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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 l.jpg

Phase Contrast Optics

Theory & Appl. Light Microscopy

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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

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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

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Phase Objects

  • Do not absorb light

  • Difference in index of refraction between specimen and background

Theory & Appl. Light Microscopy

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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

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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

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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

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Zernike Phase Vector Diagram

For propagation of light through phase object


S = incindent wave

P = particle wave

P = phase shift of ray through specimen

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


Length of P = amplitude specimen/amplitude medium =

transmission ratio

Theory & Appl. Light Microscopy

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Calculate P by vector addition


U + D = P

By the law of sines



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

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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

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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

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In microscope

At image plane

In specimen










U' P'


U = P

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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

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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

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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

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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

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Positive Phase







U = P

U'> P'

Retard D relative to U (move D vector clockwise)

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Negative Phase







U = P

U'< P'

Advance D relative to U (move D vector counterclockwise)

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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

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Anoptral Phase


No phase shifts on ring






U = P

U'< P'

Produces delicate image against brown background

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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

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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

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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

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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

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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

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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

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Interference Microscopy

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

  • Quantitative Techniques

  • Qualitative Techniques

Theory & Appl. Light Microscopy

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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

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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

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  • 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

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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

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Vector Diagrams

R = reference beam = U = P = A0







U' = 2 A0 1.4 A0

Interference between P and R produces P' 1.8 A0

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  • 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

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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

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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

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Theory & Appl. Light Microscopy

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Not Commonly Used field:

  • 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

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Jamin-Lebedeff Microscope field:

  • 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

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Problems with Designs field:

  • 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

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Common Biological Use field:

  • 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

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Georges (Jerzy) Nomarski (1919 field: –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

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Robert Day Allen (1927 field: –1986)

  • Pioneered practical applications of Nomarski’s system

Theory & Appl. Light Microscopy

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DIC field:

  • 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

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  • Lower wollaston also modified to separate two beams in space field:

  • 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

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Nomarski Image field:

  • 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

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Shear in Image field:

  • 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

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Phase Contrast field:


Easier to set up

Uses less than full aperture of objective

Phase Halo — surrounds specimen and other changes in i.r.


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

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Phase Contrast field:

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


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