Correction of Distortion Aberration in Electron Magnetic Lenses

Transcription

1 SSRG Intenational Jounal of Applied Physics ( SSRG IJAP ) Volume 3 Issue May to Aug 016 Coection of Distotion Abeation in Electon Magnetic Lenses TalibMohsen Abbas Depatment of Physics, College of Education fo pue Sciences, Univesity of Babylon, PO Box 4, Hilla-Babylon, IRAQ consisted of cylindical double polepiece magnetic lenses[]. Afte that many studies have been submitted using simila pocedue in the ecent study but lenses wee, one was double pole piece and the othe wassingle polepiece by using cylindical polepiece[3],spheical polepieces [4] and cone polepieces with plane face [5]. With the woth to mention that all the pevious studies wee following the conventional pocedue in designing and studying the optical popeties of fee distotion doublet magnetic electon lenses. In fact, moden studies have appeaed ecently to tackle the subject of studying pojecto optical popeties of fee distotiondoublet magnetic lenses by using invese design and though suggesting of axial magnetic function like scala magnetic potential [6,7]. In this study, one of the known functions has been used in the field of electon optics to epesent the axial magnetic field of fee distotion doublet axial lens. II. MATHEMATICAL MODEL Using analytic mathematical function in this eseach as a taget function to epesent axial magnetic field fo magnetic lens and it's mathematical fom as follows: B max B ( )...(1) 1 ( ) W Fom the elation above it is noticed that this model is epesent distibution of axial magnetic flux density and it s a function of maximum magnetic flux density (B max ) and a half width of axial magnetic field(w) which epesent optimiation paametes in which can change the fom of the field, and () epesents the length of optical axial of the lens. This function has been used to have an axial magnetic field fo doublet lens whee the optical axial has been divided into two egions, the fist epesents the negative flux of the optical axial ( the field of the fist single lens) and the second egion epesents the positive flux ( the field of the second sigle lens). Hee each egion woks away alone,i.e, the taget function has been epesented values Z at B max1 and W 1 wheeas B max and W used to negative values. by changing the geometical and physical paamete fo its single lens. The equation which descibes Abstact In this eseach, a theoetical investigation had been done to study and coect distotion abeation which happened in electon magnetic lenses while it is used as pojecto lenses in tansmission electon micoscope. In this study, invese design had been used MATLAB envionment and by epesenting the axial magnetic field fo doublet magnetic lens with axial magnetic function as a taget function. Keywods: electon optics, electon magnetic lens, doublet magnetic lens. I. INTRODUCTION The pojecto magnetic lens is egaded as one of the most impotant lenses of tansmission electonic micoscope afte the objective lens which magnifying the image poduced by objective lens and falling on the sceen of electon micoscope, but this suffes fom defects which made fom distotion in the poduced image but it doesn't effect on esolving powe of micoscope. One of the most defects which appea on the image duing stating the lens beside its otation ound the optical axis is the adial and spial distotion.spial distotion is consideed as one of special defects of magnetic lenses due to the unequivalent otation of the image though adius of axial boe of the lens and it inceases convesely with the excitation of the lens. Because the pojecto lens woks at the minimum of its focal length to get the geatest magnifying fo the image, the spial distotion will be high at the excitations and to impove the quality of the final image, the distotion must be detected o educed. Among the ways which used in educing the spial distotion is using the doublet magnetic lens. The fist sincee tial to get id of adial and spial distotion in the image of electonic micoscope was done by Tsuno and Haada whee they designed a doublet magnetic lens with unequal axial boes which give in the fist otation distotion images and with a pecentage of spial distotion 0,07% [1]. Al Obadi was able to get images fee spial and adial distotion in the fist egion of otation only by designing doublet magneticlens In fact this situation gives the ability of changing doublet lens popeties o its opeational pefomance ISSN: Page 1

2 SSRG Intenational Jounal of Applied Physics ( SSRG IJAP ) Volume 3 Issue May to Aug 016 show half width of axial magnetic field. (W =,4,6,8,10 mm) with the constancy of the maximum magnetic flux density B max = -0.5 T. Figue (1) shown the distibutions of axial magnetic field B fo the doublet lens and it is noticed that the change of second lens field accoding to the change half width of axial magnetic field in addition to that, the figue explains that the distance between the cente of both lenses ( the fist and second) is fixed at 40mm and it is the focal length fo fist and second single lens and also the doublet when both lenses ae identical. The most featue of doublet lens fom the single is that having cuves of pojecto focal popeties (D s,d,f p ) two loops at the same peiod of excitation paamete NI/ SQRT(V). The fist otation called the fist magnification egion and the othe called second magnification egion. In this eseach, it has been teated with each otation in a single way egading that each one is epesenting independent opeation mode.pojecto lenses ae woking at minimum of pojecto focal length (F P ) min to get maximum magnification whee pojecto focal length is known as invese of electon beam tajectoy gadient afte penetation the lens field. Figue () shows cuves of pojecto focal length as a function ofexcitation paamete NI/SQRT(V ) in the fist otation egion 0.01NI/SQRT(V) 4.5 and fo each value of W. It is noticed fom the Figue that each cuve has minimumvalue in the fist otation egion (F P ) min1 and deceases with the incease values W, see table (1). The eason behind that is elated to deceases the values of electon motion in the magnetic field paaxial ays equation, which is given in: ( 8 e mv ) B 0 called the () epesents electon tajectoy inside magnetic field andv epesents elativistically coected acceleation voltage. In solving the paaxial ays equation numeically by using ( Rung-Kutta) fo the fouth ode, then electon tajectoy has been counted inside the magnetic lens at the initial conditions ( = 1, / = 0). Finally adial distotion coefficient has been counted (D )and spial (D s ) numeically by using technology of (Simpson's ule)[8] D D s 18 V f s 18 f s 4 B 3 B V ( )( ( ) 8 B 1 16 V ( ) ) d 3 / 1 / 3 3 V whee α ae solutions of paaxial ays equation. III. RESULTS AND DISCUSSIONS Optimiation paametes have been fixed fo the fist single B 3...( )...( 3) B d,......( 4 ) acceleation voltage(v ), and also noticed that the minimum of pojecto focal length in fist otation egion(f P ) min1 at value W =mm is equal to the distance between position magnetic of lens at the values W 1 =mm, B max1 =0.5 T ( axial maximum valuesof two fieldswhen the lenses ae identical magnetic field in the negative pat of optical axial) while in geometical figue. the second single lens ( axial magnetic field in the positive pat of optical axial),diffeent values have been chosen to Figue (1): Distibutions of Axial Magnetic Fieldfo Doublet Lens at The Diffeent Valuesof Half Width of Second Field W ISSN: Page

3 SSRG Intenational Jounal of Applied Physics ( SSRG IJAP ) Volume 3 Issue May to Aug 016 Figue ():Cuves of Pojecto Focal Length F p fo Doublet Lens as a Function of Excitation Paamete N1/SQRT(V ) in the Fist Rotation Regionat The Diffeent Values of Half Width of Second Field W B fo diffeent values of W. It is noticed hee that each cuve has a eosvalueof spial distotion coefficient D s which happens at diffeent excitation paamete and also noticed the inceasing W which leads to get eo spial distotion coefficient at the same excitation paamete which we get eo adial distotion and minimum value ofpojecto focal length at value W =6vmm, see table (1). Doublet magnetic lenses can be got fom the pevious infomation which give fee adialand spial distotion images at the same excitation paamete which gives minimum valueof the pojecto focal length in the fist otation egion and accoding suggested mathematical model in this study and at the following values: W 1 =mm, W =6mm,B max1 =0.5 T, B max = -0.5 T Cuves of adial distotion coefficient D has been dawn as function of excitation paamete NI/SQRT(V) in the fist otation egionand fo each distibution B as shown in figue (3), and it is noticed fom the figue that each cuve has eosvalue (D =0) happens at diffeent of excitation paamete and also noticed that adial distotion coefficient disappea at the same excitation paamete which gives minimum of pojecto focal length when both lenses ae identical and also at the value of half width W =6mm (i.e. both lenses ae not identical),see table (1). Figue (4) shows that cuves of spial distotion coefficient D s in fist otation egion as a function of excitation paamete fo each distibution ISSN: Page 3

4 SSRG Intenational Jounal of Applied Physics ( SSRG IJAP ) Volume 3 Issue May to Aug 016 Figue (3): Cuves adial distotion coefficientd fo doublet lens as a function of excitation paamete N1/SQRT(V ) in the fist otation egionat thediffeent values of half width of second field W Figue (4): Cuves spial distotion coefficientd s fo doublet lens as a function of excitation paamete N1/SQRT(V ) in the fist otation egionat thediffeent values of half width of second field W Table(1): Pojecto optical popeties of the doublet magnetic lens in fist otation egionat thediffeent values of half width of second field W ISSN: Page 4

5 SSRG Intenational Jounal of Applied Physics ( SSRG IJAP ) Volume 3 Issue May to Aug 016 At NI/V (1/) W (mm) (F p ) min1 mm (F p ) min1 D =0 D s = REFERENCES [1] Tsuno, K. and Haada Y. (1981b) "Elimination of Spial Distotion Electon in Micoscopy using an Asymmetical Tiple Polepiece Lens", J. Phys. E:Sci. Instum., 14, [] Al-Obadi, H N. (1991) "Design of Electomagnetic Lenses ". M.Sc. Thesis. Univesity of Al-Mustansiiya, Iaq, Baghdad. [3] Al-Saady, A K. (1996). "Computations on The Popeties of Magnetic Doublet Lenses fo The Tansmission Electon Micoscope ". Ph.D. Thesis. Univesity of Al-Mustansiiya, Iaq, Baghdad. [4] Zain-Alabdeen F. S. (1997). "Rotation an Distotion fee Spheical Tiple Polepiece pojecto Lenses ". M.Sc. Thesis. Univesity of Al-Mustansiiya, Iaq, Baghdad. [5] Al-Shummay, B. A. (00) "A Study of Distotion fo The Pojecto Lenses in The Tansmission Electon Micoscope ". M.Sc. Thesis. Univesity of Babylon, Iaq, Babylon. [6] Rashid M. H. and Malik C. (010)"New Magnetic Einel Lens and its Beam optical Featues ", Poc. Cyclotons, Lanhou, China [7] Rashid M. H. and Chakabaty A. (013)"Beam Optical Simulation in Poposed Magnetic Einel lens ", Poc. Cyclotons, Vancouve,Canada. [8] Silagyi, M. (1988) "Electon and Ion Optics",Plenum Pess: New Yok. [9] El-Kaeh, A. B. and El-Kaeh, J. C. (1970)"Electon BeamsLenses and Optics", vol. 1 and, Academic Pess: New Yok and London. IV. CONCLUSIONS In this study, we can conclude the following points: 1- Ability of using analytic mathematical functions to epesent axial magnetic field fo distotion fee doublet magnetic lens as a taget function in technology of establishing and with high efficiency. - Getting axial magnetic field fofee adialdistotion doublet magnetic lens at excitation paamete giving minimum valueof pojecto focal length in fist otation egion when the fields of lens ae equal with the value of half width and maximum value of axial magnetic flux density. 3- Getting axial magnetic field fo doublet magnetic lens fee adial and spial distotion at excitation paamete which happened at minimum pojecto focal length at the fist otation and at diffeent values fo half width of field and maximum of axial magnetic flux density to the field of the lens. ISSN: Page 5