Camera Simulation

1. Camera Simulation References Photography, B. London and J. Upton Optics in Photography, R. Kingslake The Camera, The Negative, The Print, A. Adams University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

2. Topics • Ray tracing lenses • Focus • Field of view • Depth of focus / depth of field • Exposure University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

3. Lenses

4. Snell’s Law Refraction University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

5. Paraxial Approximation Rays deviate only slightly from the axis University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

6. Incident Ray Angles: ccw is positive; cw is negative The sum of the interior angles is equal to the exterior angle. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

7. Refracted Ray University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

8. Derivation • Paraxial approximation University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

9. Derivation • Paraxial approximation • Snell’s Law University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

10. Ray Coordinates University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

11. Gauss’ Formula • Paraxial approximation to Snell’s Law • Ray coordinates • Thin lens equation Holds for any height, any ray! University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

12. Vergence Diverging Converging • Vergence • Thin lens equation • Surface Power equation University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

13. Lens-makers Formula Refractive Power Diverging Converging University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

14. Conjugate Points • To focus: move lens relative to backplane • Horizontal rays converge on focal point in the focal plane University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

15. Gauss’ Ray Tracing Construction Parallel Ray Focal Ray Chief Ray Image Object University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

16. Ray Tracing: Finite Aperture Focal Plane Aperture Plane Back Plane University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

17. Real Lens Cutaway section of a Vivitar Series 1 90mm f/2.5 lens Cover photo, Kingslake, Optics in Photography University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

18. Double Gauss Data from W. Smith, Modern Lens Design, p 312 University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

19. Ray Tracing Through Lenses 35 mm wide-angle 200 mm telephoto 16 mm fisheye 50 mm double-gauss From Kolb, Mitchell and Hanrahan (1995) University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

20. Thick Lenses Equivalent Lens Refraction occurs at the principal planes University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

21. Field of View

22. Field of View From London and Upton University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

23. Field of View From London and Upton University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

24. Field of View Redrawn from Kingslake, Optics in Photography • Field of view • Types of lenses • Normal 26º Film diagonal  focal length • Wide-angle 75-90º • Narrow-angle 10º University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

25. Perspective Transformation • Thin lens equation • Represent transformation as a 4x4 matrix University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

26. Depth of Field

27. Depth of Field From London and Upton University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

28. Circle of Confusion Focal Plane Back Plane Circle of confusion proportional to the size of the aperture University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

29. Depth of Focus [Image Space] • Depth of focus  Equal circles of confusion • Two planes: near and far University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

30. Depth of Focus [Image Space] • Depth of focus  Equal circles of confusion University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

31. Depth of Focus [Image Space] • Depth of focus  Equal circles of confusion University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

32. Depth of Field [Object Space] • Depth of field  Equal circles of confusion University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

33. Hyperfocal Distance When H is the hyperfocal distance University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

34. Depth of Field Scale University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

35. Factors Affecting DOF From http://www.kodak.com/global/en/consumer/pictureTaking/cameraCare/cameCar6.shtml University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

36. Resolving Power • Diffraction limit • 35mm film (Leica standard) • CCD/CMOS pixel aperture University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

37. Exposure

38. Image Irradiance University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

39. Image Irradiance Solid angle subtended by the lens, as seen by the patch dA Power from patch dA through the lens Irradiance at the sensor element University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

40. Image Irradiance University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

41. Image Irradiance On axis University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

42. Relative Aperture or F-Stop • F-Number and exposure: • Fstops: 1.4 2 2.8 4.0 5.6 8 11 16 22 32 45 64 • 1 stop doubles exposure University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

43. Camera Exposure • Exposure • Exposure overdetermined Aperture: f-stop - 1 stop doubles H Decreases depth of field Shutter: Doubling the open time doubles H Increases motion blur University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

44. Aperture vs Shutter f/4 1/125s f/2 1/500s f/16 1/8s From London and Upton University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

45. High Dynamic Range • Sixteen photographs of the Stanford Memorial Church taken at 1-stop increments from 30s to 1/1000s. • From Debevec and Malik, High dynamic range photographs. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

46. Simulated Photograph Adaptive histogram With glare, contrast, blur University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

47. Camera Simulation Sensor response Lens Shutter Scene radiance University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell