Geometrical Optics and Basic Imaging Light Paths of the Bright

Field MicroscopeE. D. Salmon

University of North Carolina at Chapel Hill

Major Imaging Functions of the Microscope

• Magnification: Needed to overcome resolution limitations produced by finite size of recording sensors- rods and cones in eye, silver grains in film; pixels in CCDs

• Resolution: Limited by lens aberrations and finite wavelength of light

• Contrast: How to make resolvable structural detail visible-absorbing stains, phase contrast, DIC, Pol., immunofluorescence, fluorescent analogs, GFP-fusion proteins, other fluorescent molecular probes

Camera

Camera AdapterBinocular

Eyepiece

Beam Switch

Filter Cube ChangerSlot for Analyzer

Slot for DIC Prism

Objective Nosepiece

Objective

Stage

Condenser: Diaphragm&Turret Centering Focus

Field Diaphragm

Coarse/Fine Specimen Focus

Filtersand Diffuser

Lamp: Focus, Centering

Mirror:Focus andCentering

Mirror:Focus andCentering

Focus, Centering

Trans-Lamp Housing

Epi-Lamp HousingEpi-Field Diaphragm

Epi-CondenserDiaphragm

ShutterFilters& Centering

Slot for Polarizer

Upright Microscope Stand

Body Tube

MICROSCOPE COMPONENTS

Magnification Changer

IMAGING LIGHT PATHS ILLUMINATING LIGHT PATHS

Eyeor

Camera

Eyepiece

IntermediateImage plane

Objective Lens

Specimen

Condenser Lens

CondenserDiaphragm.

FieldDiaphragm

Collector Lens

Lamp

Objective Back FocalPlane

Tube Lens

MICROSCOPE ALIGNMENT FORTRANSMITTED LIGHT KOEHLER ILLUMINATION

Some Visible Spectrum Light Sources

The eye is most sensitiveto green light!

Primer on Geometrical Optics

• Light moves in straight lines through homogeneous media at velocity: v = c/n()

• Example values for n(546nm):Air 1.0Water 1.3333Cytoplasm 1.38Glycerol 1.46Crown Glass 1.52Immersion Oil 1.515Protein 1.51-1.53Flint Glass 1.62

Reflection

N

r i

reflecting surface

N

mirror

r = 45

i= 45

o

o

Reflection and Refraction at Transparent Surface

N N

r

i

n1

n2

n1

n2

r

i

a. n2 n1 <> n2 n1b.

i

i

Reflecting

Refracting

Reflecting

Refracting

Snell’s Law of Refractionn1sin(i) = n2sin(r)

Total Internal Reflection Can Occur

Snell’s Law of Refractionn1sin(i) = n2sin(r)

N

n1

n2

r

i

N

n1

n2

b.a.

r = 90o

i c=

N

n1

n2

c.

r

i

Total Internal Reflection is Used to Re-Direct Light

N

r i = 45

Prism

Fiber OpticLight Guide

Homework

1. A beam of light in glass hits a surface at an angle. At what angle does the light just become total internally reflected if the glass has a refractive Index of 1.52 and the interface has a refractive index of :

a. Airb. Waterc. Immersion oil

In each case, what is the numerical aperture (NA) of the beam relative to the normal to the interface?

Refraction is Usually Greater at Shorter Wavelengths

n

blue

red

1

n2

1 2

Refraction at Curved Lens Surfaces: Action of Convex or Concave Lenses

F'

F'

F'

a.

b.

c.

d.

e.

F'

F'

F’ is Primary Front Focal Point of Lens

Basic Action of Converging Lenses

F'

a.

b.

f

optical axis

f

F'

a a = f sin

Back FocalPlane(BFP)

Light parallel to the optical axis comes into focus at a point F’, the back focal point, located one focal length, f, from principle plane (PPL) of the lens.

Parallel light at angle, , to the optical axis comes into focus at a point, F”, located in the back focal plane and ata distance a = fsin() from the focalpoint, F’.

Homework: What is an easy way to measure the approximate focal length of

a lens

Basic Action of Converging Lenses (cont.)

Light emanating from the front focal point, F’, located a distance, f, on the optical axis from the PPL will emerge Parallel to the optical axis.

Light emanating from a point in the front focal plane, FFP, at distance a from the optical axis, will emerge as aparallel beam of light at angle, , tothe optical axis, where a = fsin().

a.

b.

f

optical axis

f

a

optical axis

FrontFocalPlane(FFP)

F

F

Example: Flashlight

Real-Image FormationAs Object Moves Closer to Lens

Three Light Rays Can Define Real Image Formation

PPL

f

o i

s2

F'FO

I

1

2

3

S1

f

M = I/O =i/o

1/i +1/o = 1/f

Image Formation in the Human Eye

Resolution Limitations of the Human Eye

250 mm

O' O"

I

I'

I"

ConventionalViewingDistance

O

³ 2.0 m

A B

Limits to Accommodation

Unresolved Resolved

COARSE FINE

Resolution Test

Ocular is a Single Lens Magnifier

250 mm

O'

I

I'

O

f

O

Magnification (angular) = 250 mm/f

Homework: What is The Ocular Focal Length for the Following

Magnifications?• 5X _________

• 10X _________

• 20X _________

• 25X _________

The Objective Forms a Real Image At the Ocular Front Focal Plane: The Primary or

Intermediate Image Plane (IIP)

PPL

fob

OTL

s2

F'FO

I

1

2

3

S1

fob

IIP

foc

Conventional OpticsObjective with finite Focal Length(Optical Tube Length, OTL, Typically 160 mm)

Mob = OTL/fob

Total Magnification = Mob x Moc = OTL/fob x 250mm/foc

Homework: For Finite Focal Length Objective and OTL = 160 mm, what is focal length for the following Objective

Magnifications• 4X _________

• 10X ________

• 20X ________

• 40X ________

• 60X ________

• 100X _______

How to Insert Filters Above

Objective Without Inducing

Image Aberration

a. Conventional objective (no Telan Lenses)

b. Conventional objective with Telan lenses

c. Infinity Corrected objectives

OBJ

Glass Filter

PIP

Glass Filter

Glass Filter

PIP

PIPFocusing Lens

(Neg.) (Pos.)

Telan lenses

Mob = ffocusing/fob

Zeiss introduced infinity corrected objective for biomedical scopes in late

1980’s, Nikon, Leica and Olympus followed by Mid-1990’s

Also, field of view in ocular enlarged from 18 mm to 24-25 mm.

Numerical Aperture (NA) of Collection (a) or Illumination (b)

F'

f

NA = nSinobj

BFP

n

Iris Diaphragmor Stop

a.

cond

FFP

f

NA = nSin

b.

How to Measure Objective NA

Low PowerObjective

Specimen Slide

Microscope Stage

Black Dotson White Card

n = 1

w w

h

1 2 3

3 2 1

White Card Set OnCondenser CarrierLowered All theWay Down.

(1) (2)

m

m

Lamp

IMAGING LIGHT PATHS ILLUMINATING LIGHT PATHS

Eyeor

Camera

Eyepiece

IntermediateImage plane

Objective Lens

Specimen

Condenser Lens

CondenserDiaphragm.

FieldDiaphragm

Collector Lens

Lamp

Objective Back FocalPlane

Tube Lens

MICROSCOPE ALIGNMENT FORTRANSMITTED LIGHT KOEHLER ILLUMINATION

Homework for Thursday: Go to http://micro.magnet.fsu.edu/primer/index.html

and work through:• Light and color• Anatomy of Microscope:

-Introduction

-concept of Magnification

-Microscope Optical components:

-Geometrical construction of Ray Diagrams

-Perfect Lens Characteristics

-Perfect 2 Lens Characteristics