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1/13/2008 2-1 ECE 415 EXPERIMENT NO. 2 LENS-PINHOLE SPATIAL FILTERS AND BEAM EXPANDERS PURPOSE : To study the operations of beam expanders and lens-pinhole spatial filters and to practice alignment of simple optical components. REFERENCES : 1. C. L. Chen, Elements of Optoelectronics & Fiber Optics , Irwin, (1996), Sections 2.4 and 2.8, pp. 49-55 and 68-74. 2. A. Nussbaum and R. A. Philips, Contemporary Optics for Scientists and Engineers , Prentice-Hall, Inc., Englewood, NJ (1976), Chapter 10. 3. E. Hecht, Optics , Addison-Wesley, 4th edition, (2002), Chapter 11. 4. F. L. Pedrotti and L. S. Pedrotti, Introduction to Optics , Second edition, Prentice Hall, (1993), Section 16-3. 5. B. J. Pernick, "Irradiance uniformity and power loss with a spatially filtered laser beam," Rev. Sci. Instrum ., Vol. 45, pp. 1344-47, (1974). 6. Notes on "Autocollimation of convex lens." (Attached) 7. M. E. Cox, "The lens-pinhole spatial filter," Physics Education , Vol. 14, pp. 56- 57, (1979). (Attached) 8. J. M. Yaeli, "Method for designating the optical axis of a refracting system," Opt. Eng. , Vol. 19, pp. 438-439 No. 3, (1980) REMARKS : The beams emitted by typical HeNe lasers may be approximated accruately as Gaussian beams. A detailed discussion of the properties of Gaussian beams can be found in Section 2.4 of Ref. [1]. We briefly discuss the key properties of Gaussian beams here. The irradiance distribution of a Gaussian beam is: ) z ( w / r 2 2 2 2 e w P 2 ) z , r ( I π = (1) where I(r,z) is the irradiance (W/m 2 ) at a distance r from the beam axis and at a distance z from beam waist, P is the total beam power (W), and w(z) is the beam radius at which the irradiance reduces to e 2 of the on-axis value. The beam diameter at
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1/13/2008 2-2 z is to 2w(z). A derivation of (1) is given in p. 52 of Ref. [1]. In fact, (1) is exactly (2.60) of Ref. [1]. Outside the Rayleigh range, a Gaussian beam diverges or spreads at a half angle (Figure 1), θ h = λ π w o (2) where 2 θ h is the full cone angle to the e 2 irradiance points and w o is the beam waist radius. (Also see (2.62) of Ref. [1]).
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