1. Frequency analysis of optical imaging system Dinesh Ganotra

2. Imaging System

3. Lens Design Software Effective Focal Length Max. Field Angle Stop Surface Number Afocal EFL Back Focal Length Zoom Surface Working Distance Wavelength (Primary) No. of Zoom Positions Telephoto Ratio Refractive Index (Primary) Overall Physical Length Abbe Number Entrance Pupil Diameter No. of Glass Elements Max. Parax Image Height Overall Glass Length Lateral Magnification No. of Optical Surfaces Angular Magnification No. of Physical Surfaces Zoom Ratio No. of Cemented Groups Numerical Aperture Number of Examples

4. Imaging system   v u zozo zizi

7. Point Spread

8. Geometrical optics  Diffraction optics : image amplitude : amplitude at image coordinates in response to a point source object at Amplitude point spread function

9. Amplitude Point Spread Function : Pupil function : unity inside and zero outside the projection aperture. Superposition integral

10. MTF PSF

11. Reduced coordinates ; Ideal image

12. Amplitude PSF in reduced coordinates

15. Diffraction limited system regard the image as being a convolution of the image predicted by geometrical optics with an impulse response that is the Fraunhofer diffraction pattern of the exit pupil.

16. Spatial coherence where  is the time delay associated with propagation from to in general,  is a function of the coordinates involved.

17. Intensity

18. Drop time delays where known as mutual intensity.

19. Take time-varying phasor at the origin as reference For a perfectly coherent illumination Thus

20. Coherent object illumination is linear in complex amplitude

22. Frequency response Coherent illumination Incoherent illumination

23. Coherent illumination Define Amplitude transfer function Fourier transform of PSF

24. Coherent imaging … Taking Fourier transform on both the sides and using convolution theorem

25. Substituting h(u,v)‏ Take and ignore negative signs

26. Cut off frequency Example = 10 -4 cm w=1 cm z i = 10cm give cut off frequency of 100 cycles / mm

27. Incoherent illumination Convolution of intensity impulse response with ideal image intensity

28. Define

29. Take FT on both sides and use convolution theorem Optical transfer function

30. Relationship between OTF and amplitude transfer function Amplitude Transfer Function Point Spread Function Optical Transfer Function OTF is normalized autocorrelation function of amplitude transfer function

31. Why frequency analysis?