Wavefront detection & modulationweb.mit.edu/2.710/Fall06/2.710-wk13-b-sl.pdf · 2005-11-27 ·...
Transcript of Wavefront detection & modulationweb.mit.edu/2.710/Fall06/2.710-wk13-b-sl.pdf · 2005-11-27 ·...
MIT 2.71/2.710 Optics11/30/05 wk13-b-1
Wavefront detection & modulation
Detection• Types of photodetectors• Digital imaging• Color
Modulation• Photographic film• Spatial light modulators• Binary optics
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Imaging: detection of light
a) photothermal (pyroelectric)b) photoconductivity
c) photoresistivity (bolometers)d) photomechanical
B. Jähne & H. Haußecker, “Computer Vision and Applications,”
Academic Press 2000
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Digital imagingChargeCoupledDevices(CCDs)
B. Jähne & H. Haußecker, “Computer Vision and Applications,”
Academic Press 2000
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Digital imagingCMOS
APS=active pixel sensor
microlens arrays improvesensitivity
B. Jähne & H. Haußecker, “Computer Vision and Applications,”
Academic Press 2000
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Color
B. Jähne & H. Haußecker, “Computer Vision and Applications,”
Academic Press 2000
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Color
http://www.dpreview.com/news/0202/02021102foveonx3tech.asp
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Improved color: the Foveon
http://www.dpreview.com/news/0202/02021101foveonx3.asp
MIT 2.71/2.710 Optics11/30/05 wk13-b-8
Improved color: the Foveon
US Patent 5,965,875
http://www.dpreview.com/news/0202/02021102foveonx3tech.asp
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Improved color: the Foveon
http://www.dpreview.com/news/0202/02021102foveonx3tech.asp
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Light modulation
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Photographic films / platesprotective layer
emulsion with silver halide (e.g. AgBr)grains
base (glass, mylar, acetate)
Exposure: Ag+ + e– → Ag (or 2Ag+ + 2e– → Ag2 )
development speckCollection of development specks = latent image
Development (1st chemical bath): converts specks to metallic silver
Fixing the emulsion (2nd chemical bath): removal of unexposed silver halide
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Photographic film / plates• Exposure (energy) : energy incident per unit area on a photographic
emulsion during the exposure process (units: mJ/cm2)
• Intensity transmittance : average ratio of intensity transmitted over intensity incident after development
• Photographic density
Exposure = incident intensity × exposure time E=Iexpose × T
( )⎭⎬⎫
⎩⎨⎧
=yxIyxIyx
,at incident ,at ed transmitt
averagelocal
,τ
DD −=⇔⎟⎠⎞
⎜⎝⎛= 10 1log10 ττ
MIT 2.71/2.710 Optics11/30/05 wk13-b-13
Photographic film / plates• Hurter-Driffield curve • Gamma curve
log E
D
Gross fog
ToeLinear region(slope γ)
Shoulder
Saturationregion
development time
γ
1
2
5 10 15 (min)
γ high/low : high/low contrast film
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Kelley model of photographic processOptical imagingduring exposure
(linear)
H&D curve
(nonlinear)
additional blurdue to chemicaldiffusion(linear)
log E
DH&D curve
measureddensity
inferred logarithmicexposure
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The Modulation Transfer Function
xuEEE 010 2cos π+=
( ) xuEuMEE 0100 2cos π+=′u0
M
Exposure:
“Effective exposure”:
1.0
0.5
adjacency effect(due to chemical diffusion)
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Bleaching / phase modulation
emulsion
exposure
tanning bleach(relief grating)
non-tanning bleach(index grating)
( )zyx ,,ε∆
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Spatial Light Modulators
• Liquid crystals• Magneto-Optic• Micro-mirror• Grating Light Valve• Multiple Quantum Well• Acousto-Optic
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Liquid crystal modulators
• Nematic• Smectic (smectic-C* phase: ferroelectric)• Cholesteric
crossed polarizers
OFF
crossed polarizers
V(acts as λ/2 plate;rotates polarizationby 90°)
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Micro-mirror technology
Texas Instruments DMD/DLP
Lucent (Bell Labs)
Sandia
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Micro-mirror display
http://www.howstuffworks.com
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Micromirrors for adaptive optics
Véran, J.-P. & Durand, D. 2000, ASP Conf. Ser 216, 345 (2000).
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Grating Light Valve (GLV) display
Silicon Light Machines, www.siliconlight.com
www.meko.co.uk
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Binary Optics
Refractive Diffractive Binary(prism) (blazed grating)
⎟⎠⎞
⎜⎝⎛= N2
1sinc21η
efficiency of 1st diffracted order fromstep-wise (binary) approximation toblazed grating with N steps over 2π range
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Binary Optics: binary grating
0
1( )xtAmplitude maskAmplitude mask X
x
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Binary Optics: binary grating
( ) ( )[ ]xixt φ exp=
–1
1( )xtPhase maskPhase mask X
0
π( )xφ X
x
x
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Fourier series for binary phase grating
1( )xt X
x
–1
⎟⎠⎞
⎜⎝⎛
⎟⎠⎞
⎜⎝⎛= ∑
+∞
−∞= Xnxin
nπ2exp
2sinc
0≠n
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Fourier series for binary phase grating
1( )xt X
x
–1
identify physical meaning:• plane waves• orientation of nth plane wave:
• diffracted orders
Xnn λθ =sin
⎟⎠⎞
⎜⎝⎛
⎟⎠⎞
⎜⎝⎛= ∑
+∞
−∞= Xnxin
nπ2exp
2sinc
0≠n
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Fourier series for binary phase grating
1( )xt X
x
–1
identify physical meaning:• plane waves• orientation of nth plane wave:
• diffracted orders
Xnn λθ =sin
nθ
⎟⎠⎞
⎜⎝⎛
⎟⎠⎞
⎜⎝⎛= ∑
+∞
−∞= Xnxin
nπ2exp
2sinc
0≠n
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Fourier series for binary phase grating
1( )xt X
x
–1
identify physical meaning:• plane waves• orientation of nth plane wave:
• diffracted orders
Xnn λθ =sin
nθ
⎟⎠⎞
⎜⎝⎛
⎟⎠⎞
⎜⎝⎛= ∑
+∞
−∞= Xnxin
nπ2exp
2sinc
0≠n
only! orders odd 2
sinc ⇒⎟⎠⎞
⎜⎝⎛ n
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Fourier series for binary phase grating
1( )xt X
x
–1
Fourier transform:•
• result is
( ) ( )002exp uuxui −↔δπ
⎟⎠⎞
⎜⎝⎛ −⎟
⎠⎞
⎜⎝⎛∑
+∞
−∞= Xnun
nδ
2sinc
0≠n
(Fourier series)
⎟⎠⎞
⎜⎝⎛
⎟⎠⎞
⎜⎝⎛= ∑
+∞
−∞= Xnxin
nπ2exp
2sinc
0≠n
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Diffracted spectrum from binary phase grating
1( )xt X
x
–1
1( ) uT
1/X
u
0
⎟⎠⎞
⎜⎝⎛
2sinc n
ℑ ℑ
⎟⎠⎞
⎜⎝⎛ −⎟
⎠⎞
⎜⎝⎛= ∑
+∞
−∞= Xnun
nδ
2sinc
0≠n
⎟⎠⎞
⎜⎝⎛
⎟⎠⎞
⎜⎝⎛= ∑
+∞
−∞= Xnxin
nπ2exp
2sinc
0≠n
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Fourier-plane diffraction from finite binary phase grating
f f
(x” not to scale)
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The Fresnel Zone Plate (FZP)
( )⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛+=
fryxgλ
π2
cossgn121,
( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛=
fryxgλ
π2
cossgn,
amplitude FZP:
phase FZP:
22 yxr +=
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Field diffracted from the FZP
monochromatic, coherentplane wave illumination
0th order (DC):plane wave
(amplitude FZP only)
–1st order:converging,
focal point at f
–3rd order:converging,
focal point at f/3
+1st order:diverging,
focal point at –f(virtual)
+3rd order:diverging,
focal point at –f/3(virtual)
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FZP relationships
2fmrm
λ=
mfrr mmm 22
λδ ≈−≡ −
mth zone radius
mth zone width
x”
zonelast of width
22.1widthhalf lobemain PSF
∝
≈−Mfλ
–1st diffraction order, assuming FZP radius = rM: