1. Theory & Appl. Light Microscopy Phase Contrast Optics

2. Theory & Appl. Light Microscopy Abbé Theory Designed optics for amplitude objects Absorb light without change in phase of light waves Based on assumption of no difference in index of refraction between specimen and background

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7. Criterion for Resolution Lens must capture undiffracted light plus at least first order of diffracted rays Combine these in image plane by interference But — most biological specimens (esp. living) are not amplitude objects Phase Objects

8. Theory & Appl. Light Microscopy Phase Objects Do not absorb light Difference in index of refraction between specimen and background

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10. Example: Cell Object 1.25  m thick, i.r. = 1.35; i.r. water = 1.30 (0.05 difference) Difference in path length for light = 1.25 (0.05) = 0.0625  m 62.5/500 nm = 1/8 wavelength /8 =  /4 radians = 45° This is difference in phase of wave passing through cell against wave passing next to cell

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12. Phase Differences Our eyes cannot see this Eyes set for amplitude differences, so cell is essentially transparent But — information is present in light beams from specimen and in image How do we see this?

13. Theory & Appl. Light Microscopy Frits Zernike (1888–1966) Dutch physicist Developed vector notation for theory of light propagation through phase objects Invented phase contrast optics in 1930; not manufactured until 1941 by Zeiss

14. Theory & Appl. Light Microscopy P S  Zernike Phase Vector Diagram For propagation of light through phase object Length of P = amplitude specimen/amplitude medium =  transmission ratio S = incindent wave P = particle wave  P = phase shift of ray through specimen (S = U, undiffracted (0- order) ray

15. Theory & Appl. Light Microscopy P  U D D =  of all diffracted orders of light from specimen U = undiffracted light P = resulting specimen light, produced by interference between U and D in image formation Calculate P by vector addition U + D = P By the law of sines

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17. Brightfield Optics Shifts all vectors in phase equally, and may change all amplitudes equally: U + D = P U = P No amplitude image Information in P is present in , not in amplitude — eye cannot see this

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19. Phase Contrast Imaging Basic principle: –Shift phases (  s) and/or amplitudes of U and D differentially –This can produce a change in amplitude of P (length of vector)

20. U'U' D P  U D P'P' U'U' D'D'D'D' In specimen In microscopeAt image plane U = P U'  P' Amplitude!

21. Theory & Appl. Light Microscopy Phase Contrast Optics Physically separates U and D light and subjects one or the other to phase shift and/or amplitude shift In theory, any shift of U and D are possible In practice, a shift of  90° ( /4) is appropriate for most biological specimens

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23. Optical Arrangements Several possible, but major design challenge to keep U and D rays separate and handled differently In practice, use a hollow cone of light to illuminate specimen –Phase Annulus below condenser –Phase plate at back focal plane of objective Only 0 order rays from annulus pass through plate

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27. Phase Plate Rings in phase plate can include –Attenuating layer (absorption but no phase shift), or –Phase-shifting layer (no absorption, phase shift only), or –Any combination of the two

28. Theory & Appl. Light Microscopy Positive/Negative Phase Positive Phase Specimen dark against light background (usual now) Negative Phase Specimen bright against dark background (looks like darkfield optics)

29. P  U D U = P P'P' U'U' D'D' U' > P' Positive Phase Retard D relative to U (move D vector clockwise)

30. P  U D U = P P'P' U'U' D'D' U' < P' Negative Phase Advance D relative to U (move D vector counterclockwise)

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35. Example Systems Anoptral Phase Contrast Change amplitude of U (soot on ring), no phase shifts for either U or D rays. Bright image — negative phase Popular among algae workers in Great Britain in 50s–60s

36. P  U D U = P P'P' U'U' D'D' U' < P' Anoptral Phase Produces delicate image against brown background No phase shifts on ring

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38. Example Systems Zernike Phase Contrast Differential changes in amplitude and phase of U and D rays. All combinations possible: –Amplitude absorption with no phase shift (metal coating) –Phase shift wavefront with no absorption (silica coating)

39. From: Rose & Pomerat (1960) J. Biophys. Biochem. Cytol. 8:423.

40. Theory & Appl. Light Microscopy Use/Limitation of Phaseco Use for qualitative, not quantitative evaluation of specimens Reasons: –Intensity differences in image not uniquely related to index of refraction differences of specimen –Phase halo — optical artifact Cannot completely separate U and D rays in optics

41. Theory & Appl. Light Microscopy Intensity Differences Two points may have same image intensity, but have different  values (different i.r.s) I.e., if IP/IU of  at 240° identical to ratio at 320°, then how distinguish different i.r.?

42. Theory & Appl. Light Microscopy Phase Halo Serious artifact, most prominent at boundaries of sharp differences in i.r. Exceeds ability of optics to produce an accurate image So identification of exact boundary of specimen from image is very difficult

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45. Reducing Phase Halo Modification of design of phase plate Apodized Phase Contrast Addition of neutral density filters to phase plate to suppress halo Optical Process

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48. Reducing Phase Halo Modification of specimen and medium Worst halo comes from abrupt i.r. difference between specimen (cell) and medium it is in Match i.r. of medium to i.r. of specimen to reduce halo Barer & Joseph (1957) Symp. Soc. Exp. Biol. 10:160–184. Use of non-osmotic solutes to increase medium index of refraction

49. Theory & Appl. Light Microscopy Interference Microscopy Like phaseco in that imaging produces amplitude differences from phase differences in specimen Quantitative Techniques Qualitative Techniques

50. Theory & Appl. Light Microscopy Optical Path Difference Specimen vs. medium  ' = (  s -  m )t  ' = optical path length t = physical thickness Can measure  ', then calculate  s = (  '/t) +  m

51. Theory & Appl. Light Microscopy Dry Mass Calculations Derived from  ' Need to determine , the refractive increment (difficult) (For most biological specimens,  = 1.8 x 10 -3 i.r./gm solute/100 ml)

52. Theory & Appl. Light Microscopy C (dry weight concentration) = (  specimen -  water )/  = (  s – 1.33)/1.8 x 10 -3 = gm/100 ml = gm solids x 100/(area x thickness)  ' =  C t Mass of solids per cell = (  ' x area)/100  = (  ' x area)/0.18

53. Theory & Appl. Light Microscopy Double Beam Interference Phaseco — image formed from interference between 0 order and diffracted orders from specimen Double Beam Interference — image arises from interference between light from specimen and from a reference beam that does not pass through specimen (No phase halos from incomplete separation of U and D rays)

54. Vector Diagrams U'U' U R R = reference beam = U = P = A 0 U' =  2 A 0  1.4 A 0 P' P R Interference between P and R produces P'  1.8 A 0

55. Theory & Appl. Light Microscopy Image –Specimen bright against background –Ratio of intensities (1.8/1.4) 2  1.6 Can vary amplitude and phase of R vector to produce negative contrast as well

56. Theory & Appl. Light Microscopy Coherent Optics For this to work, the specimen and reference beams must be coherent to one another (Not needed for phaseco: U and D emerge from same point in specimen and are automatically coherent) Light from source must be split into 2 beams and reunite these in image

57. Theory & Appl. Light Microscopy Mach-Zender Double Microscope Classical form Difficult to construct Difficult to set up optics Difficult to interpret images Beam splitter system must have twin matched objectives and condensers (and add appropriate compensators)

58. Theory & Appl. Light Microscopy Image contains interference fringes in a gradient across field: /2, 3 /2, 5 /2, 7 /2, etc. Displacement of fringe is related to difference in optical path through the specimen:  ' Measure physical thickness of specimen and calculate C and dry weight

59. Theory & Appl. Light Microscopy Not Commonly Used Mach-Zender expensive and specialized More commonly used systems: split beam interference optics Single condenser and objective used Reference and Specimen beams present in same system Double Beam Interference Optics

60. Theory & Appl. Light Microscopy Jamin-Lebedeff Microscope Special attachments applied to condenser and objective, as well as polarizer and analyzer system About 2/3 of field has useable image (rest has ghost image) Rotation of analyzer allows quantification of image information Angle information produces  ' Then measure vertical thickness of specimen to calculate dry weight

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62. Problems with Designs Image deteriorates with higher magnification objectives (40x max) Optical path differences in different scopes Contrast is lost with open aperture Condenser and Objective must be specially modified and are not useable for other optics

63. Theory & Appl. Light Microscopy Common Biological Use Nomarski Differential Interference Contrast (DIC) Qualitative, not quantitative use Nomarski 1952 patent (Allen, et al. (1969) Zeit. fur Wiss. Mikros. 69:193) DIC sensitive to d  /ds, so shows refractive gradients or interfaces

64. Theory & Appl. Light Microscopy Georges (Jerzy) Nomarski (1919–1997) Polish-born, lived in France after World War II Physicist, many inventions Developed modification of interference microscopes now known as differential interference contrast (DIC) optics

65. Theory & Appl. Light Microscopy Robert Day Allen (1927–1986) Pioneered practical applications of Nomarski’s system

66. Theory & Appl. Light Microscopy DIC Complicated optical arrangement involving polarizer, analyzer, double wollaston prisms. Polarizer produces light; lower wollaston prism separates that into 2 component beams polarized at right angles to one another

67. Theory & Appl. Light Microscopy Lower wollaston also modified to separate two beams in space Each beam is R for the other Displacement of beams is set for each objective’s resolution: –100x, NA 1.25 — 0.2  m –40x, NA 0.65 — 0.55  m –16x, NA 0.32 — 1.32  m Upper wollaston recombines 2 beams into same path, but is adjustable Usually displace from precise recombination

68. Theory & Appl. Light Microscopy Nomarski Image Result is extinction (shadow) on one side of specimen and reinforcement (bright) on the other Shear of image False relief 3D image Consider wavefront diagrams

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72. Shear in Image Degree of shear is set by wollaston combination Bias of shear adjustable by shifting upper wollaston position to retard one beam more or less relative to other Cannot be used for quantitative measurements of dry mass But extremely useful for observing living cells

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76. Comparison of Nomarski and Phase Contrast Optics Phase Contrast Cheaper Easier to set up Uses less than full aperture of objective Phase Halo — surrounds specimen and other changes in i.r. Nomarski More expensive Fussy alignment Uses full aperture — closet to theoretical limit Shadow Effect — contrast greatest at shear direction maximum

77. Phase Contrast Insensitive to birefringence in specimen or slides Extremely large depth of field — sensitive to artifacts far out of plane of specimen Doesn’t work well with stained specimens Nomarski Optics disrupted by birefriengence Extremely shallow depth of field — useful for optical sectioning of specimen Works well with stained specimens; optics can be adjusted to enhance contrast

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