IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.24 (2) 2011 The Effect of Spot Size on the Fractal Optical Modulation A. A S Mohammad , K. H Harby ,T.A. K Al-Aish Department of Physics ,College of Education Ibn Al-Haitham ,University of Baghdad Received in : 30, October , 2010 Accepted in : 27, February, 2011 Abstract The present paper analyzes the signal emitting from the Reticle during changing the spot size of laser falling on the disk and shows the optimum frequency and the amount of energy window in different patterns of modulator (Reticle). All results are obtained by establishing a special program named “Disk optical modulator version 3" using the language visual basic 6 ahich contains many parameters. All models of optical modulator consist of twenty sectors, ten sectors are opaque and other ten sectors are transmitted for the laser. The number of sectors depends on several factors as chopping frequency, power transparent and modulation transfer function. It has been demonstrated by simulations, the optimal value of modulation transfer function is achieved when spot size of laser 0.3 mm and any increasing in spot size lead to decrease in MTF value. Keywords: Fractal Optical Modulator, Chopping frequency, Spot size, power transparent, the Modulation Transfer Function MTF Introduction In any electro- optical tracking systems the optical modulation disk (Reticle) is used as optical filter for background discrimination. The design and movement of the Reticle is to enhance the object and suppress the background. The detection of Reticle is limited to point sources of radiation and to achieve the best efficiency of the disk [1]. In practice, it must not exceed the size of Reticle sector at three times the size of target image. The ideal situation, in fact, occurs when the dimensions of object image is equal to the dimensions sectors Reticle, but the increase in the volume of object image as a result of the approaching electro- optical system is the real motive behind the reduced dimensions of its image in order to start a third remove sections of Reticle, should not exceeding the dimensions spot dimensions of disk sectors [2]. IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.24 (2) 2011 Design of Reticle There are some factors of spot size affecting on the Reticle design, usually the design of Reticle depends on the following [2, 3, 4]: 1. The nature of work of electro-optical system (negative or positive mode). 2. The type and nature of the objects to be pursued and sources of ambient noise. 3. The dimensions of Reticle. 4. The rotation speed and the number of sectors of Reticle. 5. The requirements of the speed of response of the system. 6. The field of vision to be covered. 7. The nature of the electronic circuits used in signal processing The dimensional ideal for Reticle design which is based on the progress of the above factors will assume number of assumptions, in electro-optical tracking systems with active mode, the target is illuminated by an external source of lighting, often the source is one type of lasers. Where the principle in such systems, is based on the target (as a reflecting surface diffuse type), thus the source represented as radiation source or lambertian source [4]. Since the proposed range of electro-optical tracking systems is about 5 km therefore has been chosen one solid-state lasers (CW), which is Nd-Yag laser, high energy and wavelength (1.06 micrometers). This wavelength is located within the limits of the optical response detector made of silicon with distinctive characteristics and cheap price [5,6]. Two models has been designed for Reticle; the first design is normal way, so as to compare the results obtained from this model with the results of the second model, which was designed by using Fractal Function,( a new technique) [7,8]. The normal optical modulator is a circular disc which has a radius R, which assumes the number of sector is (twenty sectors), ten sectors are opaque and the other ten sectors are transmitted for the light as shown in Fig (1). One may consider these ten sectors also as opaque for the other regions of electro -magnetic wave spectrum. By using this concept and IFS (Iterated Function Sys tem) kit program [9], we have designed optical modulator as shown in Fig (2). This optical modulator consists of two pattern circles. Each circle is divided into ten transparents and ten opaque sectors (q). The first pattern, is (inner pattern) designed in a circle with data as shown in Table (1). After conducting the operations of scaling, rotation and iteration (for many times) the obtained pattern is as shown in Fig (2). The second pattern (outer pattern) is designed in an equilateral triangle with data as shown in Table (2).After (many times) of conducting the operations of scaling, rotation and iteration, the result is as shown in Fig. (2). Result and Discussion To get work it has been established a special program named “Disk optical modulator version 3" using the language visual basic 6 which contains many parameters and as shown in Table (3). When calculating the frequency it has been converted to units (Rev / s), as well as for angular velocity w, The Law of frequency is given by[10]: IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.24 (2) 2011 2/wfr  ……..…. (1) qfrfc  …………. (2) Where fc chopping Frequency, fr rotation Frequency and q number of sectors. The basic idea in this research requires expansion the spot size of laser to cover the full Reticle with radius equals to 90 mm and by assuming the power of laser emission from source about PL= 50 Watt and diameter of spot is r = 3 mm with wavelength , and distribution of the power density in the near field given by [2, 11]: ………….. (3) for r = 1.5 mm When extended the spot laser to cover all effective area of reticle become for r = 90 mm The great part of the laser energy will loss as a result of the processes of reflection, absorption, and that will suffer, when passed through the optical components of the transmitter unit, if the transmittance of the lens of an expanded package are and , its means lost 20% of the power energy in lens And approximately 80% of the energy falls on a Reticle which have transparent for transparent sectors. The power transparent P of each sector is given by the equation [2,11]: p = Sn τr …………………….(4) Where =0.729 and Sn area of sub sector The modulation transfer function MTF is calculated for each pattern by calculating the transmittance intensity by using the equation:- minmax minmax II II MTF    Where: Imax: is transmittance maximum intensity and Imin : is oblique minimum intensity .we calculate Imax (the ratio between the spot size and the transmittance area), and Imin (the ratio between the spot size and oblique area [12,13]. Then we measure the modulation transfer function MTF by using eq (5). The results that were obtained based on a number of information assumed as shown in Table (4) and Table (5). First, we may draw the relationship between the rotation frequency and Chopping frequency with number of sectors, we got the curve shown in Fig(3) ……………………….…….. (5) IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.24 (2) 2011 The movement of any section in a circular motion takes approximately 0.0001 seconds (for the disc consists of 10 sections of dark does not allow passage of the power and 10 section window allows passage power) that would lead to cut the signal on an ongoing basis every 0.0001 seconds as shown in Table ( 6 ) and Figs (4, 5), which represents the relationship between power transparent and the time, also it shows, that the power transparent is directly proportional with size of sector, consequently the power transparent from fractal Reticle is larger from normal Reticle. Changing spot size of laser Theoretically, the best detection occurs when sectors of the disk is determined periodically and the forms and dimensions similar to the form and dimensions of spot, this leads to complete the modulation continues process and reduce the frequency bandwidth occupied by the optical signal to the lowest extent possible, or in other words, reduce the impact of noise to a minimum [2,9,8]. To explain the impact of changing spot size of laser on the fractal modulator frequency, we will change the spot size between 0.3 mm 2 to 0.6 mm2 from area of sector as shown in Table (7), and then evaluate the best value of MTF depending on Eq.5 In order to unify the values for all models we'll take stairs gradually to cover these Values, depending on the minimum value (0.376 mm 2) and maximum value (0.93mm2) and between them in the following manner Spot size in mm2 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008 0.0009 Tables (8, 9, 10 and 11) shows the results of the fc and modulation transfer function MTF which was obtained as a result of changing the spot size from 0.3 mm 2 to 0.6 mm2 (as shown in Figure (6)to fig.(13)). We note that the best value for the MTF was obtained when the size of the section is equal to 0.3 mm2 and any increase in spot size after this value leads to adversely affects on MTF for all models, and this supports what we assumed theoretically for the case of an ideal fit between the spot size and area of the section of the disk. Conclusion 1 - The outer pattern of fractal Reticle is used to detect the target , which requires that the aperture sizes are larger than the target by three times to achieve the following:  early detection of distant targets situated within the range of Reticle  The ability to detect more than one objective, and determine the coordinates of based on its initial size and shape  Keep the targets under monitoring, especially when approaching where the bigger size  Give adequate time for the reorientation of the visual system in order to drop in body image exposed on the inner pattern of fractal model by object-oriented lens. 2 - The inner pattern of fractal Reticle is used for the purpose of the lock on the target, and this IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.24 (2) 2011 requires that the expulsion of the target equals to the dimensions of sectors to achieve the following:  Complete the modulation continues process and this leads to reduce the impact of noise to a minimum.  Access to the regular signal and nearly constant frequency. 3. The power transparent is directly proportional with size of sector; consequently the power transparent from fractal Reticle is larger from normal Reticle References 1. Harry, L. VAN TREES, (2001), Detection, Estimation, and Modulation Theory", Book: George Mason University , ISBNs: 0-471-10793-X (Paperback); 0-471-22109-0 (Electronic), Library of Congress, USA. 2. Reyad, N. Ali, (2004), Design Study on Laser Guidance System Employing an Optical Reticle, PH.D Thesis, Al- Rasheed College of engineering. 3. Hyun, K. Hong, Sung, H . Han, Gyoung, P. Hong, and Jong, S. Choi, (1996), Simulation of Reticle Seekers Using the Generated Thermal Images, Proceedings I E E E Conference on Circuits and Systems, Seoul. 4. Marvin, K. Simon, (2001), Bandwidth-Efficient Digital Modulation with Application to Deep-Space Communications, Book, Publisher : Wiley, California Institute of Technology 5. Biberman, L. M. (1966) Reticles in Electro-Optical devices, ergamon Press, Published Pergamon Press in Oxford, Toronto. 6. Wolfe w, and Zissis G, (1978), The Infrared Handbook, IRIA center, Environmental research Institute of Michigan. 7. Mandelbrot, B.B (1982),The Fractal Geometry of Nature. W.H. Freeman and Company.. ISBN 0-7167-1186-9, New York. 8. Thair, A.A.(2002), Fractal Image Synthesis by Iterated Function System, MSc Thesis, University of Baghdad. 9. IFS kit program, http://ecademy.agnesscott.edu/~lriddle/ifskit/ 10. Gramm, C.F. (1965), Infrared Equipment , Chapter 9 Volume Two of Applied Optics and Optical Engineering , R. kingslake editor, Academic. 11. George, M. Siouris, (2004), M issile Guidance and Control Systems, ISBN 0-387-00726-1 (hc. : alk. paper), Springer, Verlag New York, Inc. 12. Fadl, W. (2004), Design Optical Modulator by Using Fractal Function Geometry, MSc Thesis, Al-Mustansiryah University. IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.24 (2) 2011 13. Ahmed, S.A. (2008), Calculation of MTF for Optical Disk Modulator by Using Fractal Function, MSc Thesis, University of Technology. Table (1): The initial shape of the first pattern Table (2): The initial shape of the second pattern Table( 3) data of Disk optical modulator v.2 Program Table( 4): The results of normal and Reticle disk IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.24 (2) 2011 State Normal Reticle Fractal Reticle Inner Pattern Outer Pattern radius 0.09 m 0.03 m 0.09 m Time 0.002 sec 0.002 sec 0.002 sec Number of sector 20 20 20 spot size of laser 0.5 mm 0.5mm 0.5 mm Angle of sector 18 degree 18 degree 18 degree Circumference 0.5652 m 0.1884 m 0.5652 m Area of disk 0.025434 m2 0.002826 m2 0.025434 m2 Angular velocity 1744.44 rad/sec 5233.33 rad/sec 1744.44 rad/sec Rotational frequency 277.77 833.33rad/sec 277.77 Chopping frequency 2777.7 rad/sec 8333.3 rad/sec 2777.7 rad/sec Table (5): data of sub sector for normal and fractal reticle State Normal Reticle Fractal Reticle Inner Pattern Outer Pattern Circumference sub sector 0.02826 m 0.1884 m 0.02826 m Area of transparent sub sector 0.0012717 m2 0.00001256m2 0.00001558842m2 Area of transparent sector 0.0012717 m2 0.001256m2 0.001558842m2 Table (6) : The power transparent of Reticle disk No of sector Time in sec Pow er transparent of Normal in Watt Pow er transparent of inner fractal in wa tt Pow er transparent of outer fractal in wat t 1. 0.0001 0 0 0 2. 0.0002 1.82 1.7999 2.234 3. 0.0003 0 0 0 4. 0.0004 1.82 1.7999 2.234 5. 0.0005 0 0 0 6. 0.0006 1.82 1.7999 2.234 7. 0.0007 0 0 0 8. 0.0008 1.82 1.7999 2.234 9. 0.0009 0 0 0 10. 0.001 1.82 1.7999 2.234 11. 0.0011 0 0 0 12. 0.0012 1.82 1.7999 2.234 13. 0.0013 0 0 0 14. 0.0014 1.82 1.7999 2.234 15. 0.0015 0 0 0 16. 0.0016 1.82 1.7999 2.234 17. 0.0017 0 0 0 18. 0.0018 1.82 1.7999 2.234 19. 0.0019 0 0 0 20. 0.002 1.82 1.7999 2.234 Table(7): data of (0.3 - 0.6 )area of sub sector for normal and fractal reticle IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.24 (2) 2011 Area of transparent sector 0.0012717m2 0.001256m2 0.001558842m2 Outer pattern Inner pattern Normal reti cle Spot size State Spot size State Spot size State 0.00046 0.3 0.000376 0.3 0.000381 0.3 0.00062 0.4 0.0005024 0.4 0.000508 0.4 0.00073 0.5 0.000628 0.5 0.000635 0.5 0.00093 0.6 0.0007536 0.6 0.000763 0.6 Table(8 ):The MTf of Normal and fractal Reticle when Spot size = 0.0003 m Normal Reticle Fractal Reticle Inner Pattern Outer Pattern R Fc MTF R Fc MTF R Fc MTF 0.009 27777.7 0.096 0.03 8333.33 0.32 0.09 2777.7 0.96 0.018 13888.8 0.192 0.02906 8602.89 0.309 0.08720 2866.97 0.930 0.027 9259.25 0.288 0.026477 9442.15 0.282 0.0794 3148.61 0.846 0.036 6944.44 0.384 0.02287 10931.35 0.243 0.0686 3644.31 0.731 0.045 5555.55 0.48 0.01946 12846.86 0.207 0.05840 4280.82 0.622 0.054 4629.62 0.576 0.018 13888.88 0.192 0.054 4629.62 0.576 0.063 3968.25 0.672 0.01946 12846.86 0.207 0.05840 4280.82 0.622 0.072 3472.22 0.768 0.02287 10931.35 0.243 0.0686 3644.31 0.731 0.081 3086.41 0.864 0.026477 9442.15 0.282 0.0794 3148.61 0.846 0.09 2777.77 0.96 0.02906 8602.89 0.309 0.08720 2866.97 0.930 Table(9 ):The MTf of Normal and fractal Reticle when Spot size = 0.0004 Normal Reticle Fractal Reticle Inner Pattern Outer Pattern R Fc MTF R Fc MTF R Fc MTF 0.009 27777.77 0.075 0.03 8333.33 0.25 0.09 2777.77 0.75 0.018 13888.88 0.15 0.02906 8602.89 0.242 0.08720 2866.97 0.726 0.027 9259.25 0.225 0.026477 9442.15 0.22 0.0794 3148.61 0.661 0.036 6944.44 0.3 0.02287 10931.35 0.190 0.0686 3644.31 0.571 0.045 5555.55 0.375 0.01946 12846.86 0.162 0.05840 4280.82 0.486 0.054 4629.62 0.45 0.018 13888.88 0.15 0.054 4629.62 0.45 0.063 3968.25 0.525 0.01946 12846.86 0.162 0.05840 4280.82 0.486 0.072 3472.22 0.6 0.02287 10931.35 0.190 0.0686 3644.31 0.571 0.081 3086.41 0.675 0.026477 9442.15 0.22 0.0794 3148.61 0.661 0.09 2777.77 0.75 0.02906 8602.89 0.242 0.08720 2866.97 0.726 Table(10 ):The MTf of Normal and fractal Reticle when Spot size = 0.0005 Normal Reticle Fractal Reticle Inner Pattern Outer Pattern R Fc MTF R Fc MTF R Fc MTF 0.009 27777.77 0.06 0.03 8333.33 0.2 0.09 2777.77 0.6 0.018 13888.88 0.12 0.02906 8602.89 0.193 0.08720 2866.97 0.581 0.027 9259.25 0.18 0.026477 9442.15 0.176 0.0794 3148.61 0.529 0.036 6944.44 0.24 0.02287 10931.35 0.152 0.0686 3644.31 0.457 0.045 5555.55 0.3 0.01946 12846.86 0.129 0.05840 4280.82 0.389 0.054 4629.62 0.36 0.018 13888.88 0.12 0.054 4629.62 0.36 0.063 3968.25 0.42 0.01946 12846.86 0.129 0.05840 4280.82 0.389 0.072 3472.22 0.48 0.02287 10931.35 0.152 0.0686 3644.31 0.457 0.081 3086.41 0.54 0.026477 9442.15 0.176 0.0794 3148.61 0.529 0.09 2777.77 0.6 0.02906 8602.89 0.193 0.08720 2866.97 0.581 IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.24 (2) 2011 Table(11):The MTf of Normal and fractal Reticle when Spot size = 0.0006 Normal Reticle Fractal Reticle Inner Pattern Outer Pattern R Fc MTF R Fc MTF R Fc MTF 0.009 27777.77 0.05 0.03 8333.33 0.166 0.09 2777.77 0.5 0.018 13888.88 0.1 0.02906 8602.89 0.161 0.08720 2866.97 0.484 0.027 9259.25 0.15 0.026477 9442.15 0.147 0.0794 3148.61 0.441 0.036 6944.44 0.2 0.02287 10931.35 0.127 0.0686 3644.31 0.381 0.045 5555.55 0.25 0.01946 12846.86 0.108 0.05840 4280.82 0.324 0.054 4629.62 0.3 0.018 13888.88 0.1 0.054 4629.62 0.3 0.063 3968.25 0.35 0.01946 12846.86 0.108 0.05840 4280.82 0.324 0.072 3472.22 0.4 0.02287 10931.35 0.127 0.0686 3644.31 0.381 0.081 3086.41 0.45 0.026477 9442.15 0.147 0.0794 3148.61 0.441 0.09 2777.77 0.5 0.02906 8602.89 0.161 0.08720 2866.97 0.484 Fig. (1): The Normal optical modulator Fig. (2): The fractal optical modulator IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.24 (2) 2011 Fig.( 3) :The relation between No. of sector versus frequency Fig .(4): The relationship between power transparent and the time for Normal Reticle Fig. (5): The relationship between power transparent and the time for fractal Reticle IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.24 (2) 2011 Fig .(6): The MTF versus fc with spot size 0.0003 (Normal Reticle) Fig. (7): The MTF versus fc with spot size 0.0003 (fractal Reticle) Fig .(8): The MTF versus fc with spot size 0.0004(Normal Reticle) Fig. (9): The MTF versus fc with spot size 0.0004(fractal Reticle) IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.24 (2) 2011 Fig .(10): The MTF versus fc with spot size 0.0005(Normal Reticle) Fig. (11): The MTF versus fc with spot size 0.0005(fractal Reticle) Fig. (12): The MTF versus fc with spot size 0.0006(Normal Reticle) Fig. (13): The MTF versus fc with spot size 0.0006(fractal Reticle) للعلوم الصرفة والتطبیقیة المجلد 2011) 2( 24مجلة ابن الھیثم التضمین البصري الكسوري في تأثیر حجم البقعة السالم محمد، خالد هالل حربي ،ثائر عبد الكریم خلیل العایشعبد الرزاق عبد د –كلیة التربیة ابن الهیثم -قسم الفیزیاء جامعة بغدا 2010، تشرین االول ،30: استلم البحث في 2011، شباط، 27: قبل البحث في الخالصة اإلشارات المنبعثة من قرص التضمین البصري من خالل تغییر حجم بقعة اللیزر الساقطة حللت في هذا البحث .تردد من خالل مقدار الطاقة النافذة من قرص التضمین البصري فضلاوحسب على القرص قرص التضمین البصري االصدار الثالث الذي یحتوي هطة انشاء برنامج خاص اسمینااجمیع النتائج استحصلت بواس . عشرة منها مضیئة واالخرى معتمة لضوء اللیزر، "امقطع 20جمیع نماذج قرص التضمین تتألف من . العدید من البارمترات .مثل تردد القطع، القدرة النافذة ودالة االنتقال الضمني عدیدة ان عدد المقاطع یعتمد على عوامل ي 0.3یكون حجم بقعة اللیزر ماوقد ثبت عن طریق المحاكاة ان افضل قیمة لدالة االنتقال الضمني تتحقق عند ملم وا .زیادة في حجم المقطع یودي الى انخفاض في قیمة دالة االنتقال الضمني ، دالة االنتقال الضمني التضمین البصري الكسوري ، تردد القطع، حجم المقطع ، القدرة النافذة: كلمات مفتاحیةال