Technical Data
Factors Influencing the Optical Efficiency
of Fresnel Lens Concentrators
Introduction
Draft Angle
In the production of Fresnel lens solar concentrators,
several factors influence the theoretical design efficiency
- this technical bulletin describes those factors and 3M’s
approach to measure the effect of the factors on overall
expected lens efficiency.
Losses due to the unused (draft) facet for several draft
angles are illustrated in the following graph. The ideal case
of 0° draft angle is difficult to meet in lens production.
Lens Efficiency (%)
Fresnel Losses
Fresnel losses are due to fresnel reflections from the
air/acrylic interfaces.
0.90
0.88
0 degree draft
2 degree draft
4 degree draft
0.86
0.7
0.9
1.1
1.3
F Number (µm)
1.5
1.7
1.9
Facet Corner Rounding
f/#2
0
f/#1
40
20
60
80
100
120
The blue line shows reflective losses at discrete radial
positions and cumulative lens losses, in red, for a 100 mm
focal length lens.
95%
94%
93%
92%
91%
90%
89%
88%
0.7
0.9
1.1
1.3
1.5
1.7
1.9
94%
92%
90%
88%
86%
84%
82%
0 µm Radius
3 µm Radius
10 µm Radius
80%
78%
200 mm Focal Length
400 mm Focal Length
76%
0.5
87%
86%
85%
0.5
Facet corner rounding is an indication of replication fidelity.
It is difficult in most molding processes to get high fidelity
replication with the fast cycle times required to produce
lenses at low cost.
Lens Efficiency (%)
50%
40%
30%
20%
10%
0%
0.92
0.84
0.5
Cumulative Loss – Square Lens
Cumulative Loss – Circular Lens
Single Point Loss
Radial Position (mm)
Lens Efficiency (%)
Data for all charts
were generated at a
wavelength of 630 nm
for an acrylic lens.
Calculations are based
on square lenses, with
the f/# based on the
diagonal length of
the lens.
Reflective Loss (%)
100%
90%
80%
70%
60%
0.94
2.1
F Number
This graph shows lens throughput as a function of
f/# (focal length/diameter) for two different lens designs.
The relationship between f/# and reflective losses is
relatively unaffected through large changes in lens size and
focal length.
0.7
0.9
1.1
1.3
F Number (µm)
1.5
1.7
Losses due to the rounding of facet corners, assuming
that no light from a rounded corner reaches the target,
are illustrated in the above graph.
1.9
3M™ Solar Concentrator Lens Panels
Absorption
Lens Panel Spectral Absorption
100%
90%
Optical Transmission (%)
Note: The following
technical information
and data should
be considered
representative or
typical only and
should not be used for
specification purposes.
Shown at right are absorption and fresnel losses through
the center of an acrylic Fresnel lens panel. The short
wavelength cutoff is dependent on the amount of UV
protection required. The other absorption peaks are typical
of acrylics.
80%
70%
60%
50%
40%
30%
20%
10%
0%
0
200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400
Wavelength (nm)
Production Results
3M has constructed a production scale quality control
system for measuring fresnel lens efficiency. This
system scans a collimated light source across the lens
aperture, measuring transmission at discrete points.
Focal position, aperture size, and sampling resolution
are adjustable.
Wavelength: 630 nm
Spot Size: 5 mm diameter
Aperture: 25 mm in focal plane
Results in the graph below, from a production lens,
show that the best measurements at any radial position
are within a few tenths of a percent of the maximum
throughput predicted by modeling that takes into account
Fresnel losses, draft angle, and vertex rounding.
Modeling based on a target design including a minimum
draft angle and anticipated facet corner rounding is
sufficient to predict lens efficiency at a single wavelength
to better than 1% accuracy.
Error Analysis
300
250
Frequency
Lens Efficiency (% of Incidence)
Measured vs. Modeled Lens Throughput
Measured
Modeled
200
150
100
50
0
Radial Distance from Center
0
0.4
0.8
1.2
1.6
Relative Error (%T:Modeled-Measured)
2.0
For more information on our solar manufacturing product line, contact 3M Renewable Energy at 800-755-2654 or visit us at www.3M.com/solar.
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3
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