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ECEG105 & ECEU646 Optics for Engineers Course Notes Part 10: Fourier Optics

ECEG105 & ECEU646 Optics for Engineers Course Notes Part 10: Fourier Optics. Prof. Charles A. DiMarzio Northeastern University Fall 2003. Fourier Optics. Review Fraunhofer Diffraction Review Pupils and Windows Concepts of Fourier Optics Point Spread Function Transfer Function Examples

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ECEG105 & ECEU646 Optics for Engineers Course Notes Part 10: Fourier Optics

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  1. ECEG105 & ECEU646 Optics for EngineersCourse NotesPart 10: Fourier Optics Prof. Charles A. DiMarzio Northeastern University Fall 2003 Chuck DiMarzio, Northeastern University

  2. Fourier Optics • Review Fraunhofer Diffraction • Review Pupils and Windows • Concepts of Fourier Optics • Point Spread Function • Transfer Function • Examples • Experimental Techniques Chuck DiMarzio, Northeastern University

  3. Fraunhofer Diffraction (1) Chuck DiMarzio, Northeastern University

  4. Fraunhofer Diffraction (2) Chuck DiMarzio, Northeastern University

  5. Linear Systems Approach to Imaging x’ x Any Optical System Exit Window Entrance Window Isoplanatic Chuck DiMarzio, Northeastern University

  6. Terminology • h is called the point spread function (PSF) • H is called the optical transfer function (OTF) • Magnitude is called Modulation Transfer Function (MTF) • Phase is Phase Transfer Function (PTF) • fx and fy are spatial frequencies Uimage Uobject Uimage Uobject Chuck DiMarzio, Northeastern University

  7. Concepts of Fourier Optics Any Isoplanatic Optical System Exit Window Exit Pupil Entrance Pupil Entrance Window Scale x,y and Multiply by OTF Fourier Transform Fourier Transform Chuck DiMarzio, Northeastern University

  8. Coherent and Incoherent Imaging Coherent Case: Incoherent Case: Chuck DiMarzio, Northeastern University

  9. Spatial Frequency Domain f,g are fields, V/m finc,ginc are irradiances, W/m2 H Hinc Chuck DiMarzio, Northeastern University

  10. Coherent and Incoherent OTF • h(x,y) is real: H(-fx,-fy) = H*(fx,fy). • Convolution of H and H* is Autocorrelation of H • The incoherent PSF is the squared magnitude of the coherent PSF. • Thus the incoherent OTF is the autocorrelation of the coherent OTF. Chuck DiMarzio, Northeastern University

  11. Measure OTF or MTF Sinusoidal Objects... Plus DC (No E<0) Complete but Tedious Bar Charts Radial Bar Charts AF Resolution Chart Measure PSF Point Object(s) Scan image or use CCD Slits (Line Objects) Knife Edge Scan or CCD Differentiate Comparison Diffraction Limit (XDL) Characterizing Optical Systems Chuck DiMarzio, Northeastern University

  12. Some Resolution Charts (1) Edge Point and Lines Sinusoidal Chart Bar Charts Chuck DiMarzio, Northeastern University

  13. Some Resolution Charts (2) Air Force ISO Bar Charts Chuck DiMarzio, Northeastern University

  14. 1 0.9 20 0.8 40 0.7 60 0.6 80 20 0.5 100 40 0.4 20 120 60 0.3 40 140 80 0.2 60 160 0.1 100 80 180 0 120 20 40 60 80 100 120 140 160 180 100 140 120 160 140 180 20 40 60 80 100 120 140 160 180 160 180 20 40 60 80 100 120 140 160 180 Radial Target and Image Colorbar for all Object Image Point-Spread Function of System Chuck DiMarzio, Northeastern University

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