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Phase Contrast Optics. Abb é 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. Criterion for Resolution.

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phase contrast optics

Phase Contrast Optics

Theory & Appl. Light Microscopy

abb theory
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

Theory & Appl. Light Microscopy

criterion for resolution
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

Theory & Appl. Light Microscopy

phase objects
Phase Objects
  • Do not absorb light
  • Difference in index of refraction between specimen and background

Theory & Appl. Light Microscopy

example cell
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

Theory & Appl. Light Microscopy

phase differences
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?

Theory & Appl. Light Microscopy

frits zernike 1888 1966
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

Theory & Appl. Light Microscopy

slide14
Zernike Phase Vector Diagram

For propagation of light through phase object

S

S = incindent wave

P = particle wave

P = phase shift of ray through specimen

(S = U, undiffracted (0-order) ray

P

Length of P = amplitude specimen/amplitude medium =

transmission ratio

Theory & Appl. Light Microscopy

slide15
Calculate P by vector addition

D

U + D = P

By the law of sines

U

P

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

Theory & Appl. Light Microscopy

brightfield optics
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

Theory & Appl. Light Microscopy

phase contrast imaging
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)

Theory & Appl. Light Microscopy

slide20
In microscope

At image plane

In specimen

D'

D'

D

D

P'

U

U'

U'

P

U' P'

Amplitude!

U = P

phase contrast optics21
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

Theory & Appl. Light Microscopy

optical arrangements
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

Theory & Appl. Light Microscopy

phase plate
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

Theory & Appl. Light Microscopy

positive negative phase
Positive/Negative Phase
  • Positive Phase Specimen dark against light background (usual now)
  • Negative Phase Specimen bright against dark background (looks like darkfield optics)

Theory & Appl. Light Microscopy

slide29
Positive Phase

D

D'

U'

U

P

P'

U = P

U'> P'

Retard D relative to U (move D vector clockwise)

slide30
Negative Phase

D'

D

P'

U'

U

P

U = P

U'< P'

Advance D relative to U (move D vector counterclockwise)

example systems
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

Theory & Appl. Light Microscopy

slide36
Anoptral Phase

D

No phase shifts on ring

D'

U

U'

P

P'

U = P

U'< P'

Produces delicate image against brown background

example systems38
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)

Theory & Appl. Light Microscopy

use limitation of phaseco
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

Theory & Appl. Light Microscopy

intensity differences
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.?

Theory & Appl. Light Microscopy

phase halo
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

Theory & Appl. Light Microscopy

reducing phase halo
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

Theory & Appl. Light Microscopy

reducing phase halo48
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

Theory & Appl. Light Microscopy

interference microscopy
Interference Microscopy
  • Like phaseco in that imaging produces amplitude differences from phase differences in specimen
  • Quantitative Techniques
  • Qualitative Techniques

Theory & Appl. Light Microscopy

optical path difference
Optical Path Difference
  • Specimen vs. medium
  • ' = (s - m)t

' = optical path length

t = physical thickness

Can measure ', then calculate s = ('/t) + m

Theory & Appl. Light Microscopy

dry mass calculations
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)

Theory & Appl. Light Microscopy

slide52
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

Theory & Appl. Light Microscopy

double beam interference
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)

Theory & Appl. Light Microscopy

vector diagrams
Vector Diagrams

R = reference beam = U = P = A0

R

R

U

P

U'

P'

U' = 2 A0 1.4 A0

Interference between P and R produces P' 1.8 A0

slide55
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

Theory & Appl. Light Microscopy

coherent optics
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

Theory & Appl. Light Microscopy

mach zender double microscope
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)

Theory & Appl. Light Microscopy

slide58
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

Theory & Appl. Light Microscopy

not commonly used
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

Theory & Appl. Light Microscopy

jamin lebedeff microscope
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

Theory & Appl. Light Microscopy

problems with designs
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

Theory & Appl. Light Microscopy

common biological use
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

Theory & Appl. Light Microscopy

georges jerzy nomarski 1919 1997
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

Theory & Appl. Light Microscopy

robert day allen 1927 1986
Robert Day Allen (1927–1986)
  • Pioneered practical applications of Nomarski’s system

Theory & Appl. Light Microscopy

slide66
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

Theory & Appl. Light Microscopy

slide67
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

Theory & Appl. Light Microscopy

nomarski image
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

Theory & Appl. Light Microscopy

shear in image
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

Theory & Appl. Light Microscopy

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

Comparison of Nomarski and Phase Contrast Optics
slide77
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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