Anya ndọda

thumb|231x231px|Isi iyi nke ìhè na agafe n'azụ oghere ndọda (ihe a na adịghị ahụ anya nke a na etinye n'etiti onyinyo ahụ). Okirikiri mmiri bụ isi iyi ìhè dịka a ga ahụ ya ma ọ bụrụ na enweghị oghere anya, ebe ntụpọ ọcha bụ ọtụtụ ihe oyiyi nke isi iyi (lee Mgbaaka Einstein).
Igwe ndọda ndọda bụ ihe, dị ka ụyọkọ ụyọkọ kpakpando ma ọ bụ ihe dị n’ebe dị anya, nke na ehulata ìhè si n’ebe dị anya ka ọ na agakwuru onye na ekiri ihe. Ọnụ ọgụgụ nke lensing ndọda bụ nke Albert Einstein n'ozuzu echiche nke relativity kọwara n'ụzọ ziri ezi karịa Newtonian physics, nke na emeso ìhè dị ka corpuscles na ejegharị na ọsọ nke ìhè.

8Orest Khvolson (1924) na Frantisek Link (1936) bụ ndị a na ekwukarị na ha bụ ndị mbụ tụlere mmetụta dị na mbipụta, mana ọ na ejikọkarị ya na Einstein, bụ onye mere mgbako na ebipụtaghị ya na 1912 wee bipụta otu akụkọ banyere isiokwu a na 1936.

N'afọ 1937, Fritz Zwicky kwuru na ụyọkọ ụyọkọ kpakpando nwere ike ịrụ ọrụ dị ka lenses ndọda, nkwupụta a kwadoro na 1979 site na nyocha nke Twin QSO SBS 0957+561.

## Nkọwa
thumb|Nlegharị anya ndọdali   ụyọkọ kpakpando na etinye aka na agbanwe ọdịdị ụyọkọ kpakpando dị n'azụ ya (vidiyo; echiche nke onye na ese ihe).
áká_èkpè|thumb|Ihe onyonyo a na eme atụmatụ na egosi ka ọkụ sitere na ụyọkọ kpakpando dị anya si agbagọ site na mmetụta ndọda nke ụyọkọ kpakpando nke dị n'ihu, bụ́ nke na eme ka oghere na eme ka ebe dị anya yie ihe gbagọrọ agbagọ, ma na ebuwanye ibu, na akpụ mgbanaka ìhè e ji mara ya, nke a maara dị ka mgbanaka Einstein.
thumb|Ntụle nke mgbagha nke SDP.81 kpatara site na mmetụta a ekpughere ihe ndị na emepụta kpakpando.
N'adịghị ka oghere anya anya, oghere oghere dị ka gravitational lens na emepụta ngbanwe kachasị elu nke ìhè na agafe nso na etiti ya, na ngbanwe kacha nta nke ìhè na aga n'ebe dị anya site na etiti ya. N'ihi ya, oghere ndọda enweghị otu ebe mgbadoro anya, kama ọ bụ ahịrị gbadoro anya. Okwu ahụ bụ "lens" n'ọnọdụ mgbapụ ọkụ ndọda bụ nke mbụ O.J. Lodge, bụ onye kwuru na ọ bụ "agaghị ekwe omume ịsị na ike ndọda anyanwụ na eme ka oghere anya, n'ihi na ọ nweghị ogologo oge". Ọ bụrụ na isi iyi (ìhè), nnukwu ihe lensing, na onye na ekiri ihe na edina n'ahịrị kwụ ọtọ, ìhè mbụ ga apụta dị ka mgbanaka gburugburu nnukwu ihe lensing (ọ bụrụ na oghere ahụ nwere symmetry okirikiri). Ọ bụrụ na enwere ngbanwe ọ bụla, onye na ekiri ya ga ahụ akụkụ arc kama

Ọ bụ onye St. Petersburg physicist Orest Khvolson kwuru nke mbụ na 1924,  ma Albert Einstein kwuru ya na 1936. A na akpọkarị ya n'akwụkwọ dị ka Mgbaaka Einstein, ebe ọ bụ na Khvolson echeghị na flux ma ọ bụ radius nke onyinyo mgbaaka ahụ. Karịsịa, ebe oghere anya dị mgbagwoju anya (dị ka Ìgwè ụyọkọ kpakpando ma ọ bụ ụyọkọ) ma ọ naghị akpata mgbagwoju mgbagwoju nke oghere oge, isi iyi ahụ ga adị ka akụkụ arcs gbasasịrị gburugburu oghere anya. Onye na-ekiri ihe na emenụ nwere ike ịhụ ọtụtụ ihe oyiyi gbagọrọ agbagọ nke otu isi iyi ahụ; ọnụ ọgụgụ na ọdịdị nke ndị a dabere na ọnọdụ nke isi iyi ahụ, oghere anya, na ọdịdị ya nke olulu nke ihe anya.

: he microlensing effect.

Anya anya ndọda na eme otu ihe n'ụdị radieshon ọ bụla, ọ bụghị naanị ìhè a na ahụ anya, yana na radieshon na abụghị nke elektrọnik, dị ka ebili mmiri ndọda. A na amụ mmetụta lensing na adịghị ike maka ndabere microwave na mbara igwe yana nyocha nke ụyọkọ kpakpando. A hụla lensị siri ike na usoro redio na x-ray. Ọ bụrụ na oghere siri ike na emepụta ọtụtụ ihe oyiyi, a ga enwe oge igbu oge n'etiti ụzọ abụọ: ya bụ, n'otu foto a ga ahụ ihe lensed n'ihu ihe oyiyi nke ọzọ.

## Akụkọ ihe mere eme
áká_ịkẹngạ|thumb|193x193px|Otu n'ime foto Eddington nke nnwale ọnwa 1919 nke anyanwụ, nke e gosipụtara n'akwụkwọ ya 1920 nke na ekwupụta ihe ịga nke ọma ya.
Emere nlebanya mbụ nke ntugharị ọkụ site n'ịhụ mgbanwe ọnọdụ kpakpando ka ha na agafe n'akụkụ anyanwụ n'elu mbara igwe. Achọpụtara ihe ndị ahụ na 1919 site n'aka Arthur Eddington, Frank Watson Dyson, na ndị ha na ha na arụkọ ọrụ n'oge chi jiri n'ehihie zuru ezu na May 29. Igwe n'ehihie mere ka a hụ kpakpando ndị dị nso na anyanwụ. Emere nleba anya n'otu oge n'obodo Sobral, Ceará, Brazil na na São Tomé na Principe dị n'ụsọ oké osimiri ọdịda anyanwụ nke Africa. Nlebanya ndị ahụ gosipụtara na ìhè sitere na kpakpando na agafe nso anyanwụ gbadara ntakịrị, nke mere na kpakpando pụtara ntakịrị n'ọnọdụ.
áká_èkpè|thumb|Na ehulata ọkụ gburugburu nnukwu ihe sitere n'ebe dị anya. Àkụ oroma na egosi ọnọdụ pụtara ìhè nke isi iyi ndabere. Akụ na acha ọcha na egosi ụzọ nke ìhè si n'ezi ọnọdụ nke isi iyi.
thumb|Na nhazi a maara dị ka Einstein's Cross, ihe oyiyi anọ nke otu quasar dị anya na apụta gburugburu ụyọkọ kpakpando nke dị n'ihu n'ihi lensing ike ndọda.
E weere nsonaazụ ya dị ka akụkọ dị egwu ma mee ka peeji nke mbụ nke ọtụtụ akwụkwọ akụkọ bụ isi. O mere Einstein na ozizi ya nke nkwekọ n'ozuzu ka ama ama n'ụwa. Mgbe onye na enyere ya aka jụrụ ya ihe mmeghachi omume ya gaara abụ ma ọ bụrụ na Eddington na Dyson akwadoghị mmekọ ọnụ n'ozuzu ya na 1919, Einstein kwuru "Mgbe ahụ, m ga enwe ọmịiko maka Onyenwe anyị hụrụ n'anya. Ozizi ahụ ziri ezi na agbanyeghị." N'afọ 1912, Einstein ekwuola na onye na ekiri ihe nwere ike ịhụ ọtụtụ ihe oyiyi nke otu isi iyi ọkụ, ma ọ bụrụ na ọkụ na atụgharị gburugburu otu ọkụ. Mmetụta a ga eme ka uka ahụ na eme ihe dị ka ụdị oghere anya ndọda. Agbanyeghị, ebe ọ tụlere naanị mmetụta ntụgharị n'akụkụ otu kpakpando, ọ dị ka ọ na ekwubi na ihe a na atụghị anya ya maka ọdịnihu a na ahụ anya ebe ọ bụ na nhazi dị mkpa n'etiti kpakpando na onye na ekiri ihe ga abụ ihe na agaghị ekwe omume. Ọtụtụ ndị ọkà mmụta sayensị ndị ọzọ tụlekwara anya gbasara lensing ndọda, mana ha niile ruru otu nkwubi okwu ahụ na ọ ga abụ ihe na agaghị ekwe omume ịhụ.

Ọ bụ ezie na Einstein mere ngụkọta a na ebipụtaghị na isiokwu ahụ,  mkparịta ụka mbụ banyere oghere ike ndọda na ebi akwụkwọ bụ nke Khvolson, n'otu edemede dị mkpirikpi na atụle "mmetụta halo" nke ike ndọdịrị mgbe isi iyi, oghere, na onye na ekiri ihe na eme ihe fọrọ nke nta ka ọ bụrụ nhazi zuru oke,  nke a na akpọ ugbu a Mgbaaka Einstein.

'afọ 1936, mgbe Rudi W. Mandl gbara ume, Einstein bipụtara obere isiokwu "Lens Like Action of a Star By the Deviation of Light In the Gravitational Field" na akwụkwọ akụkọ Science.

'afọ 1937, Fritz Zwicky bu ụzọ tụlee ikpe ebe ụyọkọ kpakpando ndị a chọpụtara ọhụrụ (nke a na akpọ 'nebulae' n'oge ahụ) nwere ike ịrụ ọrụ dị ka isi iyi na oghere anya, na nke ahụ, n'ihi oke na nha ya, o yikarịrị ka a ga ahụ mmetụta ahụ.

Na 1963 Yu. . Klimov, S. Liebes, na Sjur Refsdal ghọtara n'onwe ha na quasars bụ ezigbo ihe na enye ìhè maka mmetụta anya ndọda.

Ọ bụghị ruo n'afọ 1979 ka a ga achọpụta oghere mbụ nke ike ndọda. A maara ya dị ka "Twin QSO" ebe ọ bụ na ọ dị ka ihe abụọ yiri ibe ya.  (A na-akpọ ya SBS 0957+561.) Dennis Walsh, Bob Carswell, na Ray Weymann chọpụtara oghere a site na iji onyokomita Kitt Peak National Observatory 2.1 mita.

N'afọ 1980, ndị na enyocha mbara igwe ghọtara na njikọta nke ndị na ese foto CCD na kọmputa ga eme ka a tụọ ìhè nke ọtụtụ nde kpakpando kwa abalị. N'ọhịa jupụtara, dị ka etiti ụyọkọ kpakpando ma ọ bụ igwe ojii Magellanic, enwere ike ịchọta ọtụtụ ihe omume microlensing kwa afọ. Nke a dugara na mgbalị ndị dị ka Optical Gravitational Lensing Experiment, ma ọ bụ OGLE, nke gosipụtara ọtụtụ narị ihe omume dị otú ahụ, gụnyere nke OGLE-2016-BLG-1190Lb na OGLE 2016BLG-1155Lb.

## Nkọwa nke Newtonian
Newton wondered if light, in the form of corpuscles, would be bent due to gravity. The Newtonian prediction for light deflection refers to the amount of deflection a corpuscle would feel under the effect of gravity, and therefore one should read "Newtonian" in this context as the referring to the following calculations and not a belief that Newton held in the validity of these calculations.

Maka oghere oghere nke ịdị arọ 

M 

{\Mhttps://wikimedia.org/api/rest_v1/media/math/render/svg/f82cade9898ced02fdd08712e5f0c0151758a0dd 

, a corpuscle nke mass 

m 

{\displaystyle m} 

na enwe mmetụta nke ike

: \vec F = -\frac{GMm}{r^2} \hat r ~,

ebe 

r 

{\r 

bụ nkewa nke lens corpuscle. Ọ bụrụ na anyị jiri ike a tụnyere Iwu nke abụọ nke Newton, anyị nwere ike idozi maka ọsọ nke ìhè na agafe

: 

Ìhè na emekọrịta ihe na oghere site n'oge mbụ 

t = 0 

{\t=0} 

na 

t 

{\displaystyle t} 

, na ọsọ na akwalite corpuscle na-enweta bụ

: \Delta \vec v = -\int_0^{t} dt' ~ \frac{GM}{r(t')^2} \hat r(t') ~.

Ọ bụrụ na mmadụ na eche na na mbụ ìhè dị anya site na oghere anya iji leghara ike ndọda anya, anya dị n'etiti ụzọ mbụ nke ìhè na oghere bụ b (ihe mmetụta), na anya dị nro bụ 

r 

Ọdịdị 

{\displaystyle r_{\parallel }} 

dị ka nke ahụ 

r 

2 

=

b 

2 

+ 

r 

Ọdịdị 

2 

{\displaystyle r^{2}=b^{2}.+r_{\parallel }^{2}} 

. Anyị na ekwukwa na ọsọ ọsọ nke ìhè na adịgide adịgide n'akụkụ ihu. 

d 

r 

Ọdịdị 

≈ c d t 

{\displaystyle dr_{\parallel }\approx cdt} 

, nakwa na a na eme ka ìhè dị obere. Mgbe etinyechara echiche ndị a n'ime usoro dị n'elu ma mee ka ọ dịkwuo mfe, mmadụ nwere ike idozi maka mmụba ọsọ na ntụziaka kwụ ọtọ. N'ihi ya, akụkụ nke ntụgharị n'etiti ụzọ mbụ na nke ikpeazụ nke corpuscle bụ (lee, dịka, M. Meneghetti 2021) 

: \theta = \frac{2GM}{c^2 r} ~.

Although this result appears to be half the prediction from general relativity, classical physics predicts that the speed of light c is observer-dependent (see, e.g., L. Susskind and A. Friedman 2018) which was superseded by a universal speed of light in special relativity.

## Nkọwa n'ihe gbasara oghere na oge
áká_èkpè|thumb|Igwe anya na adọkpụ (oghere ojii na agafe n'ihu ụyọkọ kpakpando).
N'ozuzu, ìhè na agbaso mgbagwoju anya nke ohere na oge, ya mere mgbe ìhè na agafe gburugburu nnukwu ihe, ọ na agbaji. Nke a pụtara na ìhè sitere n'ihe dị n'akụkụ nke ọzọ ga agbanye n'anya onye na ekiri, dịka oghere anya nkịtị. N'ozuzu, ọsọ nke ìhè na adabere na ikike ndọda (ya bụ, metric) na a pụrụ ile ntụgharị a anya dị ka nsonaazụ nke ìhè na'okporo ụzọ na agagharị na ọsọ ọsọ. Ìhè bụ ókèala dị n'etiti ọdịnihu, mbara igwe, na mpaghara gara aga. Enwere *ike* ile ike ịdọrọ mmasị dị ka mmegharị nke ihe ndị a na emetụbeghị n'azụ *geometry* ma ọ bụ n'ụzọ ọzọ dị ka nzaghachi nke ihe na ike dị na geometry dị larịị. Akụkụ ntụgharị bụ:

: \theta = \frac{4GM}{c^2 r}

*G* na oke *r*">M na anya r site na radiation metụtara, ebe G bụ ihe na adịgide adịgide nke ike ndọda na *c* bụ ọsọ nke ìhè na ikuku.

Ebe ọ bụ na Radius Schwarzschild 

r 

s 

{\displaystyle r_{\text{s}}} 

akọwapụtara dị ka 

r 

s 

=

2 G m 

/ 

c 

2 

{\displaystyle r_{\text{s}}={2Gm}/{c^{2}}} 

na ọsọ mgbapụ 

v 

na 

{\displaystyle v_{\text{e}}} 

akọwapụtara dị ka 

v 

na 

=

2 G m 

/ 

r 

=

β 

na 

c 

{\textstyle v_{\text{e}}={\sqrt {2Gm/r}}=\beta _{\text {e}}c} 

, a pụkwara ịkọwa nke a n'ụzọ dị mfe dị ka

: \theta = 2 \frac{r_\text{s}}{r} = 2 \left(\frac{v_\text{e}}{c}\right)^2 = 2\beta_\text{e}^2

## Ịchọ anya na adọkpụ
[thumb|Foto a sitere na NASA / ESA Hubble Space Telescope na egosi ụyọkọ kpakpando [MACS J1206.]]
A chọtara ọtụtụ n'ime oghere ndị nwere ike ndọda n'oge gara aga na mberede. Ọchụchọ maka oghere anya na mpaghara ugwu (Cosmic Lens All Sky Survey, CLASS), nke e mere na redio site na iji Very Large Array (VLA) na New Mexico, dugara na nchọpụta nke usoro oghere anya ọhụrụ 22, nnukwu ihe dị ịrịba ama. Nke a emegheela ụzọ ọhụrụ maka nyocha site na ịchọta ihe ndị dị anya na ịchọta ụkpụrụ maka usoro mbara igwe ka anyị wee nwee ike ịghọta eluigwe na ala nke ọma.

Nchọgharị yiri nke ahụ na mpaghara ndịda ga abụ nzọụkwụ dị mma iji gbakwunye nyocha nke mpaghara ugwu yana inweta ebumnuche ndị ọzọ maka ọmụmụ. Ọ bụrụ na a na eme nchọpụta dị otú ahụ site na iji ngwá ọrụ na data a haziri nke ọma, enwere ike ịtụ anya nsonaazụ yiri nke nyocha ugwu. Ojiji nke Australia Telescope 20 GHz (AT20G) Survey data anakọtara site na iji Australia Telescop Compact Array (ATCA) na eguzo ka ọ bụrụ nchịkọta data dị otú ahụ. &nbsp;Ka a na anakọta data site na iji otu ngwá ọrụ ahụ na edebe àgwà data siri ike anyị kwesịrị ịtụ anya inweta ezigbo nsonaazụ site na ọchụchọ ahụ. Nnyocha AT20G bụ nyocha kpuru ìsì na 20 GHz ugboro na ngalaba redio nke electromagnetic spectrum. &nbsp;N'ihi oke ugboro eji eme ihe, ohere ịchọta anya ndọda na abawanye ka ọnụ ọgụgụ nke ihe ndị dị n'etiti (dịka quasars) dị elu (Sadler et al. 2006). Nke a dị mkpa ebe ọ bụ na lensing dị mfe ịchọpụta na ịmata na ihe ndị dị mfe ma e jiri ya tụnyere ihe ndị dị mgbagwoju anya na ha. Ọchụchọ a na agụnye iji usoro interferometric amata ndị na achọ ma soro ha na mkpebi dị elu iji mata ha. Nkọwa zuru ezu nke ọrụ ahụ na arụ ọrụ ugbu a maka mbipụta.
áká_èkpè|thumb|Ìgwè kpakpando SDSS J0915+3826 -enyere ndị na enyocha mbara igwe aka ịmụ banyere mmalite kpakpando na ụyọkọ kpakpando.
Microlensing techniques have been used to search for planets outside our solar system.  A statistical analysis of specific cases of observed microlensing over the time period of 2002 to 2007 found that most stars in the Milky Way galaxy hosted at least one orbiting planet within 0.5 to 10 AU.

'afọ 2009, e ji oghere anya na adịghị ike mee ihe iji gbasaa mmekọrịta nke oke-X-ray ìhè na ihe ndị okenye na obere karịa ka o kwere omume na mbụ iji melite nha nke ụyọkọ kpakpando ndị dị anya.

  a chọtara ụyọkọ kpakpando anya kachasị anya, J1000+0221, site na iji Hubble Space Telescope">Hubble Space Telescope nke NASA. Ọ bụ ezie na ọ ka bụ ụyọkọ kpakpando na ahụ anya nke nwere ihe oyiyi anọ a maara, otu ìgwè mba ụwa nke ndị na enyocha mbara igwe mechara chọpụta ụyọkọkọ kpakpade na ahụ maka ihe oyiyi Hubble Space Telescope na Keck telescope na spectroscopy. E bipụtara nchọpụta na nyocha nke oghere IRC 0218 na Astrophysical Journal Letters na June 23, 2014. 

Nnyocha e bipụtara na Septemba 30, 2013 na mbipụta ntanetị nke Physical Review Letters, nke Mahadum McGill dị na Montreal, Quebec, Canada, duziri, achọpụtala Ụdị B, nke e guzobere n'ihi mmetụta nke gravitational lensing, site na iji South Pole Telescope nke National Science Foundation na enyemaka nke Herschel space observatory.  a ga-emeghe ohere nke ịnwale echiche nke otu eluigwe na ala anyị si malite.

## Anya na adọkpụ
Albert Einstein buru amụma  1936 na ụzarị nke ìhè sitere n'otu ụzọ ahụ nke na agba gburugburu ọnụ Anyanwụ ga-agbakọta na ebe a na elekwasị anya ihe dịka 542 AU site na anyanwụ.  mere, nyocha nke dị n'ebe dị anya (ma ọ bụ karịa) site na Anyanwụ nwere ike iji Anyanwụ dị ka oghere ndọda maka ime ka ihe ndị dị anya dị n'akụkụ nke ọzọ nke Anyanwụ. Ebe nyocha nwere ike ịgbanwe dị ka ọ dị mkpa iji họrọ ihe dị iche iche gbasara anyanwụ.

Ogologo a karịrị ọganihu na ikike ngwá ọrụ nke nyocha mbara igwe dị ka Voyager 1, na karịa mbara ala ndị a maara na mbara ala ndị dị mkpụmkpụ, ọ bụ ezie na n'ime ọtụtụ puku afọ 90377 Sedna ga aga n'ebe dị anya na orbit ya dị elu. Nnukwu uru maka ịchọpụta akara site na oghere a, dị ka microwaves na Akara hydrogen 21cm, dugara na aro Frank Drake n'oge mmalite nke SETI na enwere ike iziga nyocha na ebe a.  tụụrụ ESA aro nyocha SETISAIL na mgbe e mesịrị FOCAL na 1993, mana a na atụ anya na ọ ga abụ ọrụ siri ike.  bụrụ na nyocha gafere 542 AU, ikike mmụba nke oghere ahụ ga anọgide na arụ ọrụ n'ebe dị anya, ka ụzarị ndị na abịa na ebe dị anya karịa gafere n'ebe mgbagwoju anya nke corona anyanwụ.  nyere nkatọ nke echiche ahụ, [1] onye tụlere okwu gụnyere mgbochi nke corona anyanwụ, nnukwu mmụba nke ebumnuche ahụ, nke ga eme ka imewe nke ụgbọ elu ahụ sie ike, yana nyocha nke aberration spherical nke oghere anya.

N'afọ 2020, onye sayensị NASA Slava Turyshev gosipụtara echiche ya nke Direct Multipixel Imaging na Spectroscopy nke Exoplanet nwere Solar Gravitational Lens Mission. Ogwe anya nwere ike ịmegharị onyinyo mbara ala ahụ  ~25 km-scale surface resolution, nke zuru ezu iji hụ ihe ndị dị n'elu na ihe ịrịba ama nke obibi.

## Ịtụle anya anya na adịghị ike
thumb|Ìgwè kpakpando MACS J2129-0741 na ụyọkọ kpakpando nwere oghere MACS2129-1 .
Kaiser, Squires and Broadhurst (1995),  Luppino & Kaiser (1997)  na Hoekstra et al. (1998) nyere iwu usoro iji gbanwee mmetụta nke ọrụ na-agbasa isi (PSF), na eweghachi onye na eme atụmatụ nke na enweghị mmerụ ahụ site na mgbagwoju anya nke PSF.   (KSB +) bụ usoro a na ejikarị eme ihe na nyocha nke lensing na adịghị ike.

Ụyọkọ kpakpando nwere ntụgharị na ntụgharị na enweghị isi. N'ihi ya, mmetụta shear na lensing na adịghị ike kwesịrị ikpebi site na ntụziaka ndị a họọrọ. Isi ihe na eme ka njehie dị na nyocha anya bụ n'ihi nkwekọrịta nke PSF na onyinyo anya. Usoro KSB na atụle ellipticity nke onyinyo ụyọkọ kpakpando. Akpụkpọ ahụ kwekọrọ na ellipticity. A na ahazi ihe ndị dị na ihe oyiyi ndị nwere oghere dịka oge quadrupole ha dị arọ. Maka ellipse zuru oke, oge quadrupole dị arọ nwere njikọ na ellipticity dị arọ. KSB -agbakọ otu esi ejikọta ihe ellipticity dị arọ na shear ma jiri otu usoro ahụ wepụ mmetụta nke PSF.

Uru ndị bụ isi nke KSB bụ ịdị mfe ya na mmejuputa ya dị mfe. Otú ọ dị, KSB dabeere na isi echiche na PSF bụ okirikiri na mgbagwoju anya anisotropic. Nke a bụ echiche ezi uche dị na ya maka nyocha nke cosmic shear, mana ọgbọ na esote nke nyocha (dịka LSST) nwere ike ịchọ izi ezi karịa ka KSB nwere ike inye.

## Ihe ngosi

Usòrò:The_Sunburst_Arc_PSZ1_G311.65-18.48.jpg|alt=Sunburst Arc galaxy.|Sunburst Arc na-agba ụta.
Usòrò:Hubble’s_view_on_distant_quasar_J043947.08+163415.7.tif|alt=Gravitationally lensed Quasar.|nwere oghere ike ndọda.
Usòrò:On_the_hunt_for_newborn_stars.tif|alt=In SDSS J0952+3434, the lower arc-shaped galaxy has the characteristic shape of a galaxy that has been gravitationally lensed.|SDSS J0952+3434, ụyọkọ kpakpando dị ala nwere ọdịdị nke ụyọkọ nke e ji ikike ndọda mee.
Usòrò:Warped_and_distorted_SDSS_J1050+0017.jpg|alt=Warped and distorted around SDSS J1050+0017.|Gbagọrọ agbagọgbagọọ gburugburu SDSS J1050+0017 . [1]
Usòrò:Stretched_out_image_of_distant_galaxy.jpg|alt=Galaxy SPT0615-JD existed when the Universe was just 500 million years old.|__ibo____ibo____ibo__ Ọ bụ ezie na ọ bụSPT0615-JDdị mgbe eluigwe na ala dị naanị na afọ 500.
Usòrò:Cosmic_snake_pregnant_with_stars.tif|alt=Gravitational lenses found in the DESI Legacy Survey data|Igwenke ike ndọda a hụrụ na data DESI Legacy Survey [1]
Usòrò:Gravitational_lenses_found_in_the_DESI_Legacy_Survey_data.jpg|alt=Gravitational lenses found in the DESI Legacy Survey data|Lensị ike ndọda hụrụ na data DESI Legacy Survey [1]
Usòrò:Hubble_captures_gallery_of_ultra-bright_galaxies.jpg|alt=The lensing phenomenon allows for features as small as about 100 light-years or less.|Ihe omume lensing-enye ohere maka atụmatụ ndị dị obere dị ka ihe dị ka 100 light-years ma ọ bụ obere.
Usòrò:Detailed_look_at_a_gravitationally_lensed_supernova.jpg|alt=Detailed look at a gravitationally lensed type Ia supernova iPTF16geu.|Nchịkọta zuru ezuụdị nke supernovaiPTF16geu.
Usòrò:HST-Smiling-GalaxyClusterSDSS-J1038+4849-20150210.jpg|alt="Smiley" image of galaxy cluster (SDSS J1038+4849) & gravitational lensing (an Einstein ring) (HST).|"Smiley" onyinyo nke ụyọkọ kpakpando (SDSS J1038+4849) & gravitational lensing (Mgbaaka Einstein) (HSTỌpụpụ ọzọ [1]
Usòrò:Gravitationell-lins-4.jpg|alt=Abell 1689 - actual gravitational lensing effects (Hubble Space Telescope).|Abell 1689- mmetụta nke ikike ndọda (Hubble Space TelescopeỌpụpụ ọzọ
Usòrò:COSMOS_3D_dark_matter_map.jpg|alt=Dark matter distribution - weak gravitational lensing (Hubble Space Telescope).|NkesaIhe gbara ọchịchịrị- lensing na-adịghị ike (Hubble Space TelescopeỌpụpụ ọzọ
Usòrò:The_most_distant_gravitational_lens_yet_discovered.jpg|alt=Gravitational lens discovered at redshift z = 1.53.|Anya na-ahụ maka ikike ndọdaredshiftz = 1.53.
Usòrò:PIA23641-GravitationalLensing-20200108.jpg|alt=Gravitational Lensing Graphic (January 8, 2020)|Gravitational Lensing Graphic (Jenụwarị 8, 2020)
Usòrò:Hubble_Showcases_Hamilton’s_Object.jpg|alt=Hubble Showcases Hamilton's Object|Hubble na-egosi Ihe Hamilton
Usòrò:Gravitational_lensing_by_a_black_hole.jpg|alt=Illustration of gravitational lensing|osise nke gravitational lensing [1]
Usòrò:Gravitationally-lensed_distant_star-forming_galaxy.jpg|alt=Gravitationally-lensed distant star-forming galaxies.|Ìgwè kpakpando ndị anya na-emepụta kpakpando.


## Hụkwa

* Anya ikuku nke ụwa
* Anya kpakpando   Ọdịdị nke ụyọkọ kpakpando
* Ọdịdị nke oghere ike ndọda   ụdị usoroPeeji na-egosi nkọwa wikidata dị ka ọdịda azụ
* Igwe anya ike ndọda   mmetụta siri ike iji mepụta ọtụtụ ihe oyiyi, arcs, ma ọ bụ ọbụna mgbanaka EinsteinPeeji na egosi nkọwa wikidata dị ka ọdịda azụ
** Obe Einstein   Foto nke nwere oghere na adọkpụPeeji ndị na egosi nkọwa dị mkpirikpi nke ndị a na achọ ịlaghachi
** Mgbaaka Einstein   Akụkụ a na ahụ mgbe ihe na eme ka ìhè nwee ikike ndọda
* Lens nke ike ndọda na adịghị ike   ntụgharị nke ìhè n'enweghị ịmepụta ihe oyiyi ndị ọzọ a na ahụ anyaPeeji na egosi nkọwa wikidata dị ka ọdịda azụ
* Microlensing nke ikike ndọda   Ihe na eme na mbara igwe n'ihi mmetụta nke ikike ndọda
* SN Refsdal   Supernova nke e mebiri
* Euclid (ụgbọ mbara igwe)    Ebe a na ahụ anya na mbara igwe na Europe

## Akwụkwọ akụkọ ihe mere eme na ntụaka

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## Ihe odide

; Ihe edeturu

; Ịgụ ihe ọzọ

* 
* 
* [Ihe e dere n'ala ala peeji] "Site na Fundamental Theorem nke Algebra gaa na Astrophysics: Ụzọ "Harmonious" (PDF). Nkwupụta nke AMS. 55 (6): 666–675. E debere ya (PDF) site na nke mbụ na 2008-09-07.
* 
* Ngwá ọrụ maka nyocha nke ohere nke iji ọnụọgụ parallax nke isi mmalite ndị nwere oghere (Stein Vidar Hagfors Haugan. June 2008)
Òtù:Pages with unreviewed translations