Project Report. AVAQW&r ETS-21. Real-Time, Intermediate-Field Astrometry ESD ACCESSION LIST ' ESkpy NO. ^_of. ,cys. EEST AVAILABLE COPY F.

Transcription

1 F.SD-TR ESD ACCESSION LIST ' bhjdri Call N. <%~7'#"l3i ESkpy NO. ^_f.,cys. Prject Reprt ETS-21 Real-Time, Intermediate-Field Astrmetry Prepared fr the Department f the Air Frce under Electrnic Systems Divisin Cntract F C-0002 by Lincln Labratry MASSACHUSETTS INSTITUTE OF TECHNOLOGY LEXINGTON, MASSACHUSETTS Apprved fr public release; distributin unlimited. AVAQW&r EEST AVAILABLE COPY

2 The wrk reprted in this dcument was perfrmed at Lincln Labratry, a center fr research perated by Massachusetts Institute f Technlgy, with the supprt f the Department f the Air Frce under Cntract F C This reprt may be reprduced t satisfy needs f U.S. Gvernment agencies. The views and cnclusins cntained in this dcument are thse f the cntractr and shuld nt be interpreted as necessarily representing the fficial plicies, either expressed r implied, f the United States Gvernment. This technical reprt has been reviewed and is apprved fr publicatin. FOR THE COMMANDER f V^c^-<^-C. Raymnd L. Liselle, Lt. Cl., USAF Chief, ESD Lincln Labratry Prject Office

3 MASSACHUSETTS INSTITUTE OF TECHNOLOGY LINCOLN LABORATORY REAL-TIME, INTERMEDIATE-FIELD ASTROMETRY J. M. SORVARI Grup 94 PROJECT REPORT ETS OCTOBER 1977 Apprved fr public release; distributin unlimited. LEXINGTON MASSACHUSETTS

4 ABSTRACT An experiment t test the accuracy f a very simple calibratin scheme is described. It is cncluded that a meanffset, three-star calibratin wrking frm a catalg f 1600 reference stars can prvide psitinal accuracy f ten secnds f arc with the ETS equipment. in

5 CONTENTS ABSTRACT iii I. INTRODUCTION 1 II. INTERMEDIATE FIELD CALIBRATION 4 III. THE OBSERVATIONS 7 IV. CONCLUSIONS 15 REFERENCES 17

6 I. INTRODUCTION Once a celestial bject has been detected by an ptical system, there remain just tw quantities t be measured: brightness (as a functin f wavelength and time) and psitin (as a functin f time). Each measurement requires the establishment f a reprducible measuring system and a set f reference standards. This reprt deals with sme aspects f the psitin measurement astrmetry. Fr astrmetry, the measuring system can be the usual astrnmical crdinate system measured with encders n the telescpe munt. Mechanical flexure and plar misalignment can be mdeled and remved via bservatins f the reference standards. The irreprducible mechanical errrs (hysteresis) must be made negligible by prper design f the telescpe and munt. The set f reference standards is prvided by a fundamental catalg f star psitins such as the FK4 (ref.l). Althugh nt a fundamental catalg, the SAO catalg (ref.2) is prbably satisfactry fr use as an astrmetric reference in the GEODSS prgram (see ref.3). There are essentially tw appraches t calibratin. One is t bserve reference standards ver the entire sky and cnstruct a "mdel" t prduce true psitins as a functin f bserved psitins. This glbal calibratin prcedure is unlikely t be capable f the degree f accuracy desired, primarily due t its great sensitivity t hysteresis effects. The secnd apprach is

7 t arrange fr each field f interest t cntain several reference standards and t make essentially differential crrectins t measured psitins. This small field calibratin has been exhaustively studied (see, fr example, ref.4) and is capable f a high degree f accuracy. The preceding cnsideratins wuld seem t indicate that small field astrmetry was the desired apprach. There are, hwever, sme pssible disadvantages t small field astrmetry in the cntext f the ETS missin. The requirement fr "several" stars in each small field f interest implies a need fr a quite large catalg f standards. Fr each unknwn bject, many standard stars must be measured and extensive calculatins perfrmed n the data. In a real-time system, this can mean an undesireably large prprtin f system verhead and perating time devted t calibratin. The accuracy achieved by the measurement and calibratin system is determined primarily by tw surces f errr: the accuracy f the astrmetric calculatins (the mdeling errr) and the accuracy with which data can be taken (the instrumental errr). Fr the current ETS cnfiguratin, typical small field astrmetry can make the mdeling errr much smaller than the instrumental errr. In light f the prblems with small field astrmetry, it makes sense t cnsider less sphisticated calibratin schemes. This Reprt describes the results f an experiment which addresses

8 the questin: Hw simple a calibratin scheme may be used and still prduce psitinal accuracy sufficient fr the GEODSS prgram?

9 II. INTERMEDIATE FIELD CALIBRATION Falling shrt f failing t calibrate at all, the simplest scheme is t assume d = a" + Aa ' + A6 where the naught subscripts refer t the true psitins, and the primes refer t the bserved psitins. Values fr Aa and A6 are btained frm bservatins f ne r mre standard stars. It shuld be nted that even a simple displacement f the crdinate ple requires a mre cmplicated transfrmatin than this. The mdel is thus extremely crude, and wuld be expected t fail badly fr distances in excess f 0.1 radian (^350') r near the ple. The psitins prduced by this calibratin technique wuld be expected t shw effects f bth the mdeling errr and the instrumental errr. The instrumental errr shuld be the same fr all bjects while the mdeling errr t first apprximatin shuld increase linearly with the separatin between unknwn bject and calibratin star. A plt f the errr in psitin f the unknwn (d) vs. separatin (r) shuld shw d increasing linearly with r fr large r and "bttming ff" t sme minimum value fr small r. The minimum errr, E, shuld be given by E = e/1 + 1/n where e is the instrumental errr and n is the number f reference stars used.

10 In rder t test these expectatins and t evaluate the pssibility f using this simple calibratin scheme fr GEODSS peratin, nine test stars were bserved. Tw different reductins were used n the data: the simple averaging described abve and the same averaging preceded by a crrectin fr atmspheric refractin. There are several telescpe independent crrectins t a star's psitin which may be made entirely independently f the telescpe mdel. Mst f these, hwever, are either very small r have very small first derivatives and thus are just as well lumped int the mdel crrectin. Atmspheric refractin, hwever, has a significant first derivative and may be easily crrected, as it is a functin nly f the telescpe elevatin. The data are presented in Sectin III. It will be useful t have a relatinship between the average distance, r, frm test star t reference star and the star density,. Cnsider stars distributed at randm n the plane with density a. A circle with radius, p, given by p = l//t will cntain, n the average, ne star. The mean distance frm the center f a circle t all pints in the circle is 2/3 f the radius, s the relatin between mean distance between test bject and nearest ne star, r l,is given by ri, = 2/3/Fa =.376//a.

11 If we want three reference stars, we must bviusly cnsider a circle with three times the area. Thus, the mean distance between test bject and nearest three stars, r 3, is given by r 3 = /3rj =.651//" The distributin f stars n the sky is nt cmpletely randm, especially fr the brighter stars, and the cmpilatin f a catalg f reference stars will include sme srt f attempt t make the distributin mre unifrm. It might, therefre, be argued that the assumptin f randmness abve is nt well satisfied and that the relatinships shwn are inaccurate. T test the effect f rder in the star distributin n the calculatins, the nearest neighbr calculatin has been dne fr the case f backgrund stars arranged at the vertices f a square grid. The result is n - {/2 + ln(l + /2)}/6/ =.383//a It can be seen that even this extreme case f nn-randm distributin affects the numbers nly minimally.

12 III. THE OBSERVATIONS The nine stars used as test bjects fr this experiment are listed in Table 1. The psitinal data were btained frm reference (5) updated t The set f reference stars was the S-20 phtmetric catalg cmpiled at ETS (ref. 6). The psitinal data in this catalg are als updated data frm reference (5), s bth test and reference stars are in the same crdinate system. Observatins were made as fllws: The telescpe was driven t a test star, centered, and the time and psitin recrded. The autmatic extinctin package (ref. 7) was then used t drive the telescpe t the three nearest stars read frm the phtmetric catalg. These stars were centered and time and psitin recrded. Mean values fr Aa and A6 were calculated frm the reference stars and applied t the bservatin f the test star. The discrepancy, d, between the crrected psitin f the test star and its catalg value was then calculated. All nine stars were bserved n each f tw nights. On ne night this was dne nrmally and n the ther the mean separatin was increased by using nly dd numbered stars frm the phtmetric catalg. A few stars were als bserved n each f several additinal nights. There is n indicatin that any particular night was significantly better r wrse than the thers. The calculatin was carried ut using bth the mean f the three nearest stars and als using nly the single nearest star.

13 TABLE I [ EST STARS FOR INTERMEDIATE FIELD CALIBRATION, RA DEC GC 1 15 h 37 m 02? ' 27"

14 As mentined in Sectin II, it makes sense t crrect the raw data fr atmspheric refractin befre prceeding with the data reductin. This was dne fr all nine stars n the night when all catalg stars were used and fr Star 7 n each f three different nights. The crrectin was made in bth the three star and ne star versins f the reductin. The discrepancy, d, in the test bject psitin was then cmpared t the crrespnding value calculated withut first making the refractin crrectin. The mean value f the rati f d (with refractin crrectin) t d (withut refractin crrectin) was This is a rather surprising result, but ne which has been fund by ther wrkers as well (L. G. Taff, private cmmunicatin). Only data reduced withut the refractin crrectin is referred t in the remainder f this Reprt. Table II lists the data fr the bservatins. The primed star numbers refer t the bservatins made n the "dd nly" night. One bservatin f Star 4 culd nt be reduced in the ne star versin because the raw data was inadvertently destryed after the three star reductin had been carried ut. Als listed are the azimuth and elevatin at which each test star was bserved. Figure 1 shws a plt f d fr the three star reductin as a functin f azimuth and elevatin. The nly crelatin apparent is a mild tendency tward larger d in the

15 TABLE II POSITION DISCREPANCIES AND MEAN DISTANCES TO REFERENCE STARS FOR TEST STARS 3 Star 1 Star a e d r d r " 448' 13" 209' * '

16 TABLE II (Cntinued) 3 Star 1 Star a e d r d r 3' " 535' 14" 310' 4' ' ' ' ' '

17 tfl 0) 4J <4-l u Id CO - c u <u m c H c H id > 0) 13 (D T3 >1 C U (0 C (0 X! Cb-P QJ 3 u e U -H U) N rh (C T c 0 H c 4-> H H W -P O O a c E-" id t (0 i-h CO u H 4J fr. en 12

18 nrth. Figure 2 shws a plt f d as a functin f r. this graph is the basis fr the cmments in Sectin IV. Data fr the 3 star reductin and fr the 1 star reductin are pltted tgether, but with different symbls. 13

19 1 1 ' c en X US -*-x _ 00 (N 1 CO w X i > X X X XX V x xx * x LD x C\J x x x ^~ _ en C CD 0 -P u rh t c 4-> CO CD CD (-1 13 <D T3 <4-l iw (1) 0 <u M S-l,^-^ K U TS id u c +-> (0 (0 t <4-l 4-1 (U 0 t c <u 0 en +J T> 0 IX) C C +J 0 CD O 0) M <D S a) CO 4J 144 w CD C XI M H c t» 0 T3 -H 10 t s_ +J t c CO >i u 5-1 -H O (0 U 4-) c a (0 CD p a t T> <D,-. <D u c O ^ U (C M t <D <ti U H S (0 t) > r C 0 O t 0 t CD H C <D <D > M H -H 3 X! O to 4-> C 4J O O U H CSJ CX C e O 3 4-> 0) 44 C x; rh CO E-i (0 CD -rh O n ^ U 1 (0 ' M (N H t t U >-l M tr> ic (0 T> H 4-> 4-1 C t. t t id 14

20 IV. CONCLUSIONS The data btained here are insufficient fr a thrugh analysis f the errrs invlved in the mean ffset calibratin. Nnetheless, several cnclusins may be reached upn examining Figure 2. In this analysis, the "target" accuracy is taken t be ten secnds f arc. Our expectatins regarding the discrepancy as a functin f mean separatin seem t be brne ut. The value f d appears t increase linearly with r fr large r, and t reach a minimum fr small r. The data indicate an instrumental errr f apprximately eight secnds f arc, cnsistent with the knwn prperties f the eguipment and with ther studies (L. G. Taff, private cmmunicatin). The calibratin using a single star des nt appear capable f reaching the target accuracy. Use f three stars des appear capable f reaching target accuracy if the mean separatin is less than abut 200'. This translates int a required star density f star per square degree, r abut 1600 stars distributed ver the entire sky. One way f evaluating the prpsed calibratin scheme is t ask if it can prvide sufficient accuracy. Fr the current parameters the answer is clearly yes. If the target accuracy is made smaller withut an imprvement in instrumental accuracy, the answer is clearly n. It is nt presently pssible t decide what 15

21 the result wuld be if bth target accuracy and instrumental accuracy were imprved. Anther way f evaluating the calibratin scheme is t ask if it can prvide the best pssible accuracy. Because the instrumental accuracy and target accuracy are apprximately the same, the answer is still yes. Again, it is unclear what the answer wuld be if instrumental accuracy were imprved. The ultimate test f these cnclusins is bviusly the installatin in RTS f a mean-ffset, three-star calibratin wrking frm a reference catalg f 1600 stars. Observatins with this system wuld als prvide data which culd reslve the uncertainties in the scaling f results with imprvement in the instrumental accuracy. 16

22 REFERENCES (1) W. Fricke and A. Kpff, Vierter Fundamental Katalg (Publ. Astrn. Rechen-Institut,[Heidelberg, W. Germany, Number 10, 1963]). (2) Smithsnian Astrphysical Observatry, Star Catalg (Publ. Smithsnian Inst., Nr 4562, Washingtn, D.C., 1966). (3) L. G. Taff, "The Handling and Uses f the SAO Catalg," Prject Reprt ETS-6, Lincln Labratry, M.I.T. (5 Nvember 1976), DDC AD-A035871/3. (4) L. G. Taff, "Astrmetry in Small Fields," Technical Nte , Lincln Labratry, M.I.T. (14 June 1977), DDC AD-A (5) A. Becvar, Atlas f the Heavens-II Catalg , (Sky Publishing Crp., Cambridge, Mass., 1964). (6) J. M. Srvari, "Magnitudes f Stars n the S-20 System," Prject Reprt ETS-19, Lincln Labratry, M.I.T. (14 September 1977). (7) J. M. Srvari and C. E. Beane, "Autmatic Real-Time Extinctin Measurement," Prject Reprt ETS-17, Lincln Labratry, M.I.T. (12 September 1977). 17

23 UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered, 1. REPORT NUMBER ESD-TR REPORT DOCUMENTATION PAGE r READ INSTRUCTIONS BEFORE COMPLETING FORM 2. GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBER 4- TITLE (and Subtitle) 7. AUTHORS) Real-Time, Intermediate-Field Astrmetry Jhn M. Srvari 5. TYPE OF REPORT & PERIOD COVERED Prject Reprt 6. PERFORMING ORG. REPORT NUMBER Prject Reprt ETS CONTRACT OR GRANT NUMBER^sy F C PERFORMING ORGANIZATION NAME AND ADDRESS Lincln Labratry, M.I.T. P.O. Bx 73 Lexingtn, MA CONTROLLING OFFICE NAME AND ADDRESS Air Frce Systems Cmmand, USAF Andrews AFB Washingtn, DC U. MONITORING AGENCY NAME & ADDRESS (if different frm Cntrlling Office) Electrnic Systems Divisin Hanscm AFB Bedfrd, MA PROGRAM ELEMENT, PROJECT, TASK AREA & WORK UNIT NUMBERS Prgram Element N F Prject N REPORT DATE 28 Octber NUMBER OF PAGES SECURITY CLASS, (f this reprt) Unclassified 15a. DECLASSIFICATION DOWNGRADING SCHEDULE 16. DISTRIBUTION STATEMENT (f this Reprt) Apprved fr public release; distributin unlimited. 17. DISTRIBUTION STATEMENT (f the abstract entered in Blck 20, if different frm Reprt) 18. SUPPLEMENTARY NOTES Nne 19. KEY WORDS (Cntinue n reverse side if necessary and identify by blck number) astrmetry ETS mean-ffset calibratin GEODSS RTS 20. ABSTRACT (Cntinue n reverse side if necessary and identify by blck number) An experiment t test the accuracy f a very simple calibratin scheme is described. It is cncluded that a mean-ffset, three-star calibratin wrking frm a catalg f 1600 reference stars can prvide psitinal accuracy f ten secnds f arc with the ETS equipment. DO, j A^M, EDITION OF 1 NOV 65 IS OBSOLETE UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered)