Optics and Image formation - Université de...

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Optics and Image formation

Pascal Chartrand

chercheur-agrégéDépartement de Biochimie

email: [email protected]

The Light Microscope

• Four centuries of history• Vibrant current development• One of the most widely used research tools

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Main issues of Microscopy

In order to observe “small objects”, three preconditions have to befulfilled

- Magnification- Resolution- Contrast

Only fulfillment of these three conditions allows translation of information as accurately as possible from object into an image which represents thatobject.

Light as a wave

Quantum wave-particle duality of light

Rays: photon trajectories

Rays: propagation direction of waves

Waves vs. Photons vs. Rays

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Light waves

frequency = v = oscillations per seconds (Hz)

Rays are perpendicular to wavefronts

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shorter , higher v

longer ,lower v

The electromagneticspectrum

Energy of photons

E = hv

where: h= Planck’s constant (6,63x10-34 J.sec)v= frequency of photons

Therefore, blue light is more energetic than red light

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Light interacts with matter

It can be: - absorbed- diffracted- reflected- refracted

Refraction

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Light velocity

c =

where: c= speed of light in a vacuum (3x108 m/sec)= wavelenght= frequency of photons

However, the speed of light is not constant and varydepending on the medium

Index of refraction: velocity of light in a materialcompared to the velocity of light in air

v= c/n

where v= velocity of light in a mediumin the air or in a vacuum, n=1

n = 1 n > 1 n = 1

Light travels more slowly in matter

v = c/n

The speed ratio is the Index of Refraction, n

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Refractive Index Examples

Depends on wavelength and temperature

• Vacuum 1• Air 1.0003

• Water 1.333• Cytoplasm 1.35–1.38 ?• Glycerol 1.475 (anhydrous)• Immersion oil 1.515

• Fused silica 1.46• Optical glasses 1.5–1.9

• Diamond 2.417

Wave Front

90o

Air

Glass Glass

Not 90o

Air

How refraction works

Refraction occurs when a wave front moves into an interface between twosubstances with different refractive indices

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Reflected wave

r

Refraction by an Interface

Refractive index n1 = 1Speed = c

Refractive index n2Speed = c/n

Incident wave1

Refracted wave2

n1 Sin(1) = n2 Sin(2) Snell’s law:

/n

r = 1

Mirror law:

Which Direction?

n1

n2 > n1

Refraction goestowards the normal

in the higher-index medium

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Refraction and lenses

Parallellight rays coming frominfinity

F= focal plane or focal point

FL= focal length

Axis: axis of the lens

Lenses

Refraction of light rays on the surface of the glass of a bi-convex lensleads to the convergence of the rays toward a point beyond the lens, called focal plane

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Ray Tracing Rules of Thumb(for thin ideal lenses)

f f

Parallel rays convergeat the focal plane

Rays that cross in the focal planeend up parallel

Rays through the lens center are unaffected

What happen if you put an object in front of a lens?

The three rules of refraction:

1) an incident ray traveling parallel to the axis of the lens will refract through the lens and travel through the focal point on the opposite side of the lens

2) an indicent ray travelling through the center of the lens will continue in the samedirection that when it entered the lens

3) an incident ray travelling through the focal point on the way to the lens will refractthrough the lens and emerge parallel to the axis of the lens

1

2

3

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What happen if you put an object in front of a lens?

When a set of incident and refracted rays are drawn for several points upona vertical object, each reflected ray intersect at locations which form a vertical image

To simplify ray diagrams, only two sets of rays from a single point are usuallyshowed

Lenses and magnification

An object located over 2X the distance of the focal point (2F) forms a smallinverted image of an object on the opposite side of a lens

An object located between F and 2Fforms a large inverted image of an objecton the opposite side of a lens

The closer an object is to the focal point, the larger its image will be

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f f

p q


object image

The lens law:1

p+

1

q=

1

fMagnification:

d1

d2

d1

d2 q

pM = =


What happen if an object is at the focal point of a lens?

At the focal point, all the refracted rays are parallel, and do not converge toward a specific point to form an image of the object

- therefore, there is no image of the object

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What happen if an object is between the focal point and the lens?

All the refracted rays are divergent, and do not converge toward a specific point to form an image of the object

- However, there is a virtual image of the object is formed. This virtual image is bigger than the image, upright and located in front of the lens

f f

specimen

objective

Intermediate image plane(I.I.P)

f f

I.I.P

ocular

The compound microscope

f f f f

specimen I.I.P

objective ocular

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Back focal plane

Object

f0

f0 f0

Back focal plane

Rays that leave the object with the same anglemeet in the objective’s back focal plane

Tube lensobjective

The Compound Microscope

Sample

Objective

Tube lens

Primary or intermediateimage plane

Eyepiece

Back focal plane (pupil)

Exit pupil

Object plane

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Sample

Objective

Tube lens

Intermediate image plane

Eyepiece

Object plane


Exit pupil

Eye

Final image

Sample

Objective

Tube lens


Eyepiece

Object plane


Exit pupil

Eye

Final image


Microscopeconjugate

planes:

Planeswhich

are in focus witheach other

Field or Image formingconjugate set

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Sample

Objective

Tube lens


Eyepiece

Object plane


Exit pupil

Eye

Final imageMicroscopeconjugate

planes:

Planeswhich

are in focus witheach other

Aperture or Illuminationconjugate

set

specimen I.I.P

objective ocular

Finite vs infinity-corrected microscope

Finite-tube lenght microscope

160 mm

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specimenI.I.P

objective ocular

Parallel lightbeam

(infinity space)

Infinity-corrected microscope

tubelens

Magnification of microscope = magnification of objective x magnification of the ocular

Finite vs infinity-corrected microscope

• Function of any microscopy is NOTsimply to magnify!

• Function of the microscope is to RESOLVE fine detail.

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Resolution

Resolution

RESOLUTION means objects can be seen as separate objects

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

MORE IMPORTANT THAN MAGNIFICATION !!

Well resolved just resolved Not resolved

d

N.A.

Resolution

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WHAT DETERMINES RESOLUTION?

1. Contrast is necessary to detect detail (edges) frombackground

2. Diffraction fundamentally limits resolution diffraction occurs at the objective lens aperture

Diffraction

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The Huygens principle and diffractionHuygens’ Principle All points on a wave front act as point sources of spherically

propagating “wavelets”. At a short time Δt later, the new wave front is the unique surface tangent to all the forward-propagating wavelets.

InterferenceIn phase

Opposite phase

+

+

=

=

constructive interference

destructive interference

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Diffraction of waves passing through a single slit

negative interference

positiveinterference

Single-slit diffraction pattern

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Diffraction by an aperture

Larger aperture

weaker diffraction

Light spreads to new angles

drawn as waves

Diffraction by an aperture

The pure, “far-field”diffraction pattern

is formed at infinity…

…or can be formedat a finite distance

by a lens…

…as happens in a microscopeObjective pupil

Intermediateimage

Tube lens

drawn as rays

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Tube lens

Back focal plane aperture


Diffraction spoton image plane

Sample

Objective

Aperture and Resolution


Tube lens



Sample

Objective


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Tube lens



Sample

Objective



• Image resolution improves with aperture size

Sample

Objective Tube lens




Numerical Aperture (NA)

NA = n sin() = light gathering anglen = refractive index of samplewhere:

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Numerical Aperture of objectives

4X / 0.20 NA = 11.5°

100X / 0.95 NA = 71.8°

NA=n sin (α)

Refractive indices:

Air: 1.003Water: 1.33Glycerol: 1.47 Oil: 1.52

Immersion media increases the NA of an objective or a condenser by bringing the beams with higher incidence angle intothe light path

Role of immersion medium

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Central maximum of one peak overlies 1st minimum of neighboring peak

Just resolved

The Rayleigh criterion and resolutionGenerally accepted criterion of resolution

Well resolvedSingle point source

d

Rayleigh criterion: d = 0.61 for self-luminous object)

N.A.

N.A. : Numerical aperture of the objective

Ex. : NA = 1.4, = 520 nm (GFP, FITC…)

d = 226 nm (human eye: d ~ 100 μm)

Thus, the best resolution that can be achieved by an optical microscope is~ 200 nm

Minimal distance between two points of an object that can be resolved

The Rayleigh criterion and resolution

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Objective of NA 0.95 d = 190 nm @ 360 nmd = 320 nm @ 600 nm

Effect of wavelength on resolution

Decreasing wavelength increases the resolution between two points

The point spread function (PSF)

The Airy disk correspond to a slice of a point spread function

zx

yx

The PSF correspond to the image produced by the microscope of a point source of light

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PSF and axial (Z) resolution

The axial resolution can be defined as FWHM= the full width at half maximal intensity of a z line of a point source

INTENSITYZ

-PO

SIT

ION

FWHM

or d = 2n for = 520 nm, NA= 1,4, n= 1,52 NA2 the axial resolution is ~ 820 nm

ContrastLive cells are largely transparent, absorbing almost no light andscatter relatively little

- little contrast between cell and surrounding medium

How can we increase this contrast?

brightfield darkfield

phase contrast Differential interference contrast

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Which properties of light can we change to increase contrast

• Amplitude => increase illumination intensity or put in an absorbent stain

• Wavelength => use fluorescent molecules

• Direction of propagation: Look only at light refracted by sample (dark field microscopy)

• Velocity=> Phase; Altering phase of incident light can lead to interference with background light (Phasecontrast, DIC)

Effect of the specimen on the phase of incident light

- Amplitude specimen changes the intensity of incident light

- Phase specimen changes the phase of incident light

- Most unstained biological specimens are phase ones

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Phase Contrast

1/4

1/2

DiffractedLight

Background Light

DiffractedLight

Background Light

Phase Contrast produces destructive interference.

Destructiveinterference

A) When incident light pass through a specimen, the diffracted light is ¼wavelength out of phase with the background light.

B) A Phase plate, at the back focal plane of the objective, further retards diffracted light by ¼ wavelength

- This creates a ½ wavelength difference between the background and diffracted light.

A

B

Phase Contrast

Brightfield Phase Contrast

Benefits Negatives

Much better resolution

(dark edges)

White halo around the edges

Good for unstained cells

(Tissue Culture)

A Phase Ring Equipped Objective is required

Better Contrast Optimized for 548nm wavelength

Benefits and Negatives of Phase Contrast Microscopy

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Differential interference Contrast (DIC)

1) A single ray of light is split by theWollaston prism

- generates 2 rays separated bya distance of ~ 0,2 um and slightlyout of phase (90 )

2) Both rays go through the specimen

3) A second Wollaston prism combinesthe split rays

4) An analyzer brings the rays in the sameplane

- if both rays are in phase, thisresults in positive interference

1

2

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Differential interference Contrast (DIC)

A) If both rays go through a medium with the same refractive index, bothray will stay in phase, leading to positive interference when both rayscombine (bright)

B) If one of the two rays goes through the cytoplasm of a cell, this willresult in a shift of its phase compared to the sister ray, leading tonegative interference when both rays combine (dark-grey)

C) If both rays go through a cell, both will have the same phase alteration,leading to positive interference when both rays combine (bright)

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Differential Interference ContrastPhase Contrast DIC

Benefits Negatives

Best Resolution (3D effect) Cannot do both low power and high power DIC (lower Wallaston)

Best depth discrimination (but be careful - What you see is NOT

always what you get)

Due to use of polarizers, DIC cannot be used with plastic

dishes.

Good contrast Change in RI can be mistaken for depth

Benefits and Negatives of DIC Microscopy

Optics and Image formation - Université de...

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