In this study,the potential application of shaped charge jets as transient antennas for electromagnetic signal transmission was explored and an electromagnetic pulse radiation system with a shaped charge jet as a tran...In this study,the potential application of shaped charge jets as transient antennas for electromagnetic signal transmission was explored and an electromagnetic pulse radiation system with a shaped charge jet as a transient antenna was proposed.During the research,crucial characteristics of the transient antenna formed by a shaped charge with a 30 mm diameter,such as resonant frequency,radiation pattern,and radiation efficiency,were evaluated.The typical shaped charge jet morphology was obtained based on the simulations,in which it could insight the dynamic behavior of the shaped charge jet selected.An equivalent model experiment was employed to test the radiation efficiency,and it showed that a shorting pin loading method could increase the relative bandwidth of the jet antenna to 32.8%,and the experimental results correlate with the theoretical predictions for half-wave dipole antennas reasonably well.Additionally,variations in the diameter of the shaped charge jet were found to affect the input impedance and impedance bandwidth,while the length of the jet influenced the resonant frequency of the antenna.This suggests that altering these parameters can achieve reconfigurability of the jet antenna.展开更多
Shaped charge has been widely used for penetrating concrete.However,due to the obvious difference between the propagation of shock waves and explosion products in water and air,the theory governing the formation of sh...Shaped charge has been widely used for penetrating concrete.However,due to the obvious difference between the propagation of shock waves and explosion products in water and air,the theory governing the formation of shaped charge jets in water as well as the underwater penetration effect of concrete need to be studied.In this paper,we introduced a modified forming theory of an underwater hemispherical shaped charge,and investigated the behavior of jet formation and concrete penetration in both air and water experimentally and numerically.The results show that the modified jet forming theory predicts the jet velocity of the hemispherical liner with an error of less than 10%.The underwater jets exhibit at least 3%faster and 11%longer than those in air.Concrete shows different failure modes after penetration in air and water.The depth of penetration deepens at least 18.75%after underwater penetration,accompanied by deeper crater with 65%smaller radius.Moreover,cracks throughout the entire target are formed,whereas cracks exist only near the penetration hole in air.This comprehensive study provides guidance for optimizing the structure of shaped charge and improves the understanding of the permeability effect of concrete in water.展开更多
The cavity characteristics in liquid-filled containers caused by high-velocity impacts represent an important area of research in hydrodynamic ram phenomena.The dynamic expansion of the cavity induces liquid pressure ...The cavity characteristics in liquid-filled containers caused by high-velocity impacts represent an important area of research in hydrodynamic ram phenomena.The dynamic expansion of the cavity induces liquid pressure variations,potentially causing catastrophic damage to the container.Current studies mainly focus on non-deforming projectiles,such as fragments,with limited exploration of shaped charge jets.In this paper,a uniquely experimental system was designed to record cavity profiles in behind-armor liquid-filled containers subjected to shaped charge jet impacts.The impact process was then numerically reproduced using the explicit simulation program ANSYS LS-DYNA with the Structured Arbitrary Lagrangian-Eulerian(S-ALE)solver.The formation mechanism,along with the dimensional and shape evolution of the cavity was investigated.Additionally,the influence of the impact kinetic energy of the jet on the cavity characteristics was analyzed.The findings reveal that the cavity profile exhibits a conical shape,primarily driven by direct jet impact and inertial effects.The expansion rates of both cavity length and maximum radius increase with jet impact kinetic energy.When the impact kinetic energy is reduced to 28.2 kJ or below,the length-to-diameter ratio of the cavity ultimately stabilizes at approximately 7.展开更多
An analysis of the interaction mechanisms between a Shaped Charge Jet(SCJ) and a single Moving Plate(MP) is proposed in this article using both experimental and numerical approaches. First, an experimental set-up is p...An analysis of the interaction mechanisms between a Shaped Charge Jet(SCJ) and a single Moving Plate(MP) is proposed in this article using both experimental and numerical approaches. First, an experimental set-up is presented. Four collision tests have been performed: two tests in Backward Moving Plate(BMP) configuration, where the plate moves in opposition to jet, and two tests in Forward Moving Plate(FMP) configuration, where the plate moves alongside the jet. Based on the virtual origin approximation,a methodology(the Virtual Origin Method, VOM) is developed to extract quantities from the X-ray images, which serve as comparative data. γSPH simulations are carried out to complete the analysis, as they well capture the disturbance dynamics observed in the experiments. Based on these complementary experimental and numerical results, a new physical description is proposed through a detailed analysis of the interaction. It is shown that the SCJ/MP interaction is driven at first order by the contact geometry. Thus, BMP and FMP configurations do not generate the same disturbances because their local flow geometries are different. In the collision point frame of reference, the BMP flows in the same direction as the jet, causing its overall deflection. On the contrary, the FMP flow opposes that of the jet leading to an alternative creation of fragments and ligaments. An in-depth study, using the VOM shows that deflection angles, fragment-ligament creation frequencies, and deflection velocities evolve as the interaction progresses through slower jet elements.展开更多
The Explosive Reactive Armors(ERA)are really efficient at reducing Shaped Charge Jet(SCJ)performance.The main destabilizing mechanism is the transverse movement of the front and rear moving plates(MP)on the SCJ.Theref...The Explosive Reactive Armors(ERA)are really efficient at reducing Shaped Charge Jet(SCJ)performance.The main destabilizing mechanism is the transverse movement of the front and rear moving plates(MP)on the SCJ.Therefore,a good understanding of the interaction SCJ/MP is essential for improving both weapon and armor systems.In a previous article,we have shown that interaction regimes are mainly influenced by the local collision geometry.Thus,in the collision point frame,the angle of collision be-tween the continuous SCJ and the MP is a key parameter.This flow angle is acute for the Backward Moving plate(BMP)moving against the SCJ and obtuse for the Forward Moving Plate(FMP)moving alongside it.In the former,the jet is simply deflected,which is the regime 1 of deflection.In the latter,the interaction turns on an alternative creation of fragment and ligament,which is the regime 2.Fragments are parts of the jet that are only slightly deflected while ligaments are the curved material bridges that connect two consecutive fragments.When stretching,the jet is systematically subject to instabilities that disturb its surface,creating necks along it.Their growth finally leads to the jet fragmentation.In this article,we focus on this jet distur-bance and its consequences on the SCJ/MP interaction.An experimental set-up was built to implement the interaction between a SCJ and a moving plate for different collision points,at different stand-off distances.The plate can interact with a smooth SCJ or a disturbed SCJ at a close and a far stand-off distance,respectively.One of the main results is the visualization of a regime change in SCJ/BMP interaction.A regime 1(deflection)interaction changes into a ligament regime interaction(similar to a FMP regime 2)when the collision point stand-off is increased.It is proposed that this change can be attributed as the increase of the amplitude of the jet surface disturbances.This phenomenon is well captured by the gSPH simula-tions.Finally,using both experimental and numerical approaches,we propose a new detailed analysis of the different phenomena occurring during the interaction between a disturbed-surface jet and a moving plate.Interaction regime changes are linked to jet local geometry changes.The interactions of a BMP with a smooth SCJ or with a disturbed surface SCJ are geometrically not the same and,thus,generate different local flows and interaction mechanisms.However,some other simulations have been carried out with constant velocity jet whose surface has been previously disturbed.These simulations underline the influence of both disturbance wavelength l and amplitude A on the interaction regimes.Surface disturbances of the SCJ,linked to its stretching,have a major influence on its interaction with a moving plate.展开更多
Reactive armour is a very efficient add-on armour against shaped charge threats.Explosive reactive armour consists of one or several plates that are accelerated by an explosive.Similar but less violent acceleration of...Reactive armour is a very efficient add-on armour against shaped charge threats.Explosive reactive armour consists of one or several plates that are accelerated by an explosive.Similar but less violent acceleration of plates can also be achieved in a completely inert reactive armour.To be efficient against elongated jets,the motion of the plates needs to be inclined against the jet such that a sliding contact between the jet and the plates is established.This sliding contact causes a deflection and thinning of the jet.Under certain circumstances,the contact will become unstable,leading to severe disturbances on the jet.These disturbances will drastically reduce the jet penetration performance and it is therefore of interest to study the conditions that leads to an unstable contact.Previous studies on the interaction between shaped charge jets and flyer plates have shown that it is mainly the forward moving plate in an explosive reactive armour that is effective in disturbing the jet.This is usually attributed to the higher plate-to-jet mass flux ratio involved in the collision of the forward moving plate compared to the backward moving plate.For slow moving plates,as occurs in inert reactive armour,the difference in mass flux for the forward and backward moving plate is much lesser,and it is therefore of interest to study if other factors than the mass flux influences on the protection capability.In this work,experiments have been performed where a plate is accelerated along its length,interacting with a shaped charge jet that is fired at an oblique angle to the plate’s normal,either against or along the plate’s velocity.The arrangement corresponds to a jet interacting with a flyer plate from a reactive armour,with the exception that the collision velocity is the same for both types of obliquities in these experiments.The experiments show that disturbances on the jet are different in the two cases even though the collision velocities are the same.Numerical simulations of the interaction support the observation.The difference is attributed to the character of the contact pressure in the interaction region.For a backward moving plate,the maximum contact pressure is obtained at the beginning of the interaction zone and the contact pressure is therefore higher upstream than downstream of the jet while the opposite is true for a forward moving plate.A negative interface pressure gradient with respect to the jet motion results in a more stable flow than a positive,which means that the jet-plate contact is more stable for a backward moving plate than for a forward moving plate.A forward moving plate is thus more effective in disturbing the jet than a backward moving plate,not only because of the higher jet to plate mass flux ratio but also because of the character of the contact with the jet.展开更多
Shaped charge liner(SCL)has been extensively applied in oil recovery and defense industries.Achieving superior penetration capability through optimizing SCL structures presents a substantial challenge due to intricate...Shaped charge liner(SCL)has been extensively applied in oil recovery and defense industries.Achieving superior penetration capability through optimizing SCL structures presents a substantial challenge due to intricate rate-dependent processes involving detonation-driven liner collapse,high-speed jet stretching,and penetration.This study introduces an innovative optimization strategy for SCL structures that employs jet penetration efficiency as the primary objective function.The strategy combines experimentally validated finite element method with machine learning(FEM-ML).We propose a novel jet penetration efficiency index derived from enhanced cutoff velocity and shape characteristics of the jet via machine learning.This index effectively evaluates the jet penetration performance.Furthermore,a multi-model fusion based on a machine learning optimization method,called XGBOOST-MFO,is put forward to optimize SCL structure over a large input space.The strategy's feasibility is demonstrated through the optimization of copper SCL implemented via the FEM-ML strategy.Finally,this strategy is extended to optimize the structure of the recently emerging CrMnFeCoNi high-entropy alloy conical liners and hemispherical copper liners.Therefore,the strategy can provide helpful guidance for the engineering design of SCL.展开更多
Testing rocket and space technology objects in ground conditions for resistance to the impact of meteoroids and fragments of space debris can be carried out using shaped charges. To substantiate the design parameters ...Testing rocket and space technology objects in ground conditions for resistance to the impact of meteoroids and fragments of space debris can be carried out using shaped charges. To substantiate the design parameters of shaped charges that ensure the formation of aluminum particles in a wide velocity range(from 2.5 to 16 km/s), numerical modeling of the formation process was carried out within the framework of a two-dimensional axisymmetric problem of continuum mechanics using three different computing codes to increase the reliability of the results. The calculations consider shaped charges with a diameter of 20-100 mm with aluminum liners of various shapes. It is shown that the formation of particles with velocities close to the lower limit of the considered range is ensured by gently sloping segmental liners of degressive thickness. To form higher-velocity particles with velocities over 5 km/s, it is proposed to use combined liners, the jet-forming part of which has the shape of a hemisphere of constant thickness or the shape of a semi-ellipsoid or semi-superellipsoid of rotation of degressive thickness.展开更多
In order to accurately measure an object’s three-dimensional surface shape,the influence of sampling on it was studied.First,on the basis of deriving spectra expressions through the Fourier transform,the generation o...In order to accurately measure an object’s three-dimensional surface shape,the influence of sampling on it was studied.First,on the basis of deriving spectra expressions through the Fourier transform,the generation of CCD pixels was analyzed,and its expression was given.Then,based on the discrete expression of deformation fringes obtained after sampling,its Fourier spectrum expression was derived,resulting in an infinitely repeated"spectra island"in the frequency domain.Finally,on the basis of using a low-pass filter to remove high-order harmonic components and retaining only one fundamental frequency component,the inverse Fourier transform was used to reconstruct the signal strength.A method of reducing the sampling interval,i.e.,reducing the number of sampling points per fringe,was proposed to increase the ratio between the sampling frequency and the fundamental frequency of the grating.This was done to reconstruct the object’s surface shape more accurately under the condition of m>4.The basic principle was verified through simulation and experiment.In the simulation,the sampling intervals were 8 pixels,4 pixels,2 pixels,and 1 pixel,the maximum absolute error values obtained in the last three situations were 88.80%,38.38%,and 31.50%in the first situation,respectively,and the corresponding average absolute error values are 71.84%,43.27%,and 32.26%.It is demonstrated that the smaller the sampling interval,the better the recovery effect.Taking the same four sampling intervals in the experiment as in the simulation can also lead to the same conclusions.The simulated and experimental results show that reducing the sampling interval can improve the accuracy of object surface shape measurement and achieve better reconstruction results.展开更多
基金supported by the"Fundamental Research Funds for the Central Universities"(Grant No.30924010801).
文摘In this study,the potential application of shaped charge jets as transient antennas for electromagnetic signal transmission was explored and an electromagnetic pulse radiation system with a shaped charge jet as a transient antenna was proposed.During the research,crucial characteristics of the transient antenna formed by a shaped charge with a 30 mm diameter,such as resonant frequency,radiation pattern,and radiation efficiency,were evaluated.The typical shaped charge jet morphology was obtained based on the simulations,in which it could insight the dynamic behavior of the shaped charge jet selected.An equivalent model experiment was employed to test the radiation efficiency,and it showed that a shorting pin loading method could increase the relative bandwidth of the jet antenna to 32.8%,and the experimental results correlate with the theoretical predictions for half-wave dipole antennas reasonably well.Additionally,variations in the diameter of the shaped charge jet were found to affect the input impedance and impedance bandwidth,while the length of the jet influenced the resonant frequency of the antenna.This suggests that altering these parameters can achieve reconfigurability of the jet antenna.
基金supported by the National Science Foundation of China(Grant Nos.12372361,12102427,12372335 and 12102202)the Fundamental Research Funds for the Central Universities(Grant No.30923010908)Postgraduate Research&Practice Innovation Program of Jiangsu Province(Grant No.KYCX23_0520).
文摘Shaped charge has been widely used for penetrating concrete.However,due to the obvious difference between the propagation of shock waves and explosion products in water and air,the theory governing the formation of shaped charge jets in water as well as the underwater penetration effect of concrete need to be studied.In this paper,we introduced a modified forming theory of an underwater hemispherical shaped charge,and investigated the behavior of jet formation and concrete penetration in both air and water experimentally and numerically.The results show that the modified jet forming theory predicts the jet velocity of the hemispherical liner with an error of less than 10%.The underwater jets exhibit at least 3%faster and 11%longer than those in air.Concrete shows different failure modes after penetration in air and water.The depth of penetration deepens at least 18.75%after underwater penetration,accompanied by deeper crater with 65%smaller radius.Moreover,cracks throughout the entire target are formed,whereas cracks exist only near the penetration hole in air.This comprehensive study provides guidance for optimizing the structure of shaped charge and improves the understanding of the permeability effect of concrete in water.
基金financial support from the National Natural Science Foundation of China(Grant No.11572159).
文摘The cavity characteristics in liquid-filled containers caused by high-velocity impacts represent an important area of research in hydrodynamic ram phenomena.The dynamic expansion of the cavity induces liquid pressure variations,potentially causing catastrophic damage to the container.Current studies mainly focus on non-deforming projectiles,such as fragments,with limited exploration of shaped charge jets.In this paper,a uniquely experimental system was designed to record cavity profiles in behind-armor liquid-filled containers subjected to shaped charge jet impacts.The impact process was then numerically reproduced using the explicit simulation program ANSYS LS-DYNA with the Structured Arbitrary Lagrangian-Eulerian(S-ALE)solver.The formation mechanism,along with the dimensional and shape evolution of the cavity was investigated.Additionally,the influence of the impact kinetic energy of the jet on the cavity characteristics was analyzed.The findings reveal that the cavity profile exhibits a conical shape,primarily driven by direct jet impact and inertial effects.The expansion rates of both cavity length and maximum radius increase with jet impact kinetic energy.When the impact kinetic energy is reduced to 28.2 kJ or below,the length-to-diameter ratio of the cavity ultimately stabilizes at approximately 7.
基金supported by the Ministère des Armées,and the Agence de l'Innovation de Défense(AID).
文摘An analysis of the interaction mechanisms between a Shaped Charge Jet(SCJ) and a single Moving Plate(MP) is proposed in this article using both experimental and numerical approaches. First, an experimental set-up is presented. Four collision tests have been performed: two tests in Backward Moving Plate(BMP) configuration, where the plate moves in opposition to jet, and two tests in Forward Moving Plate(FMP) configuration, where the plate moves alongside the jet. Based on the virtual origin approximation,a methodology(the Virtual Origin Method, VOM) is developed to extract quantities from the X-ray images, which serve as comparative data. γSPH simulations are carried out to complete the analysis, as they well capture the disturbance dynamics observed in the experiments. Based on these complementary experimental and numerical results, a new physical description is proposed through a detailed analysis of the interaction. It is shown that the SCJ/MP interaction is driven at first order by the contact geometry. Thus, BMP and FMP configurations do not generate the same disturbances because their local flow geometries are different. In the collision point frame of reference, the BMP flows in the same direction as the jet, causing its overall deflection. On the contrary, the FMP flow opposes that of the jet leading to an alternative creation of fragments and ligaments. An in-depth study, using the VOM shows that deflection angles, fragment-ligament creation frequencies, and deflection velocities evolve as the interaction progresses through slower jet elements.
基金supported by the Ministère des Arméesthe Agence de l'Innovation de Défense (AID)
文摘The Explosive Reactive Armors(ERA)are really efficient at reducing Shaped Charge Jet(SCJ)performance.The main destabilizing mechanism is the transverse movement of the front and rear moving plates(MP)on the SCJ.Therefore,a good understanding of the interaction SCJ/MP is essential for improving both weapon and armor systems.In a previous article,we have shown that interaction regimes are mainly influenced by the local collision geometry.Thus,in the collision point frame,the angle of collision be-tween the continuous SCJ and the MP is a key parameter.This flow angle is acute for the Backward Moving plate(BMP)moving against the SCJ and obtuse for the Forward Moving Plate(FMP)moving alongside it.In the former,the jet is simply deflected,which is the regime 1 of deflection.In the latter,the interaction turns on an alternative creation of fragment and ligament,which is the regime 2.Fragments are parts of the jet that are only slightly deflected while ligaments are the curved material bridges that connect two consecutive fragments.When stretching,the jet is systematically subject to instabilities that disturb its surface,creating necks along it.Their growth finally leads to the jet fragmentation.In this article,we focus on this jet distur-bance and its consequences on the SCJ/MP interaction.An experimental set-up was built to implement the interaction between a SCJ and a moving plate for different collision points,at different stand-off distances.The plate can interact with a smooth SCJ or a disturbed SCJ at a close and a far stand-off distance,respectively.One of the main results is the visualization of a regime change in SCJ/BMP interaction.A regime 1(deflection)interaction changes into a ligament regime interaction(similar to a FMP regime 2)when the collision point stand-off is increased.It is proposed that this change can be attributed as the increase of the amplitude of the jet surface disturbances.This phenomenon is well captured by the gSPH simula-tions.Finally,using both experimental and numerical approaches,we propose a new detailed analysis of the different phenomena occurring during the interaction between a disturbed-surface jet and a moving plate.Interaction regime changes are linked to jet local geometry changes.The interactions of a BMP with a smooth SCJ or with a disturbed surface SCJ are geometrically not the same and,thus,generate different local flows and interaction mechanisms.However,some other simulations have been carried out with constant velocity jet whose surface has been previously disturbed.These simulations underline the influence of both disturbance wavelength l and amplitude A on the interaction regimes.Surface disturbances of the SCJ,linked to its stretching,have a major influence on its interaction with a moving plate.
基金funded by the Swedish Armed Forces under Contract No AT.9220620。
文摘Reactive armour is a very efficient add-on armour against shaped charge threats.Explosive reactive armour consists of one or several plates that are accelerated by an explosive.Similar but less violent acceleration of plates can also be achieved in a completely inert reactive armour.To be efficient against elongated jets,the motion of the plates needs to be inclined against the jet such that a sliding contact between the jet and the plates is established.This sliding contact causes a deflection and thinning of the jet.Under certain circumstances,the contact will become unstable,leading to severe disturbances on the jet.These disturbances will drastically reduce the jet penetration performance and it is therefore of interest to study the conditions that leads to an unstable contact.Previous studies on the interaction between shaped charge jets and flyer plates have shown that it is mainly the forward moving plate in an explosive reactive armour that is effective in disturbing the jet.This is usually attributed to the higher plate-to-jet mass flux ratio involved in the collision of the forward moving plate compared to the backward moving plate.For slow moving plates,as occurs in inert reactive armour,the difference in mass flux for the forward and backward moving plate is much lesser,and it is therefore of interest to study if other factors than the mass flux influences on the protection capability.In this work,experiments have been performed where a plate is accelerated along its length,interacting with a shaped charge jet that is fired at an oblique angle to the plate’s normal,either against or along the plate’s velocity.The arrangement corresponds to a jet interacting with a flyer plate from a reactive armour,with the exception that the collision velocity is the same for both types of obliquities in these experiments.The experiments show that disturbances on the jet are different in the two cases even though the collision velocities are the same.Numerical simulations of the interaction support the observation.The difference is attributed to the character of the contact pressure in the interaction region.For a backward moving plate,the maximum contact pressure is obtained at the beginning of the interaction zone and the contact pressure is therefore higher upstream than downstream of the jet while the opposite is true for a forward moving plate.A negative interface pressure gradient with respect to the jet motion results in a more stable flow than a positive,which means that the jet-plate contact is more stable for a backward moving plate than for a forward moving plate.A forward moving plate is thus more effective in disturbing the jet than a backward moving plate,not only because of the higher jet to plate mass flux ratio but also because of the character of the contact with the jet.
基金supported by the NSFC Basic Science Center Program for"Multi-scale Problems in Nonlinear Mechanics" (Grant No.11988102)the NSFC (Grant Nos.U2141204,12172367)+2 种基金the Key Research Program of the Chinese Academy of Sciences (Grant No.ZDRW-CN-2021-2-3)the National Key Research and Development Program of China (Grant No.2022YFC3320504-02)the opening project of State Key Laboratory of Explosion Science and Technology (Grant No.KFJJ21-01 and No.KFJJ18-14 M)。
文摘Shaped charge liner(SCL)has been extensively applied in oil recovery and defense industries.Achieving superior penetration capability through optimizing SCL structures presents a substantial challenge due to intricate rate-dependent processes involving detonation-driven liner collapse,high-speed jet stretching,and penetration.This study introduces an innovative optimization strategy for SCL structures that employs jet penetration efficiency as the primary objective function.The strategy combines experimentally validated finite element method with machine learning(FEM-ML).We propose a novel jet penetration efficiency index derived from enhanced cutoff velocity and shape characteristics of the jet via machine learning.This index effectively evaluates the jet penetration performance.Furthermore,a multi-model fusion based on a machine learning optimization method,called XGBOOST-MFO,is put forward to optimize SCL structure over a large input space.The strategy's feasibility is demonstrated through the optimization of copper SCL implemented via the FEM-ML strategy.Finally,this strategy is extended to optimize the structure of the recently emerging CrMnFeCoNi high-entropy alloy conical liners and hemispherical copper liners.Therefore,the strategy can provide helpful guidance for the engineering design of SCL.
文摘Testing rocket and space technology objects in ground conditions for resistance to the impact of meteoroids and fragments of space debris can be carried out using shaped charges. To substantiate the design parameters of shaped charges that ensure the formation of aluminum particles in a wide velocity range(from 2.5 to 16 km/s), numerical modeling of the formation process was carried out within the framework of a two-dimensional axisymmetric problem of continuum mechanics using three different computing codes to increase the reliability of the results. The calculations consider shaped charges with a diameter of 20-100 mm with aluminum liners of various shapes. It is shown that the formation of particles with velocities close to the lower limit of the considered range is ensured by gently sloping segmental liners of degressive thickness. To form higher-velocity particles with velocities over 5 km/s, it is proposed to use combined liners, the jet-forming part of which has the shape of a hemisphere of constant thickness or the shape of a semi-ellipsoid or semi-superellipsoid of rotation of degressive thickness.
文摘In order to accurately measure an object’s three-dimensional surface shape,the influence of sampling on it was studied.First,on the basis of deriving spectra expressions through the Fourier transform,the generation of CCD pixels was analyzed,and its expression was given.Then,based on the discrete expression of deformation fringes obtained after sampling,its Fourier spectrum expression was derived,resulting in an infinitely repeated"spectra island"in the frequency domain.Finally,on the basis of using a low-pass filter to remove high-order harmonic components and retaining only one fundamental frequency component,the inverse Fourier transform was used to reconstruct the signal strength.A method of reducing the sampling interval,i.e.,reducing the number of sampling points per fringe,was proposed to increase the ratio between the sampling frequency and the fundamental frequency of the grating.This was done to reconstruct the object’s surface shape more accurately under the condition of m>4.The basic principle was verified through simulation and experiment.In the simulation,the sampling intervals were 8 pixels,4 pixels,2 pixels,and 1 pixel,the maximum absolute error values obtained in the last three situations were 88.80%,38.38%,and 31.50%in the first situation,respectively,and the corresponding average absolute error values are 71.84%,43.27%,and 32.26%.It is demonstrated that the smaller the sampling interval,the better the recovery effect.Taking the same four sampling intervals in the experiment as in the simulation can also lead to the same conclusions.The simulated and experimental results show that reducing the sampling interval can improve the accuracy of object surface shape measurement and achieve better reconstruction results.
