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

Laser White light

Phase

Direction

Polarization

Chromatic

Both lasers and white light sources used in microscopy

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

s= horizontalp= vertical

for propagationParallel to floor

Circular polarization:H,V (s,p) 90 degreesout of phase

Vertical

horizontal

elliptical polarization: less than 90 out of phase

This nature used extensivelyIn microscopy: pol microscopy, DIC, SHG

Particle (Quantized) Behavior

Light interacting with matter: absorption, reflectionphoton smallest unit- energy corresponds to frequency ()

   

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)

hvE

chE

0, 180 degrees Limiting cases for complete constructive, Destructive interference, respectively

Constructive, destructive interference

Wave Behavior

Underlies image formation in almost all forms of microscopy: phase, DIC, polarization,Some advanced forms of confocal

Representations of Light

Good for modelingLight propagation:Ray TracingNot real form

Interference,Image formation

Absorption,lasers

Wave, particle duality physically importantSome phenomenon described by both

Robert Hooke

Hooke made the first optical microscope

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 atThis point become parallel to the axis after the lens.

To an eye on the right-hand side, these diverging rays will Appear to be coming from the point F’: the second focal point.

Diverging (defocusing) Lens

Focal length is negative

where 1 is the angle of incidence,

2 is the angle of refraction

Snell’s Law

                                           

medium index

air (STP) 1.00029

water (20° C) 1.33

crown glass 1.52

flint glass 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 planeand can be projected onto some surface in image plane

Virtual Image: if rays diverge, but backwards extensionsconverge and intersect behind specimen

Two-lens Imaging system

Eye is part of optical system of microscope

A slightly more complicated imaging system aka old microscope

Infinity Corrected Microscopes: last 15 Years

Infinity optics allows insertion ofFilters, analyzers without changing tube length, or final image

Infinity=parallel

Thin lens formula 

Basic Formulae in airObject plane Image plane

Lensmakers equation 

''

111

ssf

h

h

s

sm

''''

2121

)1(111 )1( RnRdn

RRf n

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

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

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

Refractive Index Depends on the Wavelength

This is called dispersion

Dispersion of Air

Dispersion of Glass

All but quartz

Quartz

Sellmeier Equations

How to Calculate?

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 backgroundlight 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

Objectivelens

specimen

d n sin N.A. = n sin

Numerical Aperture (N.A.)

Image plane

NA= radius/focal length

NAd

2

22.1min

Resolution only determined by NA and wavelength

From diffraction theory

Abbe` Limit

Minimum spot

~250 nm in visible

Electromagnetic Spectrum

Visible region used for Light microscopy smallPart of EM spectrum

Resolution limit : λ/2~200 nm:

Ideal for micron sizedstructures

Visible good forLive specimens:Cells, organelles

EM, X-ray cannotdo live imaging

S=3 microns S=12 microns

Inverse relationship (transform) of object spacing (or size) and diffraction pattern

Spacing of Grating and Diffraction Pattern

Consider microscope object as simple grating

Condition for Constructive interference:

Double-slit Experiment

a sinθ = nλ

n = 0, 1, 2, 3 …

After focusing:

d = f λ / a

Multiple-slit is not Too Different

Abbe’s Diffraction Pattern from White Light

TubeLens

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.

a) No specimen diffraction: no imageb) Specimen diffraction: no collection, no imagec) 0th and first order diffractiond) 0th and first and second order diffraction

better resolution

Diffracted Spots in back focal plane

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

800 nm

Subresolution beadsAppear same size

Diffraction from self-luminous spot: delta function source

Central spot is 0th order diffraction or Airy diskContains 84% of power

Impossible to remove interference rings:Separated exactly by n

Absence of light betweenRings 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

Full aperture

Reduced aperture

Aperture size, Interference, and Resolution

Maxima larger, max, min further apart:Covers more cone cellsor camera pixels: less resolution

Interference inimage plane

Always fillLens apertureFor highestresolution

Con inter at P’Destr at P’’

P’-P’’ distanceSmaller for fullaperture

The resolution of a microscope is the shortest distance two points can be separated and still be observed as 2 points.

MORE IMPORTANT THAN MAGNIFICATION !!

Well resolved just resolved Not resolved

RESOLUTION

Limits on NA and Resolution?

Air: NA= 0.95 for =70 degrees

Immersion increase n: NA= 1.4 =67 degrees (oil) n~1.5

1.2 (water) n=1.33

Higher index materials for greater resolution?

Some exist: methyl iodide, smelly, toxicAlso need higher index coverslips, slides

Low NAHigh NA

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 powerDefined only by NA2

Focusing critical at high NA

Small Depth of Field at high NA

Gromit captured at f/22 (left) and at f/4 (right).

f = image distance / effective diameter of the lens