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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

MIT 2.71/2.710 Optics11/30/05 wk13-b-2

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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MIT 2.71/2.710 Optics11/30/05 wk13-b-3

Digital imagingChargeCoupledDevices(CCDs)

B. Jähne & H. Haußecker, “Computer Vision and Applications,”

Academic Press 2000

MIT 2.71/2.710 Optics11/30/05 wk13-b-4

Digital imagingCMOS

APS=active pixel sensor

microlens arrays improvesensitivity

B. Jähne & H. Haußecker, “Computer Vision and Applications,”

Academic Press 2000

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MIT 2.71/2.710 Optics11/30/05 wk13-b-5

Color

B. Jähne & H. Haußecker, “Computer Vision and Applications,”

Academic Press 2000

MIT 2.71/2.710 Optics11/30/05 wk13-b-6

Color

http://www.dpreview.com/news/0202/02021102foveonx3tech.asp

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MIT 2.71/2.710 Optics11/30/05 wk13-b-7

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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MIT 2.71/2.710 Optics11/30/05 wk13-b-9

Improved color: the Foveon

http://www.dpreview.com/news/0202/02021102foveonx3tech.asp

MIT 2.71/2.710 Optics11/30/05 wk13-b-10

Light modulation

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MIT 2.71/2.710 Optics11/30/05 wk13-b-11

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

MIT 2.71/2.710 Optics11/30/05 wk13-b-12

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

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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

MIT 2.71/2.710 Optics11/30/05 wk13-b-14

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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MIT 2.71/2.710 Optics11/30/05 wk13-b-15

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)

MIT 2.71/2.710 Optics11/30/05 wk13-b-16

Bleaching / phase modulation

emulsion

exposure

tanning bleach(relief grating)

non-tanning bleach(index grating)

( )zyx ,,ε∆

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MIT 2.71/2.710 Optics11/30/05 wk13-b-17

Spatial Light Modulators

• Liquid crystals• Magneto-Optic• Micro-mirror• Grating Light Valve• Multiple Quantum Well• Acousto-Optic

MIT 2.71/2.710 Optics11/30/05 wk13-b-18

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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MIT 2.71/2.710 Optics11/30/05 wk13-b-19

Micro-mirror technology

Texas Instruments DMD/DLP

Lucent (Bell Labs)

Sandia

MIT 2.71/2.710 Optics11/30/05 wk13-b-20

Micro-mirror display

http://www.howstuffworks.com

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MIT 2.71/2.710 Optics11/30/05 wk13-b-21

Micromirrors for adaptive optics

Véran, J.-P. & Durand, D. 2000, ASP Conf. Ser 216, 345 (2000).

MIT 2.71/2.710 Optics11/30/05 wk13-b-22

Grating Light Valve (GLV) display

Silicon Light Machines, www.siliconlight.com

www.meko.co.uk

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MIT 2.71/2.710 Optics11/30/05 wk13-b-23

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

MIT 2.71/2.710 Optics11/30/05 wk13-b-24

Binary Optics: binary grating

0

1( )xtAmplitude maskAmplitude mask X

x

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MIT 2.71/2.710 Optics11/30/05 wk13-b-25

Binary Optics: binary grating

( ) ( )[ ]xixt φ exp=

–1

1( )xtPhase maskPhase mask X

0

π( )xφ X

x

x

MIT 2.71/2.710 Optics11/30/05 wk13-b-26

Fourier series for binary phase grating

1( )xt X

x

–1

⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛= ∑

+∞

−∞= Xnxin

nπ2exp

2sinc

0≠n

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MIT 2.71/2.710 Optics11/30/05 wk13-b-27

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

MIT 2.71/2.710 Optics11/30/05 wk13-b-28

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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MIT 2.71/2.710 Optics11/30/05 wk13-b-29

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

MIT 2.71/2.710 Optics11/30/05 wk13-b-30

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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MIT 2.71/2.710 Optics11/30/05 wk13-b-31

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

MIT 2.71/2.710 Optics11/30/05 wk13-b-32

Fourier-plane diffraction from finite binary phase grating

f f

(x” not to scale)

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MIT 2.71/2.710 Optics11/30/05 wk13-b-33

The Fresnel Zone Plate (FZP)

( )⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛+=

fryxgλ

π2

cossgn121,

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=

fryxgλ

π2

cossgn,

amplitude FZP:

phase FZP:

22 yxr +=

MIT 2.71/2.710 Optics11/30/05 wk13-b-34

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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MIT 2.71/2.710 Optics11/30/05 wk13-b-35

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: