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