nonimaging optics - unlimited opportunities! — school of engineering
TRANSCRIPT
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Nonimaging optics departs from the methods of traditional optical design by instead developingtechniques for maximizing the collecting power of illumination elements and systems. Nonimaging
designs exceed the concentration attainable with focusing techniques by factors of four or more andapproach the theoretical limit (ideal concentrators).
Roland WinstonSchools of Engineering & Natural Science
University of California, Merced
Thermodynamically efficient
NONIMAGING OPTICSDan David Symposium
UC MERCEDSeptember 26, 2008
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Limits to Concentration
• from λ max sun ~ 0.5 μ we measure Τsun ~ 6000° (5670°)
• Then from σ T4 - solar surface flux~ 58.6 W/mm2
– The solar constant ~ 1.35 mW/mm2
– The second law of thermodynamics– C max ~ 44,000– Coincidentally, C max = 1/sin2θ
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1/sin2θ Law of Maximum Concentration
Nonimaging Optics 3
• The irradiance, of sunlight, I, falls off as 1/r2 so that at the orbit of earth, I2 is 1/sin2θ xI1, the irradiance emitted at the sun’s surface.
• The 2nd Law of Thermodynamics forbids concentrating I2 to levels greater than I1, since this would correspond to a brightness temperature greater than that of the sun.
• In a medium of refractive index n, one is allowed an additional factor of n2 so that the equation can be generalized for an absorber immersed in a refractive medium as
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During a seminar at the Raman Institute (Bangalore) in 2000,Prof. V. Radhakrishnan asked me:How does geometrical optics know the second law of thermodynamics?
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First and Second Law of ThermodynamicsNIO is the theory of maximal efficiency radiative
transferIt is axiomatic and algorithmic based
As such, the subject depends much more on thermodynamics than on optics
`
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Chandra
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B1
B2
B3
B1
B2
B3
B4
P
Q
Q’P’
(a) (b)
Radiative transfer between walls in an enclosure
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Strings 3-walls
1
2
3
qij = AiFij
Fii = 0
F12 + F13 = 1F21 + F23 = 1 3 EqsF31 + F32 = 1
Ai Fij = Aj Fji 3 Eqs
F12 = (A1 + A2 – A3)/(2A1)
F13 = (A1 + A3 – A2)/(2A1)
F23 = (A2 + A3 – A1)/(2A2)
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Strings 4-walls
1
2
3
456
F14 = [(A5 + A6) – (A2 + A3)]/(2A1)F23 = [(A5 + A6) – (A1 + A4)]/(2A2)
F12 + F13 + F14 = 1F21 + F23 + F24 = 1
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Limit to Concentration
F23 = [(A5 + A6) – (A1 + A4)]/(2A2)• = sin(θ) as A3 goes to infinity• This rotates for symmetric systems• To sin 2(θ)
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the string method
ϑ
2D concentrator with acceptance (half) angle ϑ
absorbing surface
slider
string
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the string method
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the string method
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the string method
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the string method
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stop here, because slope becomes infinite
the string method
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the string method
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Edge-ray wave front
BB’
A’ A
C
ϑ===
+=+
sinA'AACBB'ABAB'
Α'ΒΒΒ'ΑCΑΒ'
ϑ=→ sin/'BB'AA
Nonimaging Optics FundamentalsThe Edge-Ray Principle
ϑ
Compound Parabolic Concentrator (CPC)
(tilted parabola sections)
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Edge-ray wave front
BB’
A’ A
CNonimaging Optics Fundamentals
The Edge-Ray Principle
ϑ 2D étendue = A’A sin ϑ
2D étendue = B’B sin(π/2) = B’B
ϑsin/'BB'AA =→
concentration limit in 2D !
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21
sliderϑ
tubularlight source
R
2D cylindrical optics: nonimaging optics basics: the string
method
kind of “involute”of the circle
étendueconserved ideal design!
2πR/sinϑ
example: collimator for a tubular light source
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Availability of Solar Flux over a range 1 – 105 Suns
Solar Furnace, Materials, Lasers, Space Propulsion, Experiments
2 axis trackingConc.= 20,000 –100,000
Power generationHigh CPV
2 axis tracking (dish&tower)
Conc.= 500 -10,000
Power generation, Heating&Cooling, Low CPV
1 axis tracking and seasonal
Conc.= 4 -150
Heating&Cooling, PV
FixedConc.= 1 - 4
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Analogy of Fluid Dynamics and Optics
Nonimaging Optics 23
fluid dynamics optics
phase space (twice the dimensions of
ordinary space )
general etendue
positions positions momenta directions of light rays
multiplied by the index of refraction of the medium
incompressible fluid volume in “phase space” is conserved
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Imaging in Phase Space
• Example: points on a line.– An imaging system is required to
map those points on another line, called the image, without scrambling the points.
• In phase space– Each point becomes a vertical
line and the system is required to faithfully map line onto line .
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Edge-ray Principle
• Consider only the boundary or edge of all the rays.
• All we require is that the boundary is transported from the source to the target.– The interior rays will come along . They
cannot “leak out” because were they to cross the boundary they would first become the boundary, and it is the boundary that is being transported.
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Edge-ray Principle
• It is very much like transporting a container of an incompressible fluid, say water.
• The volume of container of rays is unchanged in the process. – conservation of phase space volume.
• The fact that elements inside the container mix or the container itself is deformed is of no consequence.
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Edge-ray Principle
• To carry the analogy a bit further, suppose one were faced with the task of transporting a vessel (the volume in phase-space) filled with alphabet blocks spelling out a message. Then one would have to take care not to shake the container and thereby scramble the blocks.
• But if one merely needs to transport the blocks without regard to the message, the task is much easier.
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Nonimaging Optics 28
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BRIGHTER THAN THE SUN
an experiment on the roof of the U of C HEP Building
Roof top Physics
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Ultra High Flux Experiment
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Heat sink
Solar cell on heat spreader
Secondary mirror
Primary mirror
PMMA cover
3D Rendering of Our New Design
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Features of Our New Design
Light impinging on the primary mirror is not focused onto the cell, but onto the secondary mirror
This results in a uniform cell illumination with an average concentration of 500 suns
Primary mirror
Secondary mirror
Light radially distributed along cell
Focal ring on secondary mirror
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Dimensions (in mm)
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PALO ALTO WATERSolFocus Array
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0
1
2
3
4
5
6
7
8
0 200 400 600 800 1,000 1,200 1,400
Accep
tance half‐angle [degrees]
Geometrical concentration
Optical Performance Comparison of Various CPV Designs (1)
Theoretical limit (n=1.5; 60° exit angle)
Theoretical limit (n=1; 60° exit angle)
Dielectric TIR Aplanat (circular)
XR (circular)
Two aplanatic (air filled) mirrors + prism
Two aplanatic (glass filled) mirrors
Fresnel lens without secondary
AR=0.6AR=0.3
AR=0.3
AR=1.9
AR ... Aspect ratio (depth/aperture diameter)
AR=0.3
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With Apologies to Benny Goodman
It don’t mean a thingIf it doesn’t have Sin θ=n/√C
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Sarah Kurtz and Jerry Olson, Dan David Laureates 2007