Basic light microscopy
Department of Mechatronics
GIST
Yong-Gu Lee
References:
1. “Fundamentals of light microscopy and electronic imaging,”
Chapters 1-6, Douglas B. Murphy, Wiley-Liss, 2001
2. “Fundamental of photonics,” Chapter 4 Fourier optics, Bahaa E. A.
Saleh and Malvin Carl Teich, John Wiley & Sons, 1991
3. http://www.microscopyu.com/
4. http://www.bio.unc.edu/courses/2005Spring/Biol188/
5. http://support.svi.nl/wiki/ImageFormation
6. Handbook of optics second edition, McGraw Hill, Vol II, Chapter 17
Contents
•
•
•
•
History
Köhler illumination
Selection of objective lens
Spatial resolution
Janssen microscope was one of the first
Objective lens and
a focusable eyepiece telescope
Hooke microscope had a
resolution of about 5 mm
“Cells” discovered
perceived and interpreted
by the brain as a magnified
virtual image about 25 cm
in front of the eye
Köhler illumination
• The light microscope contains two distinct
sets of interlaced focal planes
– eight planes in all – between the illuminator
and the eyes
• Köhler illumination:
Illumination that gives bright, uniform
illumination of the specimen and
simultaneously positions the sets of image
and diffraction planes at their proper
locations.
Two sets of
conjugate focal planes
• Four object or field planes:
– Viewed by eyepieces (normal, orthoscopic mode)
• Four aperture or diffraction planes
– Viewed by eyepiece telescope or Bertrand lens,
which is focused on the back aperture of the
objective lens (aperture, diffraction, conoscopic
mode)
• The planes are called conjugate, because all
of the planes of a given set are seen
simultaneously when looking in the
microscope
The locations of conjugate focal planes
in a light microscope adjusted for
Koehler illumination
Köhler illumination
• Bright and even illumination in the specimen plane and in the
conjugate image plane
– Even when illumination is provided by an irregular light source such
as a lamp filament, illumination of the object is remarkably uniform
across an extended area. Under these conditions of illumination, a
given point in the specimen is illuminated by every point in the light
source, and, conversely, a given point in the light source
illuminates every point in the specimen.
• Positioning of two different sets of conjugate focal planes at
specific locations along the optic axis of the microscope
– This is a strict requirement for maximal spatial resolution and
optimal image formation for a variety of optical modes. As we will
see, focusing the stage and condenser positions the focal planes
correctly, while adjusting the field and condenser diaphragms
controls resolution and contrast. Once properly adjusted, it is
easier to locate and correct faults such as dirt and bubbles that can
degrade optical performance.
Aligning for Köhler illumination
You will need an
eyepiece telescope
or Bertrand lens to
examine the lamp
filament
II: Z(objective) X-Y(condenser)
III: Z(condenser)
IV: Open(field diaphragm)
V: Open/Close (condenser aperture) to
set specimen contrast and resolution
Ref. http://www.microscopyu.com/tutorials/java/kohler/index.html
I : θ –Z-X-Y
Optical Aberrations
• Lens errors in modern optical microscopy are an unfortunate
problem caused by artifacts arising from the interaction of
light with glass lenses. There are two primary causes of nonideal lens action: Geometrical or Spherical aberrations are
related to the spherical nature of the lens and approximations
used to obtain the Gaussian lens equation; and Chromatic
aberrations, which arise from variations in the refractive
indices of the wide range of frequencies found in visible light.
Ref: http://micro.magnet.fsu.edu/primer/anatomy/aberrations.html
• Coma
• In optics (especially
telescopes), the coma
(aka comatic aberration)
in an optical system refers
to aberration inherent to
certain optical designs or
due to imperfection in the
lens or other components
which results in off-axis
point sources such as
stars appearing distorted.
http://en.wikipedia.org/wiki/Coma_(optics)
Curvature of field
• Field curvature indicates that the image plane is not flat, but has
the shape of a concave spherical surface as seen from the
objective. Different zones of the image can be brought into
focus, but the whole image cannot be focused simultaneously
on a flat surface as would be required for photography. Field
curvature is corrected by the design of the objective and
additionally by the tube or relay lens and sometimes the oculars.
Objective correction for optical
aberration
Objective
Type
Spherical
Aberration
Chromatic
Aberration
Field
Curvature
Achromat
1 Color
2 Colors
No
Plan Achromat
1 Color
2 Colors
Yes
Fluorite
2-3 Colors
2-3 Colors
No
Plan Fluorite
3-4 Colors
2-4 Colors
Yes
Plan
Apochromat
3-4 Colors
4-5 Colors
Yes
Ref: http://micro.magnet.fsu.edu/primer/anatomy/objectives.html
Objective specifications
Dry objectives must correct for
refractions at air/coverslip interface; Oil
immersion Increases NA
Multi-Immersion and variable
coverslip thickness objectives
Airy Disk
1.22
D/d
D
d
A simple way to see an “Airy Disk” is to direct a laser beam through a pinhole in a
piece of brass--An Airy Disk is the diffraction pattern of a circular hole
Wave optical resolution limits for
point sources
• Lateral resolution (Rayleigh Limit):
1.22 0.61 0.61


D
D/d
NA
/d
2
• Effect of increasing D/d or decreasing
wavelength on resolution of tiny point
sources of light
Low NA or Long Wavelength ----->High NA or Short Wavelength
Abbe’s theory for image
formation in the microscope
• Abbe’s Rule: Resolution of a spatial frequency
requires interference between the zero and at
least one of the first diffraction orders

sin   i
ith order

nd
,
i  1, 2,3
d
i

n
d
d

n sin 

NA
Ref: http://micro.magnet.fsu.edu/primer/java/imageformation/gratingdiffraction/index.html
Summary: wavelength and NA limit
resolution in the light microscope
• For a fluorescent or self-luminous specimen or for
nonluminous points that are examined by brightfield microscopy in transmitted light where
the NAcond >= NAobj:
-Lateral resolution:
p = 0.61/ NAobj
• For a trans-illuminated specimen where
the NAcond < NAobj :
-Lateral resolution:
p = / (NAobj + NACond)
Depth of Field and Depth of
Focus
• When considering resolution in optical
microscopy, a majority of the emphasis is
placed on point-to-point lateral
resolution in the plane perpendicular to
the optical axis. Another important aspect
to resolution is the axial (or longitudinal)
resolving power of an objective, which is
measured parallel to the optical axis and
is most often referred to as depth of field.
• Depth of field is determined by the
distance from the nearest object plane in
focus to that of the farthest plane also
simultaneously in focus. In microscopy
depth of field is very short and usually
measured in units of microns. The term
depth of focus, which refers to image
space, is often used interchangeably with
depth of field, which refers to object
space.
Ref. http://www.microscopyu.com/articles/formulas/formulasfielddepth.html
Airy pattern
 2J v 
I  v   I0  1

 v 
NA
v  2
ri
M
ri  Mro
2
M is the magnification of the objective lens
ri is the radial distance measured in the intermediate image plane
ro is the distance in object space
Airy pattern cont’d
•
•
The two-dimensional Airy pattern that is
formed in the image plane of a point
object is, in fact, a cross section of a
three-dimensional pattern that extends
along the optical axis of the microscope .
As one focuses an objective lens for
short distances above and below exact
focus, the brightness of the central spot
periodically oscillates between bright and
dark as its absolute intensity also
diminishes. Simultaneously, the diameters
of the outer rings expand, both events
taking place symmetrically above and
below the plane of focus in an
aberration-free system (Fig . 8) .
Figure 9 c shows an isophot of the
longitudinal section of this threedimensional diffraction image . In the
graph we recognize the first minimum of
the Airy pattern which we discussed. The
intensity distribution along u
perpendicular to the focal plane has its
first minima at
u  4 , v  0
where,
NA2
u  2 2 zi
M 
Airy pattern cont’d
• The first minimum is at a distance z   2M   / NA .
To transfer distance zi in image space to
distance zo in object space, we use the
relationship zi  zo M 2 / n . (Note that for small
axial distances, to a close approximation, the
axial magnification is the square of the lateral
magnification M divided by the refractive
index n of the object medium) The distance
from the center of the three-dimensional
diffraction pattern to the first axial minimum in
object space is then given by:
n
2
1
zmin  2
NA2
2
Axial magnification
• From
imaging
equation
1 1 1
z1

z2

Object
f
Image
1
1 1
 
n1 z1 z2 f
  1
1


0
z1  n1 z1 z2 
z2
1

0
n1 z12 z22 z1
sin 1  n2 sin 2
z2
z22
M2


z1
n1 z12
n1
n1
1'
• Magnification equation
z
y2   2 y1
z1
n1 sin   sin 1
'
1
1
n1 z1  z1 z1
From “Fundamental of photonics,” pp 15, Bahaa E. A.
Saleh and Malvin Carl Teich, John Wiley & Sons, 1991
z1
Airy pattern cont’d
• The axial resolution of the microscope is closely
related to the depth of focus, which is the axial depth
on both sides of the image plane within which the
image remains acceptably sharp. The depth of focus
D is usually defined as ¼ of the axial distance
between the first minima above and below focus of
the diffraction image of a small pinhole. In the
intermediate image plane , this distance is equal to
z1 / 2. The depth of focus defined by z1 is the
diffraction-limited, or physical, depth of focus .
D
n
NA
2
Geometric depth of focus
• It is an inherent property of waves that the image of a point
cannot itself be a point, but must be a small circle, the Airy disc.
Thus a point cannot be distinguished from a small circle which
is called the circle of confusion. Any two points which fall within
the radius (not the diameter) of the circle of confusion cannot
be resolved as separate points.
M
Di 
e
NA
e : detector resolution
M
n
n
Do 
e 2 
e
NA
M
MNA
e : detector resolution
NA  n sin   sin  

Di
Me
Di tan  
Di 
Me
2
Me
Me
Me


2 tan   2 tan   NA
Depth of focus
n
n
D

e
2
NA MNA
• These values for the depth of focus, and the distribution of
intensities in the three-dimensional diffraction pattern, are
calculated for incoherently illuminated (or emitting) point
sources (i.e., NAcond  NAobj ) . In general , the depth of focus
increases, up to a factor of two, as the coherence of
NAcond  0
illumination increases (i.e., as
).
• However, the three-dimensional point spread function with
partially coherent illumination can depart in complex ways from
that so far discussed when the aperture function is not uniform.
In a number of phase-based, contrast-generating modes of
microscopy , the depth of field may turn out to be unexpectedly
shallower than that predicted from above equation and may
yield extremely thin optical sections.