Phase Contrast
Optics
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
Theory & Appl. Light Microscopy
Theory & Appl. Light Microscopy
Theory & Appl. Light Microscopy
Theory & Appl. Light Microscopy
Theory & Appl. Light Microscopy
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
• Do not absorb light
• Difference in index of
refraction between specimen
and background
Theory & Appl. Light Microscopy
Theory & Appl. Light Microscopy
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
Theory & Appl. Light Microscopy
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)
• 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
Zernike Phase Vector Diagram
For propagation of light through phase object
S
S = incindent wave

P
P = particle wave
P = phase shift of ray
through specimen
(S = U, undiffracted (0order) ray
Length of P = amplitude specimen/amplitude medium =
transmission ratio
Theory & Appl. Light Microscopy
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
Theory & Appl. Light Microscopy
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
Theory & Appl. Light Microscopy
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
In microscope
In specimen
At image plane
D'
D'
D
D
P'
U

U'
U'
P
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
Theory & Appl. Light Microscopy
Theory & Appl. Light Microscopy
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
Theory & Appl. Light Microscopy
Theory & Appl. Light Microscopy
Theory & Appl. Light Microscopy
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 Phase Specimen
dark against light background
(usual now)
• Negative Phase Specimen
bright against dark
background (looks like
darkfield optics)
Theory & Appl. Light Microscopy
Positive Phase
D
D'
U'
U

P
U=P
P'
U' > P'
Retard D relative to U (move D vector clockwise)
Negative Phase
D'
D
P'
U
U'

P
U=P
U' < P'
Advance D relative to U (move D vector counterclockwise)
Theory & Appl. Light Microscopy
Theory & Appl. Light Microscopy
Theory & Appl. Light Microscopy
Theory & Appl. Light Microscopy
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
Anoptral Phase
D
No phase shifts on ring
U
D'

P
U'
P'
U=P
U' < P'
Produces delicate image against brown background
Theory & Appl. Light Microscopy
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
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
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.?
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
Theory & Appl. Light Microscopy
Theory & Appl. Light Microscopy
Theory & Appl. Light Microscopy
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
Theory & Appl. Light Microscopy
Theory & Appl. Light Microscopy
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
• Like phaseco in that imaging
produces amplitude differences
from phase differences in
specimen
• Quantitative Techniques
• Qualitative Techniques
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
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)
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
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)
Theory & Appl. Light Microscopy
Vector Diagrams
R = reference beam = U = P = A0
R
R
U
P
U'
U' = 2 A0  1.4 A0
P'
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
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
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)
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
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
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
Theory & Appl. Light Microscopy
Theory & Appl. Light Microscopy
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
• 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)
• 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)
• Pioneered practical
applications of Nomarski’s
system
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
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
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
Theory & Appl. Light Microscopy
Theory & Appl. Light Microscopy
Theory & Appl. Light Microscopy
Theory & Appl. Light Microscopy
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
Theory & Appl. Light Microscopy
Theory & Appl. Light Microscopy
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
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
Theory & Appl. Light Microscopy
Theory & Appl. Light Microscopy
Theory & Appl. Light Microscopy