Performance modeling of electro-optical devices for military target acquisition

Revised 2 February 2007 Defence Science Journal, V ol. 57 , No. 3, May 2007, pp. 323 - 331  2007, DESIDOC 323 Performance Modelling of Electro-o ptical D evices for Military Target Acquisition S.K. Das and R.S. Singh In st itu te fo r Sy ste ms & Stu die s a nd A na lys es , De lh i-1 10 0 54 ABSTRACT Accurate predictions of electro-optical imager performance are important for defence decision- ma ki n g. T he p re di ct io ns s er ve a s a gu id e fo r s y st em d ev el op me nt a nd a re us ed i n w ar g am e, si mul ati ons th at dir ect ly in flu en ce en gag eme nt tac ti cs. In the pr ese nt stud y , mat hem ati ca l mod els h av e be e n d ev el op ed w hi ch i n vo lv es de te c ti on of di ff e re nt mi li ta r y t ar ge ts us in g th ei r o pt o- e le ct ro ni cs p ro pe rt i es i n d if fe re nt e nv i ro nm en ta l c o nd it io ns . Th e me th od f ir st c al cu l at es t he si gn a l- to -n oi se ra ti o r ec ei ve d b y t he ob se rv i ng s en so rs re fl ec t ed f r om t he ta rg et by qu an ti f yi ng t he l ig ht e n erg y i n t e rm s o f ph ot on s, wh ic h i s u se d f or e va lu at i ng t he d e te ct io n pr ob ab i li ty. Keywords: Signal-to -noise rat io, ty pe I error , type II error , Gaus s ian distribution , probabi lity of detection, probability of recognition, false alarm 1 . I N T R O D U C T I O N A cq ui si ti on o f t ar ge t is a vi ta l tas k pr io r to t arg et e ng ag e men t. T he d et ect io n o r d is co ve ry o f a t arg et is a c la ss ic al s ta ti st ic al pr ob le m of fi n di ng a signal in a background of noise 1 . A signal is a discrete a nd m ea su rab l e ev en t p ro du ce d b y a t ar ge t, wh er ea s n oi se i s an y p ro ce ss or ph en om en on u n rel at ed t o a t arg et th at c an m as k o r b e m is ta ke n fo r t he t ar get . T arg et de tect ion sys tems , re gar dle ss of whi ch s en sor s t he se a re b as ed on , me as ur e a c omb in a ti on o f b ot h s ig na l a nd no i se. R eli a bl e d et ec ti on c an on ly be accomplished when the signal can be clearly distinguished f ro m t he n oi se. J on es 2 as su me d si gn al p lu s no i se an d n oi se f ol lo w Ga us si an d is t ri bu ti on w it h ov er l ap pi ng me an an d st an da rd d ev ia ti on s. U si ng t ha t G au ss ia n n at ur e of si gn al an d n oi se h e st at ed th at o ne c an d et erm in e th e si gn al -t o- n oi se r at io ( SN R) r eq ui re d b y a n o pt o- el ec tr ic al d ev i ce t o d et ect a s ig na l w it h a g iv en r el ia bi li ty a nd a gi v en f al se a la rm ra te . T h e p r o c es s o f o p ti c a l l y d e t ec t i n g a di f f e r e n ce i n b ri g h tn e s s be t w ee n t wo a d j ac e nt ob j ec t e l em en t s d e p e n d s o n t h e a b i l i t y o f t h e s e n s o r t o d i s t i n g u i s h b e t w e e n t h e n u m b e r s o f p h o t o n s i t r e c e i v e s a n d r e g i s t e r s f r o m t h e t w o e l e m e n t s d i s c r e t e l y 3 . T h e d i f f e r e n c e b e t w e e n t h e t w o q u a n t a o f p h o t o n s g i v e s r i s e t o a s i g n a l . S i n c e t h e e m i s s i o n o f photons is a random process, the statistical fluctuations i n t h e s e n u m b e r s c a u s e a n a s s o c i a t e d n o i s e . S t a t i s t i c a l f l u c t u a t i o n s i n t h e a r r i v a l o f p h o t o n s l i m i t t h e c o n t r a s t p e r c e p t i o n o f t h e e y e . R o s e 4 m a d e s o m e a p p r o a c h e s t o t h e q u a n t i t a t i v e e f f e c t o f t h e s e f l u c t u a t i o n s . T ar g et ac q u is i t i on is c o mp l e x . M an y m od e l s o f t h e p r o c es s h a ve b e e n d e v e lo p e d , a n d o f te n t h es e a r e s p e ci a l i s ed to o n ly a fe w m i l i ta r y s c en a r i o s. F o r m o st m o d el s o n l y p a r t ia l v a l i da t i o n e x i st s d u e t o t h e d if f i c u lt i e s i n c a rr y i n g o u t r ea l i s t ic f i el d t e s t s 5 . 324 DE F S CI J , V OL . 5 7, N O. 3 , M AY 20 07 R ec en tl y , S he ff er 6 , et a l . a nd B ir ke ma rk 7 s tu di e d t h e r o b u s tn e s s o f d i f fe r e n t s t a t is t i c a l c r i te r i a s u c h as signal-to-clutter ratio (SCR), Mahalanobis distance, B h at t a c h ar y a di s t a n ce , a n d I n f o r ma t i on c r i t er i a fo r target and background seperability in different spectral w a ve l e n g t h o f e l e ct r o ma g n e t ic r a d i at i o n . T o e v a lu a t e t h e t a rg e t d e t e ct i o n c a p a b il i t y b y v a ri o u s se n s o r s l i k e b i n o cu l a r, i ma g e in t e n s i fi e r (II), night vision devices (working in visual wavelength) a n d t h e r m a l i m a g e r s ( w o r k i n g i n t h e t h e r m a l w a ve l e n gt h ) , s o me m a t he m at i c a l mo d e l s ha v e b e e n d e v el o p e d a n d d i sc u s s e d b e l o w . 2 . A P P R O A C H P e rf o r m an c e o f a s e n so r i s d e fi n e d i n t e rm s o f t h e p r o b a b il i t y o f d e t e c ti o n , o r P d , w h i ch i s t h e l i k el i h o o d t h a t a d e v i c e w i l l d e t e ct a r e a l t a r ge t o f g i v en s i z e a t d e f i ne d r a n g e g i v e n a p r o b a bi l i t y o f f a ls e a l a r m, w h e r e P f a , w h i ch i s t h e l i k el i h o o d t h a t a d e v ic e m a y d e c l a re t h e p r e se n c e o f a t a r ge t o f a g i ve n d i me n s io n a t so m e r a n ge a n d p r e va l e n t e n v ir o n m en t a l c o n d it i o n s f a l se l y . Th e ma tri x i n Fig . 1 s ho ws t he po ss ibl e o ut come s o f a t a rg e t d e t e ct i o n t e s t. W h e n t h e m ea s u r em e n ts ma t c h a c tu a l c o n d i t io n s , t h e r e s u lt i s a c o r re c t t e s t d e ci s i o n , e i t he r t h e d e t e ct i o n o f a n a c t ua l t a r ge t o r the confirmation that none exists. If the measurements d o n o t m at c h a c t u a l c on d i t i o n s, t h e t e st d e c is i o n i s i n co r r ec t –e i t he r a mi s s ed de t e ct i on or a f a l se a l ar m . L e t i t b e a s s u me d t h a t t h e n o i s e i n v o l v es a G a us s i a n d i s t r ib u t i o n o f a mp l i t u d es . To b e su r e t he distribution of photons is Poisson rather than Gaussian, b u t e x ce p t w h e n t h e n u mb e r o f p h o t on s i s s m al l , the two distributions are practically indistinguishable. S u p p os e n o w t h a t o n e w i sh e s t o d e t e ct a s i g na l i n t h e p r e se n c e of G a u ss i a n n oi s e . Th e s i t ua t i o n is i l lu s t r a t ed i n F i g . 2 . I n F i g . 2 , t h e Ga u s s i an c u rv e o n t h e l e ft r ep r e s en t s t h e d i s t ri b u t i o n o f a mp l i t ud e s w h en t h e s i g n a l i s a b s en t , a n d t h e s i mi l a r c u rv e o n the right is the distribution of signal-plus-noise amplitudes w h en th e s i g n al is p re s e nt . I f t h e d e c is i o n t h r es h o l d i s a t t h e p o s it i o n T , t h e n t h e sh a d e d a r e a t o t h e r i g h t o f th e v e rt i c a l l i n e a t T i s t h e p r o b a b i li t y P f a t h at th e d e v i c e f a l se l y c o n cl u d e s t h a t a si g n a l i s p r es e n t w h e n i t i s n o t [ T y pe I e r r or, F i g 2 ( a ) ], a n d the area to the left of the vertical line is the probability 1 - P d t h a t t h e d e v i c e c o n cl u d e s th a t a s i g n a l i s n o t p r es e n t w h e n a c t u a ll y it i s [ T y pe I I e r r o r , F i g 2( b ) ] . Fi gu re 2 est ab li sh es a gr ap hi ca l r el at io n b et we en t h e s i g n a l- t o - n o is e r a t io ( S N R ) k , t h e f a l s e a l a r m f r ac t i o n P fa , an d t he d e t ec t i o n p r o b a bi l i t y P d . To o b t ai n t h e c o r r e sp o n d i n g r e l a t io n , o n e d e f i n e x = e r f -1 ( y ) a s t h e r e l at i o n t h a t i s i n v er s e t o y = e r f ( x ) ≡ )du 2 u exp( 2ð 1 x 2 ∫ ∞ − − (1) w h er e e r f ( x ) i s t h e w e l l - kn o w n e r ro r f u n c ti o n . W e DETECTION FALSE ALARM (TYPE II) MISSED DETECTION (TYPE I) ( NO DETECTION TARGET NO TARGET TARGET NO TARGET ACTUAL CALCULATED Fi gure 1. P oss ible o utco mes of a t arg et d ete ctio n t est . Fi gure 2. Determining the SNR: (a) probability of false alarm, and (b ) p roba bili ty o f de tect ion. 325 DA S & S ING H: PE RF ORM AN CE MO DEL IN G O F E LEC TRO -O PT ICA L D EVI CE S F OR MI LIT ARY T AR GE T AC QU IS ITI ON s u p p os e , t h e l e f t G au s s i a n c u r v e t o b e e x p r es s e d by Y = ( 2 π ) - 1/ 2 e x p [ - x 2 / 2 ] ~ N ( 0 , 1 ) ( 2) a n d t h e r i g h t G a u ss i a n c u r v e b y Y = ( 2 π ) - 1/ 2 e x p [ - ( x - k ) 2 / 2 ] ~ N ( k , 1 ) ( 3) B o t h G a u s s i a n c u r v e s h a v e u n i t a r e a a n d u n i t s t a n d a r d d e v i a t i o n , w h e n k i s t h e r a t i o o f t h e s i g n a l a m p l i t u d e t o t h e r o o t m e a n s q u a r e ( r m s ) n o i s e a m p l i t u d e s . F o r a n i d e a l d e v i c e , i f t h e m e a s u r e d a m p l i t u d e s i s a b o v e t h e t h r e s h o l d , t h e d e v i c e c o n c l u d e s t h a t t h e s i g n a l i s p r e s e n t , o t h e r w i s e n o i s e i s p r e s e n t . T he n i t is e a sy t o s ho w t ha t t h e S NR , k re q u ir e d b y t h e i d e a l d e v ic e o f F i g. 1 t o a c h i e ve a d e t e ct i o n p r o ba b i l i t y P d w i t h a f a l se a l a rm f r a c t io n P f a i s d e ri v e d as 1 – P d = du k u ) 2 ) - ( exp( 2ð 1 T 2 ∫ ∞ − − ( 4) Let u – k = v , t he n du = dv , Wh en u → T , v → T – k Thus, 1 - P d = dv v T-k ) 2 exp(- 2ð 1 2 ∫ ∞ − ( 5) ∴ 1 - P d = e r f ( T - k ) ( 6) o r P d = 1 - e r f ( T - k ) ( 7) S i mi l a r ly f r o m E qn ( 1 ) 1 - P f a = )du T 2 2 u exp( 2ð 1 ∫ ∞ − − = e r f ( T ) ( 8) T h e r e f o r e , T = e r f - 1 ( 1 – P f a ) ( 9) ∴ P d = 1 - e r f [ e r f - 1 ( 1 - P f a ) - S N R ] ( 1 0) T h u s b y i n v er s e i n te r p o l at i o n o f n o r m al t a b l es o n e c a n d e t er m in e t h e S N R r eq u i r e d b y a n i d e a l d e v ic e t o d et e c t a s i g n al w i t h a g i v e n f a l s e a l a r m f r a ct i o n P f a . 3 . DE TE CT IO N MODE L FOR HUMA N EYE, BINOCULAR, AND IMAGE INTENSIF IER T h e ba s ic p r e mi se o f t h is mo d el i s t o d et e rm i ne p r o b ab i l i t y o f d et e c t i on o f a t a r g et , b y a v i e w i n g d e v ic e , i n s p e c i fi e d e n v i r o nm e n t al c o n di t i o n s , a t d if fe re n t ra ng e s. Th e mod e l is b as ed on t he q ua n tu m me c h a n i cs o f l ig h t . T h e m o de l u s e s t h e f o l lo w i n g pa ra met er s, in pr oc es sin g th e si gn al , fo r as cer ta in in g t h e p r o b a bi l i t y o f d et e c t i on : ( a ) S u n o r mo o n i l l um i n at i o n ( I i n l u x ) ( b) R a n g e , R ( k m) ( c ) T a rg e t s i z e , s ( c m 2 ) ( d) Ta rg e t r e f l e c t a n c e, R t ( e ) B a ck g r o u n d r e f le c t an c e , R b ( f ) A p er t u r e o f t he s e n so r / p u pi l r a di u s , r ( mm ) ( g) D e t e c t o r e f f ic i e n c y , θ 2 ( h) I n te gr a ti o n t i me ( e ye re sp o ns e ti me ) 4, 8 τ, ( s) (i) P h o to n i n t e n si t y 8 ( i . e. , n u mb e r o f p h ot o n s p e r l u me n p er s ec o n d ) , P (j) F a ls e a l a r m r a t e , P f a ( k) A t t e n ua t i o n c o e ff i c i en t , A C T h e a l g o ri t h m f o r v is u a l de t e c t io n p r o ce e d s a s follows: (i) Based on ambient illumination, target reflectance and background reflectance, the brightness status o f t h e t ar g e t [ L t = ( R t * I ) / π i n c d / m 2 ] a n d t h e b a ck g r o u n d [ L b = ( R b * I ) / π ] i s ev a l u at e d . Fr o m these, the contrast ratio [ C =( L t – L b )/( L t + L b )] between t h e t a r g et a n d b a c k g ro u n d i s evaluated. T h en , using range and attenuation coefficient, apparent c o n tr a s t [ C '= C * e x p ( – AC * R ) ] o f t h e t a r g et i s c a l cu l a t e d. (ii) D e pe n d i n g o n t he r a ng e an d t a rg e t s i ze , t he a n g le ( a = 57 . 3 * 6 0 s / R ) p r o j e ct e d b y t h e t a r ge t o n t h e d e t e ct i n g d e vi c e i s d e t e r mi n e d . U s i ng t h e i n f or m a t io n o n v i e w i ng d e v i c e a pe r t u r e o r p u p i l d i a me t e r a n d t h e l i g h t e n e r gy r e f l e ct e d by target and background, the number of photons i n t h e t w o e n e r g i es i s c a l cu l a t e d. C o n s id e r i n g the efficiency of the viewing system, eye response t i me a n d p h o t o n s r e ce i v e d , t h e s i gn a l s t re n g t h c a n b e q u a nt i f i e d . 326 DE F S CI J , V OL . 5 7, N O. 3 , M AY 20 07 (iii) From signal strength, noise component is identified a n d S N R i s c a l c u l a t e d . B a s e d o n S N R = { 2 .6 6 * 1 0 - 11 L m 2 C 2 a 2 θ P r 2 τ } 1 /2 a n d a s s u me d f a ls e a l a r m r a te ( P f a ) , p r o b ab i l i t y o f d e t e ct i o n 3 ( P d = 1 – er f ( e rf -1 ( 1 – P fa ) – SN R ) ) c an b e e v a l ua t e d u si n g t he a p pr o a ch o u tl i n ed i n S e ct i on 2 ; w he r e L m i s t h e m e a n b r i g ht n e s s a n d e r f s t a nd s f or e r ro r f u nc t i o n . 4 . RE COG NIT IO N M OD EL FOR THERM AL I M A G E R Detection is less important for thermal acquisition o f t a r ge t s . T e mp e r a tu r e d i ff e r e n ce o f t a rg e t s a n d b a ck g r o u n d a r e t h e i mp o r t a n t f a ct o r s f o r t h e r ma l r ec og n it i on . T h e b as i c p r em i s e o f t hi s m o d el i s t o d e t e rm i n e p r o b ab i l i t y o f r e c og n i t i o n o f a t a r g et , b y a t h e r ma l imager, in specified environmental condition, at different r a ng e s . T h e mo d e l u s e s t h e f o ll o w i n g p a r a me t e rs , f o r a s ce r t a i n in g t h e p r o ba b i l i ty o f r e c og n i t i o n . ( a ) I n h er e n t t e mp e r a t ur e d i f f e re n c e o f t ar g e t a n d b a ck g r o u n d ( ∆ T i ) ( b ) R an g e ( R ) ( c ) T a rg e t h e i g h t ( H t arg ) ( d ) Parameters of minimum recognisable temperature d i ff e r en c e ( M R T D ) c u rv e o f t he r m al i m ag e r ( a , b ) . T h e s e a r e t h e o r d i n ar y l e a s t s q u a re ( O LS ) e s t i ma t o rs ( s e e A p p e nd i x I ) . ( e ) A t te n u a t i on c o ef f i c ie n t ( AC ) T he a l g or i th m fo r t h er ma l r ec o gn i t io n p r oc e ed s a s f o l lo w s : ( i ) Determine the target critical dimension (H targ /R) , an d a pp are nt te mp era tu re d iff er enc e [ ∆ T a = ∆ T i * (- AC * R )], using knowledge of the atmospheric at ten ua tio n c oef fic ie nt ( AC ) a nd r ang e ( R ) ( ii) Calculate or measure the system MRTD [ a *exp ( b * S F) ] wh e re S F st an d s fo r s pa ti a l fr e qu e nc y which is reciprocal of the target critical dimension. From the apparent ( ∆ T a ) and the MRTD determine t h e m a xi m u m r e so l v a b l e s p a ti a l f r e q u en c y [ f x = ( 1 / b ) *l o g ( ∆ T a / a ) ] o f t h e s e n s o r ( iii) U s in g t h e a n g ul a r s u b t e nd s ( f x ) o f t h e t a r ge t c r it i c a l d i me n si o n a n d H t arg / R , c a l c u la t e t h e m a x i m u m n u m b e r o f r e s o l v a b l e c y c l e s [ N = f x * ( H t ar g / R ) ] a c r o s s t h e t a r g e t ( iv) D et er mi n e t he p ro b ab i li t y o f r ec og n it i on f ro m the target transform probability function (TTPF) c u r v e 5 a s E E r N N N N P ) / ( 1 ) / ( 50 50 + = wh ere , P r is probability of recognition; N is maximum r es o l va b l e cy c le s a cr o s s th e t ar g e t; N 50 i s r es o lv a b l e c y cl e s f o r 5 0 p e r c en t p r o b ab i l i t y o f r e co g n i t i o n; a n d E = 2 . 7 + 0 . 7 ( N / N 5 0 ) 5 . R E S U LT S I n t h i s p a p e r a n a t t e m p t h a s b e e n m a d e t o e v a lu a t e t h e p e r fo r m an c e o f hu m a n e y e i n d i ff e r e n t i l l u m i n a t i o n c o n d i t i o n s f o r s o m e t a r g e t s . T h e p e r f o r m a n c e i s d e t e r m i n e d i n t e r m s o f d e t e c t i o n p r o b a b i l i t y, w h i c h i s r e p r e s e n t e d a s a f u n c t i o n o f r a n g e . N i g h t - s e e i n g c a p a b i l i t y o f h u m a n e y e c a n b e e n h a n c e d u s i n g i m a g e i n t e n s i f i e r. F i g u r e s 3 ( a ) - 3 ( d ) s h o w t h e p e r f o r m a n c e o f h u m a n e y e , i m a g e i n t e n s i f i e r , a n d b i n o c u l a r , u s i n g t h e p a r a m e t e r s v a l u e g i v e n i n Ta b l e 1 . T h e h u m a n e y e c a n d e t e c t t h e t a r g e t a c c o r d i n g t o t h e i r s i z e u p t o 1 . 5 k m ( w i t h 1 0 0 % d e t e c t i o n p r o b a b i l i t y ) i n d a y l i g h t w i t h o u t u s i n g v i e w i n g d e v i c e s . I f v i e w i n g d e v i c e s ( b i n o c u l a r ) a r e u s e d , t h e n t h e r a n g e e n h a n c e s t o 5 km u n d e r t h e s am e w e a t h e r c o n d i t i o n s . S i m i l ar l y h u m a n e y e c a n d e t e c t t h e t a r g e t s a c c o r d i n g t o t h e i r s i z e u p t o 5 0 0 m ( w i t h 1 0 0 % d e t e c t i o n p r o b a b i l i t y ) i n f u l l m o o n c o n d i t i o n s w i t h o u t u s i n g a n y n i g h t v i s i o n d e v i c e s . I f i m a g e i n t e n s i f i e r i s u s e d , t h e n t h e r a n g e e n h a n c e s t o 2 k m u n d e r t h e s a m e w e a t h e r c o n d i t i o n s . F u r t h e r, i t i s a p p a r e n t f r o m t h e c u r v e s t h a t a s t h e r a n g e i n c r e a s e s , t h e d et ec ti on p ro ba bi l it y de cr ea se s s ha rp ly an d be co me s a s y m p t o t i c a r o u n d 2 0 p e r c e n t . A si mi la r ex er c is e ha s be en c on d uc te d fo r ta r ge t r eco g ni ti on us i ng th e th er ma l i ma ge r at ni g ht . F i gu re 4 s h o w s t h e p e r f or m an c e o f t h e r ma l i ma g e r f o r r ec o gn i s in g a ta n k ta r ge t u s in g t he p a ra me te r s va l u e 327 DA S & S ING H: PE RF ORM AN CE MO DEL IN G O F E LEC TRO -O PT ICA L D EVI CE S F OR MI LIT ARY T AR GE T AC QU IS ITI ON g i v en i n T a b l e 2 . Un d e r c l e a r w e a t he r c on d i t i o ns , a n a v er a g e t h er m a l d e v i ce c a n r e co g n i s e a t an k a t a d i s t a n ce a r o u n d 3 5 0 0 m , w h e r ea s i n p o o r w ea th er c o nd it i on , th e th er ma l de v ic e c an r ec og n is e a t a n k o n l y a t a d i st a n c e a r o u nd 2 0 0 0 m . 6 . C O N C L U S I O N S S o me o f t h e s i gn i f i c an t o b s e r va t i o n s a r e : ( a ) C o n tr a s t is t h e o n ly r e l at i v e me a su r e o f ta r g et ' s b ri gh tn es s wi th un if or m b ac kg ro u nd br ig ht ne ss , (a) (c) (b) (d) Fig ure 3. Detec tion pro babi lity o f d iff erent t arge ts a t cl ear we ather c ondit ion, as a f unct ion of r ange (k m): (a) da yli ght w ith cle ar w eather by an un aided hu man eye, ( b) f ullm oon n ight by an un aided hu man eye , (c) d aylig ht w ith bi nocul ar , and (d ) f ull moon nig ht b y a n ima ge inte nsif ier -II. 328 DE F S CI J , V OL . 5 7, N O. 3 , M AY 20 07 Sl. No. Parameters Specifications Daylight Fullmoon 1 Illumination Day light 10.0E+2 lux 3.1E - 01 lux 2 Range 0- 5 km 0- 2 km 3 Target size Person Tank 1 Toner Mortar 1.6 m 2 2.5 m 2 2.0 m 2 1.4 m 2 1.6 m 2 2.5 m 2 2.0 m 2 1.4 m 2 4 Target reflectance Person T ank 1 Toner Mortar 23.6 % 20 % 19.6 % 19 % 23.6 % 20 % 19.6 % 19 % 5 Background Desert, reflectance 26 % 26 % 6 Sensors aperture Pupil radius Binocular/image intensifier (II) NOD MK I 0.1 cm 8.0 cm 0.4 cm 20 cm 7 Sensors efficiency Photophic vision/me sophic vision (1/4200) (1/4200) 8 Integration time -- 0.1 s 0.2 s 9 Photon intensity Photophic vision/mesophic vision 4.073E+13 photons/ lumen -s 4.073E+13 photons/ lumen -s 10 Probability of false alarm -- 1.00E -1 1.00E -1 11 Attenuation coefficient Clear environment 1.118 1.071 w h ic h i s u s ed f o r t h e v i s u a l de t e c ti o n . A s S NR i s d i r ec t l y p r o po r t i o n al t o t h e s q u ar e o f t a r g e t' s c o n t r as t , m i n o r c h a ng e s i n c o n t r as t l e a d t o s i gn i f i c an t c h a n g e i n S N R . ( b) The detection probability is highly sensitive to the b ac kg r ou nd i ll um in at io n . Un d er ni g ht co n di t io n s u ch a s s t a rl i g h t , h u ma n e ye c a n de t ec t a t an k at a di st anc e a ro un d 2 00 m, wh er e as a t fu l lm oo n c o nd i t io n , t h e b a ck g r o un d i l lu m i na t i on is hi g h , t h e h um a n e ye i n f u l l mo o n i l lu m i n at i o n c an d et ec t a t a nk a t a d is t an ce a ro u nd 1 5 0 0 m w i t h 5 0 p e r c e n t p r o b ab i l i t y o f d e t ec t i o n . ( c ) T h e e f f i ci e n c y o f p h o t op i c v i s i o n i s m a x i mu m a t w a v e le n g t h a r o u n d 6 0 0 n m, at th i s r a n g e, t h e p h o t on i n t e n s it y i s 4 . 2 x 1 0 13 p e r l u me n - s e c o n d . W h e r e a s t h e e f f i c i en c y o f s c o t o p i c vision is maximum at wavelength around 500 nm, a t t h i s r a n g e t h e p h o t on i n te n s i t y i s 3 . 5 x 1 0 1 3 p e r l u m e n - s e c o n d . A s t h e S N R i s d i r e c t l y p ro po r ti o na l to t he ph o to n in t en s it y , un d er t he se c o n d it i o n s , h u ma n e y e c a n d e t e c t t h e s a me t a rg e t a t l o n g e r r a n g e i n d a y a s c o m pa r e d t o a t n i g ht . ( d) A n g le s u bt e n d e d b y a t a r g e t t o t h e d e t ec t o r i s a n i m p o rt a n t f a ct o r a s c o m p ar e d t o t a rg e t ' s s i ze . A n gl e i s a fu n c t i o n o f t a rg e t ' s s i ze an d T ab le 1. Param eter s value for evaluatin g per forman ce of human eye, image inten sifier , and binoc ular f or day and night vision . Fi gure 4. Pro bab ilit y of r ecog niti on of a ta nk i n c lea r nigh t b y S y st e ms I a nd I I t he r ma l i m a ge r us i ng t h e pa ram eter va lue s g iv en in th e T ab le 2. 329 DA S & S ING H: PE RF ORM AN CE MO DEL IN G O F E LEC TRO -O PT ICA L D EVI CE S F OR MI LIT ARY T AR GE T AC QU IS ITI ON d i st a n c e . D i f fe r e n t t a r g et s c a n p r o d u c e s a me a n g le a t d i f f er e n t d i st a n c e s. S N R i s d i r e ct l y p r o p or t i o n a l t o t h e s q u a r e o f t a r g et ' s a n g l e . S o l i tt l e c h a ng e i n t a rg e t ' s a n g l e c a n c h a n g e t h e S N R s i g n i f ic a n t l y . ( e ) Number of photons captured by the pupil (human ey e) de pen d s o n it s di ame ter. T he p upi l di ame te r o f t h e h um a n e ye ch a n g es wi t h t h e b a ck g r o u nd i l lu m i n at i o n . N um b e r o f p h o t o ns c a p t ur e d b y h um an e ye is d ir e ct ly p ro p or t io na l t o t h e sq ua r e o f t h e p u p i l d i a me t e r . T h e p u p i l d i am e t er c a n b e i n c r ea s e d u s i n g a n a r ti f i c ia l p u p i l t h a t w i l l c a pt u r e m a x i mu m n u mb e r o f p h o t o n s . U s in g a n a r t i fi c i a l p u p i l o f 8 0 m m d i a , t h e d e t e c ti o n r an g e of a t an k c an b e i nc r ea se d u p t o 5 00 m i n s t ar l i g h t co n d i t i on a n d 2 5 00 m i n f u ll mo o n co n di ti on wi th 5 0 p er ce n t d et ec ti on p ro ba bi li ty . ( f ) Under good weather condition, an average thermal d ev i ce c an r ec o gn i se a t an k a t a ro u nd 3 50 0 m , wh er eas at p oor w eat her c ond it io n, t h e t her mal d e v ic e c a n r e co g n i s e a t a n k o n l y a t a r o u n d 2 0 0 0 m . A C K N O W L E D G E M E N T S T h e a u t h o rs t ha n k f u l ly a c k n ow l e d g e t h e h e l p o f S h . R a j i v G u p t a a n d S h . D e ba s h i s h D u t t a, b o t h S c ie n t i s t F , I S S A , i n c o n d uc t i n g t h i s r e s e ar c h a n d t h e c o n s t r u c t i v e c o m m e n t s r e c e i v e d f r o m t h e a n o n y mo u s r e f e r e e s. R E F E R E N C E S 1 . F i er r o , M . & G u t h a rt , H . D e te c t i n g l e a k s f r o m t a nk s a n d p i p e li n e s : T h e s t a ti s t i c al n a t ur e of t h e t e s ti n g p ro c e s s. V i s ta R e s . T e c h . Me m o r . N o . 5 1 , 1 9 7 5 , 4 0 8 , 8 3 0 . 2 . Jo ne s, R .C. Qu ant um e ffi cie ncy of hu man vis ion . J . O p t . S o c . Am . , 1 9 5 9 , 4 9 , 6 4 5 . 3 . S c ha g e n , P . E l e ct r o n i c a i d s t o n i g h t v i s i on . P h i l . Tr a n s . R o y . S o c . , 1 9 7 1 , 2 6 9 , 2 3 3 . 4 . R o se , A . T h e r e la t i v e s e n s it i v i t i es o f t e le v i s i o n p ic k up t u be s , ph o to g r ap h ic f il m, a n d t he h u ma n e y e. P ro c e e d i n g s I . R . E . , 1 9 4 2 , 3 0 , 2 9 5 . 5 . H o we , D . J . I R /E O H a n d b oo k , C h . 2 , 1 9 9 9 , 5 7 . 6 . S h ef f e r, D . & U l t c h in , Y . C o m p ar i s o n o f b a n d s el ec t io n re s ul ts u si n g di f fe re nt c l as s se pa r at io n me a s u r es i n v a r i o u s d a y a n d n i gh t c o n d i t io n . P ro c ee d i n g s S P I E , 2 0 0 5 , 5 0 9 3 , 4 5 2 . 7 . B i r ke m a r k, C . M . C A M EV A , a m e th o d o l o g y f o r es t im at i n g o f ta rg e t d et e c ta b il i t y . O p t . E n g ., 2 0 0 1, 4 0 ( 9 ) , 1 8 3 5 . 8 . S c ha d e , O. H . A n ev a l u a ti o n o f p h o t og r a p h i c i ma g e q u a l i t y a n d r e s o lv i n g p o w e r. J . O p t . S o c . Am . , 1 9 5 6 , 4 6 , 7 21 . Sl No. Parameters Specifications Values 1. Inherent temperature difference of target and background Tank 1.25 °C 2. Range -- 3 km 3. Target height Tank 2.5 m 4. Parameters (a, b) of minimum recognisable temperature difference (MRTD) curve of thermal i mager (i) System I (ii) System II (0.0106, 0.584) (0.0145, 1.1942) 5. Attenuation coefficient Clear 1.071 T abl e 2 . Pa ramet ers val ue f or eva luat ing per for mance o f th erma l im ager 330 DE F S CI J , V OL . 5 7, N O. 3 , M AY 20 07 A p p e n d i x 1 P a r a m e t e r s o f T h e r m a l I m a g e r s S y s t e m I A n o p t ic a l s y s te m u s in g F / 2 .0 , 2 0 0 m m f oc a l l e n g th a n d h a v in g a n o v e r a ll t r an s m i ss i o n o f 0 . 5 h a s b e en c h o s en . T h e d e t ec t o r e l em e n t ( MC T - PV t y p e ) c ho s e n i s 2 x 1 5 s e r i al - p a r al l e l s c a n t yp e w i t h a s c an n i n g e f f ic i e n c y o f 0 . 6 6 f o r a 1 4 - f ac e t o p t o - me c h a ni c a l s ca n n e r . T h e e l e me n t a l s i z e o f t h e d e t e ct o r i s 3 5 µ x 3 5 µ w i t h a g a p o f 1 0 µ b e t w ee n t w o s u cc e s s i ve r o w s a nd 1 0 0 µ b e t w e en t h e t w o c o l u mn s . T h e d e te c t i v it y o f t h e d e t ec t o r h a s b e e n a s su m e d t o b e 6 x 1 0 1 0 c m H z 1 /2 W -1 . T h e s ca n n i n g f r am e r a t e h a s b e en t a k e n a s 2 5 c y c l e s/ s . Tab l e 3 a n d F i g . 5 s h o w t h e o b se r v e d a n d p r e d i ct e d m i n i mu m r e co g n i s a bl e t e mp e r at u r e d i ff e r e nc e ( M RTD ) f o r S y s te m I . Spatial frequency Observed MRTD Predicted MRTD 1.0 0.047863 0.0517 1.5 0.08696 0.0950 2.0 0.157993 0.1632 2.5 0.287048 0.2751 3.0 0.521521 0.4672 3.5 0.947521 0.8151 4.0 1.721495 1.5000 4.5 3.127686 3.0400 5.0 5.682512 7.4950 T abl e 3 . M inimum recognisable temperature difference data f or Sys tem I 0 0 .5 1 1 .5 2 2 .5 0 2 4 6 8 1 0 S P AT IA L FREQ UENCY ( MRAD- 1 ) MRTD OBS E RV E D M R T D P RED ICT E D M R T D Fig ure 5 . Obs erv ed a nd p redi cted MR TD f or th e Sy stem I . S y s t e m I I A n o p t ic a l s y s te m u s in g F / 2 .0 , 4 0 0 m m f oc a l l e n g th a n d h a v in g a n o v e r a ll t r an s m i ss i o n o f 0 . 5 h a s b e en c h os e n . T h e d e t ec t o r e l e me n t ( M C T - P C t y p e ) c h o s en is 1 x 10 0 el e me n t pa r a l l el sc a n t y p e w i t h 1 : 2 i n t e rl a c i n g a n d h a v i n g a s c a n e f f ic i e n c y o f 0 . 5 f o r a 1 2 - f a ce t o p t o -m e c h an i c a l s c an n e r. T h e e l e me n t a l s i ze of th e de t e c t or is 35 µ x 3 5 µ w i t h a g a p of 3 5 µ b e t w ee n t w o s u c ce s s i ve r o ws . T h e d e t ec t i v i ty i s ta k e n as 8 x 1 0 10 c m H z 1 /2 W -1 a n d th e s c an n i n g f r am e ra t e i s as s u me d t o b e 25 c y c le s / s . F i g u re 6 a n d T a b l e 4 s h o w t h e o b s e r ve d a n d p r e d ic t e d mi n i mu m r e c o g ni s a b l e t e mp e r at u r e d if f e re n c e ( M R T D ) f o r S y st e m I . 331 DA S & S ING H: PE RF ORM AN CE MO DEL IN G O F E LEC TRO -O PT ICA L D EVI CE S F OR MI LIT ARY T AR GE T AC QU IS ITI ON 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 S P AT I AL FREQUENCY (M R A D-1 ) MRTD OB S E R V ED M R T D P REDICT E D MRT D Figure 6 . Obs erved an d pred icted MRTD for t he Sys tem II. Spatial frequency Observed MRTD Predicted MRTD 1 0.01612 0.019008 2 0.03740 0.034085 3 0.06878 0.061121 4 0.11780 0.109602 5 0.19810 0.196538 6 0.33490 0.352431 7 0.58350 0.631978 8 1.06800 1.133260 9 2.20000 2.032159 T abl e 4 . Minimum recognisable temperature difference data f or Sy stem I I D r S . K . D a s o b t a i n e d P h D ( A g r i c u l t u r a l S t a t i s t i c s ) f r o m t h e I n d i a n A g r i c u l t u r a l R e s e a r c h I n s t i t u t e , N e w D e l h i , i n 2 0 0 5 . H e j o i n e d D R D O a t I n s t i t u t e f o r S y s t e m s Stu dies and An aly ses (IS SA), De lhi , i n 2 002 . H is ar eas of res ear ch in clu de: Mat hem ati cal m o d e l l i n g f o r m i l i t a r y t a r g e t d e t e c t i o n , a r m o u r w a r f a r e , a n d d i g i t i s e d b a t t l e f i e l d . M r R. S . S i n gh o b t a i ne d M S c ( M a t h e m at i c s ) i n 1 9 7 7 . He j o i n e d D R D O a t t h e I S S A , D e l hi , i n 1 9 8 4 . H e h a s wo r k e d f o r r e l i a b il i t y e v a l ua t i o n o f va r i o u s s y s t e ms d e si g n e d a n d d e v e l o p e d b y D R D O s y s t e m s l a b s . P r e s e n t l y, h e i s w o r k i n g f o r m a t h e m a t i c a l m o d e l s d e v e l o p m e n t . C on t r ib u to r s