Understanding Optical Quality and Accommodation in the Eye: Sensitivity and Resolution Trade-Offs

1. Outline • Focus • Photo-transduction • Sensitivity / resolution trade-off • Measuring the optical quality of the eye • Linear systems analysis

3. Focus - the lens equation

4. Accommodation - bringing objects into focus Focused on Focused on

5. Some numbers • Refractive power of cornea • 43 diopters • Refractive power of lens • 17 - 25 diopters • Other eyes • Diving ducks - 80 diopter accommodation range • Anableps - two pairs of eyes with different focusing power

6. Accommodation errors(focus problems) • Myopia • Near-sightedness • Emmetropia • Far-sightedness

8. Accomodation errors(focus problems) • Myopia • Near-sightedness • Emmetropia • Far-sightedness • Presbyopia • Hardening of lense with age (cannot accommodate to near objects)

9. Depth of Field (DOF) • DOF = range of depths at which objects are “reasonably” in focus • E.g., at which blur is less than some threshold limit. • How can one increase one’s depth of field?

10. Transduction in the retina

13. Isomerized (bleached) photopigment retinal opsin

15. Sensitivity / resolution trade-off • Increase sensitivity => decrease resolution • Increase resolution => decrease sensitivity

16. Sensitivity / resolution trade-off • Increase sensitivity => decrease resolution • Increase resolution => decrease sensitivity • One example - changing pupil size Increased spatial resolution Shrink pupil Decreased sensitivity

17. Other examples

18. Other examples • Wavelength • Time • Wavelength

19. Duplicity Theory: Two receptor systems • Cones • Encode wavelength information • High resolution image coding in fovea • Low sensitivity • Rods • High sensitivity • Concentrated in periphery • Lower resolution coding in periphery

22. Part 2 of solution to sensitivity / resolution trade-off • Foveal coding • One-to-one connections from cone receptors to bipolar cells and from bipolar cells to ganglion cells • Peripheral coding (neural pooling) • Many-to-one connections from receptors to bipolar cells Periphery Fovea Receptors Bipolar cells

23. General solution to sensitivity / resolution trade-off • Place high resolution / low sensitivity system in fovea • Place high sensitivity / low resolution system in periphery • Use eye movements to obtain high resolution images of peripheral objects

25. Measuring the resolution of the eye • The point spread function • Spatial frequency analysis - the modulation transfer function

26. Measuring the resolution of the eye • The point spread function • Spatial frequency analysis - the modulation transfer function

27. Visual angle

32. Point spread

33. Point spread function