Results of quality assessment tasks of the optical -electronic complex using complex instrumentation background and astroclimatic conditions

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1 Results of qulity ssessment tsks of the opticl -electronic complex using complex instrumenttion bckground nd stroclimtic conditions Chirov D.S., Grigoroshenko V.M. Abstrct The report presents the results of the evlution of the limit of instrumentl performnce nd the qulity of execution of tsks in the stges of testing nd tril opertion of the opticl-electronic complex under complicted bckground nd stroclimtic conditions. The dependences of the qulity of problem solving of OEC from the bckground nd stroclimtic conditions, nd the boundry vlues of the bckgrounds nd chrcteristics of the tmosphere, in which the OEC performs tsks, for estblishing n cceptble level. *** One feture of the observtions of smll-sized spce debris is the need to consider fctors ffecting the decrese in the detectbility performnce of the opticl sensors (OS), when plnning their work nd in the ppliction. These fctors re stronomicl-bllistic, bckground, nd meteorologicl conditions in the plce of the OS deployment. Accounting for these conditions during testing nd opertion of OS cn be relized in the following wys: mthemticl modeling; bsed on mesurements of specil devices (systems); combined (ccording to the models nd mesuring instruments) method. Reserch in this re [1, 2] showed tht the most effective wy to ccount for stronomicl-bllistic, bckground, nd meteorologicl conditions during testing nd opertion of the OM, is the combined method. Adoption of this pproch hs been crried out with the opticl-electronic complex (OEC) "elenchuk" since 27. As result of the use of hrdwresoftwre complex (HSC), ccounting for the stronomicl-bllistic nd bckground conditions in the softwre lgorithms nd the complex specil equipment estimtes the limit of the instrumentl chrcteristics nd the qulity of the HSC tsks in difficult bckground nd stroclimtic conditions.

2 The work of the HSC ccounting for the stronomicl-bllistic nd bckground conditions cn be divided into two stges. At the first (preprtory) stge, before the observtions, it clcultes limiting power of the sensor t ech point in the sky through the whole observtion period of the dte. For this it tkes into ccount the phse illumintion of the sky domins, brightness of the sky bckground, the decrement of the signl level due to tmospheric bsorption, the decrement of the cquisition threshold due to moonlight, nd some other cuses. The fll of the signl D (mgnitudes) s function of the phse ngle, reducing the detection threshold M c (given the sky bckground of 21 mgnitudes/sq.deg.) due to chnges in the brightness of the sky bckground illumintion M m by the Moon, or other cuses, ws estimted for HSC in the computtionl method. Reduction of the detection threshold is clculted in ccordnce with the expression [2]: where rel 21 F M = f, (1) 2 M - lowering the threshold of detection (limiting power) OEC, rel vlue of the sky bckground. rel F f - the To estimte the signl decrese, D, s function of the phse ngle, priori informtion bout the brightness of the spce objects nd its overll dimensions, obtined from the control center, is used. According to the results of clcultions, tble of vlues of the limiting power of the sensor depending on the coordintes of the elevtion, zimuth, nd time is prepred. The result is mp of the projected visibility the stellites. When plnning work, the opticl sensors for the detection of smll spce debris use selected res, in which limiting power is mximl. Simultneously with the clcultion of the visibility mps t this stge, estimte is mde of the probbility of the bsence from the line of sight of the OEC-stellite cloud formtions, using the forecst of cloud cover in the loction of the OEC.

3 A verticl section of the cloud field nd the corresponding model screen with nontrnsprent ( ( x) = ) nd the trnsprent res ( ( x) = 1) in the plne H is shown in Figure 1. Figure 1 - The model of cloud heterogeneities. In this cse, the trnsmission of the field in given direction, ξ, depends on the sptil structure of the field nd is rndom vlue. When the selected model trnsmission cloud field shows no clouds in the line of sight, it cn be compred to the probbility, tht rndom rrngement of the opticl zone of the contct in the field of the cloud intersect with the line of sight to the screen, hits the site with = 1. This probbility is equl to the rtio of the re of trnsprent sections of the opticl contct re to the whole of its re, A. If you hve two shdes of trnsmission ( r) = {,1}, where r = { x, y}, nd x, y - coordintes in the rectngulr coordinte system, the probbility of the product is determined by the verge pssing over the re, A, of the zone, Ω Ω а ~ 1 = ( r) dr. (2) A For the Poisson distribution centers of cloud heterogeneities (with only their two-dimensionl structure) t A re ~ 2πµ d = e [ 1 F ( x) ] rdr, (3)

4 where µ - density of the filled re of cloud centers; F (r) - distribution function d of the size of the horizontl cloud heterogeneities. When the size of cloud heterogeneities re identicl, it follows from (2) = e ( µ πd d 2 / 4). The verge trnsmittnce,, of the cloud field corresponds to tht used in meteorology the bsolute cloud grde j, which is ssocited with it s = j / 1. The 1 verged trnsmittnce,, chrcterizes the probbility of the product in "windows" ( = 1) cloud cover on the stellite line of sight, which is fixed nd psses ner the zenith ( ξ << 1 on Figure 1). At ngles ξ > 1 to consider threedimensionl cloud formtions, (ξ ), for which the verge trnsmission, consistent with reltive grde of meteorology, j, is where ~ π 2 = P( ξ ) sin ξd ξ (4) P( ξ ) ~ 2 ( µ dπd / 4+ 2dhtgξ ( ξ ) = e ) = - probbility of bsence of clouds in the line of sight through the "window" of trnsprency in given direction ξ ; the prmeters The vlue µ, d d и h re function of the grde of clouds, j. ~ = chrcterizes the probbility tht the product in n rbitrry ~ j direction is unknown, ξ, nd is ssocited with reltive grde of cloudiness, j, over the re s P АТМ ~ = = 1 j /1. (5) j The likelihood of work OS in given direction is define by (5), s P АТМ ~ ( ξ ) sinξ = (1 j /1) sinξ = j. (6) The reltive grde, which hs grdes from to 1 in increments of one point, determine if ground-bsed observtions re possible. At the second stge, the model ccomplishes dynmic correction of the chrt in rel time by dt from the Sky Monitoring System (SMS) t the fcility

5 loction. SMS provides clcultion of the cloudiness density distribution, ngulr rte, nd direction of the cloudiness field motion, detection nd prediction of the cler spces dynmics, estimtion of the tmosphere trnsprency coefficient vlue nd its distribution ll over the sky, nd n estimte of the opticl sky bckground level distribution. SMS uses specil object-glss of the fish eye type nd the rdition receiver with CCD mtrix, which obtins high resolution imge (see Figure 2). All these opertions re utomted nd the dt bse of sky imges is used. Figure 2 Imge of the sky The estimte of the tmosphere trnsprency coefficient vlue nd its distribution over the sky, nd the estimte of the opticl sky bckground level distribution re mde using the photometric ctlog of strs in the imge of the sky. The determintion of the presence nd distribution of clouds in the sky, speed, nd direction of movement of the clouds, detection nd prognosis of the dynmics of gps in the cloud field, the djustment vlue P АТМ (ξ ) e mde in the utomted mode using dtbse of imges of the sky. The determintion of the presence nd distribution of clouds re mde by the seprtion of the sky

6 brightness fluctutions in the imge by wy of contrsts, in prticulr the method of Roberts, which consists in crrying out the opertions of two-dimensionl discrete differentition [3]: ( 2 ) 2 ( j, k ) = [ I( j, k ) I( j + 1, k + 1) ] + [ I( j, k + 1) I( j 1, k )] I R +, (7) where I ( j, k) - the brightness vlue of imge pixel coordintes ( j, k). Roberts' method is to perform two liner opertions of differentition in vrious directions t n ngle of 45. Determintion of the ngulr rte nd direction of the cloudiness field motion, nd detection nd prediction of the cler spces dynmics re performed by nlyzing the dynmics of the chnge in the opticl stte of the sky from the imges obtined from the dtbse, nd the vlues of the wind speed nd direction t the pproprite heights. According to the results of SMS n opertionl mp of stellite visibility is mde. Simultneously with the work of SMS there is n ssessment of the meteorologicl conditions t the site of deployment of OEC: wind speed nd direction, nd prmeter 2 Cn. These estimtes, together with mp of the stellites visibility, re used to djust the opertionl plns of the OEC, in order to chieve the best ccurcy nd qulity mesurements. One of the importnt prmeters ffecting the qulity of OEC functionl tsks, estimted in the second stge of the HSC, is the probbility of obtining n opticl imge with high ngulr resolution. This prmeter, ccordnce with [4]: D 3.5. r P oi, is evluted in P oi 5.6exp.1557 D, (8) r where D - perture dimeter, r - Fried prmeter. Eqution (8) is vlid for The probbility of obtining n opticl imge with high ngulr resolution is crried out promptly (before the strt of session of observtion) of the evlution r. This informtion llows the opertor to tke the OEC with the fesibility of

7 obtining opticl imges in the session. Tble 1 presents estimtes of the probbility of obtining qulity opticl imge, depending on the prmeter D r [4]. Tble 1 D P oi r 2.986± ± ±.14 5 (9.38±.33) (1.915±.84) (2.87±.57) (1.7±.48) (3.4±.59) 1-15 Anlysis of the work of the HSC in 211 led to the following conclusions: 4% of the time the wind speed t the site of the loction OEC is 3 m/s nd bove (see Figure 3), which does not llow high-qulity opticl imges. In these times, OEC should be used for ngle nd photometry mesurements; for the period nlyzed, OEC observtions of stellites would be under the cloud cover bout 46% of the time (see Figure 4); conditions of tmospheric turbulence, llowing to obtin opticl imges, with mximum ngulr resolution, on the order of 19% of the nlyzed time period (see Figure 5). The probbility of obtining high-qulity imges is of the order of Reference: 1. Михельсон Н.Н. Оптические телескопы. Теория и конструкция. М.: Наука, O.Aksenov, S.Veniminov, А.Rykin, D.Chirov. Some results of testing the model for tking into ccount stro-bllistic nd sky-bckground conditions

8 when plnning spce debris observtions // 27 session of IADC, Drmstdt, Germny, Лучин А.А., Тимошенко А.С., Перевозчиков Н.И., Чиров Д.С. Информационные технологии обработки оптических и радиолокационных изображений в задаче распознавания космических аппаратов // «Информационные технологии», 11, 24 г, Москва. 4. Dvid L. Fried. Probbility of getting lucky short-exposure imge through turbulence // J. Opt. Soc. Am., Vol. 68, No. 12, December 1978, pp

9 Men wind speed Number of hours Wind speed, м/с Figure Number of hours Bll of clouds Figure 4

10 % number of hours Norm Сn Figure 5