theory & appl. light microscopy phase contrast optics

Theory & Appl. Light Microscopy

Phase Contrast Optics


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


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


Phase Objects

• Do not absorb light

• Difference in index of refraction between specimen and background


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


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?


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


P

S

Zernike Phase Vector DiagramFor 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


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


Brightfield Optics

• Shifts all vectors in phase equally, and may change all amplitudes equally:

U + D = PU = P

• No amplitude image• Information in P is present in

, not in amplitude — eye cannot see this


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)

U'

D

P

U

D

P'

U'

D'D'

In specimen In microscope At image plane

U = P U' P'

Amplitude!


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


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


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


Positive/Negative Phase

• Positive Phase Specimen dark against light background (usual now)

• Negative Phase Specimen bright against dark background (looks like darkfield optics)

P

U

D

U = P

P'

U'

D'

U' > P'

Positive Phase

Retard D relative to U (move D vector clockwise)

P

U

D

U = P

P'

U'

D'

U' < P'

Negative Phase

Advance D relative to U (move D vector counterclockwise)


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

P

U

D

U = P

P'

U'

D'

U' < P'

Anoptral Phase

Produces delicate image against brown background

No phase shifts on ring


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)

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


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


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.?


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


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


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


Interference Microscopy

• Like phaseco in that imaging produces amplitude differences from phase differences in specimen

• Quantitative Techniques

• Qualitative Techniques


Optical Path Difference

• Specimen vs. medium' = (s - m)t

' = optical path length

t = physical thickness

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


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)


• 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


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)

Vector Diagrams

U'

U

R

R = reference beam = U = P = A0

U' = 2 A0 1.4 A0

P'

P

R

Interference between P and R produces P' 1.8 A0


• 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


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


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)


• 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


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


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


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


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


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


Robert Day Allen (1927–1986)

• Pioneered practical applications of Nomarski’s system


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


• 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


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


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

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

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

theory & appl. light microscopy phase contrast optics

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