AD-A MASSACHUSETTS INST OF TECH LEXINGTON LINCOLN LAB FIG 20/6 ZERN IKE ABERRATIONS AND THEIR FAR FIELDS INTENSITIES.(U) SEP So J HERRMANN

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1 AD-A MASSACHUSETTS INST OF TECH LEXINGTON LINCOLN LAB FIG 20/6 ZERN IKE ABERRATIONS AND THEIR FAR FIELDS INTENSITIES.(U) SEP So J HERRMANN F C-0002 UNCLAS I TN ESD-TR-8-88 L

2 iiii'.,!ii -U -2 1~2.2 M36* MR LA,.IIII lll I I III MICROCOPY RESOLUTION TEST CHART NATIONAL BUREAU OF STANDARD',1963-A

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5 MASSACHUSETTS INSTITUTE OF TECHNOLOGY - LINCOLN LABORATORY ZERNIKE ABERRATIONS AND THEIR FAR FIELD INTENSITIES w J. HERRMANN Group 55 TECHNICAL NOTE SEPTEMBER 1980 Appowed for public eisue; 1stribetion mlimitod. LEXINGTON MASSACHUSETTS IIV

6 ZERNIKE ABERRATIONS AND THEIR FAR FIELD INTENSITIES. We present in this report the phase of a wave front as described by the Zernike polynomials I and the corresponding intensities in the focal plane. All aberration up to n=8 are included. The numbering of the Zernike aberration is shown in Table I. If the phase is expressed in terms of Zernike polynomials n = mo Anm Rm cos me then the variance of the phase becomes 2 E E A + mo n=l m=o n+- 2 We present two sets of figures: The phase of the aberrations on the unit circle (in radians) and the intensity in the focal plane on a grid spaced by RAI/D (with a contourline spacing of 2dB). A uniform intensity distribution is assumed for the aperture. The Strehl" ratio (peak intensity) is indicated on each figure and also given in Table I. The extended Mar6chal formula exp-0 2 ) gives a value for the Strehl ratio. Only the cos me terms are presented because the sin me terms can be obtained by a rotation. The assignment of the orders is in accordance with Ref. 1. Sec. 5.1 which was uses m + n for the order of wave aberrations. The far field intensities were calculated using a descrete Fourier transform with a 256 by 256 computational mesh for most cases. For some aberrations (k=16, 29, 37, 42) 512 by 512 mesh points were used. The most striking feature of the irradiances is the shape of the Accession For central lobe which is nearly constant for higher aberrations (nz5). NTIS DTIC T48 CPI&I Unlannounced Justif iatiol_ F1 'I Distribution/ Avaiibilit," CoI M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1965), Sec p i

7 Table I lernike Aberrations k n m Aka) Strehl Ratio 2 I is " " " s " s " " " " " a) Chosen to give a nman-$quare phase deformation of A/10 for each aberration. a

8 * f b ~~1~ = I-zw = -- w w 0 6~ p4 p 3 I

9 CI It-s--- 7Z ~S

10 LA

11 fni C _L U

12 La C-L~ C'I

13 Oisic -X)T) '7-7 pzb

14 ~Ia LLJ ;z LJ -L)J 00 (.4

15 C3-4 It 10

16 0z 0 LAJ LA CL~ OD 0:m

17 /a,. 12

18 0L -- 0,J q 20 zc c- 13

19 I - kn: IL IHI 14 7W

20 156 I t z

21 al UC 16

22 LaJ CT 17

23 4 1- QI CC4 /I- -

24 LI p.r4 54 LL'I

25 LiJ C36 02

26 LJ CI- 211

27 LiJU 'I 22

28 I- cz LL e- LLJJ 00 0% 23

29 col-- (flaj cn I LLJ 9 AJ LII Id, C O If oco ODg 24

30 - 0 lg, -j tjlj lq/ if 0t a"h z 64 25

31 0 55 Lk C4 26

32 0 0m )V ui = C Uv 340 I& 0 NY27

33 LINCLASSIFIED SECURI TV CLASSIFICATION OF THIS PAGE (When Doe. Sowed) REPOT MmAT~N PAE REPOT ENTAION PM AGEBEFORV RAD INSTIRUCTIONS COIPLETNO FM I. REPORT kw GOVT ACCE1SSON N0. 3. RECIPIENT'S CATALOG NUMBER E T 0100 cov8 4-TILEfed-ibul). TYPE Of REPO*T PEIDC RED Zetnike Aberrations and Thefr Far Field htensidesp / 7". ftwo Oo. REPORT NUM&ER Tecluical, Note hi Jan/ierrmann I) ~ FJ C -OS 9. PERFORMING ORGANIZATION NM AND is. P 1 PR.1'". Infcoln Laboratory. M.1. T.AEAWOKNINUER P.O. Box 73 Lexingtons MA It. CONTROLLING OPFICE NAME AND ADDRESS - 2 UE5 T PormEeetN.674 PormEemtN.674 Naval Sea Systems Command 2 Sep gg$w 10 High Energy Laser Project Office Washington. DC MONITORING AGENCY NAME & ADORES$ (if diffwens f~ea Coamreagf OffpeJ IS. SECURITY CLASS. (alhi tdpw Electronic Systems Divislo Hlanscom AFB A)~ I~ Bedfod, MA DISTRIBUTION STATEMENT (el dia Rspe.N) -Unclassifed ~ 7/ /v-j/y,7-7'decla.. SSFICATION OImGRAOING Approved for public release; distribution Unlinited. 17. DISTRIBUTION STATEMENT ( g,.. eaaetedi a lck 29. fffuaf..rp) 18. SUPPLEMENTARY NO0TES None 19. KEY WORDS lcoohiow on revers side, ifsaacss..y aid id"naj 4y Week member) Zeruike poynomials focal, plane Fouarier transform 20. ABSTRACT (C.,mone *a revewe side if neetaa.y aid dianulfy by Weoek numb) We preses= in this report the phase of a wave frot as described by the Zerniba polynomials and the correspomlisig lutanshies In the focal plane. IO JAN 723 EITOOPINV4ISOOEE UNCLASSIFIED SECURITY CLASSIPICAYION OP?"IS PAGE (Wen Daft Sautedj

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