▁The ▁contrast ▁transfer ▁function ▁can , ▁to ▁some ▁extent , ▁be ▁experiment ally ▁approxim ated ▁through ▁techniques ▁such ▁as ▁Fourier ▁transform ing ▁images ▁of ▁am orph ous ▁material , ▁such ▁as ▁am orph ous ▁carbon . ▁ ▁More ▁recently , ▁adv ances ▁in ▁aber r ation ▁correct or ▁design ▁have ▁been ▁able ▁to ▁reduce ▁spher ical ▁aber r ations ▁and ▁to ▁achieve ▁resolution ▁below ▁ 0 . 5 ▁Å ng str ö ms ▁( 5 0 ▁pm ) ▁at ▁magn ifications ▁above ▁ 5 0 ▁million ▁times . ▁Im pro ved ▁resolution ▁allows ▁for ▁the ▁imag ing ▁of ▁l ighter ▁atoms ▁that ▁scatter ▁electrons ▁less ▁efficiently , ▁such ▁as ▁l ith ium ▁atoms ▁in ▁l ith ium ▁battery ▁materials . ▁The ▁ability ▁to ▁determine ▁the ▁position ▁of ▁atoms ▁within ▁materials ▁has ▁made ▁the ▁H R TE M ▁an ▁ind isp ens able ▁tool ▁for ▁nan ote chn ology ▁research ▁and ▁development ▁in ▁many ▁fields , ▁including ▁heter ogeneous ▁catal ysis ▁and ▁the ▁development ▁of ▁sem icon duct or ▁devices ▁for ▁electron ics ▁and ▁phot on ics . ▁ ▁See ▁also ▁ ▁References ▁ ▁External ▁links ▁ ▁The ▁National ▁Center ▁for ▁Electron ▁Micro sc opy , ▁Ber keley ▁California ▁USA ▁The ▁National ▁Center ▁for ▁Mac rom ole cular ▁Im aging , ▁Houston ▁Texas ▁USA ▁The ▁National ▁Resource ▁for ▁Autom ated ▁M ole cular ▁Micro sc opy , ▁New ▁York ▁USA ▁T utorial ▁courses ▁in ▁Trans mission ▁Electron ▁Micro sc opy ▁Cambridge ▁University ▁Te aching ▁and ▁Learning ▁Package ▁on ▁T EM ▁Online ▁course ▁on ▁Trans