A Review of Optics

1. A Review of Optics Austin Roorda, Ph.D. University of Houston College of Optometry

2. These slides were prepared by Austin Roorda, except where otherwise noted. Full permission is granted to anyone who would like to use any or all of these slides for educational purposes.

3. Geometrical Optics Relationships between pupil size, refractive error and blur

4. Optics of the eye: Depth of Focus 2 mm 4 mm 6 mm

5. Optics of the eye: Depth of Focus Focused behind retina In focus Focused in front of retina 2 mm 4 mm 6 mm

6. 7 mm pupil Bigger blur circle Courtesy of RA Applegate

7. 2 mm pupil Smaller blur circle Courtesy of RA Applegate

8. Demonstration Role of Pupil Size and Defocus on Retinal Blur Draw a cross like this one on a page, hold it so close that is it completely out of focus, then squint. You should see the horizontal line become clear. The line becomes clear because you have made you have used your eyelids to make your effective pupil size smaller, thereby reducing the blur due to defocus on the retina image. Only the horizontal line appears clear because you have only reduced the blur in the horizontal direction.

9. Physical Optics The Wavefront

10. What is the Wavefront? parallel beam = plane wavefront converging beam = spherical wavefront

11. What is the Wavefront? parallel beam = plane wavefront ideal wavefront defocused wavefront

12. What is the Wavefront? parallel beam = plane wavefront ideal wavefront aberrated beam = irregular wavefront

13. What is the Wavefront? diverging beam = spherical wavefront aberrated beam = irregular wavefront ideal wavefront

14. The Wave Aberration

15. What is the Wave Aberration? diverging beam = spherical wavefront wave aberration

16. Wavefront Aberration 3 2 1 mm (superior-inferior) 0 -1 -2 -3 -3 -2 -1 0 1 2 3 mm (right-left) Wave Aberration of a Surface

17. Diffraction

18. Diffraction “Any deviation of light rays from a rectilinear path which cannot be interpreted as reflection or refraction” Sommerfeld, ~ 1894

19. Fraunhofer Diffraction • Also called far-field diffraction • Occurs when the screen is held far from the aperture. • Occurs at the focal point of a lens!

20. Diffraction and Interference • diffraction causes light to bend perpendicular to the direction of the diffracting edge • interference due to the size of the aperture causes the diffracted light to have peaks and valleys

21. rectangular aperture square aperture

22. circular aperture Airy Disc

23. The Point Spread Function

24. The Point Spread Function, or PSF, is the image that an optical system forms of a point source. The point source is the most fundamental object, and forms the basis for any complex object. The PSF is analogous to the Impulse Response Function in electronics.

25. The Point Spread Function The PSF for a perfect optical system is the Airy disc, which is the Fraunhofer diffraction pattern for a circular pupil. Airy Disc

26. Airy Disk q

27. As the pupil size gets larger, the Airy disc gets smaller. 2.5 2 1.5 separatrion between Airy disk peak and 1st min (minutes of arc 500 nm light) 1 0.5 0 1 2 3 4 5 6 7 8 pupil diameter (mm)

28. Point Spread Function vs. Pupil Size 1 mm 2 mm 3 mm 4 mm 5 mm 6 mm 7 mm

29. Small Pupil

30. Larger pupil

31. Point Spread Function vs. Pupil SizePerfect Eye 1 mm 2 mm 3 mm 4 mm 5 mm 6 mm 7 mm

32. Point Spread Function vs. Pupil SizeTypical Eye 1 mm 2 mm 3 mm 4 mm pupil images followed by psfs for changing pupil size 5 mm 6 mm 7 mm

33. Demonstration Observe Your Own Point Spread Function

34. Resolution

35. Unresolved point sources Rayleigh resolution limit Resolved

36. uncorrected corrected AO image of binary star k-Peg on the 3.5-m telescope at the Starfire Optical Range About 1000 times better than the eye!

37. Keck telescope: (10 m reflector) About 4500 times better than the eye! Wainscott

38. Convolution

39. Convolution

40. Simulated Images 20/20 letters 20/40 letters

41. MTF Modulation Transfer Function

42. low medium high object: 100% contrast image 1 contrast 0 spatial frequency

43. The modulation transfer function (MTF) indicates the ability of an optical system to reproduce (transfer) various levels of detail (spatial frequencies) from the object to the image. • Its units are the ratio of image contrast over the object contrast as a function of spatial frequency. • It is the optical contribution to the contrast sensitivity function (CSF).

44. MTF: Cutoff Frequency cut-off frequency 1 mm 1 2 mm 4 mm Rule of thumb: cutoff frequency increases by ~30 c/d for each mm increase in pupil size 6 mm 8 mm modulation transfer 0.5 0 0 50 100 150 200 250 300 spatial frequency (c/deg)

45. Effect of Defocus on the MTF 450 nm 650 nm Charman and Jennings, 1976

46. PTF Phase Transfer Function

47. low medium high object image 180 phase shift 0 -180 spatial frequency

48. Relationships Between Wave Aberration, PSF and MTF

49. The PSF is the Fourier Transform (FT) of the pupil function The MTF is the real part of the FT of the PSF The PTF is the imaginary part of the FT of the PSF