Freeform Optics – Controlling Illumination Distribution
Melissa N Ricketts1, Roland Winston1,2, Vladimir Oliker3
1School of Natural Sciences, UC Merced
2School of Engineering, UC Merced
3Mathematics Department, Emory University
ABSTRACT
Light pollution is a serious problem in our world. In Yosemite National Park, it is very important to minimize the disturbance to the wildlife,
specifically with artificial lighting. The ability to control light and eliminate light spillage is highly desired. Special freeform optical lenses and mirrors
can be used for this purpose. Freeform optics is a relatively new field that addresses the methods necessary to describe surfaces lacking symmetry,
and/or surfaces that create non-symmetrical irradiance distributions. These surfaces are ideal for the prescribed irradiance problem. The Supporting
Quadrics Method (SQM) developed by Oliker uses an envelope of quadrics to create prescribed irradiance distributions. A single quadric can take
incoming parallel light and focus it to a pixel on a target plane. Quadrics can be combined, and their envelope becomes a lens used to make up an
image on the target plane with a 1:1 ratio of pixels to quadrics. Using SQM, we will generate prototype freeform optics to implement in Yosemite
National Park. These lighting demonstrations will not only improve the park lighting efficiency by using the latest LED technology, but also
incorporate freeform optics to control the light, and thus decrease light pollution.
Background: Light Emitting Diodes
Yosemite National Park
Freeform Optics
• When LEDs emerged as a competitor they boasted 45-80 lm/W
• Now, the record holder is 303 lm/W
• They have become the best lighting option for replacements – high
efficiency, high light output, color control, tune-able
Freeform Optics: Optical systems that do not adhere to prior imposed symmetry constraints or that require
nonsymmetrical irradiance output distributions.
# of photons
Freeform Optics
Light Distribution in Light Tools
SQM: Supporting
Quadrics Method
2.0mm
Lambertian Distribution
3.5mm
Direct Optimization
• LED light does not have a direction
• LEDs possess a Lambertian Distribution
Half Dome
Target Flux Mapping
SMS: simultaneous
multi-surface
• The LED distribution curve is that of Cosθ
Supporting Quadrics Method (SQM)
Background: Prescribed Irradiance
A quadric is a D-dimensional surface defined by an equation of the second degree ( paraboloid, ellipsoid,
hyperboloid, etc)
• Light pollution in National parks has a division devoted to studying and maintaining natural levels of light in the parks.
• A significant amount of lighting in Yosemite is not only very outdated thus inefficient but also possess no distribution
control over where the light goes.
• The light pollution can have a drastic effect on surrounding wildlife which is often more sensitive to lighting as well as
campers and nature enthusiasts who visit places like this to see the night skies.
The ‘z-Sag’ defines the surface of a quadric:
• In nonimaging optics, a central challenge for optical systems design is controlling the output irradiance with lenses and mirrors.
A majority of Yosemite’s lighting is outdated, installed in the 1980s.
Parallel incoming light incident on the hyperboloid, is sent to point p on the target plane.
• The ability to do this is highly desired, and offers many benefits.
Demonstration Project:
• The prescribed irradiance problem – Transforming a given input irradiance into a prescribed output distribution
• Index of refraction: n
• Freeform optics will be prototyped and retrofitted into several lighting fixtures in the park.
• x is a point on α
Using Freeform Optics
• Comparisons will be made between the control and freeform LED to evaluate lighting
pollution and energy consumption reduction.
• Point p, located on the target plane, is set by
the user .
• The focal parameter f, can be adjusted to
Gray scale Image
increase or decrease the intensity of the light
arriving to p.
Input beam
Target plane
Lens
• Distance to target plane: d
Prescribed Irradiance Pattern
Acknowledgements
Images from [1]
A special thank you to UC Light for providing funding, as well as
UC Solar for its support, and Yosemite National Park for their
collaboration.
References:
A freeform reflector and LED source. Image from [3]
• Two hyperboloid lenses focus to two points p1 and p2
Freeform lens converting light
into the Lena-picture [4]
on a target plane.
• R1 is concave, R2 is neither concave nor convex.
• We work with R1
Freeform lens before and after optimization [5]
• The combination of multiple quadrics makes a single lens R, taking light and prescribing it to the target plane.
A freeform lens and its intensity distribution [6]
• Ray mapping, 1:1, incoming light irradiance is mapped into a prescribed output distribution.
[1] Oliker, Vladimir I. "Controlling Light with Freeform Optics: Recent Progress in Computational Methods for Optical Design of Freeform
Lenses with Prescribed Irradiance Properties." Nonimaging Optics: Efficient Design for Illumination and Solar Concentration XI Conference Proc.
9191.919105 (2014): SPIE.
[2] Oliker, Vladimir. "Differential Equations for Design of a Freeform Single Lens with Prescribed Irradiance Properties." Optical Engineering
53.3 (2014): 031302.
[3] Yang, Bo. “Automating Design of Free-form Optics for LED lighting.” Optical Design & Engineering, SPIE: 2008.
[4] Michaelis, D., P. Schreibner, Chen Li, and A. Brauer. "Construction of Freeforms in Illumination Systems via Generalized Cartesian Oval
Representation." Nonimaging Optics: Efficient Design for Illumination and Solar Concentration VIII 8124.812403 (2011): n. pag. SPIE. Web. 18
Jan. 2015.
[5] Qin, Zong, Kai Wang, Shang Wang, and Sheng Liu. "Energy-saving Bottom-lit LED Backlight with Angle-control Freeform Lens." Renewable
Energy and the Environment Technical Digest (2011). Optics InfoBase: Journal of the Optical Society of Korea, OSA.