1. CS348B Lecture 7Pat Hanrahan, 2005 Camera Simulation EffectCause Field of viewFilm size, stops and pupils Depth of field Aperture, focal length Motion blurShutter ExposureFilm speed, aperture, shutter References Photography, B. London and J. Upton Optics in Photography, R. Kingslake The Camera, The Negative, The Print, A. Adams

2. CS348B Lecture 7Pat Hanrahan, 2005 Topics Ray tracing lenses Focus Field of view Depth of focus / depth of field Exposure

3. Lenses

4. CS348B Lecture 7Pat Hanrahan, 2005 Refraction Snell’s Law

5. CS348B Lecture 7Pat Hanrahan, 2005 Paraxial Approximation Rays deviate only slightly from the axis

6. CS348B Lecture 7Pat Hanrahan, 2005 Incident Ray Angles: ccw is positive; cw is negative The sum of the interior angles is equal to the exterior angle.

7. CS348B Lecture 7Pat Hanrahan, 2005 Refracted Ray

8. CS348B Lecture 7Pat Hanrahan, 2005 Derivation Paraxial approximation

9. CS348B Lecture 7Pat Hanrahan, 2005 Derivation Paraxial approximation Snell’s Law

10. CS348B Lecture 7Pat Hanrahan, 2005 Ray Coordinates

11. CS348B Lecture 7Pat Hanrahan, 2005 Gauss’ Formula Paraxial approximation to Snell’s Law Ray coordinates Thin lens equation Holds for any height, any ray!

12. CS348B Lecture 7Pat Hanrahan, 2005 Vergence Thin lens equation Surface Power equation DivergingConverging

13. CS348B Lecture 7Pat Hanrahan, 2005 Lens-makers Formula Converging Diverging Refractive Power

14. CS348B Lecture 7Pat Hanrahan, 2005 Conjugate Points To focus: move lens relative to backplane Horizontal rays converge on focal point in the focal plane

15. CS348B Lecture 7Pat Hanrahan, 2005 Gauss’ Ray Tracing Construction Parallel Ray Focal Ray Chief Ray Object Image

16. CS348B Lecture 7Pat Hanrahan, 2005 Ray Tracing: Finite Aperture Focal PlaneBack PlaneAperture Plane

17. CS348B Lecture 7Pat Hanrahan, 2005 Real Lens Cutaway section of a Vivitar Series 1 90mm f/2.5 lens Cover photo, Kingslake, Optics in Photography

18. CS348B Lecture 7Pat Hanrahan, 2005 Double Gauss Radius (mm) Thick (mm) ndnd V-noaperture 58.9507.5201.67047.150.4 169.6600.24050.4 38.5508.0501.67047.146.0 81.5406.5501.69930.146.0 25.50011.41036.0 9.00034.2 -28.9902.3601.60338.034.0 81.54012.1301.65857.340.0 -40.7700.38040.0 874.1306.4401.71748.040.0 -79.46072.22840.0 Data from W. Smith, Modern Lens Design, p 312

19. CS348B Lecture 7Pat Hanrahan, 2005 Ray Tracing Through Lenses From Kolb, Mitchell and Hanrahan (1995) 200 mm telephoto 50 mm double-gauss 35 mm wide-angle 16 mm fisheye

20. CS348B Lecture 7Pat Hanrahan, 2005 Thick Lenses Refraction occurs at the principal planes Equivalent Lens

21. Field of View

22. CS348B Lecture 7Pat Hanrahan, 2005 Field of View From London and Upton

23. CS348B Lecture 7Pat Hanrahan, 2005 Field of View From London and Upton

24. CS348B Lecture 7Pat Hanrahan, 2005 Field of View Field of view Types of lenses Normal26º Film diagonal  focal length Wide-angle75-90º Narrow-angle 10º Redrawn from Kingslake, Optics in Photography

25. CS348B Lecture 7Pat Hanrahan, 2005 Perspective Transformation Thin lens equation Represent transformation as a 4x4 matrix

26. Depth of Field

27. CS348B Lecture 7Pat Hanrahan, 2005 Depth of Field From London and Upton

28. CS348B Lecture 7Pat Hanrahan, 2005 Circle of Confusion Circle of confusion proportional to the size of the aperture Focal Plane Back Plane

29. CS348B Lecture 7Pat Hanrahan, 2005 Depth of Focus [Image Space] Depth of focus  Equal circles of confusion Two planes: near and far

30. CS348B Lecture 7Pat Hanrahan, 2005 Depth of Focus [Image Space] Depth of focus  Equal circles of confusion

31. CS348B Lecture 7Pat Hanrahan, 2005 Depth of Focus [Image Space] Depth of focus  Equal circles of confusion

32. CS348B Lecture 7Pat Hanrahan, 2005 Depth of Field [Object Space] Depth of field  Equal circles of confusion

33. CS348B Lecture 7Pat Hanrahan, 2005 Hyperfocal Distance When H is the hyperfocal distance

34. CS348B Lecture 7Pat Hanrahan, 2005 Depth of Field Scale

35. CS348B Lecture 7Pat Hanrahan, 2005 Factors Affecting DOF From http://www.kodak.com/global/en/consumer/pictureTaking/cameraCare/cameCar6.shtml

36. CS348B Lecture 7Pat Hanrahan, 2005 Resolving Power Diffraction limit 35mm film (Leica standard) CCD/CMOS pixel aperture

37. Exposure

38. CS348B Lecture 7Pat Hanrahan, 2005 Image Irradiance

39. CS348B Lecture 7Pat Hanrahan, 2005 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

40. CS348B Lecture 7Pat Hanrahan, 2005 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

41. CS348B Lecture 7Pat Hanrahan, 2005 Aperture vs Shutter From London and Upton f/16 1/8s f/4 1/125s f/2 1/500s

42. CS348B Lecture 7Pat Hanrahan, 2005 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.

43. CS348B Lecture 7Pat Hanrahan, 2005 Simulated Photograph Adaptive histogramWith glare, contrast, blur

44. CS348B Lecture 7Pat Hanrahan, 2005 Camera Simulation Sensor response Lens Shutter Scene radiance