1. Design of photographic lens Shinsaku Hiura Osaka University

2. Design of photographic lens What is photographic lens? Artifacts of the lens Aberration Photometric issues Basic lens calculation Paraxial analysis Lens design Wide angle / telephoto Zoom lens

3. Intro. of optics design software

4. What is ideal lens? The image is similar to the object on a plane perpendicular to the optical axis No distortion No blur

5. Pinhole camera Common model of ideal lens in Computer Vision area Amount of the incoming light is very limited Diffraction limit

6. Artifacts of actual lens Failure of the similarity of the image Geometric degradation (aberration) Distortion Blur Photometric degradation (vignetting) Non-uniform sensitivity h  aberration

7. Definition of focal length Definition of focal length must be constant to Aperture settings aberration

8. Elements of the optics Optical system Typically 3-10 elements, 20 for zoom For aberration correction, + function Aperture For the trade-off of the both amount of light and defocus Nikkor

9. Example of a zoom lens Combination of various types of glasses, shape of the surfaces

10. Why we need many elements? For correcting monochromatic aberration Thin lens with high index glass Thick lens with low index glass For correcting chromatic aberration There are some differences for aberration even if the focal length is same White light F spectrum(blue) d spectrum(green) C spectrum(red) Longitudinal chromatic aberration of single lens

11. Parameters of optical glass Basically two parameters (index, dispersion) Dispersion Early optical glass Jena glass 1890- New glass After WW-II Extra-low dispersion Fluorite 1970- Optical glass chart Abbe number

12. Correction of chromatic aberration Balanced out by using two different dispersion Non-linear dispersion can not be corrected White light Red light Blue light Crown flint Low disp. High disp.

13. Definition of focal length Focal length is determined by the limit of very small ray height. Paraxial optics : small ray height and angle Focal length Intersection of incoming and exiting light h  0 Curve of intersection effective diameter Thin lens h Intersection of optical axis and exiting light

14. Aperture and F no. Aperture is not an actual diameter of diaphragm, but the diameter of incoming light F no = focal length / aperture diameter Smaller F no, higher speed lens Twice F no = quarter incoming light 1, 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, 32, 45, 64, … Aperture

15. Image circle Diameter of permissible quality of image is limited Limit of vignettingLimit caused by aberration lens Image plane

16. Focusing Light from a point is always focused at one point Focused at infinity Focused at close range

17. Focused plane For ideal lens, focused plane is always flat plane Image plane focused plane Image plane Focused surface misunderstanding

18. Thin lens law(1) Focal length = ｆ ba

19. Front and rear focal plane Focal length = ｆ ba Front focal plane and front principal point Rear focal plane and rear principal point

20. Thin lens equation and principal points Thin lens law still works for complex lens Rear p.p.Front p.p. ba

21. Magnification ratio Ratio of the size of object and image M=1 : life size ba Magnification ratio

22. Newton’s lens formula Definition from the focal plane f ba f x y ⇔

23. Practice (0) Prove Newton’s lens formula. to then

24. Practice(0) And expand it, we have Finally, Caution : some textbooks define x, y as signed values, So it is described as

25. Practice (1) Lens with focal length 50mm. If the lens is moved 5mm forward, how is the focused distance?

26. Practice (1) answer 1/50 = 1/b + 1/55 b = 550 (mm) For usual camera, object distance is defined from the film to the object. Object distance is 550 + 55 = 605mm If we can not ignore the distance between two principal points, we must add it.

27. Practice(2) If we want to focus the 10mm lens to the object with distance 1m, how is the lens movement forward? If the focal length is 20mm, how?

28. Practice (2) answer Focal length is much smaller than the object distance, so let us ignore it. 1/10 = 1/1000 + 1/a a = 10.101 Therefore, the lens motion is 0.101mm 1/20 = 1/1000 + 1/a a = 20.408 Therefore 0.408mm Lens motion is proportional to the square of focal length

29. Practice (3) If the photo is life size (M=1), how is the lens movement forward?

30. Practice (3) answer 1/f = 1/b + 1/a, a=b so a = b = 2f Lens movement is as same as the focal length The distance from the object to the film is 4 times as long as of focal length This is the minimum distance between film and the object

31. Tilt (swing) technique Scheimflüg law Normal setting : S at infinity Object Image Principal plane of the lens

32. Examples of tilting (1) Focused to the whole of the object

33. Examples of tilting (2) Pseudo shallow depth of field

34. View camera ARCA-SWISS M-line 4x5

35. Lenses for 35mm SLR Canon Nikon

36. Proof of Scheimflüg law In the figure above, all values are positive a b h x Thin lens lawMagnificationFlat image

37. Proof From the Eq. of planar image,,and we have ---(x) On the other hand, from the thin lens law, is used to substitute h of is used to substitute a of eq.(x), then. Solve this equation for b, finally we have. It is the linear equation of b and x.

38. Scheimflüg law In case α=0 (plane perpendicular to the optical axis),. Of course, this is the thin lens law. Solve this equation for b=0 (intersection of object and lens plane),. Therefore, two intersections get together. Solve for a=0 (intersection of image and lens plane),.

39. Perspective effect By the perspective effect, the projection is nonlinear