the michelson interferometer best known and historically most important best known and historically...

The Michelson The Michelson interferometerinterferometer

Best known and historically most importantBest known and historically most important Utilizes arrangement of mirrors (M) and beam splitters Utilizes arrangement of mirrors (M) and beam splitters

(O)(O) Compensator plate (C): each beam passes through Compensator plate (C): each beam passes through

equal thicknesses of glass equal thicknesses of glass actual path difference actual path differenceM2

OC

M1

Source

Detector

Conceptual rearrangementConceptual rearrangement

SS11 and S and S2 2 = images of source= images of source ssoo = s = sii, s, soo’ = s’ = sii’, s’, soo’ = s’ = soo + d + d

M2 M1’ S2S1Source

so’ si’

so si

d2d

Path difference

Optical path differenceOptical path difference

If beamsplitter is If beamsplitter is uncoated glass plate, uncoated glass plate, phase shift from two phase shift from two reflections = reflections = radians.radians.

Destructive Destructive interference when interference when 2dcos2dcos = m = m

Extremely accurate Extremely accurate length measurements: length measurements: d = N(d = N(/2)/2) N = number of fringes N = number of fringes

that have moved past a that have moved past a reference pointreference point

CamerasCameras

Pinhole cameraPinhole camera Well-defined, Well-defined,

practically practically undistorted imageundistorted image

Wide angular field, Wide angular field, great depth of fieldgreat depth of field

No image results if No image results if entrance pupil is entrance pupil is very largevery large

Image forms and Image forms and grows sharper with grows sharper with decrease in decrease in diameterdiameter

0.5 mm diameter hole 0.5 mm diameter hole at 0.25 m from film is at 0.25 m from film is convenientconvenient

Slow speed (f/500)Slow speed (f/500)

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Field of viewField of view

To focus the camera, To focus the camera, the entire lens is the entire lens is moved toward or moved toward or away from the film away from the film plane.plane.

Angular field of view Angular field of view = angle subtended = angle subtended at lens by a circle at lens by a circle encompassing the encompassing the sensor areasensor area

Fraction of scene Fraction of scene included in included in photographphotograph

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Viewing areaViewing area

Standard SLR lens Standard SLR lens has focal length f has focal length f in the range 50 to in the range 50 to 58 mm, field of 58 mm, field of view = 40view = 40oo to 50 to 50oo

Wide-angle SLR Wide-angle SLR lenses f = 40 to 6 lenses f = 40 to 6 mm, mm, = 50 = 50o o to to 220220oo

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Depth of fieldDepth of field Standard Standard

photographic photographic objective must objective must have a large have a large relative aperture relative aperture 1/(f/#) to keep 1/(f/#) to keep exposure times exposure times short.short.

Lens should have a Lens should have a wide angular field wide angular field of view.of view. abc.net.au

AperturesApertures

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Single Lens Reflex camerasSingle Lens Reflex cameras When shutter release is pressed, diaphragm When shutter release is pressed, diaphragm

closes down to a preset value.closes down to a preset value. Built-in light-meter arrangement coupled to the Built-in light-meter arrangement coupled to the

diaphragm and shutterdiaphragm and shutter

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Focal lengthsFocal lengths

50mm50mm is the " is the "normalnormal" " focal length, neither wide focal length, neither wide angle nor telephoto. angle nor telephoto.

Any focal length Any focal length shorter shorter than 50mmthan 50mm is is wide anglewide angle

Any focal length Any focal length shorter shorter than about 25mmthan about 25mm is is ultra ultra wide anglewide angle; ;

Any focal length Any focal length longer longer than 50mmthan 50mm is technically is technically telephototelephoto; ;

85mm to 135mm85mm to 135mm is is considered a considered a portrait lensportrait lens; ; (daystarvisions.com)(daystarvisions.com)

Compact digitals have a Compact digitals have a "normal" focal length "normal" focal length about 1/5th or 1/6th that of about 1/5th or 1/6th that of 35mm.35mm.

Lens barrel of a Canon Lens barrel of a Canon A720 says 5.8-34.8A720 says 5.8-34.8

5.8mm x 6 = 35mm and 5.8mm x 6 = 35mm and 34.8 x 6 = 210mm. 34.8 x 6 = 210mm.

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Camera sensorCamera sensor

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Charge-coupled device (CCD) Charge-coupled device (CCD) arraysarrays

Most common Most common sensor type sensor type currently used in currently used in machine vision machine vision

Basic building Basic building block: metal-oxide-block: metal-oxide-semiconductor semiconductor (MOS) capacitor(MOS) capacitor olympusmicro.com

Interline transfer CCDInterline transfer CCD

Each row in the Each row in the array represents a array represents a single line in the single line in the resulting image.resulting image.

Charge Charge accumulated by accumulated by each element is each element is proportional to light proportional to light intensity and intensity and exposure time.exposure time.

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HolographyHolography

Developed prior to the Developed prior to the laserlaser

Requirement for light Requirement for light with a high degree of with a high degree of spatial and temporal spatial and temporal coherencecoherence

Method of recording Method of recording information from a 3D information from a 3D object such that a 3D object such that a 3D image may be image may be reconstructed (wavefront reconstructed (wavefront reconstruction)reconstruction)

Hologram = recorded Hologram = recorded interference patterninterference pattern

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Holographic recordingHolographic recording

Exact shape and Exact shape and distribution of interference distribution of interference fringes based on shape of fringes based on shape of the object and reflected the object and reflected wavefrontswavefronts

Wavefront reflected from Wavefront reflected from the object Ethe object Eobob

UUoo(x,y) = complex (x,y) = complex amplitudeamplitude

UUrr(x,y) = reference beam(x,y) = reference beam Irradiance I(x,y)Irradiance I(x,y) Constant transmission TConstant transmission T

Transmitted light UTransmitted light UTT when hologram is when hologram is illuminated by Uilluminated by Urr

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Holography 101Holography 101

Object wavefront

Reference wavefront

Holographic medium

Hologram

Reference wavefront

Reconstructed object

Photorefractive volume Photorefractive volume holographyholography

5 Fundamental Processes:

1) Photoionization of impurities & generation of charge carriers

2) Charge carrier transport

3) Trapping of charge carriers leading to formation of space-charge density

4) Formation of photo-induced space charge field

5) Formation of index grating

Beam 1 Beam 2

I

x

x

x

ESC

Intensity

Charge Density

Space Charge Field

Index Variation

n

x

x

The Photorefractive Effect

)t,x(Ern2

1)t,x(n sceff

3o

21 kkK

Optical set-upOptical set-up

Optical data storageOptical data storage

543 nm LaserPolarizer

M1

L1

L2

BS3

M2

T L3

Fe:LiNbO3L4

CCD

Block

Object

Reference

BS2 BS1

594 nm Laser

632.8 nm Laser

Iris

Wavelength multiplexingWavelength multiplexing

High resolution dataHigh resolution data

Holographic animationHolographic animation

2.51

Fe:LiNbO3

He-Ne LaserM1

Target

Object beam

Reference Beam

ID

M2

CCDBS

L1

L2 L3

BX

block

Filter

L4

Phase multiplexingPhase multiplexing

Reference beam Ro

t1(x1,y1) L1

t2(x2,y2)

L2 Elastomer mask

O(x,y)

Lens

Photorefractive crystal

Recorded imagesRecorded images

Cyclic videoCyclic video

Special beamsSpecial beams

0 cm 5 cm 10 cm

15 cm

20 cm

25 cm

30 cm

35 cm

ApplicationsApplications

Determination of surface Determination of surface contours for complicated contours for complicated shapes with diffusely shapes with diffusely reflecting surfacesreflecting surfaces

Double exposure Double exposure holographic holographic interferometry: very small interferometry: very small distortions can be distortions can be measured by counting measured by counting interference fringesinterference fringes

Holographic computer Holographic computer memoriesmemories

Theoretically up to 10Theoretically up to 101010 bits/mmbits/mm33

Information is distributed Information is distributed across the entire hologram, across the entire hologram, not sensitive to scratches or not sensitive to scratches or dustdust

Very high readout rate: Very high readout rate: information is recovered in information is recovered in parallelparallel

Easier to align and less Easier to align and less subject to vibration problemssubject to vibration problems

Possible to record several Possible to record several holograms in different planes holograms in different planes of a thick materialof a thick material

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Future computer memoriesFuture computer memories

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Optical modulatorsOptical modulators

Electro-optic effectElectro-optic effect Introduces new optic axes into Introduces new optic axes into

birefringent materials or to make birefringent materials or to make naturally istropic crystals birefringentnaturally istropic crystals birefringent

Pockels effect: linear variation in Pockels effect: linear variation in refractive index, depends on crystal refractive index, depends on crystal structure and symmetrystructure and symmetry

Kerr effect: quadratic dependenceKerr effect: quadratic dependence