Ukuqonda iSampulu yeNyquist: Ukulinganisa i-Optical kunye neSigqibo seKhamera |

Kumfanekiso wedijithali, kulula ukucinga ukuba isisombululo esiphezulu ngokuzenzekelayo sithetha imifanekiso engcono. Abavelisi bekhamera bahlala bethengisa iinkqubo ezisekwe kumanani eemegapixel, ngelixa abenzi beelensi beqaqambisa ukusombulula amandla kunye nokubukhali. Nangona kunjalo, ekusebenzeni, umgangatho womfanekiso awuxhomekanga kuphela kwiinkcukacha zelensi okanye kwinzwa yodwa kodwa nakwindlela ehambelana ngayo.

Kulapho isampulu yeNyquist ingena khona. Ekuqaleni umgaqo wokusetyenzwa komqondiso, umgaqo kaNyquist ubeka isakhelo sethiyori ukuze ubambe iinkcukacha ngokuchanekileyo. Kumfanekiso, iqinisekisa ukuba isisombululo se-optical esiziswa ngelensi kunye nesisombululo sedijithali sesensom yekhamera sisebenza kunye ngokuhambelanayo.

Eli nqaku likhupha isampulu yeNyquist kumxholo wokucinga, ichaza ibhalansi phakathi kwesisombululo se-optical kunye nekhamera, kwaye ibonelela ngezikhokelo ezisebenzayo kwizicelo ezisusela kwifoto ukuya kumfanekiso wesayensi.

Yintoni iSampulu yeNyquist?

Umzobo 1: Ithiyori yesampulu yeNyquist

Phezulu:Isignali ye-sinusoidal (cyan) ilinganiswa, okanye isampuli, kumanqaku amaninzi. Umgca ompunga omde ubonisa umlinganiselo we-1 ngomjikelezo wesiginali ye-sinusoidal, ukubamba kuphela iincopho zesignali, ukufihla ngokupheleleyo ubume bokwenyani bomqondiso. Ijika elibomvu elicoliweyo libamba imilinganiselo ye-1.1 ngesampulu nganye, iveza i-sinusoid kodwa ibonakalisa kakubi ukuphindaphinda kwayo. Oku kufana nepateni kaMoiré.

Ezantsi:Kuphela xa iisampulu ezi-2 zithathwa kumjikelo ngamnye (umgca onamachaphaza amfusa) apho ubume bokwenyani bomqondiso buqala ukubanjwa.

Ithiyori yesampulu yeNyquist ngumgaqo oxhaphakileyo kuyo yonke inkqubo yesignali kwi-electronics, processing audio, imaging kunye namanye amacandelo. I-theorem yenza kucace ukuba ukwakhiwa kwakhona kwi-frequency enikiweyo kwisignali, imilinganiselo kufuneka yenziwe ubuncinane kabini loo maxesha, aboniswe kwi-Figure 1. Kwimeko yesisombululo sethu se-optical, oku kuthetha ukuba indawo yethu ye-pixel ubukhulu bendawo kufuneka ibe yincinci yeenkcukacha ezincinci esizama ukubamba, okanye, kwimeko ye-microscope, isiqingatha sesisombululo se-microscope.

Umzobo 2: Isampulu yeNyquist eneepikseli zesikwere: imiba yokuqhelaniswa

Ukusebenzisa ikhamera enegridi yeepikseli zesikwere, i-2x yesampling factor ye-Nyquist theorem iya kubamba ngokuchanekileyo kuphela iinkcukacha ezilungelelaniswe ngokugqibeleleyo kwigridi ye-pixel. Ukuba uzama ukusombulula izakhiwo kwi-engile kwigridi yepixel, ubungakanani bepixel obusebenzayo bukhulu, ukuya kuthi ga ku √2 umphinda-phinde mkhulu kwidiagonal. Ireyithi yesampulu ke ngoko kufuneka ibe ngama-2√2 umphinda-phindene we-spatial frequency oyifunayo ukuze ubambe iinkcukacha ngama-45o kwigridi yepixel.

Isizathu salokhu senziwa ngokucacileyo ngokuqwalaselwa koMfanekiso 2 (isiqingatha esiphezulu). Khawufane ucinge ukuba ubungakanani be-pixel bumiselwe kwisisombululo se-optical, sinika iincopho zemithombo yeendawo ezimbini ezingabamelwane, okanye naziphi na iinkcukacha esizama ukuzisombulula, nganye i-pixel yayo. Nangona ezi zithe zabhaqwa ngokwahlukeneyo, akukho nto ibonakalisayo kwimilinganiselo eneziphumo zokuba ziincopho ezimbini ezahlukeneyo – kwaye kwakhona inkcazelo yethu “yokusombulula” ayifikelelwanga. I-pixel phakathi iyafuneka, ibamba umkhombe wesignali. Oku kuphunyezwa ngokuphinda-phindwe kabini ireyithi yesampulu yesithuba, okt.

ISigqibo se-Optical vs. Isisombululo seKhamera

Ukuqonda indlela isampuli yeNyquist esebenza ngayo kwi-imaging, kufuneka sahlule phakathi kweentlobo ezimbini zesisombululo:

● I-Optical Resolution: Igqitywe yi-lens, i-optical resolution ibhekisela ekukwazini kwayo ukuvelisa iinkcukacha ezintle. Izinto ezinjengomgangatho welensi, ukuvuleka, kunye nokuphazamiseka kumisa lo mda. Umsebenzi wodluliselo lokumodareyitha (MTF) ukholisa ukusetyenziswa ukulinganisa ukuba ilensi iwugqithisa kakuhle kangakanani na umahluko kumaza ohlukeneyo esithuba.

● Isisombululo seKhamera: Igqitywe sisiva, isisombululo sekhamera sixhomekeke kubungakanani bepixel, i-pixel pitch, kunye ne-sensor dimensions jikelele. Ipixel inowuthi yeIkhamera yeCMOSichaza ngokuthe ngqo i-Nyquist frequency, emisela ezona nkcukacha ziphezulu inzwa inokubamba.

Xa ezi zimbini zingahambelani, kuvela iingxaki. I-lens edlula amandla okusombulula i-sensor "ichithwe" ngokufanelekileyo, kuba inzwa ayikwazi ukubamba zonke iinkcukacha. Ngakolunye uhlangothi, i-sensor-resolution ephezulu edityaniswe ne-lens ekumgangatho ophantsi iphumela kwimifanekiso engaphucukanga nangona kukho iimegapixel ezininzi.

Indlela yokulinganisa iOptical kunye neCamera Resolution

Ukulinganisa i-optics kunye ne-sensor kuthetha ukuhambelana ne-Nyquist frequency ye-sensor kunye ne-optical cutoff frequency ye-lens.

● I-Nyquist frequency ye-sensor yekhamera ibalwa njenge-1 / (2 × iphikseli pitch). Oku kuchaza elona xesha liphezulu lesithuba isivamvo esinokusampula ngaphandle kokunyelisa.
● I-optical cutoff frequency ixhomekeke kwiimpawu zelensi kunye nokwahluka.

Ukufumana iziphumo ezingcono, i-Nyquist ye-sensor frequency kufuneka ihambelane okanye igqithise kancinane isakhono sokusombulula iilensi. Ngokwenyani, umthetho olungileyo wesithupha kukuqinisekisa ukuba iphikseli inowuthi imalunga nesiqingatha selona phawu luncinci lunokulungiswa kwilensi.

Umzekelo, ukuba i-lens inokusombulula iinkcukacha ukuya kutsho kwi-4 micrometers, ngoko inzwa enobungakanani bepixel ye ~ 2 micrometers iya kulungelelanisa inkqubo kakuhle.

Ukutshatisa iNyquist kunye neSisombululo seKhamera kunye noCelomngeni lweePixels zesikwere

Ukurhweba kunye nokuncipha kwesayizi yephikseli yendawo kuyancipha isakhono sokuqokelela ukukhanya. Ngoko ke kubalulekile ukulinganisa imfuno yesisombululo kunye nokuqokelela ukukhanya. Ukongeza, ubungakanani bephikseli yendawo enkulu yento buthanda ukuhambisa indawo enkulu yokujonga isifundo somfanekiso. Kwizicelo ezinemfuno ethile yesisombululo esihle, 'umthetho wesithupha' ulungelelwaniso oluphezulu luchazwa ngolu hlobo lulandelayo: Ubungakanani bephikseli yendawo yento, xa iphinda-phindwe yinto ethile ukuze i-akhawunti yeNyquist, kufuneka ilingane nesisombululo sokukhanya. Lo bungakanani bubizwa ngokuba yisisombululo sekhamera.

Ukulinganisa i-Optics kunye ne-sensors zihlala zihla ukuze ziqinisekise ukuba isisombululo esisebenzayo sesampulu sekhamera sihambelana nomda wesisombululo se-lens. Inkqubo kuthiwa "iyahambelana neNyquist" xa:

Isisombululo sekhamera = Isisombululo esibonakalayo

Apho isisombululo sekhamera sinikezelwa ngu:

Isizathu sokuba i-akhawunti yeNyquist edla ngokucetyiswa ngu-2.3, kungekhona i-2. Isizathu soku silandelayo.

Iiphikseli zekhamera zi (ngokuqhelekileyo) isikwere, kwaye zicwangciswe kwigridi ye-2-D. Ubungakanani bepikseli njengoko buchaziweyo bokusetyenziswa kwinxaki echasayo imele ububanzi beepixels ecaleni kweeks zale gridi. Ukuba iimpawu esizama ukuzisombulula zilele nakweyiphi na i-engile ngaphandle kokuphindwa ngokugqibeleleyo kwe-90° ngokunxulumene nale gridi, ubungakanani bepixel obusebenzayo buya kuba bukhulu, ukuya kuthi ga ku√2 ≈ 1.41 umphinda-phinde ngobungakanani bepixel ku-45°. Oku kuboniswe kuMfanekiso 2 (isiqingatha esisezantsi).

Umba ocetyiswayo ngokwekhrayitheriya yeNyquist kuzo zonke izikhokelo iya kuba yi-2√2 ≈ 2.82. Nangona kunjalo, ngenxa yorhwebo olukhankanywe ngaphambili phakathi kwesisombululo kunye nokuqokelela ukukhanya, ixabiso le-compromise ye-2.3 linconywa njengomthetho wesithupha.

Indima yeNyquist yeSampulu kuMfanekiso

Isampuli yeNyquist ngumgcini-sango wokuthembeka komfanekiso. Xa ireyithi yesampulu iwela ngaphantsi komda weNyquist:

● Ukwenza iisampulu ngaphantsi → kubangela isibizo: iinkcukacha ezingeyonyani, iincam ezijijekileyo, okanye iipateni zemoiré.

● Ukwenziwa kwesampulu egqithisileyo → kubamba idatha eninzi kunokuba i-optics inokuhambisa, okukhokelela ekunciphiseni imbuyekezo: iifayile ezinkulu kunye neemfuno eziphezulu zokusetyenzwa ngaphandle kophuculo olubonakalayo.

Iisampulu ezichanekileyo ziqinisekisa ukuba imifanekiso ibukhali kwaye iyinyani ngokwenyani. Inika ibhalansi phakathi kwegalelo le-optical input kunye ne-digital capture, ukuphepha ukuchithwa kwesisombululo kwelinye icala okanye izinto zakudala ezilahlekisayo kwelinye.

Izicelo eziSebenzayo

Isampulu yeNyquist ayisiyothiyori kuphela - inezicelo ezibalulekileyo kuzo zonke iinkalo zokucinga:

● Imakroskopu:Abaphandi kufuneka bakhethe abenzi boluvo abanesampulu ubuncinane kabini kwezona nkcukacha zincinci zisonjululwa yilensi yenjongo. Ukukhetha okulungileyoikhamera yemicroscopeKubaluleke kakhulu, njengoko ubungakanani bepixel kufuneka buhambelane nesisombululo esisikelwe umda senjongo yemicroscope. Iilabhoratri zanamhlanje zihlala zikhethaIikhamera ze-sCMOS, ebonelela ngolungelelwaniso lobuntununtunu, uluhlu oluguquguqukayo, kunye nezakhiwo ze-pixel ezilungileyo zomfanekiso webhayoloji wokusebenza okuphezulu.

● Ukufota:Ukudibanisa izinzwa eziphezulu ze-megapixel kunye neelensi ezingakwaziyo ukusombulula ngokulinganayo iinkcukacha ezintle zihlala zikhokelela kuphuculo olungahoywayo kubukhali. Abafoti abachwephesha balinganisela iilensi kunye neekhamera ukunqanda ukuchithwa kwesisombululo.

● Umbono womatshini &Iikhamera zeNzululwaziKulawulo lomgangatho kunye nokuhlolwa kwemizi-mveliso, ukulahleka kweempawu ezincinci ngenxa yesampulu engaphantsi kunokuthetha ukuba iindawo ezineziphene zingabonwa. Iisampulu egqithisileyo ingasetyenziselwa ngabom ukusondeza idijithali okanye ukuqhubela phambili okuphuculweyo.

Xa kufuneka utshatise iNyquist: I-Oversampling kunye ne-Undersampling

Isampulu yeNyquist imele ulungelelwaniso olufanelekileyo, kodwa ekusebenzeni, iinkqubo zokucinga zinokuthi ngabom zigqithise okanye zibe ngaphantsi kwesampulu ngokuxhomekeke kwisicelo.

Yintoni i-Undersampling

Kwimeko yezicelo apho ubuntununtunu bubaluleke ngakumbi kunokusombulula ezona nkcukacha zincinci, ukusebenzisa indawo ye-pixel yesayizi enkulu kuneemfuno zeNyquist kunokukhokelela kuncedo olukhulu lokuqokelela ukukhanya. Oku kubizwa ngokuba yi undersampling.

Oku kuncama iinkcukacha ezintle, kodwa kunokuba luncedo xa:

● Uvakalelo lubalulekile: iipikseli ezinkulu ziqokelela ukukhanya okungakumbi, ukuphucula umlinganiselo wesignali ukuya kwingxolo kumfanekiso wokukhanya okuphantsi.
● Isantya sibalulekile: iipixels ezimbalwa zinciphisa ixesha lokufunda, nto leyo eyenza ukuba ufumaneke ngokukhawuleza.
● Ukusebenza kwedatha kuyafuneka: ubungakanani beefayile ezincinci zikhethwa kwiinkqubo ezilinganiselweyo ze-bandwidth.

Umzekelo: Kumfanekiso wekhalsiyam okanye amandla ombane, iisignali zikholisa ukunikwa iavareji kwiindawo ezinomdla, ngoko ke ukwenza isampulu iphucula ukuqokelelwa kokukhanya ngaphandle kokuphazamisa iziphumo zenzululwazi.

Yintoni i-Oversampling

Ngokuchaseneyo, izicelo ezininzi ekusombululeni iinkcukacha ezilungileyo zingundoqo, okanye izicelo ezisebenzisa iindlela zokuhlalutya emva kokufunyanwa ukufumana ulwazi olongezelelweyo ngaphaya komda we-diffraction, zifuna iipikseli zomfanekiso omncinci kuneemfuno zeNyquist, ezibizwa ngokuba yi-oversampling.

Ngelixa oku kunganyusi isisombululo sokwenyani sokubona, kunokubonelela ngeenzuzo:

● Yenza ukusondeza kwedijithali ngelahleko ekumgangatho ophantsi.
● Ukuphucula inkqubo yasemva kokwenziwa komsebenzi (umz., ukudilizwa, ukudiza, ukusombululwa okuphezulu).
● Yehlisa ukubonakala kwamagama xa imifanekiso ithotywa kamva.

Umzekelo: Kwimicroscopy, ikhamera ye-sCMOS enesisombululo esiphezulu inokugqwesa ubuninzi bezakhiwo zeselula ukuze i-algorithms yokubala ikhuphe iinkcukacha ezintle ngaphaya komda we-diffraction.

Iingcamango Eziphosakeleyo eziqhelekileyo

1, Iimegapixel ezininzi zihlala zithetha imifanekiso ebukhali.
Ayonyani. Ububukhali buxhomekeke kumandla okusombulula iilensi zombini nokuba iisampulu zoluvo ngokufanelekileyo.

2, Nayiphi na i-lens elungileyo isebenza kakuhle nayo nayiphi na inzwa yesisombululo esiphezulu.
Umdlalo ombi phakathi kwesisombululo se-lens kunye ne-pixel pitch kuya kuthintela ukusebenza.

3, Isampulu yeNyquist ifanelekile kuphela ekuqhubeni umqondiso, hayi ukucinga.
Ngokuchasene noko, ukucinga ngedijithali kuyinkqubo yesampulu, kwaye iNyquist ifanelekile apha njengakwiaudio okanye kunxibelelwano.

Ukuqukumbela

Isampulu yeNyquist ingaphezulu kokuthathwa kwezibalo - ngumgaqo oqinisekisa ukusebenza kunye nesisombululo sedijithali. Ngokulungelelanisa amandla okusombulula iilensi kunye nesampulu yamandla eenzwa, iinkqubo zokucinga zifezekisa ukucaca okuphezulu ngaphandle kwezinto zakudala okanye ukuchithwa kwamandla.

Kwiingcali kwiinkalo ezahlukeneyo njenge-microscopy, i-astronomy, ukufota, kunye nombono womatshini, ukuqonda isampuli yeNyquist ngundoqo ekuyileni okanye ekukhetheni iinkqubo zokucinga ezizisa iziphumo ezithembekileyo. Ekugqibeleni, umgangatho womfanekiso awuveli ekutyhaleni inkcazo enye ukuya kugqithiso kodwa ekuphumezeni ukulingana.

Ii-FAQs

Kwenzeka ntoni ukuba isampulu yeNyquist ayonelisekanga kwikhamera?
Xa ireyithi yesampulu iwela ngaphantsi komda weNyquist, inzwa ayinakumela iinkcukacha ezintle ngokuchanekileyo. Oku kukhokelela kwi-aliasing, ebonakala njengeencam ezijijekileyo, iipateni ze-moiré, okanye ukuthungwa okungeyonyani angekhoyo kwindawo yokwenyani.

Ubungakanani bepixel buchaphazela njani isampuli yeNyquist?
Iiphikseli ezincinci zonyusa i-Nyquist frequency, okuthetha ukuba inzwa inokusombulula iinkcukacha ezingcono. Kodwa ukuba i-lens ayikwazi ukuhambisa elo nqanaba lesisombululo, iipikseli ezongezelelweyo zongeza ixabiso elincinci kwaye zinokunyusa ingxolo.

Ngaba isampulu yeNyquist yahlukile kwi-monochrome vs. izinzwa zombala?
Ewe. Kwisivamvo se-monochrome, zonke iisampulu zepixel zikhanyisa ngokuthe ngqo, ke i-Nyquist frequency esebenzayo ihambelana nepixel pitch. Kwisivamvo sombala esinesihluzi se-Bayer, itshaneli yombala nganye ingaphantsi kwesampulu, ngoko ke isisombululo esisebenzayo emva kwe-demosaicing sisezantsi kancinci.

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