1. Chapter 3 Companion site for Light and Video Microscopy Author: Wayne

2. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 2 If light were composed of Newtonian corpuscles, corpuscles propagating from the bird to observer A should make it more difficult for observer B to see the flower, since the corpuscles from the flower will cause the corpuscles coming from the bird to scatter. FIGURE 3.1

3. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 3 According to Christiaan Huygens, light radiates from luminous sources as waves. The waves must have small wavelengths since we can resolve points A, B, and C in the candle. FIGURE 3.2

4. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 4 According to Huygens, in order for light to travel so fast, the aether must be composed of highly elastic diaphanous particles. The particles must be smaller than the minimum distance between two clearly visible points. The motion from sphere A is passed to sphere D without any perceptible change in the intervening spheres B and C. FIGURE 3.3

5. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 5 According to Huygens, the propagation of light is a continuous cycle of two transformations—one involving the fission of the primary wave into numerous secondary wavelets, and the other involving the fusion of the secondary wavelets into a new primary wave. FIGURE 3.4

6. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 6 The wave theory can explain the law of reflection. According to Huygens, a wave front incident on a mirror produces secondary wavelets. By the time the last part of the incident wave strikes the mirror at B and begins producing secondary wavelets, the wavelets initiated by the portion of the wave that first struck the mirror already at A have produced many secondary wavelets. The secondary wavelets (R) formed from each consecutive region of the mirror reinforce each other (r), leading to a wave front that propagates away from the mirror so that the angle of reflection equals the angle of incidence. The incident wavelets are represented with i’s and the reflected wavelets are represented with r’s. FIGURE 3.5

7. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 7 The wave theory can explain the law of refraction. Huygens believed that the waves traveled slower in media with higher refractive indices. This resulted in the wavelets forming closer together in the medium with a higher refractive index and the consequent bending of the wave toward the normal. The secondary wavelets (T) formed from each consecutive region in the transmitting medium reinforce each other (t), leading to a wave front that propagates into the transmitting medium at an angle consistent with the Snell-Descartes Law. FIGURE 3.6

8. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 8 Because light travels more slowly through glass than through air, a converging lens converts a plane wave to a spherical wave. To visualize how a converging lens transforms spherical waves into plane waves, imagine the source being placed at f, and then reverse the direction of all the arrows to the left of f. FIGURE 3.7

9. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 9 The wavelength of a light wave increases as the light passes from water to air. This causes the waves to have a greater wavelength and curvature when in the air. Since we do not realize that the wavelength and curvature change, we imagine that the object that produced the image on our retina is along a straight line, perpendicular to the wave front that enters our eyes. This is the reason we see objects in water as being at P¢ instead of at P and why objects appear closer to us. FIGURE 3.8

10. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 10 Grimaldi saw that the shadow formed by a small opaque body was larger than it should be if light traveled only in straight lines. He noticed that the additional shadow was composed of colored fringes. FIGURE 3.9

11. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 11 Isaac Newton noticed that the shadow of a hair (x) was larger than would be expected if light traveled in straight lines. He concluded that the broadened shadow occurred because the hair exerted a repulsive force on the corpuscles that fell off with distance. Newton did not see any light fringes inside the geometrical shadow. FIGURE 3.10

12. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 12 Thomas Young illuminated a slip of card with parallel light and observed light fringes in the geometrical shadow of the card. FIGURE 3.11

13. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 13 (A) According to Huygens’ Principle, the two edges of the card used by Young act as sources of secondary wavelets. The bright spots appear where the wavelets reinforce each other. (B) Two slits in a card also act a sources of secondary wavelets forming alternating light and dark fringes. FIGURE 3.12

14. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 14 An infinitesimally thin section of the light waves radiating from the edge of the card observed from the side will appear as a sine wave with λ an amplitude (Ao) and a wavelength. The sine wave appears from the edge of the card as if an oscillator “cranked out” the sign wave. FIGURE 3.13

15. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 15 (A) At a single instant of time, we see a wave as a spatial variation in amplitude. (B) Whether we visualize the wavelength of a wave or the frequency of a wave depends on the mode of observation. At a single point in space, we see a wave as a time variation in amplitude. FIGURE 3.14

16. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 16 (A) Constructive interference occurs between two waves that are in phase. The amplitude of the resultant is equal to the sum of the individual amplitudes. Destructive interference occurs between two waves that are λ/2 out-of-phase. (B) The amplitude of the resultant vanishes. Since the intensity of light is related to the square of the amplitude of the resultant, constructive interference produces a bright fringe and destructive interference produces a dark fringe. FIGURE 3.15

17. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 17 The slip of card can be modeled as two sources of Huygens’ wavelets. Bright fringes are formed where the waves from the two sources constructively interfere and dark fringes are formed where the waves from the two sources destructively interfere. FIGURE 3.16

18. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 18 The rays NX and PX are perpendicular to the wave fronts emanating from N and P, respectively. If x is the first-order maximum, then PC is equal to 1λ. FIGURE 3.17

19. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 19 Fraunhöfer diffraction patterns of a vertical slit, a square, and a circle. FIGURE 3.18

20. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 20 The point spread function of an Airy disc. The maxima occur at non-integral numbers. FIGURE 3.19

21. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 21 The angle described by the first order maximum depends on the diameter of an organelle. FIGURE 3.20

22. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 22 Fresnel or near-field diffraction pattern of a square. FIGURE 3.21

23. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 23 A light wave at a given instant of time according to Maxwell. The electric (E) and magnetic (B) fields are transverse, in-phase with each other, and orthogonal to each other. FIGURE 3.22

24. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 24 According to Heinrich Hertz, incoming electric waves will cause an electron to oscillate. The energy of the oscillating electron can be dissipated by the atoms or molecules that house the electron or the oscillating electron can act as a secondary source of electromagnetic waves by reradiating the energy. Electromagnetic waves can also be radiated when the electrons oscillate as a result of other energy inputs (e.g., heat, friction, etc.). FIGURE 3.23

25. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 25 The electromagnetic spectrum. FIGURE 3.24

26. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 26 A square wave. FIGURE 3.25

27. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 27 A sine wave that approximates the fundamental spatial angular wave number of the square wave. FIGURE 3.26

28. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 28 The sum of two sine waves with different spatial angular wave numbers better approximates the square wave. FIGURE 3.27

29. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 29 The sum of three sine waves with different spatial angular wave numbers approximates the square wave even better. FIGURE 3.28

30. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 30 The sum of four sine waves with different spatial angular wave numbers approximates the square wave with high fidelity. FIGURE 3.29

31. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 31 No matter how complicated an object is, it can be resolved into its Fourier components. FIGURE 3.30

32. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 32 The object (G) diffracts the illuminating light. The objective lens collects the diffracted light and produces a diffraction pattern at its back focal plane. The spherical waves that emanate from the spots (s) at the back focal plane of the objective interfere with each other to produce an image at the image plane (P). This diagram emphasizes the rays normal to the wave fronts. FIGURE 3.31

33. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 33 The object diffracts the illuminating light. The objective lens collects the diffracted light and produces a diffraction pattern at its back focal plane. The spherical waves that emanate from the spots (s) at the back focal plane of the objective interfere with each other to produce an image at the image plane. This diagram emphasizes the wave fronts. FIGURE 3.32

34. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 34 The object diffracts the illuminating light. The objective lens collects the diffracted light and produces a diffraction pattern at its back focal plane. The spherical waves that emanate from the spots at the back focal plane of the objective interfere with each other to produce an image at the image plane. This diagram emphasizes the characteristic rays. FIGURE 3.33

35. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 35 Ernst Abbe’s experiment viewing the image and diffraction pattern of a grating. FIGURE 3.34

36. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 36 Abbe used a mask to block out the first-order diffraction spots produced by the coarse grating and obtained an image of the fine grating. FIGURE 3.35

37. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 37 Albert Porter’s extension of Abbe’s experiment. Porter viewed the image and diffraction pattern of a grid. FIGURE 3.36

38. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 38 Porter produced an image of a vertical grating by masking certain diffraction spots produced by the grid. FIGURE 3.37

39. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 39 Porter produced an image of a horizontal grating by masking certain diffraction spots produced by the grid. FIGURE 3.38

40. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 40 The ability of the human eye to create a faithful image of an object by collecting as many orders of diffracted light as possible depends on twice the angular aperture of the eye. The closer we move toward an object, the more diffraction orders we collect and the better we see the object. FIGURE 3.39

41. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 41 According to Ernst Abbe, a microscope cannot resolve objects smaller than a certain length (d), because the angle of the first-order diffracted light is too great for that light to be captured by the objective lens. FIGURE 3.40

42. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 42 The angular aperture (a) of a lens depends on the radius (r) of the lens and the distance (so) between the object and the lens. FIGURE 3.41

43. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 43 Because waves travel more slowly through oil than through air, the angle between the first-order diffracted wave and zerothorder diffracted wave is smaller in oil than in air. This allows oil-immersion objectives to resolve finer details than dry objectives. FIGURE 3.42

44. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 44 Illuminating a specimen with oblique illumination (b) effectively doubles the angular aperture of the objective lens compared with axial illumination (a). Illuminating a specimen with a solid cone of light (c), as is done when using Köhler illumination, produces a composite image composed of a mixture of high- and low-resolution images. FIGURE 3.43

45. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 45 Two Airy discs that are clearly resolved in the image plane (left) and two Airy discs that overlap in the image plane (right). FIGURE 3.44

46. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 46 According to Lord Rayleigh, two points that produce Airy discs can just be resolved in the image plane when the central maximum of one point lies over the first minimum of the other. Under this condition, there is sufficient contrast to resolve the two points because the sum of the point’s intensities midway between the peaks is about 80% of the intensity of each peak. When the points are too close, the Airy discs overlap so that the intensity midway between the two points is equal to or greater than the intensity of the individual points. FIGURE 3.45

47. Companion site for Light and Video Microscopy. by Wayne Copyright © 2009 by Academic Press. All rights reserved. 47 Reducing the opening of the aperture diaphragm from 60° (a) to 30° (b) increases the scattering contrast of the image. FIGURE 3.46