison between experimental results and FE simulations demonstrated a notable coherence in the trend of surface morphology variations, with discrepancies in peak surface temperatures ranging from 3.29 % to 24.63 %. The experimental tests proved that the shear strength of single-lap bonded joints reaches its maximum value when the laser power is 35 W, the scanning speed is 2500 mm/s, and the number of scans is four. The enhancement of the mechanical properties of bonded joints can be attributed to the improved wettability and higher surface free energy of the laser-treated samples.

Efficiency analysis of laser ultrasonic longitudinal wave detection based on the constraint effect

Abstract Laser ultrasound is a non-destructive inspection technique, but its application in internal defect detection and state characterization is limited by its weak body wave displacement induced by thermo-elastic mechanism. In this paper, the influence of the constraint layer on the directivity of laser induced ultrasonic force source and the excitation efficiency of longitudinal wave is analyzed by finite element modeling with transparent glass as the constraint layer. With the optimization of the parameters of the confinement layer, the longitudinal waves with energy comparable to that of the free surface ablation mechanism can be excited under the thermoelastic mechanism, which greatly improves the efficiency of the longitudinal wave of laser ultrasonic. Applying the above research results to the detection of internal defects, the imaging results of the internal defects are obvious and the location defects are accurate.

Influence of Laser Power and Rotational Speed on the Surface Characteristics of Rotational Line Spot Nanosecond Laser Ablation of TC4 Titanium Alloy.

The TC4 titanium alloy is widely used in medical, aerospace, automotive, shipbuilding, and other fields due to its excellent comprehensive properties. As an advanced processing technology, laser processing can be used to improve the surface quality of TC4 titanium alloy. In the present research, a new type of rotational laser processing method was adopted, by using a beam shaper to modulate the Gaussian spot into a line spot, with uniform energy distribution. The effects of the laser power and rotational speed on the laser ablation surface of the TC4 titanium alloy were analyzed. The results reveal that the melting mechanism of the material surface gradually changes from surface over melt to surface shallow melt with the increase in the measurement radius and the surface roughness increases first, then decreases and, finally, tends to be stable. By changing the laser power, the surface roughness changes significantly with the variation in the measurement radius. Because low laser power cannot provide sufficient laser energy, the measurement radius corresponding to the surface roughness peak of the microcrack area is reduced. Under a laser power of 11 W, the surface roughness reaches its peak when the measurement radius is 600 μm, which is 200 μm lower than that of a laser power of 12 W, 13 W, and 14 W. By changing the rotational speed, the centrifugal force generated by the rotation of the specimen affects the distribution and re-condensation of the molten pool of the surface. As the rotational speed increases, the shallow pit around the pit is made shallower by the filling of the pit with molten material and the height of the bulge decreases, until it disappears. The surface oxygen content of the material increases first and then decreases with the increase in the measurement radius and gradually approaches the initial surface state. Compared with a traditional laser processing spot, the rotational line spot covers a larger processing area of 22.05 mm2. This work can be used as the research basis for rotational modulation laser polishing and has significance for guiding the innovative development of high-quality and high-efficiency laser processing technology.

Investigate the relationship between pulsed field ablation parameters and ablation outcomes.

Pulsed field ablation (PFA) is an emerging non-thermal ablation method. The primary challenge is the control of multiple parameters in PFA, as the interplay of these parameters remains unclear in terms of ensuring effective and safe tissue ablation. This study employs the response surface method (RSM) to explore the interactions between various PFA parameters and ablation outcomes, and seeks to enhance the efficacy and safety of PFA. In vivo experiments were conducted using rabbit liver for varying PFA parameters: pulse amplitude (PA), pulse interval (PI), number of pulse trains (NT), and number of pulses in a pulse train (NP). Ablation outcomes assessed included three ablation sizes, surface temperature, and muscle contraction strength. Additionally, histological analysis was performed on the ablated tissue. We analyzed the relationship between PFA parameters and ablation outcomes, and results were then compared with those from a simulation using an electric-thermal coupling PFA finite element model. A linear relationship between ablation outcomes and PFA parameters was established. PA and NT exhibited extremely significant (P < 0.0001) and significant effects (P < 0.05) on all ablation outcomes, respectively. NP showed an extremely significant impact (P < 0.0001) on surface temperature and muscle contraction strength, while PI significantly influenced (P < 0.05) muscle contraction strength alone. Histological analysis revealed that PFA produces controlled, well-defined areas of liver tissue necrosis. Surface temperature results from simulations and experiments were highly consistent (R2 > 0.97). This study clarifies the relationship between various PFA parameters and ablation outcomes, and aims to improve the efficacy and safety of PFA.

Ablation behavior and mechanisms of Cf/(CrZrHfNbTa)C‒SiC high‐entropy composite at temperatures up to 2450°C

AbstractThe oxide layer formed by ultra‐high melt point oxides (ZrO2, HfO2) and SiO2 glassy melt is the key to the application of traditional thermal structural materials in extremely high‐temperature environment. However, the negative effect of ZrO2 and HfO2 phase transitions on the stability of oxide layer and rapid volatilization of low viscosity SiO2 melt limit its application in aerospace. In this study, the ablation behavior of Cf/(CrZrHfNbTa)C‒SiC high‐entropy composite was explored systematically via an air plasma ablation test, under a heat flux of 5 MW/m2 at temperatures up to 2450°C. The composite presents an outstanding ablation resistance, with linear and mass ablation rates of 0.9 µm/s and 1.82 mg/s, respectively. This impressive ablation resistance is attributed to the highly stable oxide protective layer formed in situ on the ablation surface, which comprises a solid skeleton of (Zr, Hf)6(Nb, Ta)2O17 combined with spherical particles and SiO2 glassy melt. The irregular particles provide a solid skeleton in the oxides protective layer, which increased stability of the oxide layer. Moreover, the spherical particles have a crystal structure similar to that of Ta2O5 and are uniformly distributed in SiO2 glassy melt, which hinder the flow of SiO2 glassy melt and enhance its viscosity to a certain degree. And it reduces the volatilization of SiO2. In summary, the stable oxide layer was formed by irregular particles oxide and the SiO2 glassy melt with certain viscosity, thereby resulting in the impressive ablation resistance of the composite. This study fills a gap in ablation research on the (CrZrHfNbTa)C system.

Tribological properties of ductile cast iron with in-situ textures created through abrasive grinding and laser surface ablation

This paper discusses the proposed abrasive grinding (AG) and laser surface ablation (LSA) method for creating in-situ textures on ductile cast iron (DCI) surfaces. LSA method removes spherical graphite of DCI’s surface, forming martensite and high residual stress on the matrix, thus increasing hardness. AG method uses Al2O3 abrasives to disrupt spherical graphite and form grinding-layer. Compared to LSA, AG method avoids residual stress and burrs, simplifies the processing technology. Tribological tests show that LSA-treated samples have a lower coefficient of friction (COF) and specific wear rate, especially under dry friction conditions, due to increased surface hardness. AG-treated samples have a more stable COF because the oxide layer reduces adhesive wear, grinding-layer provides solid lubrication and reduces localized contact stress.

Surface texture image classification of carbon/phenolic composites in extreme environments using deep learning

AbstractThe classification of ablation images holds significant practical value in thermal protection structures, as it enables the assessment of heat and corrosion resistance of composites. This paper proposes an image‐based deep learning framework to identify the surface texture of carbon/phenolic composites ablative images. First, ablation experiments and collection of surface texture images of carbon/phenolic composites under different thermal environments were conducted in an electric arc wind tunnel. Then, a deep learning model based on a convolutional neural network (CNN) is developed for ablative image classification. The pre‐trained network is ultimately employed as the input for transfer learning. The network's feature extraction layer is trained using the ImageNet dataset, while the global average pooling addresses specific classification tasks. The test results demonstrate that the proposed method effectively classifies the relatively small surface texture dataset, enhances the classification performance of ablative surface texture with an accuracy of up to 97.6%, and exhibits robustness and generalization capabilities.Highlights The paper proposes a new deep learning classification method for ablative images. A model highly sensitive to small and weak features is built. Transfer learning and data enhancement techniques are introduced into classification.

Comparative study of laser-induced graphene fabricated in atmospheric and interface-confined environments

Laser-induced graphene (LIG) has found widespread applications in various carbon-based electronics, such as sensors, optoelectronics, and energy storage devices, due to its low cost, high efficiency, and large-scale fabrication potential. Here, two laser-induced carbonization techniques are investigated in terms of structural integrity (uniformity and densification) and electrical property by a combined experimental and theoretical approach; these techniques, namely interface and surface ablation, operate in confined and ambient environments, respectively. The property of LIG for each laser-induced carbonization technique is systematically studied using optical and electrical characterization methods. The results show that the naturally confined and oxygen-free environment of interface ablation can fabricate more compact and intact LIG than surface ablation in an open and oxygen environment, thus enabling a 7.6 times reduction of the square/sheet resistance. The underlying mechanism for these improved properties is the compressive thermal stress and higher carbonization efficiency of interface ablation. The better structural integrity and electrical property of interface-ablated graphene enable a four-fold improvement in the specific areal capacitance of supercapacitors. These findings present that interface ablation is a more effective and facile method to enable the scalable preparation of intact and highly conductive LIG for its potential use in high-performance carbon-based electronics.

Ex Vivo Lenticule Customization for Stromal Lenticule Addition Keratoplasty.

The purpose of this study was to explore the optimal shape of customized lenticules for stromal lenticule addition keratoplasty (SLAK) for off-centered ectasia. Two different methods to create ex vivo models of eccentric-keratoconus were investigated. Twelve human corneas were used to create model 1 by a hyperopic photorefractive keratectomy (PRK), and model 2 by masked phototherapeutic keratectomy (PTK) on the anterior corneal surface, whereas both types received myopic ablation of the posterior surface. Keratoconus models underwent a modified femtosecond laser (FSL) flap-cut to create stromal pockets. Sixteen human corneas underwent FSL dissection to obtain four lenticule types: type I (planar) and type II (negative) lenticules were used without modifications, whereas type III (customized-planar), and type IV (customized-negative) lenticules underwent further masked-PRK to obtain an asymmetric bow-tie shape. Topographic, aberrometric analysis, and anterior segment optical coherence tomography (AS-OCT) were performed in all recipient corneas before and after lenticule implantation. Keratoconus model was successfully reproduced. Tomographic analysis showed a significant inferiorly decentered corneal steepening with coherent stromal thinning. Model 2 reproduced better the curvature of real keratoconus. Lenticules type I implantation induced a homogeneous corneal thickening, type III produced higher thickening in the inferior half of the cornea. Type II determined a maximal peripheral pachymetric increase, with a gradual reduction toward the center, and type IV presented an asymmetric peripheral thickening. Topographic assessment showed a cone apex flattening in all cases, but it was significantly higher in types II and IV. Customized lenticules improved significantly corneal surface regularity regarding types I and II. The approach of customizing lenticules by increasing their asymmetry and tailoring the re-shaping effects, may improve SLAK outcomes in eccentric keratoconus.

Late Onset Corneal Haze Post Photorefractive Keratectomy

Introduction: Photorefractive keratectomy (PRK) is a surface ablation procedure to correct refractive errors. Regardless of the safety and efficacy, corneal haze may occur after PRK, and it remains one of the most feared complications because it can impair good visual outcomes. Case Presentation: A 20-year-old woman complained of blurred vision in her right eye (RE) after undergoing PRK elsewhere six months before admission with a history of refraction of S-12.75 C-1.75 x 10° preoperatively and S-0.75 postoperatively. Six-month postoperative uncorrected visual acuity (UCVA) was 0.01, best corrected visual acuity (BCVA) was 0.5 with S-7.00 C-0.75 x 50°. A slit lamp examination revealed grade three corneal haze. Anterior optical coherence tomography (OCT) showed the hyperreflective area with 132 μm deep into the stroma. The patient underwent phototherapeutic keratectomy (PTK) and mitomycin-C (MMC) treatment to a depth of 50 μm Ø6.5mm transition zone 0.5 mm. Two months later, UCVA was 0.2, BCVA was 0.63 with S-2.50 C-0.50 x 90°, and slit lamp examination revealed no haze remaining. Conclusions: This case illustrates the potential risk for corneal haze development, mainly when PRK is performed at greater treatment depths. However, with phototherapeutic keratectomy and mitomycin-C treatment, an excellent visual outcome and vision restoration can be obtained.