The Optics of
Grating Light Valve
Displays
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Contents
„ Crash course in diffraction theory
„ How to measure the width of a hair with a laser pointer
„ How to design a grating light valve (GLV) display
„ Questions and answers (hopefully)
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Diffraction of Light
Maxwell’s equations may be reduced to the
scalar wave equation.
U may be any component of
vectors H and E
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Diffraction of light
Example solutions of the wave equation are
the plane wave and spherical wave:
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Diffraction of light
Light bends or diffracts around edges, and shrinking
the size of an aperture will increase diffraction.
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Diffraction of light
Light bends or diffracts around edges, and shrinking
the size of an aperture will increase diffraction.
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Diffraction of light
Light bends or diffracts around edges, and shrinking
the size of an aperture will increase diffraction.
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The Huygens-Fresnel principle says:
”The light disturbance at a point P arises from the
superposition of secondary waves that proceed from a
surface situated between this point and the light
source.”
Augustin-Jean
Fresnel
Christiaan Huygens
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Diffraction of Light
A mathematical representation of the HuygensFresnel principle:
Spherical wave
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Diffraction of Light
Far away from the aperture, and for small
diffraction angles we may use the Fraunhofer
approximation.
U ( β ) = C ∫ U ( x) exp(ikβ x)dx
S
x
β
S
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Diffraction of Light
Far away from the aperture, and for small
diffraction angles we may use the Fraunhofer
approximation.
U ( β ) = C ∫ U ( x) exp(ikβ x)dx
S
x
β
S
Fourier transform!
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Diffraction of Light
We may now calculate the diffraction from a slit:
⎡ ⎛ kβ a ⎞ ⎤
⎛ kβa ⎞
sin ⎜
sin ⎜
⎟
⎟⎥
⎢
2 ⎠
2 ⎠
⎥
,I = ⎢ ⎝
U= ⎝
⎛ kβa ⎞
⎢ ⎛ kβa ⎞ ⎥
⎜
⎟
⎜
⎟ ⎥
⎢
⎝ 2 ⎠
⎣ ⎝ 2 ⎠ ⎦
2π
k=
2
λ
a
β
Minima for:
β =m
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a
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Babinet’s principle
The diffracted field from an
aperture is the same as from an
obscuration of the same size
and shape
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What is the diameter of a hair?
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Diffraction from a grating light valve
d
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Diffraction from a grating light valve
h
d
⎛ kβ d ⎞
sin ⎜
⎟
4
⎠ 1
U= ⎝
⎛ kβ d ⎞ N
⎜
⎟
⎝ 4 ⎠
∑ [exp(ikβnd ) + exp(ikβ (n +
N
n =1
1
2
)d ) exp(2ikh)]
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The grating equation
mλ
sin β ≈ β =
d
d
Phase difference = an integer number
of wavelengths
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Diffraction from a grating light valve
h
d
2
I
U
4
2
=
= 2 sin (kh)
I0 U0
π
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Diffraction from a grating light valve
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Diffraction from a grating light valve
Angle given by the grating equation
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Diffraction from a grating light valve
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Diffraction from a grating light valve
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How to design a GLV display device
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How to design a GLV display device:
Design targets
„ 1000 pixels, 2000 horizontal resolution
„ 10000 lumen total = 10 lumen per pixel
„ 96 Hz refresh rate => 4 microsecond pixel time
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How to design a GLV display device:
Design constraints
„ Minimum feature size (gaps between ribbons) 0.6 µm
„ Minimum ribbon distance 3 µm gives maximum diffraction
angle and maximum throughput
„ Required yield -> Maximum chip size
„ Available laser light source (Xenon lamp is not powerful
enough)
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Two display principles
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