▁more ▁kin emat ical ▁diff raction ▁patterns , ▁but ▁both ▁the ▁capabilities ▁of ▁the ▁beam ▁t ilt ▁co ils ▁in ▁the ▁mic ros cope ▁and ▁the ▁requirements ▁on ▁the ▁pro be ▁size ▁limit ▁how ▁large ▁this ▁angle ▁can ▁become ▁in ▁practice . ▁Because ▁P ED ▁takes ▁the ▁beam ▁off ▁of ▁the ▁opt ic ▁axis ▁by ▁design , ▁it ▁acc ent u ates ▁the ▁effect ▁of ▁the ▁spher ical ▁aber r ations ▁within ▁the ▁pro be ▁forming ▁l ens . ▁For ▁a ▁given ▁spher ical ▁aber r ation , ▁Cs , ▁the ▁pro be ▁diameter , ▁d , ▁var ies ▁with ▁convergence ▁angle , ▁α , ▁and ▁pre cess ion ▁angle , ▁ φ , ▁as ▁ ▁Thus , ▁if ▁the ▁spec imen ▁of ▁interest ▁is ▁quite ▁small , ▁the ▁maximum ▁pre cess ion ▁angle ▁will ▁be ▁rest rained . ▁This ▁is ▁most ▁significant ▁for ▁conditions ▁of ▁conver gent ▁beam ▁ill um ination . ▁ 5 0   nm ▁is ▁a ▁general ▁lower ▁limit ▁on ▁pro be ▁size ▁for ▁standard ▁T EM s ▁operating ▁at ▁high ▁pre cess ion ▁angles ▁( > 3 0   m rad ), ▁but ▁can ▁be ▁sur pass ed ▁in ▁Cs ▁corrected ▁instruments . ▁ ▁In ▁principle ▁the ▁minimum ▁pre cess ed ▁pro be ▁can ▁reach ▁approximately ▁the ▁full - width - half - max ▁( F WH M ) ▁of ▁the ▁conver ged ▁un - pre cess ed ▁pro be ▁in ▁any ▁instrument , ▁however ▁in ▁practice ▁the ▁effective ▁pre cess ed ▁pro be ▁is ▁typically ▁~ 1