Global Advanced Research Journal of Management and Busness Studes (ISSN: 2315-5086) Vol. 4(3) pp. 082-086, March, 2015 Avalable onlne http://garj.org/garjmbs/ndex.htm Copyrght 2015 Global Advanced Research Journals Revew Paper Evaluate the Effectve of Annular Aperture on the OTF for Fractal Optcal Modulator Asst. Prof Dr. Abdulrazak A. S Mohammed Computer Scence- BAYAN Unversty / Erbl-Iraq Emal: mabdulrazakabdulsalam@yahoo.com Accepted 20 October 2014 The fractal optcal modulator s the optcal modulator desgn by usng the fractal functon. As well known there s an effect of aperture s shape on the OTF sgnal for optcal modulator. In present paper an aberraton-free sngle annular aperture has used and the MTF characterstcs responses nvestgate for fractal optcal modulator of IR-Seeker.The annular aperture provde several frequency transmsson bands wthn the regon up to cut-off frequency. The result compared wth the spatal frequency for crcular shape of fractal optcal modulator aperture. Keywords: Annular Aperture, OTF, Fractal Optcal Modulator, INTRODUCTION The optcal modulator s an mportant devce n optcal system for gude and control.ths devce create a frequency whch depend on type,pattern and area (sze) of the modulator. The optcal transfer functon (OTF) curve has a relaton wth area of an aperture. If we have full aperture the broad frequency response peak wll be near the cut-off frequency (Rteel, 1953). The lterature vew of usng annular aperture as follow: 1-The OTF for an annular aperture wth a sphercal aberraton was treated by (Barakat and Houston, 1965)]. 2- (Welford, 1960)], nvestgated the effect of ncreasng the depth of focus n such a type of aperture. 3-The sngle annular aperture s probablty the smplest modfed aperture. Kyung Hee Hong was found the characterstcs of the OTF of Double annular aperture (Kyung Hee Hong And Sang Soo Lee, 1980), he studed the ampltude dstrbuton the mage feld s gven by the ampltude due to the full aperture mnus the ampltude due to the nner crcular aperture. Defne the Shape of Annular Aperture The annular aperture (AA) defned by usng the reduced parameters r o, r 1 & r 2 the rad of the crcles on the aperture. r 1 =3.5cm the radus of the full crcle of aperture. r o =1.4cm the radus of annular area (the oblque area 42.8%) and r 2 =2.1cm s the radus of transmuted area of the aperture (57.2%) as shown f fg.( 4-A ). Fractal Optcal Modulator It s an optcal modulator (dsk) desgn by usng a fractal functon. There are dfferent type of fractal modulator, we choose one of them whose desgned by the reference (Jebbar, 2007) whch s sngle pattern of AM modulaton,
Abdulrazak, 083 t assumed the sze of the modulator s same sze of full annular aperture (7cm dameter, t means 3.5 cm radus).the radus of nner oblque area s 1.5cm and outer radus (transmtter area) s 2cm as shown n fg.(3). In fg.(4-b) shows the fractal modulator wth annular aperture n front of t. Some tme there wll be a condensng lenses between the aperture and the modulator.
084 Glo. Adv. Res. J. Manag. Bus. Stud. (A) (B) Fg(4 ) A- Annular aperture B-Fractal modulator wth annular aperture Fg (5). Power transparent of fractal modulator wthout annular aperture A short dea about fractal desgn s let we have an element (sngle lne) t s length (L) dvded n to (N) peces, each pece has a length (K), so The Fractal dmenson (D) equal (Razak and Ahammed, 2008) to : log( N ) D = log K ( L ) (1) By usng Iterated Functon System (IFS) t s a method of constructng fractals for the dmenson of the element (D) to get the new desgn of fractal functon modulator pattern.n order to generate the fractal pattern, let we have (x,y) mappng space of a matrx, so the f(x) wll represents all the ponts of the space. If the matrx (W for =1,2,3,.m) then : x = a W ( x) = w y c W = A X + T b x + e d y f.(2).(3)
Abdulrazak, 085 Fg 6. Power transparent of fractal modulator wth annular aperture By these sets producton operaton can be obtan of all ponts n sum operaton of two lnear transformaton. Evaluaton of OTF and MTF (Kyung Hee Hong And Sang Soo Lee, 1980) The OTF or t s modulus the modulaton transfer functon (MTF) s used as an objectve means for assessng and specfyng the magng qualty of optcal & electro-optcal system.(thermal or vsble). For a gven dstrbuton of ntensty n the object plane of modulator can be consdered as seres of supermposed sne wave gratng dstrbuton of ntensty of dfferent perodctes, phases and ampltudes Ths defned as the Fourer transform of the pont spread functon or mpulse response of the optcs and t gve the crtera, such as contrast, senstvty and resoluton. If the optcal transfer functon of the system s real and non-negatve, the optcal transfer functon s equal to modulaton transfer functon (MTF) by defnton. Also the relatve contrast s gven by the absolute value of the OTF, a functon referred to as the (MTF). On other hand when the pattern translaton s also mportant. We consder ntensty dstrbuton f(u) where (u) s a dstance n object plane, and ths can be expressed as: f( u) = 2 ν e π u F( ) ν dν (4) Where F(ν) s a complex functon whch gves the ampltude and phase of sne wave component of spatal frequency (ν). The dstrbuton of ntensty n the mage plane f (u) can be bult up from sne wave n the same way as a functon F (ν) The complex valued optcal transfer functon can be seemed as a combnaton of these valued functon PhTF( ν ) OTF where ( ν ) = MTF ( ν ) e MTF ( ν ) = OTF ( ν). (6) The defnton of transfer functon, should ndcate the fracton of lght that was detected from the pont source object. However, typcally the contrast relatve to the total amount of detected lght s most mportant. It s thus common practce to normalze the optcal transfer functon to the detected ntensty, hence
086 Glo. Adv. Res. J. Manag. Bus. Stud. MTF =. f( u) e 2πν u du (7) The MTF s then plotted aganst spatal frequency and all relevant data concernng, can be determned from that graph. DISCUSSION AND CONCLUSION By usng annular aperture wth optcal fractal modulaton we found: 1-The case gve us more accuracy result especal the optcal modulator whch has a centre oblque area, (such as our case). 2-The dfference between OTF of full aperture fg(1) and annular aperture fg (2) s n the behavor of OTF curve for full aperture s more smoothly than annular one, (for same reduced spatal frequency ) because of the central oblque area. 3-In fg (5 &6) the power transparent has been evaluated for both cases (Fractal modulator wthout annular aperture and wth t respectvely), for same nterval tme. We note that the dfferent between them s n annular aperture the power s lmted but more specfc (because less aberraton). 4-The advantage of usng annular aperture wth optcal modulator s avoded the nose that generated n the centre of the modulator and t appled n some optcal system (gude and control system) such as Laser & IR Seeker. REFERENCES Rteel W (1953). A study of the combned effects of aberraton & a central obstructon of the pupl on the contrast objectves usng mrrors Rev.Opt.,32,4-26 (1953). Barakat R and Houston A (1965). Transform functon of an annular aperture n the presence of sphercal of aberraton J. Opt. Soc. Amer, 55, 538-542, 1965. Welford (1960). Use of annular aperture to ncrease focal depth. J. Opt. Soc, Amer., 58, 749-753 (1960). Kyung Hee Hong And Sang Soo Lee (1980). Characterstcs of Optcal Transfer Functon of Double Annular Aperture. J. Of Korea Physcal Socety., V13, No. 2, October 1980. Jebbar ML (2007). Evaluaton of MTF for Fractal Optcal Modulator of Semconductor MSc. Thess, Al-Mustansrya Unversty 2007. 6xRazak AS, Ahammed S (2008). Calculaton of MTF for Optcal Dsk Modulator by usng Fractal Functon.Technology & Engneerng magazne of Technology Unversty, Baghdad, Vo.26,No. 12,2008.