Closed-loop adaptive optics using a CMOS image quality metric sensor

Transcription

1 Closed-loop adaptve optcs usng a CMOS mage qualty metc senso Chueh Tng, Mchael Gles, Adtya Rayankula, and Pual Futh Klpsch School of Electcal and Compute Engneeng ew Mexco State Unvesty Las Cuces, ew Mexco ABSTRACT When compaed to the Shack-Hatmann senso, the mage shapness feedback method has the advantage of easy mplementaton n a closed-loop adaptve optcs system. It also has the potental to be mplemented as a smat senso usng VLSI technology. In ths pape, we pesent a novel adaptve optcs testbed that uses a CMOS shapness mage bult n the ew Mexco State Unvesty (MSU) Electo-optcs Reseach Laboatoy (EORL). The adaptve optcs testbed, whch ncludes a CMOS mage shapness mage as a wavefont senso and a 37-channel defomable mo, has the capablty to apdly compensate the hgh ode phase abeaton. An expemental pefomance compason of the pnhole mage shapness feedback method and the CMOS mage s pesented. The expemental data shows that the CMOS shapness mage woks well n a closed-loop adaptve optcs system. Its oveall pefomance s bette than that of the pnhole method, and t has a fast esponse tme. Keywods: adaptve optcs, mage shapness metc, stochastc paallel gadent descent algothm 1. ITRODUCTIO Even thought adaptve optcs has been ecognzed as a pomsng technology to compensate the degaded mage caused by atmosphec tubulence; howeve, ts pefomance s stll lmted by wavefont compensaton esponse and detecto senstvty. 1 In ode to mpove system pefomance, to modfy wavefont sensng method and to mpove wavefont compensato contol algothm effcency may be a possble appoach. Compaed to use the Shack-Hatmann wavefont sensng, the mage qualty metc (o mage shapness) may have advantages of easy mplementaton n a closed-loop adaptve optcs system and moe flexblty to mplement nsde contol algothm wth VLSI technology. Appled mage qualty metc as wavefont sensng n adaptve optcs has been nvestgated by many authos and many applcatons wth adaptve optcs applcatons mplemented wth mage qualty metc wee demonstated successfully. -4 Pevous eseach esults wee demonstated the technology pomsng and applcaton mplementaton potental. Usng mage qualty metc as wavefont sensng n adaptve optcs was fst demonstated by Mulle and Buffngton and eght dffeent mage shapness functons wee descbed n the pape. 5 The concept behnd mage qualty metc method s that the undstoted mage qualty metc s always lage than the dstoted mage qualty metc at the mage plane; then, the mathematcal poblem fo mage qualty metc method can be consdeed as a stochastc seach and optmzaton poblem. A stochastc seach and optmzaton methodology based on stochastc paallel gadent descent algothm was developed by Voontsov. 6 In ode to educe stochastc seach and optmzaton pocessng tme, embedded an mage qualty optmzaton algothm nto a mage senso aay may be a possble appoach. A VLSI mage shapness senso based on the stochastc paallel gadent descent algothm appled n adaptve optcs was fst demonstated by Voontsov, Cohen and Cauwenbegehs. 7 Although pevous eseach esults show that VLSI technology povdes a pomsng futue fo the mage qualty metc senso n adaptve optcs; howeve, a quanttatve pefomance evaluaton methodology and esult fo adaptve optcs usng mage qualty metc has not been appeaed. The puposes of ths pape ae 1) we ntoduce a theoetcal system pefomance evaluaton methodology fo adaptve optcs usng mage qualty metc senso, and ) we demonstate a closed-loop adaptve optcs usng a CMOS mage qualty metc senso and evaluate ts pefomance wth ou theoetcal methodology. chtng@gauss.nmsu.edu; phone x11; fax

2 In ode to acheve ou goal, a theoetcal adaptve optcs model and an adaptve optcs testbed usng CMOS mage qualty metc senso wee developed; the methodology pefomance s vefed by the compason esults between the theoetcal computatonal esults and the expemental data. To poduce theoetcal compason esult, we also establsh an adaptve optcs theoetcal model then, we bult up an adaptve optcs testbed; and the system pefomance evaluaton analyss s based on compason esults between theoetcal smulaton data and expemental data. The theoetcal optcal system model was developed n tems of optcal modulaton functon; to evaluate the mage degadaton mpacted by atmosphec tubulence, an mage qualty metc as defned n tems of atmosphec coheence length, 0. The adaptve optcs testbed conssts of a 37 channels defomable mo and a CMOS mage qualty metc senso. In ode to epeat smla atmosphec lke tubulence envonment, a phase s taken to poduce atmosphec lke tubulence. Ths pape s oganzed as follow. The theoetcal methodology s pesented n second secton, the methodology vefcaton s descbed n the thd secton, and a concluson s ncluded.. THEORETICAL METHODOLOGY To develop a pefomance evaluaton methodology, an mage qualty metc appoach s appled. A theoetcal optcal system pefomance evaluaton model n tems of optcal tansfe functon was developed fst; n ode to evaluate mage qualty pefomance, an mage qualty met functon based on system modulaton functon was defned. To smulate a closed-loop adaptve optcs system, an adaptve phase compensaton model s descbed. -1 Optcal system pefomance evaluaton model Consde lght waves popagate though an atmosphec tubulence envonment ove a dstance z. The aveage (shot tme exposue) ntensty at the focal plane can be epesented as 8 k j k j k ρ ξ z ρ z I( ξ) = I 0 dρ e d ψ ψ ρ + U U ρ + e πz ( ) ( ) ( ) ( ),. (.1) whee ψ ( ) s the optcal wave functon acoss the apetue and U ( ) s the tansmttng apetue dstbuton of the optcal system. In equaton (1), the modulaton tansfe functon (MTF) of the optcal system wth the atmosphec tubulence can be pesented as k j = d + U U + e z ρ τ ( ψ (ρ )ψ( ) ( ) (ρ ).... (.) Snce the pefomance of an optcal system n the fa-feld egon s consdeed, the optcal system MTF n equaton (.) can be ewtten as whee W( ) τ ( = d ψ ( ρ + ) ψ( ) W ( ) W ( ρ + ),.. (.3) s a pupl functon of the optcal system and s defned as whee D s the adus of the apetue. 1 > D W ( ) =,.. (.4) 0 D Consde dstubed optcal waves on the entance pupl ae epesented as jφ( ) ψ ( ) = e,.. (.5) whee φ ( ) s the phase functon. The optcal system MTF can be epesented as j( φ( ) φ( + ) τ( = d e W ( ) W ( (.6) Assumng the atmosphec tubulence spectum follows the Kolmogoov spectum model, the atmosphec modulaton tansfe functon wthout any adaptve phase compensaton s gven as 1 1 Dφ ( A ρ = φ φ + ρ = e,... (.7) ( ) ( ) ( )

3 D ρ = φ φ + ρ s the phase stuctue functon and n tems of the atmosphec coheence length whee ( ) ( ) ( ) φ (Fed s paamete), 0, s epesented as ρ D ( = (.8) φ 0 The MTF of the optcal system come wth the atmosphec tubulence n tems of phase stuctue functon can be epesented as 1 φ ( τ( = e D d W ( ) W ( +,. (.9) whee the phase stuctue functon D φ( s defned as Dφ ( = φ( ρ + ) φ( ). (.10) The MTF of optcal system n equaton (7) can be n tems of the poduct of a dffacton-lmted optcal system MTF and the atmosphec tubulence phase plate MTF A ( ρ ), and s epesented as 1 ( φ τ( = e D dw ( ) W ( ρ + ) = A( T (,.. (.11) whee A ( ρ ) s the atmosphec tubulence phase plate MTF; and T ( ρ ) s the dffacton-lmted optcal system MTF and can be epesented as 1 cos ( ρ 1 ρ ρ D T( =.... (.1) 0 ρ > D whee D s the adus of the apetue and ρ = ρ. In ode to evaluate the mage degadaton by atmosphec tubulence, an mage qualty met whch s based on MTF s defned as 9 dρa( T ( J =,.. (.13) dρt ( and the mage qualty metc n tems of the phase stuctue functon, D φ(, and optcal system MTF, T ( ρ ), can be ewtten as 9 1 Dφ ( e T ( dρ J =... (.14) T ( dρ - Adaptve optcs system model Adaptve optcs s a eal-tme adaptve phase compensaton system and the concept behnd the adaptve phase compensaton s to look fo a phase abeaton compensatng functon, φ, such that the mnmum phase eo between these two functons (.e., the mnmzed esdual phase eo) can be obtaned wth a 5 3 ( φ φ )( φ φ ) = 0, (.15) whee a s the phase abeaton expanson coeffcent. Zenke polynomals ae the most commonly used expanson functon n tems of phase abeaton. The -tem phase abeaton compensatng functon, φ, can be expanded usng Z ρ, and s gven as 10 Zenke polynomals, ( )

4 φ ( = = 1 a Z (. (.16) The atmosphec modulaton tansfe functon wth adaptve phase compensaton n tems of an -tems Zenke polynomal, φ, s epesented as 9 AAPC ( = exp { j[ φ( ) φ ( )] j[ φ( + φ ( + ]}, (.17) and the mage qualty metc wth adaptve phase compensaton can be descbed as 9 AAPC ( T ( dρ J APC =. (.18) T ( dρ A CMOS mage senso base on mage qualty metc theoy s mplemented n VLSI labotay at ew Mexco State Unvesty. The achtectue ccut of senso s descbed n the followng secton. -3 CMOS mage senso mplement achtectue 3. EXPERIMET SETUP AD PERFORMACE EVALUATIO To evaluate the methodology pefomance, an adaptve optcs testbed wth a CMOS mage qualty metc senso s bult up and the pefomance of a closed-loop adaptve optcs usng a CMOS mage qualty metc senso s by means of the compason esults between theoetcal computaton and expemental data. 3-1 Expemental testbed setup The expemental setup whch s shown n Fgue 1 ncludes an adaptve optcs testbed and an atmosphec lke tubulence geneato. In ode to compae CMOS senso compensaton pefomance, an adaptve optcs testbed usng a 50 µm pn hole and a sngle cell photodetecto whch s shown n Fgue was also bult up. The adaptve optcs testbed conssts of a 37-actuato defomable mo, a CMOS mage qualty metc and a phase abeaton compensaton contol algothm. In ode to poduce a epeatable atmosphec lke tubulence, a laboatoy phase plate s used. The phase plate s use nea fled technology and the chaactestc of phase plate n tems of atmosphec coheence length, 0, s shown n Fgue. In Fgue, the theoetcal esult based on Kolmogoov tubulence spectum s obtaned fom equaton (.1). The wokng functon of the closed-loop adaptve optcs testbed s descbed as follows. The ncdent lght sgnal s go though an optcal elay whch conssts of lenses L 1 and L and dectly mpact nto the hgh-ode phase abeaton compensaton feedback contol loop. An optcal elay mages the entance pupl onto the defomable mo so as to fll the 1-mm damete effectve aea of the defomable mo. The phase abeaton poduced fom atmosphec lke tubulence phase plate s measued by a CMOS mage qualty metc senso. The feedback sgnals based on the sgnal stength measued fom the CMOS mage qualty metc senso ae calculated usng a stochastc paallel gadent descent algothm and delveed to the defomable mo to poduce the equed phase compensatons. The compensated wave feld fom the defomable mo s dected by the beam spltte B1 to the scence camea. Snce the pncple behnd an mage qualty metc method s a stochastc seach and optmzaton poblem and the gadent descent algothm s the most common used to solve ths poblem. To ncease compensaton pefomance, a stochastc paallel gadent descent algothm whch s used to contol phase abeaton compensato s used and descbed as followng. At evey tme-step, the contolle dffeentally petubs each element of the phase abeaton compensato u by some δu and the esultng change n the mage qualty met functon s evaluated wth 6 k k k k k k k k k k δ J = J ( u1 + δu1, u + δu,..., u + δu ) J ( u1, u,..., u )..... (3.1) Each element of the phase abeaton compensato s updated n paallel at evey tme-step accodng to the update ule, k+ 1 k k k u = u Γ( α, γ) δj δu, whee α s a petubaton paamete and γ s a leanng adaptaton ate paamete.

5 Fgue 1 Expement setup schematc dagam closed-loop adaptve optcs usng a CMOS mage qualty metc senso. Fgue Expement setup schematc dagam closed-loop adaptve optcs usng a pnhole detecto Measuement data Theoetcal data 0.7 Image Qualty Metc D/ 0 Fgue Phase plate chaactestc compason esult between theoetcal computaton and expement vesus D/ 0

6 3- Pefomance evaluaton analyss System pefomance evaluaton s pefomed by system compensaton esponse and mage compensaton qualty wth vaous D/ 0. Snce the adaptve optcs system compensaton esponse manly depends on the convegent ate of contol algothm, that s, SPGDA, the pefomance esults whch s shown n Fgue 3 ae n tems of algothm teaton numbes vesus D/ 0. The expemental esult shows the system esponse become slowly as D/ 0 (tubulence stength) nceasng. The contol algothm computaton numbes vaous fom 10 to 43; when a 66 MHz Intel Pentum 4 Pocessos s appled, the system esponse of adaptve optcs testbed shown n Fgue 4 vaes between 90 Hz and 330 Hz. Accodng to the esults shown n Fgue 3 and Fgue 4, the CMOS senso has bette system esponse than pnhole detecto as the tubulence stength nceasng CMOS senso pn hole 70 Iteaton umbes D/ 0 Fgue 3 Adaptve the teaton numbe of convegence System Response (Hz) CMOS senso Pn hole D/ 0 Fgue 4 Adaptve optcs testbed system phase compensaton esponse vesus D/ 0

7 In ode to evaluate the mage qualty compensaton pefomance, the expemental mage qualty metc s defned as the ato of the pefect mage sgnal and the dstoted sgnal and s descbed as follow Vds J exp =,.... (3.1) Vpef whee V dst s the dstoted mage sgnal stength measued fom detecto and V pef s the pefect mage sgnal stength measued fom detecto. The mage compensaton pefomance compason esults between theoetcal computatonal esults and expemental data s shown n Fgue 4. The computatonal esult wthout adaptve phase compensaton s obtaned fom equaton (.14) and the computaton esults wth adaptve phase compensaton ae obtaned fom equaton (.18). The expemental data n Fgue 4 shows that the adaptve optcs testbed usng a CMOS mage qualty senso has a capablty to compensate hgh ode abeaton to 13 th Zenke mode. The CMOS senso has the bette phase abeaton compensaton pefomance than pn hole detecto Image Qualty Metc CMOS Senso Pn Hole n=0 n=10 n= D/ 0 Fgue 4 The theoetcal data and expemental data compason fo mage qualty metc vesus D/ COCLUSIOS A theoetcal methodology to chaacteze an adaptve optcs usng mage qualty metc senso pefomance was pesented and vefed. The compason esults ae shown that thee s a hgh coelaton between expemental data and theoetcal computatonal data; the expemental data s also shown a closed-loop adaptve optcs usng a CMOS senso has the capablty n compensatng a hgh ode phase abeaton. REFERECES 1. Rodde, F, Adaptve Optcs n Astonomy, Cambdge, Weyauch, Thomas, Mkhal A. Voontsov, T. G. Bfano, J. A. Hamme, M. Cohen, and G. Cauwenbeghs, Mcoscale adaptve optcs: wave-font contol wth a µ-mo aay and a VLSI stochastc gadent descent contol, Appl. Opt., 40, 443, Weyauch, Thomas, Mkhal A. Voontsov, Fee-space lase communcatons wth adaptve optcs: atmosphec compensaton expements, J. Opt. Fbe Commun. Rep., 4, , Tng, Chueh and Mchael K. Gles, Gound-based stella ntefeomety wth adaptve optcs, Poc. SPIE, 5903, 3, Mulle, R. A. and A. Buffngton, Real-tme coecton of atmosphecally degaded telescope mages though mage shapenng, J. Opt. Soc. Am., 64, , 1974.

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