Transcript Lecture 1. Introduction. Nature of light, geometric optics.

Optical Microscopy
Lecture 1
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
Some Properties of Light
Both lasers and white light sources used in microscopy
Laser
Chromatic
Polarization
Phase
Direction
White light
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
Polarization of Light
Plane where electric field vector lies, E=Eºcos(ωt)
Perpendicular to direction of propagation
Vertical
s= horizontal
p= vertical
for propagation
Parallel to floor
horizontal
This nature used extensively
In microscopy: pol microscopy, DIC, SHG
Circular polarization:
H,V (s,p) 90 degrees
out of phase
elliptical polarization:
less than 90 out of
phase
Particle (Quantized) Behavior
Light interacting with matter: absorption, reflection
photon smallest unit- energy corresponds to frequency ()
E  hv
Eh
c

h=6x10-34 J*s
Planks constant
~10-19 J for visible light (=600 nm)
•best for describing absorption, emission of light
•Best for describing how detectors work
(photomultipliers, Diodes)
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
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
Hooke made the first optical microscope
Robert Hooke
The first image of Hooke and the birth of the term “Cell”
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.
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.
Snell’s Law
where q1 is the angle of incidence,
q2 is the angle of refraction
medium
index
air (STP)
1.00029
water (20° C) 1.33
crown glass
flint glass
1.52
1.65
Ray Tracing Rules for locating image
Only need 2 rays
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
A slightly more complicated imaging system aka old microscope
Eye is part of optical
system of microscope
Infinity Corrected Microscopes: last 15 Years
Infinity optics allows
insertion of
Filters, analyzers
without changing tube
length, or final image
Infinity=parallel
Basic Formulae in air
Object plane
Lensmakers equation
Thin lens formula
Image plane
1
f

 (n  1)
1 1 1
  ''
f s s
1
R1

1
R2

s '' h ''
m 
s
h
( n 1) d
nR1R2

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
Keplerian Telescope
Galilean telescope
Upright Microscope Geometry
Inverted Microscope Geometry
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.
Refractive Index Depends on the Wavelength
This is called dispersion
Dispersion of Air
Dispersion of Glass
How to Calculate?
Sellmeier Equations
All but quartz
Quartz
These values are tabulated (e.g. CVI Laser, Melles Griot)
Chromatic Aberration in Photography
Doublet Lens Corrects Aberration
Crown
Flint
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.
Astigmatism and coma are caused by imperfection in the lens manufacturing.
Field Curvature
Newer: CF lens – meaning Chromatic aberration Free.
The Main
Function of the
Microscope is
NOT to
MAGNIFY
What’s Important for a
Microscope?
1. 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
2. Resolution fundamentally limited by
diffraction
diffraction occurs at the objective lens aperture
Numerical Aperture (N.A.)
q
specimen
Objective
lens
Image plane
From diffraction theory
Minimum spot
d  
n sinq
d min 
1.22
2 NA
N.A. = n sinq
NA= radius/focal length
Abbe` Limit
~250 nm in visible
Resolution only determined by NA and wavelength
Electromagnetic Spectrum
Visible region used for
Light microscopy small
Part of EM spectrum
Resolution limit : λ/2
~200 nm:
Visible good for
Live specimens:
Cells, organelles
Ideal for micron sized
structures
EM, X-ray cannot
do live imaging
Consider microscope object as simple grating
Spacing of Grating and Diffraction Pattern
S=3 microns
Inverse relationship (transform) of
object spacing (or size) and diffraction pattern
S=12 microns
Double-slit Experiment
Condition for
Constructive interference:
a sinθ = nλ
n = 0, 1, 2,  3 …
After focusing:
d=fλ/a
Multiple-slit is not Too Different
Abbe’s Diffraction Pattern from White Light
Tube
Lens
d1
Fringe spacing in the image:
d2 = f’ λ / d1 = f’ λ a / f λ = M a
Requires at least one of the first order
diffraction spot in order to form the image.
Diffracted Spots in back focal plane
a)
b)
c)
d)
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
2 D diffraction of periodic structures: on road to real object
Visualizing objects below the diffraction limit
60 nm
Subresolution beads
Appear same size
800 nm
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
Aperture size, Interference, and Resolution
Full aperture
Interference in
image plane
Con inter at P’
Destr at P’’
P’-P’’ distance
Smaller for full
aperture
Reduced
aperture
Maxima larger, max, min further apart:
Covers more cone cells
or camera pixels:
less resolution
Always fill
Lens aperture
For highest
resolution
RESOLUTION
The resolution of a microscope is the shortest distance
two points can be separated and still be observed as 2
points.
Well resolved
just resolved
Not resolved
MORE IMPORTANT THAN MAGNIFICATION !!
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) n~1.5
1.2 (water)
n=1.33
Higher index materials for greater resolution?
Some exist: methyl iodide, smelly, toxic
Also need higher index coverslips, slides
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
Depth of Field:
Axial resolving power
Defined only by NA2
Small Depth of Field at high NA
Focusing critical at high NA
Gromit captured at f/22 (left) and at f/4 (right).
f = image distance / effective diameter of the lens