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

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

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

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?

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

`

Chandra

B1

B2

B3

B1

B2

B3

B4

P

Q

Q’P’

(a) (b)

Radiative transfer between walls in an enclosure

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)

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

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)

the string method

ϑ

2D concentrator with acceptance (half) angle ϑ

absorbing surface

slider

string

the string method

the string method

the string method

the string method

stop here, because slope becomes infinite

the string method

the string method

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)

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 !

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

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

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

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 .

Nonimaging Optics 24

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.

Nonimaging Optics 25

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.

Nonimaging Optics 26

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.

Nonimaging Optics 27

Nonimaging Optics 28

BRIGHTER THAN THE SUN

an experiment on the roof of the U of C HEP Building

Roof top Physics

Ultra High Flux Experiment

Heat sink

Solar cell on heat spreader

Secondary mirror

Primary mirror

PMMA cover

3D Rendering of Our New Design

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

Dimensions (in mm)

PALO ALTO WATERSolFocus Array

39

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

With Apologies to Benny Goodman

It don’t mean a thingIf it doesn’t have Sin θ=n/√C

Sarah Kurtz and Jerry Olson, Dan David Laureates 2007