Optical Microscopy

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Optical Microscopy
Lecture 1
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Concepts we will discuss in this lecture

• Natures of light
• Mechanism of Optical Imaging system
• The Use of Lenses and the Problem of Lenses
• Spatial Resolution

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Some Properties of Light
Both lasers and white light sources used in
microscopy
Laser
White light
Chromatic
Polarization
Phase
Direction
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Monochromatic vs white light
450 nm
600 nm
White light contains all, or most, of the colors
of the visible spectrum.
Lasers are Monochromatic (very narrow frequency
distribution)
Both white light, lasers used in microscopy
techniques
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Polarization of Light Plane where electric field
vector lies, EEºcos(?t) Perpendicular to
direction of propagation
s horizontal p vertical
Vertical
for propagation Parallel to floor
Circular polarization H,V (s,p) 90 degrees out
of phase
horizontal
elliptical polarization less than 90 out of phase
This nature used extensively In microscopy pol
microscopy, DIC, SHG
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• Particle (Quantized) Behavior
• Light interacting with matter absorption,
  reflection
• photon smallest unit- energy corresponds to
  frequency (?)
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• h6x10-34 Js Planks constant
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• 10-19 J for visible light (?600 nm)
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• best for describing absorption, emission of light
• Best for describing how detectors work
  (photomultipliers, Diodes)

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Wave Behavior
Constructive, destructive interference
0, 180 degrees Limiting cases for complete
constructive, Destructive interference,
respectively
Underlies image formation in almost all forms of
microscopy phase, DIC, polarization, Some
advanced forms of confocal
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Representations of Light
Absorption, lasers
Interference, Image formation
Good for modeling Light propagation Ray
Tracing Not real form
Wave, particle duality physically important Some
phenomenon described by both
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Hooke made the first optical microscope
Robert Hooke
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The first image of Hooke and the birth of the
term Cell
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Converging (focusing) Lens

• The parallel rays converge at the second focal
  point F.
• The first focal point is at the front. All rays
  originated at
• This point become parallel to the axis after the
  lens.

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Diverging (defocusing) Lens
Focal length is negative
To an eye on the right-hand side, these
diverging rays will Appear to be coming from the
point F the second focal point.
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Snells Law
where q1 is the angle of incidence, q2 is the
angle of refraction
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Ray Tracing Rules for locating image
Only need 2 rays
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Single-lens Imaging system
Real image if rays intersect and unite in image
plane and can be projected onto some surface in
image plane
Two-lens Imaging system
Virtual Image if rays diverge, but backwards
extensions converge and intersect behind specimen

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A slightly more complicated imaging system aka
old microscope
Eye is part of optical system of microscope
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Infinity Corrected Microscopes last 15 Years
Infinity optics allows insertion of Filters,
analyzers without changing tube length, or final
image
Infinityparallel
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Basic Formulae in air
Object plane
Image plane
Lensmakers equation 
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Some Conventions

• S is distance from the object S is distance
  from the image
• Sign conventions m positive for inverted
  image negative for upright
• Sign conventions f positive for converging
  lens negative for diverging lens

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Keplerian Telescope
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Galilean telescope
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Upright Microscope Geometry
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Inverted Microscope Geometry
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Inverted vs Upright Geometries

• Upright
• Move stage for focusing (unless fixed stage)
• Optical path is simpler
• Easier for immersion (long working distance)

• Inverted
• Move objective for focusing
• Better access for live cells in culture
• Electrophysiology
• Harder for oil, water immersion.

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Refractive Index Depends on the Wavelength
This is called dispersion
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Dispersion of Air
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Dispersion of Glass
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How to Calculate?
Sellmeier Equations
All but quartz
Quartz
These values are tabulated (e.g. CVI Laser,
Melles Griot)
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Chromatic Aberration in Photography
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Doublet Lens Corrects Aberration
Crown
Flint
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Spherical Aberration could also be caused by the
use of the cover glass-slip. A correction
collar might be found on the objective to set the
thickness of the glass-slip. If no correction
collar can be found, the objective is corrected
for a 0.17 mm glass-slip.
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Astigmatism and coma are caused by imperfection
in the lens manufacturing.
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Field Curvature
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Newer CF lens meaning Chromatic aberration
Free.
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The Main Function of the Microscope is NOT to
MAGNIFY
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Whats Important for a Microscope?

• Contrast is necessary to detect detail from
  background
• light from an object must either be different in
  intensity or color ( wavelength) from the
  background light
• Both used in light and fluorescence microscopy
• Resolution fundamentally limited by diffraction
• diffraction occurs at the objective lens
  aperture

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Numerical Aperture (N.A.)
q
Objective lens
specimen
Image plane
From diffraction theory
d
N.A. n sinq
?
Minimum spot
NA radius/focal length
250 nm in visible
Abbe Limit
Resolution only determined by NA and wavelength
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Electromagnetic Spectrum
Visible region used for Light microscopy
small Part of EM spectrum
Resolution limit ?/2 200 nm
Visible good for Live specimens Cells, organelles
Ideal for micron sized structures
EM, X-ray cannot do live imaging
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Consider microscope object as simple grating
Spacing of Grating and Diffraction Pattern
S3 microns
S12 microns
Inverse relationship (transform) of object
spacing (or size) and diffraction pattern
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Double-slit Experiment
Condition for Constructive interference
a sin? n?
n 0, ?1, ?2, ? 3
After focusing
d f ? / a
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Multiple-slit is not Too Different
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Abbes Diffraction Pattern from White Light
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Tube Lens
Fringe spacing in the image d2 f ? / d1 f
? a / f ? M a
Requires at least one of the first order
diffraction spot in order to form the image.
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Diffracted Spots in back focal plane

• No specimen diffraction no image
• Specimen diffraction no collection, no image
• 0th and first order diffraction
• 0th and first and second order diffraction
• better resolution

Abbe showed need for central and diffracted spot
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2 D diffraction of periodic structures on road
to real object
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Visualizing objects below the diffraction limit
Subresolution beads Appear same size
60 nm
800 nm
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Diffraction from self-luminous spot delta
function source
Impossible to remove interference
rings Separated exactly by n?
Absence of light between Rings is due to
destructive interference
Light from each point of the object is spread out
in the microscope because light diffracts at the
edges of the lens
Central spot is 0th order diffraction or Airy
disk Contains 84 of power
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Aperture size, Interference, and Resolution
Con inter at P Destr at P
Full aperture
Interference in image plane
P-P distance Smaller for full aperture
Reduced aperture
Always fill Lens aperture For highest resolution
Maxima larger, max, min further apart Covers
more cone cells or camera pixels less resolution
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RESOLUTION
The resolution of a microscope is the shortest
distance two points can be separated and still be
observed as 2 points.
Not resolved
just resolved
Well resolved
MORE IMPORTANT THAN MAGNIFICATION !!
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High NA
Low NA
Limits on NA and Resolution?
Air NA 0.95 for a 70 degrees Immersion
increase n NA 1.4 a 67 degrees (oil)
n1.5 1.2 (water) n1.33 Higher index
materials for greater resolution?
Some exist methyl iodide, smelly, toxic Also
need higher index coverslips, slides
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Useful Magnification
Useful Magnification (total) 500 to 1000 NA
(Objective)
More mag does not help, and decreases image
quality through artifacts, diffraction
Limit comes from rod separation in the eye
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Depth of Field Axial resolving power Defined
only by NA2
Small Depth of Field at high NA
Focusing critical at high NA
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Gromit captured at f/22 (left) and at f/4
(right).
f image distance / effective diameter of the
lens