ers ▁typically ▁allow ▁for ▁the ▁rotation ▁of ▁a ▁sample ▁by ▁a ▁desired ▁angle , ▁multiple ▁views ▁of ▁the ▁same ▁spec imen ▁can ▁be ▁obtained ▁by ▁rot ating ▁the ▁angle ▁of ▁the ▁sample ▁along ▁an ▁axis ▁per pend icular ▁to ▁the ▁beam . ▁By ▁taking ▁multiple ▁images ▁of ▁a ▁single ▁T EM ▁sample ▁at ▁differ ing ▁angles , ▁typically ▁in ▁ 1 ° ▁incre ments , ▁a ▁set ▁of ▁images ▁known ▁as ▁a ▁" til t ▁series " ▁can ▁be ▁collected . ▁This ▁method ology ▁was ▁proposed ▁in ▁the ▁ 1 9 7 0 s ▁by ▁Walter ▁Ho ppe . ▁Under ▁purely ▁absor ption ▁contrast ▁conditions , ▁this ▁set ▁of ▁images ▁can ▁be ▁used ▁to ▁construct ▁a ▁three - dimensional ▁representation ▁of ▁the ▁sample . ▁ ▁The ▁reconst ruction ▁is ▁accomplished ▁by ▁a ▁two - step ▁process , ▁first ▁images ▁are ▁aligned ▁to ▁account ▁for ▁errors ▁in ▁the ▁position ing ▁of ▁a ▁sample ; ▁such ▁errors ▁can ▁occur ▁due ▁to ▁v ibration ▁or ▁mechanical ▁dr ift . ▁Al ignment ▁methods ▁use ▁image ▁registration ▁algorithms , ▁such ▁as ▁aut oc or relation ▁methods ▁to ▁correct ▁these ▁errors . ▁Second ly , ▁using ▁a ▁reconst ruction ▁algorithm , ▁such ▁as ▁filtered ▁back ▁projection , ▁the ▁aligned ▁image ▁s lices ▁can ▁be ▁transformed ▁from ▁a ▁set ▁of ▁two - dimensional ▁images , ▁I j ( x ,   y ), ▁to ▁a ▁single ▁three - dimensional ▁image , ▁I ' j ( x ,   y ,   z ). ▁This ▁three - dimensional ▁image ▁is ▁of