.

.

.

.

HARMONIE VNIVERSELLE.

GQNTENANT LA THEORIE "~T LA PRATI Q";¥E

I -j DE LA MVSIQVE,

o.:rii( tnlc.& deJa Nnuredea Soc•,&dca Molit0¢ft)COS ,-du Conf"IWICcs, dn OUfonanocs, "* Gc.nrc.s. del Model, de Ia CompoC.:Uoa J de: b.

Voix•dn Cfuanu .. k de toutd (or=: d1nflrumCD$ Harmoniques.

A P A R I S, ~hez SEBASTIEN CMuotsr, lmprimcurordinlire du Roy,

l'lj~~$..IacquC3 , aux Gicogncs. M; D't:. ~XXXV I.

tAJit!~~~. Ct_tdtpr•&~Ju'D.O"'rf.. ·

1&3&

• Optical Design of JWST

SM

18 Segments

PM .----·

TM

ln1agl.!

Three-Mirror-Anastigmat (TMA} wide-field telescope design

2018

We've l ookirtg tl1.voual-1 tel esc opes tl1.at l1.aveVt't cl1.aVtged iVt basic coVtcept iVt ovev 350 yeavs. Mivvov telescopes ave too SVV\a((.)

too vigid aVtd suffev fvoVV\ excessive aevial VV\ass.

.

.

Synt he t i c Spect ra of an Eart h-li ke Pla ne t

l . E+OO ~--------------~------------~

6. E-Ol

4 .E -01

3. E-Ol

2.E -Ol

l .E -01 CH

0 cb

2

0 2

------~----------------~--~----------------

3 4 wa vel engths in mic rons

EveV\ if we do iW\o.9e O.V\ exoplo.V\et OV\ a pixel ov two O.V\d detevW\iV\e it exists iV\ t~e ~o.bito.b/e .zoV\e of its so/o.v systeW\J we CO.V\V\Ot dec/ave

it ~o.bito.b/e wit~out to.kiV\9 its spectvuW\ to fiV\d si9V\o.tuves.

Tivget telescope

L

microscope •

L lvf = ­

n

input to scope

r

~ from star-1

L

grating

telescope To take a spectruVV\ we Vteed a powerful diffractioVt 9ratiVtg. The text­books do Vtot teach usiVt9 a diffractioVt 9ratiVt9 as a priVV\ary objective.) but we built a VV\icroscope with a diffractioVt 9ratiVt9 f:?riVV\ary. The VV\icroscope works OVt gra:z.iVtg /VtcideVtce where VV\a9VtificatioVt is iVt proportioVt to the leVt9th of a gratiVtg L to aJ the iVtcideVtce aperture. A revolutiVtary telescope desigVt based gra:z.iVtg exodus rather thaVt gra:z.iVtg iVtcideVtce would eVtjoy the saVV\e levera9e as the VVlicroscope.

.

First PriYlciples

A source of disto.Vtt i{( uV\1\iVto.tioVtJ say o. star.) precesses.

How co.Vt it be V\1\o.de to proaress tlt\rou9Jt\ its spectruV\1\?

CoV\sidev aV\ object at the :z.eV\ith.

Lt9/!\t fr-oM t/!\e sour-ce ar-r-ives as plaV\e wave.

-

A

The p(aVte wave str-ikes p(aVte gv-atiVtg A.

Ltf3lt\t is disper-sed fr-oM tlt\e pfaV\e gv-atiV\9 at O.V\gfes iVlvev-sefy pv-opov-tioVla( to wave(eV\gtlt\.

DiffractioVt 9ratiVt9S v-ecoVtstruct tltte p{aVte wave at a Vtew aVt9fe wlttev-e it CaV\ be coUected .

A specific waveleV\9tlt\ is disper-sed to par-abolic V\1\ir-v-ov- B.

For- aVtotlt\ev aVt9fe of iVtcideVtce upoV\ 9vatiVt9 A par-abolic V\1\ivvov B wi{{ collect aVtotlt\ev wave{eVt&tlt\.

VavyiV\9 aV\9fes of iV\cideV\ce upoV\ 9vatiV\9 A slt\ar-iV\9 a fixed aV\d COVV\VV\OV\ aV\9fe of veCOV\StvuctioV\ v wi((

disper-se vavyiV\9 wavefeV\9tlt\s to par-abolic VV\ir-vov B.

• 1

Tlt\is coV\ft£juv-atioV\ lt\as aV\9le of iV\cideV\ce i vaV'!:jiV\9 aV\d a fixed 9V'a~iV\9 aV\9{e of

wavefv-oV\t v-eCOV\Stv-uctioV\ v-.

The Diffraction Equation

sin(i) + sin(r) = nA p

• 1

Wl--\eV\ tl--\e aV\gle of v-ecoV\stv-uctioV\ v-_, tl--\e pitcl--\ of tl--\e gv-atiV\g p _, aV\d tl--\e diffv-actioV\ ov-dev- V\ av-e fixed _, tl--\e aV\gle of iV\cideV\ce

CaV\ be calculated by a V\1\easuv-eVV\eV\t of waveleV\gtl--\ 'A.

• 1

VaviatioVts iVt tlt\e aVt9le of iVtcideVtce over- a fixed aVt9le of vecoVtstvuctioVt will disper-se a spectvuW\ of wave(eVtf}tlt\s.

FoV' gV'atiV\9 A dispeV'StV\9 to paV'abofic W\tV'V'OV' B tlt\eV'e wi{{ be a COW\W\OV\ focal poiV\t C tlt\at call\ be a spectV'aplt\ slit. A secoV\daV'!:J dispeV'seV' D call\ tlt\eV\ pV'oduce spectV'UW\ E.

.

.

As aV\ object pr-ecesses.~ its spectv-uWl CaV\ be takeVl.~ aV\d a{{ objects CaV\ be seeV\ - OV\e wave{eVl&tltt at a tiWle - over- tltte

cour-se of aV\ obsev-vatioV\ cycle.

.

.

.

• • • .•

• , • • • • • - ••• , . • .. • •

.• • • ,. • • • • - • ,. .. _,.. •• • •

• • • • .

• '. • • • - • ~ .. . ·.,.. • •

Data Reduction • -" ,

__, ., '

, • , •

~

' • ' •

" .... ••

• -., •

-~ •• • ., • ' ~ .. -· ... ,

" •

• •• .. •

-~ • ,

• • .... ~ •• • ,

• • .. . . • • ... ~ -• • • ., ... ... •

" • . ' r

Three samples of one star

• ... • • f ••• • • ... •

•

'

'

J .. •

' {

•••

, •

1.0 ,..

0.8 1-

0.6 l­

OA r-

:~ .._r- _n,&.,W,,o1_ ............................. __ 1.0

0.8

0.6

OA

0.2

0.0

1.0

0..8

0.6

0.4

0.2

0.0

r-

r-r-r-r-• r-

r-r-r-r-

I"' \

~ ~ ~ ..

J

Three frames in the data parade

A sequeVtce of fraW\eS takeVt at short iVtte,gratioVt periods results iVt a spectruW\ for each object aVtd for a(( objects .

.

.

.

Luminosity Function

Magnitude Example Stars I degree2 1 o x 90° Stars to this magnitude

-1.42 Sirius 1 6.5 Yale catalog 6,500 10.5 Hipparchus cat. 3 270 110,000 12 3" scope 12 1,080 500,000 13 6"scope 25 2,250 1,000,000 14 1 0" scope 60 5,400 2,500,000

15.5 300 27,000 10,000,000 20.5 30,000 2,700,000 1 ,000,000,000 23 Best scope 300,000 27,000,000 10,000,000,000

The MOST multiple object spectroscopy

A t/t\v-ee ov-dev- VVta_gVl.itude iVtcv-ease iVt t~e VtUVVtbev- of siVVtu(taVteous spectr-a per- obev-sev-vatioVt cycle over- aV\y coVVtpetiVt_g tec/t\Vtolo9y at a 1-0 x iVtcv-ease iVt v-esolutioVt.

.

.

A diffvactioV\ gvatiV\9 caV\ be detiveved fvoVV\ a c~liV\dev vo{{ as a gossa­VV\eV' V\1\eVV\bV'aV\e of aV\~ leV\gt~ aV\d ::LO VV\etevs ~et'g~t. How loV\g do ~ou waV\t t~e apevtuve? How big do ~ou waV\t t~e collectov? ::LOO sq. VV\etevs? soo sq VV\etevs? OV\ce deplo~ed-' gvatiV\gs ave flat-' fig~t weig~t-' COV\Ceivabl~ capable of kiloVV\etev scale iV\ t~e optical vegiV\1\e.

.

.

.

w

The MOST airborne

E

It cattt be ottt tbte dovsa{ side ov beffH of attt aivcvaft depetttditttfj ottt wbtetbtev HOU watttt Hour- spectr-a {ookitttfj up ov dowttt. Tbte aiv­fvaV\1\e is sealed_, because tbte 9vatittt9 is a vow of witttdows afottt9 tbte fusefa9e.

.

.

.

-·

Primary Objective Grating

WJ.-\at J.-\appeV\s wJ.-\eV\ tJ.-\e secoV\dar-!:J Mivvov is S!:JMMetvica((!:J opposed b!:J a secoV\d Mivvov?. Ffux coUectioV\ is doubfed. TJ.-\e fr-ee spectr-a( vaV\9e doubfes fr-oM qo de9vees to 1-80 de9vees. TJ.-\ivdJ cafibvatioV\ CaV\ be acJ.-\ieved b!:J cr-oss -covvefatioV\ betweeV\ two veadiV\9S of tJ.-\e saMe object at diffeveV\t V\1\0V\1\eV\tS iV\ tiMe.

First Mirror

secon~ ~irror FroVV\ a desi9V\eV"s poiV\t-of-view_, tVle packa9e takes OV\ a V\ice (s~a(( we sa~ "beautiful" or "VV\a9V\ificeV\t"?) balaV\ce w~ere two VV\irrors s~are t~e saVV\e telescope.

A telescope tltlat CaV\ be buried below 9rouV\d witb\ V\O doW\e _, V\O wiVtd sb\ear aVtd works esseVttiaUy witb\ V\O W\OViV\9 parts duriV\9 observatioV\ cycles

The MOST HOMES

1folo1rf:\;rh-ic r>rticf:\;t Meth-o~for Xxortf:\;net Srectroscortt

T~e dual Mir-r-or- S!:JMMetr-!:} V\OW leads us fr-oM T~e MOST T~e Multiple Object Spectv-o9v-ap~ic Telescope to HOMES_, t~e Holo9v-ap~ic Optical Met~od of ExoplaVlet Spectv-oscop!:J. T~e MOST sees aU star-s OV\e waveleV\9t~ at a tiMe. HOMES sees t~e plaVlets of OV\e star- iVl all waveleV\9t~ a(( t~e tiMe.

1 . Z

' 0 .8

0 .6 4

0 .4

o .z 4

0

' 68 u s zoz 269 336 4 0 3 470 537 6 ·04 67, 738 805 8 7 Z 939

I 1 006

06: 0 .00539 0 .00381 0 .00207 0 .00060 o .ooooo 0 .0• 0 1: ! . 00000 !.0 0000 1.00000 1.00000 1 . 00000 1 . 0 •

08 : o .oo51s o .oo389 o .oo212 o .ooo63 o .ooooo o .o• 0 9 : !.00000 !.0 0000 1.00000 1.00000 1 . 00000 1 . 0 • 10 : 0 .00557 0 .00397 0 .00218 0 .00066 0 .00000 0 .0• !!: 1.00000 !.0 0000 1.00000 1.00000 1 . 00000 1 . 0 • 1 , : 0 . 00!>66 0 . 0 010 1 0 . 00221 0 . 00069 0 . 00000 0 . 0 •

! 3 : !.ODOOO !.0 0000 1 . 00000 1 . 0 0000 1 . 00000 1 . 0 • 1 4: 0 . 0051 4 0 . 0 0 411 0 . 00229 0 . 0 0072 0 . 00000 0 . 0 •

1 5 : ! . 00000 1 . 0 0000 1 . 00000 1 . 0 0000 1 . 00000 1 . 0 • i 6: o .oo58~ o . 0 0 418 o . oo234 o . o oo7 5 o . ooooo o . o •

0 9 : ! .O~ODO ! . 0 0000 1 . 00000 1 . 0 0000 1 . 00000 1 . 0 • 10 : 0 . 00590 0 . 0 0 4 25 0 . 00238 0 . 0 007? 0 . 00000 0 . 0 •

11 : 1 .00000 1 .00000 1 .00000 1 .00000 1 .00000 1 .0 1

12 : 0 . 005 8 2 0 . 0 0 418 0.00233 0.0007 4 0 . 00000 0 . 0 •

13 : 1 .00000 1 .00000 1 .00000 1 .00000 1 .00000 1 .0• 14: 0 . 00514 0 . 0 0 411 0.00228 0.00072 0 . 00000 0 . 0 •

15: 1 .00000 1 .00000 1 .00000 1 .00000 1 .00000 1 .0 1

1 0 : 0 . 005 6 5 0 . 0 0 40 4 0.00223 0.0006! 0 . 00000 0 . 0 • 17 : 1 .00000 1 .00000 1 .00000 1 .00000 1 .00000 1 .0• ! 8 : o . oo556 o . o o396 o.oo211 o . o oo65 o . oooo.o o . o •

1 9 : 1 . 00000 1 . 0 0000 1 . 00000 1 . 0 0000 1 . 00000 1 . 0 • zo : o . oo5 4 7 o . o o388 o . oo211 o . o oo6z o . ooooo o . o • ; 1 : 1 . 00000 1 . 0 0000 1 . 00000 1 . 0 0000 1 . 00000 1 . 0 1

22: o . oo53e o . o o381 o . oo2o6 o . o oo5 9 o . ooooo o . o • ; s : 1 . ooooo 1 . o oooo 1 . ooooo 1 . o oooo 1 . ooooo 1 . 0 •

21 : o . oo5 z e o . o o372 o.oo2oo o . o oo56 o . ooooo o . o •

We star-t witlt\ tlt\e dual VV\ir-v-ov- COV\ft!Juv-atioV\ aV\d desi9V\ a cor-oV\a-9v-aplt\. AV\ exoplaV\et CaV\V\Ot be seeV\ if its Jt\ost star- is V\Ot extiV\-9uislt\ed. Wlt\eV\ two VV\ir-v-ov-s ave opposed faciV\9 a siV\9le diffv-actioV\ 9v-atiV\9_, aV\d tlt\eiv- beaVV\S COVV\biV\ed _, tlt\eV\ two equal aV\d opposite spectr-a slt\av-e OV\e spectr-al liV\e wlt\ev-e destr-uctive iV\tev-fer-eV\ce eve­ates a siV\9le extr-eVV\el!::J slt\av-p subtv-actioV\ to z.ev-o. Tlt\e iV\tev-fev-eV\ce at tlt\e liV\e wlt\ev-e tlt\e beaVV\S slt\av-e a siV\9le waveleV\9tlt\ is a siV\9u­lav-it!::j _, aV\ absolute V\UU.

In~erferogram be~ween Configura~ions ~ and 2 H~£5 Coronagraph 3/ 10/2013 0 . 5479 pm a~ 0 . 00, 0 . 00 (deg) .

~. 0000

0 .9000

0 . 8000

0 . 7000

0 .6000

0 .5000

0 .4000

0 .3000

0 .2000

0 .~000

0 . 0000

Peak to Valle y = 0 .3956 waves, Fringes/ Wave = 1 . 0000 . su rface : 24 Subaperture Sx: 0 . 0000 Sy : 0 . 0000 Sr = 0 . 1000 Coronagraph Ol. · z:mx Xtilt = 0 . 00 Y~ilt = 0 . 00 .

We see tlt\at Vtu{{ iVt tlt\is iVttev-fev-o9v-aWl .. Tlt\e iVttev-fev-oWletev- is a cov-oVta9v-aplt\ because its Vtu{{ is OV\ a siVt9fe ceVttv-a{ wavefeVt9tlt\ baVtd feaviV\9 tlt\e v-est of tlt\e field for- acquisitioVt of tlt\e p{aVtetar-!:J S!:JSteWl. A tiVt!:J ((star> is Wlav-ked iVt !:JeUow at tlt\e Vtu{{.

Nulling interferometer for coronagraphy

ESO 2001 Astronomy & Astrophysics Interferometric apodization of rectangular apertures Application to stellar coronagraphy C. Aime, R. Soummer, and A. Ferrari A&A 37Q, 697{707 (2001)

DOl: 10.1051/0004-6361:20011293

Cottttvast tlttis witltt cotttvettttiottta f tttu (( ittt9 ittttevfevoVVletvy atttd !:JOU cattt see tltte advatttta9e. Cotttvettttiotttaf tttu (( ittt9 ittt­tevfevoVVletvy Jttas VVtu(tipfe vittt9s wltticltt ittt a covottta9vaph wi(( tttu{{ ittt tltte pfatttetavy ve9iottt atttd cattt extittt9uisltt ffux fvoVVl ver-!:J pfatttets we ave fookittt9 for-.

.

Target Planetary System e D e

Off-axis sources diffract common wavelengths at disparate angles.

J Example - Second source off-axis by 2°

HOfvlES uses a Jttologr-aVV\ as a pr-iVV\ar-y objective. Wlttell\ tltte star- all\d its pial!\­etav-y systeVV\ at ill\fill\ity play back tltte Jttologr-aVV\.) tlttey focus as all\ ill\fill\ite li\UVV\bev- of iV'Aages of tltteVV\selves.) eacltt iV'Aage at diffev-ell\t wavelell\gtltt. Her-e we COVV\pav-e tltte focii for- a tar-get stav­all\d its plall\ets as coVV\pav-ed witltt a otlttev- sour-ce off-axis by 2 degr-ees

r Holographic Optical Element Primary

"St~r"

At eaclt\ foca( poiV\t is a Jt\iBJ.-\fy COVV\­pressed versioV\ of wlt\at is seeV\ at tlt\e

focus of tlt\e parabolic VV\irror of Tlt\e fvlOSTJ tlt\at is a spectra( spread

wlt\ere wavefeV\9tlt\ is propor-

portioV\a( to aV\9fe. A star slt\ares a COVV\VV\OV\ focaf

poiV\t witlt\ its pfaV\ets over a V\arrow

wavefeV\9tlt\ baV\d.

Ovtfy OV\e V\av-v-ow baV\d focuses OV\ eaclt\ fiber- tip.

Wavelength (l..rn)

lo.s lo.s

X-Field Y·Reld 10.500001

lo lo

lo lo 10.50001

lo I· 2 5e.()()5

r>fftet fiet~ r>fftet A

1000 ~-------,.--------:--------r'l

~ a; 100 1--------+-­-o

~ 0 II)

~ ~ 10 1--------~~ ----+-----~ -o 1: IU 0

0.1

0 0

1 10 100 Aperture Diameter (meters)

10000 .,......----:---------------,

5 10 15 20

Distance (parsecs)

o M Stars (163) K Stars (219)

0 G Stars (124) 0 F SWs(27) 0 ASWs(18) 0 U Slars (24)

25 30

Richard G. Lyon & Mark Clampin, ''Space telescope sensitivity and controls for exopla.net imaging" Optical Engineering 51(1), 011002 (Ja.nuru:y 2012)

Tlt\e pv-obleVV\ is VtOt v-eso{utioVt. A so to 1.00 VV\ pv-iVV\av-y objective Jt\olo9V'aVV\ Jt\as tlt\e r-equisite aV\9ulav- aV\d spectr-al v-esolutioV\ to see exop{aVtets witlt\iVt 1.0 par-secs. fVtdeedJ accov-diV\9 to L!:)OV\ & ClaVV\piV\ a 1.00 VV\etev- pv-iVV\ttV'!J could r-esolve Jt\abitable exop(aVtets out to 30 par-secs.

Table 1 Candidate stars versus aperture.

Number of stars at or outside IWA Min days

Diameter (meters) IWA (mas) A (18) F (27) G (1 24) K (219) M (163) u (24) Total (575) flt to SNR = 5

1 m 226.9 5 1 2 1 0 0 9 159.19 I~Z3x394

2m 113.4 16 8 6 1 0 0 31 120.74

4m 56.7 17 22 50 5 0 0 94 33.76

Sm 28.4 17 27 119 30 1 0 194 6.08

16m 14.2 17 27 124 132 9 0 309 0.791

Richard G. Lyon & Mark Clampin, op. cit.

Tlt\e pv-obleW\ is tlt\e flux.) because eaclt\ Jt\i9Jt\ly r-esolved HOfv1ES baV\dpass sees few plt\otoV\S. Let1s say aV\ exoplaV\et at 1-0 par-secs pr-oduces 1-0 plt\otoV\S per- squar-e W\etev- pev­WliV\ute. Tlt\at W\eaV\S witlt\ a HOfv1 ES soo squar-e W\etev­pv-iW\av-y about soo plt\otoV\S per- WliV\ute at 1-00% effi cieV\cy or- so plt\otOV\S per- WliV\ute witlt\ 1-0% tlt\v-ou9Jt\put. DividiV\9 tlt\ese iV\to spectr-a W\eaV\S pickiV\9 br-oad baV\ds to aclt\ieve iV\te9v-atioV\ tiW\es of days v-atlt\ev- thaV\ weeks or- W\OV\tlt\s.

I \VIdth • 0.03mm

T t.OOO.O.O imm

(VT}

(8x0250)

Edge Distance t0.02Smm (ED)

<{).0005mm

>0.0005 0.250 (S)

l-10.40<{).03mm (Vl)

W<{).05mm

(8 X 0.250 ) ±0.0005mm

I -1-~0.SOOiO.OOOSmm

0 19Si0.00Smm~~ A I I V 54'.74•

0 138>0 OOSmm _F---J-AJ Elehetl Pc:~mal Ctitp Tolerooeeeere !OJXIDEIIIIYI V-Gro()lle De-tail

OZ Optics

Figure 2: Detail Drawing For 16-48 Fiber Sil icon V-Groove Chips (Note: 500~m gap Is between every 8 fiber ribbon position In the chip)

. fiber-s spaV\.V\.iV\.9 W\aV\.y W\etevs. Standard Op~ICal T/1\ese bar-s der-ive fV'OW\ a COW\W\Odity pr-oduct COnneCtOr With used today for- COW\W\UV\.iCatiOV\. fiber-s. A OV\.e 500 micron W\etev bar- of fiber-s wi(( acquir-e :1- V\.W\ of spectvuW\.

OV\.e /t\uV\.dved bar-s would acquir-e a :1-00 V\.W\ eV\.OU9/t\ spacers. baV\.dwidt/1\ to see ov-9aV\.icsJ Cioldilocks' povvid9e.

We wi ( ( V\.eed t/1\ouSaV\.dS of

HOMES 4/ 4/201 2

Image Plane

Spectrograph HOEs

30 L a out

I kV\ew wMeV\ we star-ted OV\ tMis pr-oject tMat we'd V\eed a ver-y Mi[JM v-esol utioV\ secoV\dav-y spectv-oav-apM aV\d COV\Sidev-ed MeMbV'aV\e optics. ZeMaX pr-edicted tMat we could use two copies of tMe pv-i­Mar-y HOE but iV\ tv-aV\SMissioV\ v-atMev- tMaV\ v-eflectioV\.

.

2 sources separated by 1 00 mas

.?00 m,ic.rvn5

Tltte focal plaV\e diffevs fvoV\1\ tltte souvce iVV\a9e iV\ tlttat at tltte focus wlttat was a co -axial iV\put COV\taiV\iV\9 tltte waveleV\9tltt -eV\coded iVV\a9es of tltte plaV\ets ave V\OW spatially sepavated by dispevsioV\. IV\ tlttis exaV\1\ple :1...00 V\1\ilfiavcsecoV\dS aV\9ulav sepavatioV\ tvaV\slates iV\to :1... 8 CV\1\ sepavatioV\ OV\ tltte focal plaV\e avvay.

.

.

.

HOMES

.