Nkag siab Nyquist Sampling: Ntsuas qhov muag pom thiab lub koob yees duab daws teeb meem |

Hauv cov duab digital, nws yooj yim rau kev xav tias kev daws teeb meem siab dua txhais tau tias cov duab zoo dua. Cov tuam txhab lub koob yees duab feem ntau ua lag luam tshuab raws li kev suav megapixel, thaum cov neeg tsim lub lens qhia txog kev daws lub zog thiab qhov ntse. Txawm li cas los xij, hauv kev xyaum, cov duab zoo nyob tsis yog nyob ntawm qhov tshwj xeeb ntawm lub lens lossis lub sensor tus kheej tab sis kuj nyob ntawm seb lawv zoo npaum li cas.

Nov yog qhov uas Nyquist sampling los ua si. Keeb kwm yog lub hauv paus ntsiab lus los ntawm kev ua cov teeb liab, Nyquist cov txheej txheem teeb tsa lub theoretical moj khaum rau kev ntes cov ntsiab lus kom raug. Hauv kev yees duab, nws ua kom ntseeg tau tias qhov kev daws teeb meem kho qhov muag xa los ntawm lub lens thiab cov kev daws teeb meem digital ntawm lub koob yees duab sensor ua haujlwm sib haum xeeb.

Kab lus no nthuav tawm Nyquist sampling nyob rau hauv cov ntsiab lus ntawm kev yees duab, piav qhia qhov sib npaug ntawm qhov kho qhov muag thiab lub koob yees duab daws teeb meem, thiab muab cov lus qhia siv tau rau cov ntawv thov xws li kev yees duab mus rau kev tshawb fawb.

Nyquist Sampling yog dab tsi?

Daim duab 1: Nyquist sampling theorem

Sab saum toj:Lub teeb liab sinusoidal (cyan) yog ntsuas, lossis ua piv txwv, ntawm ntau lub ntsiab lus. Cov kab grey ntev-dashed sawv cev rau 1 kev ntsuas ib lub voj voog ntawm lub teeb liab sinusoidal, ntes cov teeb liab peaks nkaus xwb, zais qhov tseeb ntawm lub teeb liab. Cov liab zoo nkauj dashed nkhaus captures ntawm 1.1 kev ntsuas ib qho piv txwv, qhia ib tug sinusoid tab sis misrepresenting nws zaus. Qhov no zoo ib yam rau Moiré qauv.

Hauv qab:Tsuas yog thaum 2 cov qauv coj mus kuaj ib lub voj voog (liab dotted kab) puas qhov tseeb ntawm lub teeb liab pib raug ntes.

Nyquist sampling theorem yog lub hauv paus ntsiab lus ntawm kev ua cov teeb liab hauv electronics, audio processing, imaging and other fields. Lub theorem ua kom pom tseeb tias kom rov tsim kho qhov zaus ntawm lub teeb liab, kev ntsuas yuav tsum tau ua tsawg kawg ob zaug qhov zaus, pom hauv daim duab 1. Nyob rau hauv cov ntaub ntawv ntawm peb qhov kev daws teeb meem, qhov no txhais tau hais tias peb cov khoom qhov chaw pixel loj yuav tsum yog feem ntau ntawm ib nrab ntawm qhov tsawg tshaj plaws uas peb tab tom sim ntes, lossis, nyob rau hauv cov ntaub ntawv ntawm lub tshuab tsom, ib nrab ntawm lub tshuab ntsuas qhov kev daws teeb meem.

Daim duab 2: Nyquist sampling nrog square pixels: kev taw qhia tseem ceeb

Siv lub koob yees duab nrog ib daim phiaj ntawm square pixels, 2x sampling yam ntawm Nyquist theorem yuav tsuas yog ntes cov ntsiab lus uas zoo kawg nkaus ua raws li daim phiaj pixel. Yog tias sim daws cov qauv ntawm lub kaum sab xis rau ntawm daim phiaj pixel, qhov zoo ntawm pixel loj dua, mus txog √2 npaug loj dua ntawm kab pheeb ces kaum. Tus nqi piv txwv yuav tsum yog li ntawd 2√2 lub sij hawm qhov xav tau spatial zaus mus ntes cov ntsiab lus ntawm 45o rau pixel daim phiaj.

Yog vim li cas rau qhov no yog pom tseeb los ntawm kev txiav txim siab ntawm daim duab 2 (sab saum toj ib nrab). Xav txog cov pixel loj yog teem rau qhov kev daws teeb meem kho qhov muag, muab lub ncov ntawm ob qhov chaw nyob sib ze, lossis ib qho kev nthuav dav uas peb tab tom sim daws, txhua tus ntawm lawv tus kheej pixel. Txawm hais tias cov no tau raug kuaj pom nyias, tsis muaj qhov qhia tau hais tias qhov kev ntsuas uas lawv yog ob qhov sib txawv - thiab ib zaug ntxiv peb lub ntsiab lus ntawm "kev daws teeb meem" tsis tau raws li. Ib tug pixel nyob rau hauv nruab nrab yog xav tau, ntes ib tug trough ntawm lub teeb liab. Qhov no yog ua tiav los ntawm yam tsawg kawg yog ob npaug ntawm qhov spatial sampling tus nqi, piv txwv li ib nrab ntawm qhov chaw pixel loj.

Optical Resolution vs. Camera Resolution

Yuav kom nkag siab tias Nyquist sampling ua haujlwm li cas hauv kev kos duab, peb yuav tsum paub qhov txawv ntawm ob hom kev daws teeb meem:

● Kev daws teeb meem kho qhov muag: txiav txim siab los ntawm lub lens, qhov kev daws teeb meem kho qhov muag hais txog nws lub peev xwm los tsim cov ntsiab lus zoo. Cov yam xws li lens zoo, aperture, thiab diffraction teeb qhov kev txwv no. Cov kev hloov pauv hloov pauv (MTF) feem ntau yog siv los ntsuas seb lub lens kis qhov sib txawv ntawm qhov sib txawv ntawm qhov sib txawv.

● Kev daws teeb meem lub koob yees duab: txiav txim siab los ntawm lub sensor, lub koob yees duab daws teeb meem nyob ntawm pixel loj, pixel suab, thiab tag nrho cov sensor qhov ntev. Lub pixel suab ntawm aCMOS koob yees duabncaj qha txhais nws Nyquist zaus, uas txiav txim siab qhov siab tshaj plaws nthuav dav lub sensor tuaj yeem ntes.

Thaum ob qho no tsis sib haum, teeb meem tshwm sim. Lub lens uas tshaj qhov kev daws teeb meem ntawm lub sensor tau zoo "nkim", txij li lub sensor tsis tuaj yeem ntes tag nrho cov ntsiab lus. Hloov pauv, lub siab daws teeb meem sensor ua ke nrog lub lens tsis zoo ua rau cov duab tsis zoo txawm tias ntau megapixels.

Yuav ua li cas ntsuas qhov muag pom thiab lub koob yees duab daws teeb meem

Sib npaug optics thiab sensors txhais tau hais tias sib piv Nyquist zaus ntawm lub sensor nrog lub optical cutoff zaus ntawm lub lens.

● Lub Nyquist zaus ntawm lub koob yees duab sensor yog xam raws li 1 / (2 × pixel suab). Qhov no txhais tau qhov siab tshaj plaws spatial zaus lub sensor tuaj yeem coj mus kuaj yam tsis muaj aliasing.
● Lub optical cutoff zaus nyob ntawm lub lens yam ntxwv thiab diffraction.

Txhawm rau kom tau txais txiaj ntsig zoo tshaj plaws, lub sensor qhov Nyquist zaus yuav tsum ua raws li los yog me ntsis dhau lub lens lub peev xwm daws teeb meem. Hauv kev xyaum, txoj cai zoo ntawm tus ntiv tes xoo yog los xyuas kom meej lub pixel suab yog li ib nrab ntawm qhov me me tshaj plaws ntawm lub lens.

Piv txwv li, yog tias lub lens tuaj yeem daws cov ntsiab lus mus txog 4 micrometers, tom qab ntawd lub sensor nrog pixel qhov ntau thiab tsawg ntawm ~ 2 micrometers yuav sib npaug rau qhov system zoo.

Sib piv Nyquist nrog lub koob yees duab daws teeb meem & kev sib tw ntawm Square Pixels

Kev lag luam tawm nrog txo cov khoom qhov chaw pixel loj yog txo lub teeb sau peev xwm. Yog li ntawd nws yog ib qho tseem ceeb kom sib npaug ntawm qhov xav tau kev daws teeb meem thiab kev sau lub teeb. Tsis tas li ntawd, cov khoom loj dua qhov chaw pixel qhov ntau thiab tsawg yuav qhia qhov loj dua ntawm qhov pom ntawm cov duab. Rau cov ntawv thov uas muaj qee qhov xav tau kev daws teeb meem zoo, 'txoj cai ntawm tus ntiv tes xoo' qhov zoo tshaj qhov sib npaug tau hais tias raug ntaus raws li hauv qab no: Cov khoom siv qhov chaw pixel loj, thaum muab faib los ntawm qee yam los suav rau Nyquist, yuav tsum sib npaug rau qhov kev daws teeb meem kho qhov muag. Qhov ntau yog hu ua lub koob yees duab daws teeb meem.

Sib npaug optics thiab sensors feem ntau nqes los kom ntseeg tau tias qhov kev daws teeb meem zoo ntawm lub koob yees duab phim qhov kev daws teeb meem kho qhov muag ntawm lub lens. Ib qhov system tau hais tias "muab Nyquist" thaum:

Lub koob yees duab daws teeb meem = Optical daws teeb meem

Qhov twg lub koob yees duab daws teeb meem yog muab los ntawm:

Lub koob yees duab daws teeb meem-xws li-formula

Qhov tseem ceeb rau suav rau Nyquist uas feem ntau pom zoo yog 2.3, tsis yog 2. Qhov laj thawj rau qhov no yog raws li hauv qab no.

Lub koob yees duab pixels yog (feem ntau) square, thiab teem rau ntawm 2-D daim phiaj. Lub pixel loj raws li tau hais tseg rau kev siv nyob rau hauv kab zauv rov qab sawv cev rau qhov dav ntawm pixels raws cov axes ntawm daim phiaj no. Yog tias cov yam ntxwv peb tab tom sim daws cov lus dag ntawm ib lub kaum ntse ntse tshwj tsis yog ntau yam zoo meej ntawm 90 ° txheeb ze rau daim phiaj no, qhov zoo ntawm pixel loj yuav loj dua, mus txog √2 ≈ 1.41 npaug ntawm pixel loj ntawm 45 °. Qhov no yog qhia hauv daim duab 2 (hauv qab ib nrab).

Qhov kev pom zoo raws li Nyquist cov qauv hauv txhua qhov kev taw qhia yuav yog 2√2 ≈ 2.82. Txawm li cas los xij, vim qhov kev sib pauv tau hais dhau los ntawm kev daws teeb meem thiab kev sau lub teeb, qhov kev cuam tshuam tus nqi ntawm 2.3 raug pom zoo raws li txoj cai ntawm tus ntiv tes xoo.

Lub luag hauj lwm ntawm Nyquist Sampling nyob rau hauv Imaging

Nyquist sampling yog lub rooj vag ntawm cov duab fidelity. Thaum tus nqi piv txwv poob qis dua qhov kev txwv Nyquist:

● Undersampling → ua rau aliasing: cov ntsiab lus tsis tseeb, jagged npoo, los yog cov qauv moiré.

● Oversampling → ntes tau cov ntaub ntawv ntau dua li qhov optics tuaj yeem xa tuaj, ua rau txo qis rov qab: cov ntaub ntawv loj dua thiab kev xav tau ntau dua yam tsis pom kev txhim kho.

Cov qauv raug raug xyuas kom meej tias cov duab yog ob qho tib si ntse thiab muaj tseeb rau qhov tseeb. Nws muab qhov sib npaug ntawm cov tswv yim kho qhov muag thiab kev ntes digital, zam kev daws teeb meem khib nyiab ntawm ib sab lossis cov khoom cuav ntawm lwm qhov.

Kev siv tswv yim

Nyquist sampling tsis yog txoj kev xav xwb - nws muaj cov ntawv thov tseem ceeb thoob plaws kev qhuab qhia:

● Microscopy:Cov kws tshawb fawb yuav tsum xaiv cov sensors uas ua piv txwv tsawg kawg yog ob zaug qhov kev nthuav dav me tshaj plaws los ntawm lub hom phiaj lens. Xaiv txoj cailub koob yees duab microscopyNws yog ib qho tseem ceeb, vim tias qhov loj me ntawm pixel yuav tsum ua raws li qhov sib txawv-txhim kho qhov teeb meem ntawm lub hom phiaj tsom iav. Cov chav kuaj niaj hnub no feem ntau nyiamsCMOS koob yees duab, uas muab qhov sib npaug ntawm rhiab heev, dynamic ntau yam, thiab cov qauv zoo pixel zoo rau kev ua haujlwm zoo ntawm cov duab lom neeg.

● Kev yees duab:Pairing high-megapixel sensors nrog lo ntsiab muag uas tsis tuaj yeem daws cov ntsiab lus zoo sib npaug feem ntau ua rau muaj kev txhim kho tsis zoo hauv qhov ntse. Cov kws yees duab tshaj lij sib npaug lo ntsiab muag thiab lub koob yees duab kom tsis txhob muaj kev daws teeb meem khib nyiab.

● Tshuab Lub Zeem Muag &Cov koob yees duab scientificHauv kev tswj kom zoo thiab kev tshuaj xyuas kev lag luam, cov yam ntxwv me me uas ploj lawm vim qhov tsis zoo tuaj yeem txhais tau tias qhov chaw tsis raug kuaj pom. Oversampling tej zaum yuav siv tau txhob txwm tshaj tawm rau digital zoom lossis ua kom zoo dua.

Thaum Match Nyquist: Oversampling thiab Undersampling

Nyquist sampling sawv cev rau qhov zoo tshaj plaws tshuav nyiaj li cas, tab sis nyob rau hauv kev xyaum, imaging systems yuav txhob txwm oversample los yog undersample nyob ntawm daim ntawv thov.

Dab tsi yog Undersampling

Nyob rau hauv cov ntaub ntawv ntawm daim ntawv thov qhov rhiab heev yog qhov tseem ceeb tshaj li kev daws qhov me me ntawm cov ntsiab lus zoo, siv qhov khoom siv qhov chaw pixel loj uas loj dua qhov xav tau ntawm Nyquist tuaj yeem ua rau muaj txiaj ntsig zoo ntawm kev sau lub teeb. Qhov no yog hu ua undersampling.

Qhov no fij kom meej meej, tab sis tuaj yeem ua tau zoo thaum:

● rhiab heev yog ib qho tseem ceeb: cov pixels loj sau ntau lub teeb, txhim kho teeb liab-rau-suab nrov piv hauv cov duab qis.
● Ceev tseem ceeb: tsawg dua pixels txo lub sij hawm nyeem ntawv, ua kom tau sai dua.
● Cov ntaub ntawv yuav tsum tau ua kom zoo: cov ntaub ntawv me me yog qhov zoo dua nyob rau hauv bandwidth-limited systems.

Piv txwv li: Hauv kev ntsuas calcium lossis voltage, cov cim qhia feem ntau yog nruab nrab ntawm thaj tsam ntawm kev txaus siab, yog li kev ua haujlwm hauv qab txhim kho lub teeb sau tsis muaj kev cuam tshuam cov txiaj ntsig kev tshawb fawb.

Dab tsi yog Oversampling

Hloov pauv, ntau daim ntawv thov uas daws cov ntsiab lus zoo yog qhov tseem ceeb, lossis cov ntawv thov siv cov kev tshawb fawb tom qab tau txais cov ntaub ntawv rov qab tau cov ntaub ntawv ntxiv dhau qhov kev txwv tsis pub dhau, xav tau cov duab me me dua li Nyquist xav tau, hu ua oversampling.

Thaum qhov no tsis nce qhov kev daws teeb meem kho qhov muag, nws tuaj yeem muab qhov zoo:

● Pab kom digital zoom nrog kev poob qis dua.
● Txhim kho tom qab ua tiav (piv txwv li, deconvolution, denoising, super-resolution).
● Txo qhov pom aliasing thaum cov duab downsampled tom qab.

Piv txwv li: Hauv microscopy, lub koob yees duab sCMOS high-resolution yuav oversample cellular structures kom suav cov algorithms tuaj yeem rho tawm cov ntsiab lus zoo tshaj qhov txwv tsis pub tshaj.

Kev Ntseeg Tsis Ncaj Ncees

1, Ntau megapixels ib txwm txhais tau tias cov duab zoo dua.
Tsis muaj tseeb. Ntsej muag nyob ntawm ob lub lens daws lub zog thiab seb lub ntsuas ntsuas puas tsim nyog.

2 、 Txhua lub lens zoo ua haujlwm zoo nrog txhua qhov kev daws teeb meem siab.
Qhov kev sib tw tsis zoo ntawm lub lens daws teeb meem thiab pixel suab yuav txwv kev ua haujlwm.

3 、 Nyquist sampling tsuas yog cuam tshuam hauv kev ua cov teeb liab, tsis yog duab.
Ntawm qhov tsis sib xws, cov duab digital yog qhov tseem ceeb ntawm cov txheej txheem qauv, thiab Nyquist yog qhov tseem ceeb ntawm no xws li hauv suab lossis kev sib txuas lus.

Xaus

Nyquist sampling yog ntau tshaj li kev ua lej - nws yog lub hauv paus ntsiab lus uas ua kom pom kev kho qhov muag thiab digital daws teeb meem ua ke. Los ntawm kev ua kom lub zog daws teeb meem ntawm cov lo ntsiab muag nrog cov peev xwm ua piv txwv ntawm cov sensors, cov duab kos duab ua tiav qhov tseeb tshaj plaws yam tsis muaj khoom cuav lossis lub peev xwm khib nyiab.

Rau cov kws tshaj lij hauv thaj chaw muaj ntau yam xws li microscopy, astronomy, photography, thiab tshuab lub zeem muag, kev nkag siab Nyquist sampling yog qhov tseem ceeb rau kev tsim lossis xaiv cov duab kos duab uas xa cov txiaj ntsig zoo. Thaum kawg, cov duab zoo tsis yog los ntawm kev thawb ib qho tshwj xeeb mus rau qhov kawg tab sis los ntawm kev ua tiav qhov sib npaug.

FAQs

Yuav ua li cas yog tias Nyquist sampling tsis txaus siab rau hauv lub koob yees duab?
Thaum tus nqi piv txwv poob qis dua qhov kev txwv Nyquist, lub sensor tsis tuaj yeem sawv cev cov ntsiab lus zoo kom raug. Qhov no tshwm sim hauv aliasing, uas zoo li jagged npoo, moiré qauv, los yog cuav textures uas tsis muaj nyob rau hauv lub tiag tiag scene.

Qhov loj pixel loj cuam tshuam li cas Nyquist sampling?
Cov pixels me me ua rau Nyquist zaus, txhais tau tias lub sensor tuaj yeem daws cov ntsiab lus zoo dua. Tab sis yog tias lub lens tsis tuaj yeem xa cov kev daws teeb meem ntawd, cov pixels ntxiv ntxiv tus nqi me me thiab tuaj yeem ua kom nrov nrov.

Puas yog Nyquist sampling txawv rau monochrome vs. xim sensors?
Yog lawm. Nyob rau hauv ib tug monochrome sensor, txhua pixel qauv luminance ncaj qha, yog li qhov zoo Nyquist zaus sib tw pixel suab. Hauv cov xim sensor nrog lub lim Bayer, txhua qhov xim channel yog undersampled, yog li qhov kev daws teeb meem zoo tom qab demosaicing qis dua me ntsis.