Me Fresnel zone

Fresnel zone - suna yankunan cikin abin da farfajiya na sauti ko haske tãguwar ruwa a gudanar da wani lissafin sauti diffraction sakamakon ko haske. Wannan hanya da aka farko amfani a 1815 O.Frenel.

tarihi bayanai

Augustin-Zhan Frenel (10.06.1788-14.07.1827) - Faransa likita. Ya sadaukar da rayuwarsa ga karatu da kaddarorin jiki kimiyyan gani da hasken wuta. Ya kuma a 1811 a ƙarƙashin rinjayar E. Malus fara da kansa ya yi nazarin kimiyyar lissafi, nan da nan ya zama interested in gwaji bincike a fagen kimiyyan gani da hasken wuta. A 1814, da "sake gano" da manufa kutse, da kuma a 1816 ya kara da sanannun manufa na Huygens, wanda ya gabatar da manufar jituwar da tsangwama daga na farko tãguwar ruwa. A 1818, gina a kan aikin yi, ya ci gaba da ka'idar haske diffraction. Ya gabatar da al'adar la'akari da diffraction daga gefen, kazalika da madauwari rami. Gudanar da gwaje-gwajen, yanzu litattafansu, da biprism da bizerkalami haske tsangwama. A 1821 ya tabbatar da gaskiyar mai gangara yanayin haske tãguwar ruwa, a 1823 bude madauwari kuma elliptical rabuwa. Ya bayyana a kan tushen da kalaman wakilci chromatic rabuwa, kazalika da juyawa daga cikin jirgin sama na rabuwa da haske da kuma birefringence. A 1823, ya kafa dokoki na refraction da kuma tunani na haske a kan wani ajali lebur surface tsakanin biyu kafofin watsa labarai. Tare da Jung dauke mahaliccin kalaman kimiyyan gani da hasken wuta. Ne ya kirkiro da dama tsangwama na'urorin, kamar madubi, ko wani Fresnel biprism Fresnel. Yana dauke da kafa wani tushen sabon hanyar hasumiya mai fitila haske.

A bit da ka'idar

Ƙayyade Fresnel diffraction yiwu ga wani rami na wani siffar da kullum ba tare da shi. Duk da haka, daga cikin ra'ayi na yiwuwa shi ne mafi kyau mu bi da shi a cikin wani madauwari rami siffar. A wannan yanayin, da haske Madogararsa da kuma kallo ma'ana dole ne a kan wani layin cewa shi ne perpendicular zuwa allon jirgin, kuma ya wuce ta tsakiyar rami. A gaskiya, a cikin Fresnel zone iya karya duk wani surface ta hanyar abin da hasken tãguwar ruwa. Alal misali, equiphase surface. Duk da haka, a cikin wannan harka da shi zai yi dace da karya da lebur zone rami. Domin wannan mun yi la'akari da na farko Tantancewar matsaloli, wanda zai ba da damar mu domin sanin ba kawai radius na farko Fresnel zone, amma kuma bi-up da bazuwar lambobi.

The aiki na kayyade girman da zobba

Don fara tunanin cewa surface na lebur rami ne tsakanin haske Madogararsa (ma'ana C) da kuma masu sa ido (ma'ana H). Shi ne perpendicular zuwa layin CH. CH kashi wuce ta zagaye rami cibiyar (ma'ana Yã). Tun da mu manufa ne da axis of fasali, da Fresnel zone zai kasance a cikin nau'i na zobba. A yanke shawara za a rage zuwa tabbatar da dalilin da radius daga wadannan da'irori tare da wani sabani lamba (m). Matsakaicin darajar da aka kira da radius daga zone. Don warware matsalar ya zama dole a yi ƙarin yi, wato: zabi wani sabani nufi (A) a cikin jirgin sama na bude da kuma gama da shi mike layin segments daga batu na kallo da haske Madogararsa. A sakamakon haka ne alwatika SAN. Sa'an nan za ka iya yi da shi saboda haka cewa haske kalaman isa ga Kiyayewa tare da hanyar da SAN, hawa a daina hanya fiye da daya da za su kai ga hanya CH. Wannan ya nuna cewa hanyar bambanci CA + AN-CH ma'anar bambanci tsakanin kalaman manzilõli, sun shige daga sakandare kafofin (A kuma D) a kallo batu. Daga wannan darajar dogara resultant tsangwama tãguwar ruwa tare da matsayi na observer, ya kuma inganta hasken tsanani a wancan batu.

Lissafi na farko radius

Mun samu cewa idan hanya bambanci ne daidai da rabin hasken zango (λ / 2), hasken zuwa ga Kiyayewa a antiphase. Yana iya ƙarasa da cewa idan hanya bambancin zai zama kasa da λ / 2, da haske zai zo a wannan lokaci. Wannan yanayin CA + AN-SN≤ λ / 2, da definition, shi ne yanayin da cewa batu A aka located a cikin na farko zobe, Ina nufin shi ne na farko Fresnel zone. A wannan yanayin, ya yi iyaka da da'irar hanya bambanci ne daidai da rabin zango na haske. Saboda haka wannan lissafi domin sanin radius na farko sashi, denoted P _1. Lokacin da hanyar bambanci m zuwa λ / 2, shi zai zama daidai da kashi OA. A wannan yanayin, idan nisa ƙetare ma CO rami diamita (yawanci dauke kawai irin embodiments), da sharudda na lissafi radius na farko zone aka bayyana ta da wadannan dabara: P ₁ = √ (λ * CO + OH) / (CO + OH).

Lissafi na da radius daga Fresnel zone

Formula for kayyade dabi'u na radii na m zobba ne m tattauna a sama, kawai kara wa numerator na so zone lambar. A wannan yanayin da daidaici na hanyar bambanci zama: CA + AN-SN≤ m * λ / 2 ko CA + AH-CO-ON≤ m * λ / 2. Yana bi da cewa radius na so yanki tare da lambar "m" ma'anar wadannan dabara: P _m = √ (m * λ * CO + OH) / (CO + OH) = ₁ P √m

Summing up na tsaka-tsaki da sakamakon

Yana iya lura da cewa, ga BREAKING zone - rabuwa da sakandare haske Madogararsa to ikon kayayyaki da ciwon guda yanki, kamar yadda _m n = π * R ² _m - π * R ² _m-1 = π * ₁ P ² = P _1. Haske daga makwabciyar Fresnel zones zo a gaban zamani, saboda hanya bambancin da makwabta zobba da definition zama daidai da rabin zango na haske. Generalizing wannan sakamakon, mun kammala da cewa, warwarewarsu ga ramuka a da'irori (irin wannan haske daga makwabta kai Kiyayewa da wani ajali lokaci bambancin) zai nufin keta zobe a wannan yanki. Wannan tabbatarwa ne sauƙi tabbatar da taimakon matsalar.

Fresnel zone domin wani jirgin saman kalaman

La'akari da rashin lafiya bude yankin cikin thinner zobba na daidaita yankin. Wadannan da'ira ne secondary haske kafofin. A mawadãta daga haske kalaman isowa daga kowane zobe da Kiyayewa, kamar guda. Bugu da kari, cikin lokaci bambanci daga m kewayon a aya H ne ma wannan. A wannan yanayin, da hadaddun amplitudes a Kiyayewa lokacin da kara a wata guda hadaddun jirgin form wani ɓangare na wani da'irar - baka. A total mawadãta daga cikin guda - wata tsirkiya. Yanzu la'akari da yadda da canza juna na summation na mawadãta idan akwai canji na radius daga cikin rami, alhãli kuwa rike da wasu sigogi na matsalar. A wannan yanayin, idan rami ya buɗe daya kawai zone domin Kiyayewa, da abin kwaikwaya kara rabo da aka bayar circumferentially. A amplitude na karshe zobe da aka juya su da wani kwana π dangi zuwa tsakiyar ɓangare, watau. K. The hanya bambanci na farko sashi, da definition, daidai λ / 2. Wannan kwana za a π nufin mawadãta zai zama rabin da karkara. A wannan yanayin, da Naira Miliyan Xari da wadannan dabi'u a cikin kallo batu ne sifili - sifili tsirkiya tsawon. Idan uku zobba za su buɗe, sa'an nan hoton zai wakilci rabin da'irar da sauransu. Amplitude a Kiyayewa ta batu na wani ko da yawan zobba ne sifili. Kuma a cikin akwati a lokacin da yin amfani da wani m yawan da'ira, shi zai zama daidai da iyakar darajar da tsawon na diamita a cikin hadaddun jirgin sama na Bugu da kari amplitudes. A bisa manufofin ne Mafi bude Hanyar Fresnel zones.

A takaice game da musamman lokuta

La'akari da rare yanayi. Wani lokaci, a warware matsalar jihohin da amfani da fractional yawan Fresnel zones. A wannan yanayin, a karkashin rabin zobe yi kwata da'irar juna, wanda zai dace da rabin yankin na farko zone. Hakazalika lasafta wani fractional darajar. Wani lokaci da yanayin da shawara cewa wasu fractional yawan zobba rufe da sosai bude. A irin wannan yanayi, jimlar mawadãta daga cikin filin vector aka samu a matsayin bambanci na amplitudes na biyu ayyuka. A lokacin da duk bangarori masu bude, to, bãbu cikas a hanyar da haske tãguwar ruwa, hoton zai yi kama da wani karkace. Sai dai itace, saboda a lokacin da ka bude wani babban yawan zobba kamata la'akari da dogaro da watsi da haske Madogararsa da Kiyayewa nufi da shugabanci na sakandare Madogararsa. Mun samu cewa, haske daga zone tare da wata babbar lambar yana da kananan mawadãta. Cibiyar samu Helix ne a tsakiyar karkara na farko da na biyu zobba. Saboda haka, filin mawadãta a cikin akwati inda duk bayyane yanki ne kasa da sau biyu, fiye da a bude daya na farko faifai, da kuma tsanani da ya bambanta da sau hudu.

Fresnel diffraction haske

Bari mu dubi abin da ake nufi da wannan kalma. Kira Fresnel diffraction yanayin, a lokacin da ta cikin rami yana buɗewa da dama yankunan. Idan za mu bude wani yawa zobba, to, wannan zabin za a iya watsi da, cewa an exerted a cikin kimantawa zuwa geometrical kimiyyan gani da hasken wuta. A cikin akwati inda ta rami da aka bude ga Kiyayewa ma kasa da daya zone, wannan yanayin ne ake kira Fraunhofer diffraction. Ya aka dauke su gamsu idan haske Madogararsa da kuma batu na observer ne a wani isasshen nesa daga rami.

Kwatanta na zone farantin ruwan tabarau da kuma

Idan ka rufe duk m ko duk ko da Fresnel zone, yayin da a Kiyayewa ne hasken kalaman da mafi mawadãta. Kowane zobe daga cikin hadaddun jirgin sama ya bada rabin da'irar. Saboda haka idan ya bar bude da m zones, sa'an nan jimlar za kawai karkace halves na da'ira, wanda taimakawa ga] aukacin mawadãta daga cikin "kasa-up". A cikas a hanyar da haske kalaman, a cikin abin da daya kawai irin bude zobba, kira zone farantin. A tsanani na haske a Kiyayewa akai-akai wuce tsanani da haske a kan farantin. Wannan shi ne saboda cewa da haske kalaman na kowane bude zobe da aka yi masa alama a ga Kiyayewa a cikin wannan lokaci.

A irin wannan halin da ake ciki ne ta lura da mayar da hankali ga haske da wani ruwan tabarau. Yana, sabanin faranti, babu zobba ba rufe, da kuma motsa haske a cikin zamani da π * (+ 2 π * m) daga da'irori cewa rufe zone farantin. A sakamakon haka, da mawadãta daga haske kalaman ne ninki biyu. Bugu da ƙari, cikin ruwan tabarau gusar da ake kira na juna lokaci canjawa waɗanda ke a cikin guda zobe. Yana yana faɗaɗa kan hadaddun jirgin sama na rabin karkara domin kowane sashi a mike layin kashi. A sakamakon haka, da mawadãta ƙaruwa da π sau, kuma dukan hadaddun jirgin karkace ruwan tabarau bayyana a cikin wani madaidaiciya line.