Retroreflectors are optical components (or systems) in which the reflected rays are preferentially returned in directions close to the opposite of the direction of the incident rays, and with this property being maintained over wide variations in the direction of the incident rays. Two basic types of retroreflectors are the cat’s eye reflectors and the cube corner reflectors [1
T. W. Liepmann, “How retroreflectors bring the light back,” Laser Focus World
30, 129–132 (1994).
]. The cat’s eye reflectors typically consist of a primary lens with a secondary mirror located at the focus of the primary. The cube corner reflector, on the other hand, normally consists of three mutually perpendicular planar surfaces.
These two types of reflectors displace incoming and reflected rays, and they can be mass fabricated by, for instance, using glass beads embedded in a mirrored background or embossing microprisms into polymers. One distinction between the two, however, is that light is brought to a focus in the cat’s eye design, whereas the light traveling through a cube corner reflector is not. Since these two types of reflectors are so common their optical properties have been thoroughly investigated [2
R. Beer and D. Marjaniemi, “Wavefronts and construction tolerances for a cat’s-eye retroreflector,” Appl. Opt.
5, 1191–1197 (1966). [CrossRef] [PubMed]
G. H. Seward and P. S. Cort, “Measurement and characterization of angular reflectance for cube-corners and microspheres”, Opt. Eng.
38, 164–169 (1999). [CrossRef]
]. We have found no reference in the literature describing in detail the process of manufacturing microstructured retroreflectors, However, reference [7
] describes a double sided, bi-convex optical element in glass that could be used for retroreflecting applications, although short focal lengths is not easily obtained with this process. Typical applications for retroreflectors include increasing the visibility of traffic control devices, enhance detection in measurement systems or act as reflecting units in optical communication equipment.
Primarily a retroreflector has four appreciated properties: retroreflectance, brilliancy, divergence and angularity. Figure 1
attempts to illustrate three of these characteristics. Retroreflectance is defined as: The ratio of the reflected radiant or luminous flux to the incident flux within the narrow confines of incident and reflected geometrical conditions [8
Publication CIE 54.2-2001, Retroreflection: Definition and measurement, ISBN 3 900 734 992 (Commission Internationale de L’Eclairage, 2001).
]. Brilliancy is the term used for the reflected flux at certain observation angles, and it is normally given by the coefficient of retroreflection RA
), while the divergence is a measure of the maximum angular distribution of the reflected flux. The brilliancy (reflectance per steradian) is derived from the ratio of retroreflected luminance (lumens per steradian per square meter) to the illuminance (incident lumens per square meter). The unit reflectance per steradian is equivalent to candelas per lux per square meter. Angularity is a measure of brilliancy at various angles of incidence, where high angularity refers to the allowance of large entrance angles (and low angularity to the opposite situation).
In general, three main criteria are to be fulfilled for a successful retroreflector; it should allow large entrance angles (high angularity), it should reflect as much light as possible within a confined cone of light (high retroreflectance, high brilliancy and low divergence), and it should be manufacturable at low cost. Existing retroreflectors typically fall short in one or several of these criteria: Spherical ball retroreflectors for example, generally suffer heavily from high divergence through spherical aberration. Cube corner retroreflectors are technically advanced to manufacture and are thereby expensive.
In this work we present a type of micromachined retroreflector of cat’s eye type [9
L. Danielsson and S. Niemann, “Optical microrelief retroreflector”, International Publication Number WO 95/34006, Dec. 14, 1995.
], which can be designed to steer the four parameters mentioned over a wide range. By simply adjusting the distance between a primary spherical lens and a secondary spherical mirror we demonstrate how the brilliancy can be optimized for a given observation angle. The observation angle is the angle between the illumination axis and the observation axis, see Fig. 1
. This is also the main focus of the paper, to highlight the design possibilities of the concept.
The paper consists of the following parts: In Section 2 we describe the optical system, and we analyze three different designs of our retroreflector. Section 3 outlines the fabrication method we have devised, and Section 4 presents measurement data of a fabricated retroreflecting sheet. Finally, in Section 5, we summarize the findings.
Fig. 1. Illustration of the properties retroreflection, brilliancy, and divergence. Retroreflectance R is defined as the ratio of the reflected luminous flux to the incident flux within the narrow confines of incident and reflected geometrical conditions. Brilliancy is the term used for the reflected flux at certain observation angles, e.g. 0.2°, and it is normally given by the coefficient of retroreflection RA
(cd/lux/m2), while the divergence is a measure of the maximum angular distribution of the reflected flux.
2.1 Background theory
The basic principle of the retroreflecting geometry is shown in Fig. 2
. The sheeting material consists of a front layer of densely packed convex spherical microlenses, and a back surface of densely packed concave spherical micromirrors. Depending on the needed desired optical properties, the transparent spacer layer may or may not have a thickness equal to the focal length of the lenses. A lens and its corresponding mirror form one retroreflective element. The lens and mirror have essentially coinciding optical axes and a common aperture diameter.
Retroreflection is achieved as follows: Parallel light, incident at angle β, is refracted in the lens and paraxially focused in the plane of the reflecting mirror. This assumes the thickness to be equal to the focal length of the lens. The mirror reflects the paraxial rays symmetrically to the illumination axis. The light refracts at the lens surface and leaves the element in a direction essentially antiparallel to the incident light. The arrangement facilitates rays that enter the lens perpendicular to the surface, i.e., along the illumination axis, to retroreflect without any angular displacement. Rays that fail to leave the element along the illumination axis are referred to as diverging beams. How much of a diverging beam is acceptable is depending on the application, but normally one finds specifications for 0.2°, 0.33°, 0.5°, 1.0°, 1.5°, or 2.0°. For traffic control devices divergence within 0.2° to 0.5° is most commonly used.
The design permits five degrees of freedom; the curvature radius of the focusing lens Rl
, the curvature radius of the mirror Rm
, the aperture diameter d
of the lens and the mirror, the distance t
between a lens and its corresponding mirror, and the refractive index n
of the spacer material. However, in order to achieve a paraxial retroreflection as described above, four of the five properties are depending on each other. If one assumes that the distance t
is the same as the paraxial focal length of the lens, the focal length is determined by the lens curvature R1
and the refractive index n
. With air as surrounding medium, a first order approximation yields [10
E. Hecht, Optics , 4th Edition, (Addison Wesley Longman Inc., Reading, MA, 2002), Ch. 5 and 11.
In order to keep the paraxial focus at the mirror surface independent of incidence angle, the mirror must have its equivalent center of curvature in the center of the corresponding lens. This implies
Combining Eqs. (1
) and (2
The aperture diameter d is the only property that can be varied without displacing the paraxial focus. However, since the lens is spherical, spherical aberration will become more evident when using a large aperture diameter.
Fig. 2. Working principle of the sheeting material. The left part of the cross-section shows how the two spheres have a common center of curvature. The right part exemplifies the ray path through an element. Rl
denotes the radius of curvature for the lens, Rm
is the radius of curvature for the mirror, d is the aperture diameter, t is the total thickness, n is the refractive index of the spacer material, and β is the incidence angle of the light. It is assumed that n>1.
2.2 Design considerations
Using the proposed design, there is a trade-off between minimizing the divergence and enhancing the retroreflectance, and on the other hand optimizing the angularity. For example, the maximum entrance angle for retroreflection occurs when the paraxial focus strikes the edge of the spherical mirror. A smaller distance t, in proportion to the aperture diameter d, will give a better angularity and a larger maximum entrance angle for retroreflection. However, the divergence can be suppressed and the retroreflectance at small observation angles enhanced, by minimizing the spherical aberration in the retroreflective elements. This is achieved by choosing a larger distance t in proportion to the aperture diameter d.
In Fig. 3
this trade-off dilemma is apparent. The figure shows the calculated retroreflectance within a 2° divergence (the largest value normally found in applications), as well as the observed maximum divergence, as a function of the ratio t/d
in the design. In this case retroreflectance R
for one element is defined as the ratio between the light entering the lens and the light leaving the lens. It can be seen how the spherical aberration, and thereby the divergence, is more evident for designs allowing for larger angles of incidence. In order to attain high retroreflection and low divergence a higher ratio t/d
has to be chosen.
Fig. 3. Different designs with respect to the ratio t/d give the elements different retroreflective properties. This theoretical figure depicts the change in retroreflectance R with less than 2° divergence (open circles) for white light at 0° entrance angle, as well as change in maximum divergence in degrees (closed circles), when the ratio t/d is varied. Also, corresponding maximum entrance angle β for retroreflection is plotted for completeness. The inserted figures show a geometrical picture of the different designs. The maximum entrance angle β occurs when the paraxial focus strikes the edge of the spherical mirror. Note that when translating the maximum entrance angle (top x-axis) into corresponding t/d ratio (bottom x-axis), these values are plotted as categories rather than actual numbers. Hence, the distance between the scale marks on the bottom x-axis is not equidistant in terms of t/d values.
The data in Fig. 3
is obtained from a ray trace software [11
] with the following parameters; one element is illuminated with white light at an entrance angle β
of 0° and with Rl
equal to 380 µm and 620 µm respectively. The distance t
is 1000 µm. The refractive index is dispersive; 1.61 at a wavelength of 400 nm, and 1.57 at a wavelength of 650 nm. The information in Fig. 3
was extracted from knife edge distribution simulations (as described in Sec. 2.3). The maximum divergence is given by the value where the relative energy is 0 and 1 respectively. The retroreflectance within 2° divergence was calculated by integrating the reflected energy limited by -2° and +2° divergence and comparing it with the incident energy.
This is a commercial software and no access was given to the full nature of the software code, therefore it was only used as a tool to see how the variation of different properties affected the optical outcome. The program simply counts rays entering and leaving the optical setup, thus no corrections were made for reflection or absorption losses (Fresnel losses) etc.
2.3 Case studies
To further exemplify the wide spectra of optical properties offered by the design concept, three case studies are presented below. All examples are based on ray tracing with the same parameters as used for Fig. 3
, except for the entrance angle that is varied from 5° up to the maximum entrance angle for retroreflection for that particular design. The accompanying figures are presented in terms of knife-edge distribution, which is the normalized summation of light energy across a line (with infinitesimal width, the position is in degrees) as this is scanned from minus infinity to plus infinity, i.e., it is the normalized integral of the line spread function [10
E. Hecht, Optics , 4th Edition, (Addison Wesley Longman Inc., Reading, MA, 2002), Ch. 5 and 11.
The slope in the knife-edge distribution curve corresponds to the amount of light energy being confined in a certain angle interval. For example, if one assumes an observation angle 0.5° it is the angle interval ±0.5° from the 0° position that is of interest. The optical system is described in a right-handed coordinate system in which the incident light is traveling along the positive z-axis. In order to achieve an entrance angle >0° (in the ray tracing software) the retroreflective element is rotated around the x-axis.
2.3.1 Geometry with t/d=1.32
In certain applications high angularity is appreciated. The ratio t/d
=1.32 admits the lens to attain the shape of a hemisphere. The design allows for a retroreflection almost without deterioration up to the maximum entrance angle for retroreflection, which in this case is about 37°. However, using this design the divergence is large due to spherical aberration. The details are shown in Fig 4
. At entrance angles close to the maximum entrance angle for retroreflection some of the spherically aberrated rays fail to strike the spherical mirror. This causes less divergence in the negative y-direction and a lower retroreflectance, cf. Fig. 4
Fig. 4. Theoretical knife edge distribution curves depicting the relative energy for white light along the x- and y-axis as a function of position (in degrees) for a design with t/d=1.32. The optical system is described in a right-handed coordinate system in which the incident light is traveling along the positive z-axis. The retroreflectance R is about 1.0 (all of the light entering the lens is retroreflected back) for entrance angle β of 5°, and about 0.8 for entrance angle of 37°.
2.3.2 Geometry with t/d=3.13
If spherical aberration could be avoided a retroreflector with zero divergence would be possible. A way to diminish the spherical aberration is to use a design with a large t/d
, concentrating more of the active lens area to the paraxial region. In Fig. 3
it can be seen that the divergence for t/d
=3.13 is much less than for the t/d
=1.32 design. Figure 5
shows the knife-edge distribution given for 5° and 15° entrance angles for an element with t/d
Fig. 5. Theoretical knife edge distribution curves depicting the relative energy for white light along the x- and y-axis as a function of position (in degrees) for a design with t/d=3.13. The optical system is described in a right-handed coordinate system in which the incident light is traveling along the positive z-axis. The entrance angle β is 5° and 15°. Notice that the retroreflectance R for the two cases 5° and 15° are not the same: the ratio of light entering and leaving the lens is drastically reduced at 15°.
Utilizing a design with large t/d
will imply a smaller maximum entrance angle for retroreflection and an evident deterioration of the retroreflectance at large entrance angles. However, the rays that are blocked in such a situation are the marginal rays usually giving rise to the spherical aberration. Hence, even though the retroreflectance of such an element would decrease when increasing the entrance angle, the divergence in the y-direction would diminish, i.e., the retroreflected cone of light becomes elliptic with its minor axis in the y-direction. As seen in Fig. 5
, at entrance angle 15°, much of the incoming parallel light falls outside the extension of the lens after having been reflected. The drop in retroreflectance is quite large; from ~0.8 to ~0.3.
The standardised European passing light beam on a car is characterised by a sharp cut-off in line with the centre of the headlamp [12
Publication CIE 72-1987, Guide to the properties and uses of retroreflectors at night, ISBN 3 900 734 089 (Commission Internationale de L’Eclairage, 1987).
]. The cut-off line is horizontal on the left-hand side and goes up to 15° on the right hand side (or reverse in countries with left-hand traffic). Therefore, the maximum angle with which a traffic control sign will be illuminated, is something like 15°.
2.3.3 Color selective properties
Colored retroreflective sheeting illuminated with white light implies filtering of the light. This method does not only filter out the unwanted wavelengths but also a great part of the preferred ones. Using the applied design it is possible to suppress or bring out specific wavelengths within certain intervals of observation angles. Figure 6
shows the knife-edge distribution for an element with t/d
=3.13 illuminated with light of wavelength λ=405 nm and λ=546 nm. The spacer material is dispersive (refractive index n
of about 1.61 at a wavelength of 405 nm, and 1.58 at a wavelength of 546 nm) and therefore gives rise to chromatic aberration within the element.
If this particular sample, which has a focal distance optimized for blue reflection, were to be illuminated with white light the retroreflected light would appear bluer at smaller observation angles and more green/red at larger observation angles. An element with larger aperture diameter would preserve the property of enhancing blue color at small observation angles. However, the effect of bringing out green/red at larger observation angles is then slightly weakened. Using an element design admitting large spherical aberration, the outermost light in the retroreflected light cone would appear bluish. In order to experience this effect, the lenses must possess a very accurate sphericity.
Fig. 6. Theoretical knife edge distribution curves depicting the relative energy along the x- and y-axis as a function of position (in degrees) for a design with t/d=3.13. The optical system is described in a right-handed coordinate system in which the incident light is traveling along the positive z-axis. The entrance angle β is 5°. Illumination with light of two different wavelengths (405 nm and 546 nm) gives rise to different divergence properties. The retroreflectance R is about the same for the two wavelengths.
3. Experimental details
The idea with polymer replication is to use the accuracy and small features available from photolithographic processes in combination with production economy from the optical data storage industry (cf. CD/DVD fabrication technology) [13
O. Öhman, H. Sjödin, B. Ekström, and G. Jacobsson, “Microfluidic structure and process for its manufacture,” International Publication Number WO 91/16966, Nov. 14, 1991, and U.S. Patent 5 376 252, Dec. 27, 1994.
]. Typically, a master structure is first produced in silicon or glass with the desired geometry. Electroforming a negative copy of the master then creates a mould insert. Finally, polymer replicas can be produced in large quantities by applying these inserts in different replication methods like injection molding, casting or embossing [14
O. Rötting, W. Röpke, H. Becker, and C. Gärtner, “Polymer microfabrication technologies,” Microsystem Technologies
8, 32–36 (2002). [CrossRef]
Depending on physical and chemical requirements, there is a wide range of thermoplastic and thermosetting/UV-curing polymer materials to select from. In this work we choose to work with casting thermosetting polymers. Based on the refractive index of the chosen epoxy, the design target values were set to be Rl
=380 µm, Rm
=620 µm, d
=666 µm, and t
=1000 µm. The design target values d=620 µm and t=1000 µm were chosen in relation with the anticipated capabilities of the manufacturing process. Based on the refractive index of the epoxy and in accordance with Eqs. 1
, the to radiuses of curvature were calculated to be Rl
=380 µm and Rm
=620 µm. The refractive index is dispersive, and Eqs. 1
is fulfilled only for refractive index 1.61 (at wavelength 400 nm), but not completely for 1.57 (at wavelength 650 nm).
3.1 Fabrication of master structure
The master structure for the lens and mirror sides of the retroreflector were produced by thermal reflow of cylindrically shaped photoresist pads on silicon wafers [15
D. Daly, R.F. Stevens, M.C. Hutley, and N. Davies, “The manufacture of microlenses by melting photoresist,” IOP Short Meetings
30, 23–34 (1991).
T. R. Jay, M. B. Stern, and R. E. Knowlden, “Effect of refractive microlens array fabrication parameters on optical quality,” in Miniature and Micro-Optics: Fabrication and System Applications II, C Roychoudhuri and W B Veldkamp, Eds., Proc. SPIE
1751, 236–245 (1992).
]. Thermal reflow is an advantageous technique in this case since we are to manufacture part of a sphere, and not an aspherical shape frequently used in imaging optics. Heating the wafer forces the molten photoresist (AZ 4562 from Clariant Corp., USA) to attain the shape of a spherical segment since this minimizes the surface energy. The influence of gravitational effects is negligible at these f-numbers. By controlling the thickness of the photoresist layer, and thereby the volume, the radius of curvature could be controlled. In this work the thickness of the photoresist pads were around 50 µm for the mirrors and around 110 µm for the lenses.
Due to the relatively thick resist layers needed, a technique was developed for spinning and baking multiple layers followed by multiple exposure and development cycles. The process was in short: Each silicon wafer is primed with HMDS. The resist is dispensed statically, then spread at 250 rpm for 10 seconds with an open cover spinner (Karl S ss Gyrset RC 8/5 spinner), followed by spinning at 1500 rpm for 4 seconds with closed cover, and finally let to rest on the chuck for 6 minutes. Softbake is performed for 1 min on a 100 °C hotplate, followed by hardbake at 90 °C in an convection oven for 60 min.
The resulting layer thickness is about 25 µm. After the baking process the wafers were let to rehydrate in deionized water for about 20 minutes. The consecutive layers spun on top were each softbaked increasing the time with one minute for every layer. The exposure dose for one cycle was 4 times 540 mJ/cm2, with 60 seconds delay time. Photoresist layers thinner than 50 µm could be exposed and developed in one cycle, however, films exceeding 100 µm had to be developed and exposed up to 4 times. The development times were at room temperature about 45 minutes (in Clariant AZ400k 1:4 developer).
3.2 Replication of retroreflector
The silicon master structures were transferred into two 300 µm thick, metallic counterparts, so called stampers or mould inserts, by electroforming. In this case it was achieved by plating nickel from a sulfamate electrolyte. The silicon wafers were sputtered with a Ti/Ni seed layer prior to electroforming. Obviously, the obtained mould inserts have the negative structure of the originals. The casting of the retroreflector was then done in a cavity being limited by the respective mould inserts for the lens and mirror sides, c.f Fig. 7
. The casting was performed using a polymer that was injected into the cavity by the help of syringes.
Fig. 7. The casting set-up including the mould inserts and the spacer-ring. The casting was performed using a thermosetting epoxy that was injected into the cavity by the help of syringes. The two mould inserts are respectively fixated by steering pins, and the steel plates are equipped with a vacuum pumping capacity pressing the mould inserts flat.
The setup was composed of two steel plates on which the two mould inserts were respectively fixated by steering pins (this required corresponding holes to be drilled holes in the mould inserts). The plates were equipped with a vacuum pumping capacity pressing the mould inserts flat to their respective steel plate. Additional drilling of two more holes in the top steel plate enabled the polymer injection by connecting syringes. In order to achieve the desired thickness of the retroreflector, a spacer-ring was put between the two mould inserts. During the casting, the setup was kept together with the help of clamping devices putting pressure on the two steel plates.
Two critical dimensions had to be controlled; the alignment between the two inserts, as well as the distance between them. The obtained accuracy was determined by the mechanical tolerances of the setup. In this cavity a thermo-setting polymer (Epo-Tek 301-2 from Epoxy Technology Inc., USA) was poured and let to cure at room temperature. This epoxy is transparent for visible light. Finally, the retroreflector was sputtered with silver on its mirror side to attain a reflective surface. Silver was chosen since it has a broad reflectance spectra absorbing very little of the visible light. Figures 8
depict scanning electron micrographs of the lens and mirror side of the polymer retroreflector, respectively.
Fig. 8. Scanning electron micrographs for the lens side of the epoxy retroreflector. The lens aperture diameter is 600 µm, and the sag height 183 µm. The length of the scale bar is 1000 µm.
Fig. 9. Scanning electron micrographs for the mirror side of the epoxy retroreflector. The lens aperture diameter is 610 µm, and the sag height 92 µm. The length of the scale bar is 300 µm.
3.3 Evaluation of lens and mirror geometry
The lens and mirror deviations from a perfect sphere were measured in a Twyman-Green interferometer equipped with a 0.633 µm wavelength HeNe laser. The lens surface error is measured in reflectance mode, and the transmitted wavefront error in transmission mode. Measurements were done on 5 lenses in both modes. The numerical aperture (NA) was restricted to 0.7 in the measurement set-up. For the mirror this was enough, but since the NA of the lens is higher than 0.7 only the center of the lens could be measured; approximately 35% of the diameter in reflection mode, and 75% in transmission mode.
The curvature radius Rl
was found to be 425±2 µm. For the mirror, two different curvature radii were observed. The center is almost spherical with a radius Rm
of 575±1 µm. However, a rim at the mirror edge has a radius of 545 µm. The transmitted wavefront error was found to be within 1 µm for both the lens and the mirror. It is the deviation from a perfect spherical wavefront that is measured, not only in reflectance but also in transmittance mode.
The appearance of two different radii was observed already after the thermal reflow. On every sample a pattern of wrinkles also emerged at the rim, cf. Figures 8
. The wrinkles were about 40 µm long on the lenses while the mirror wrinkles were about 5 µm long. The reason for this phenomenon is believed to be due to a combination of two effects; the gravitational forces will strive to flatten the sphere, while the hydrophobic nature of silicon allows the melted photoresist element to shrink slightly in its base.
The diameter of the photoresist pads was indeed reduced from initially 645 µm before the melting procedure down to 600 µm and 610 µm after the reflow for the lens and mirror spheres, respectively. The result is a combination of two spherical segments with different radii. In fact, we anticipate the lens to have the same geometrical defect. The sag heights were measured in a profilometer (Alpha-Step 500 from KLA Tencor, USA) to be 183 µm for the lens, and 92 µm for the mirror. The fill-factor, i.e. the ratio of area covered by the array of retroreflective elements and the total area, is about 0.75.
Neither the target values of 620 µm and 380 µm in radii were reached, nor the lens and mirror target diameter of 666 µm. The reason for this lies within the manufacturing process, and due to the difficulties no effort was made to optimize these values.
4. Results and discussion
The retroreflection properties were measured at the Swedish National Testing and Research Institute in Borås, Sweden. The measurements were made in accordance to a suggested measurement set-up described in Technical Report 54.2 from Commission Internationale de L’Eclairage (CIE) [8
Publication CIE 54.2-2001, Retroreflection: Definition and measurement, ISBN 3 900 734 992 (Commission Internationale de L’Eclairage, 2001).
]. Two samples were characterized and tested for white light properties (wavelength between 300 nm and 830 nm) with a lamp source obeying CIE standard illuminant A (corresponding temperature 2856 K ±20 K) [17
CIE Standard Illuminants for Colorimetry, joint ISO 10526:1999 / CIE S005/E-1998 standard.
The samples differed in two aspects; sample A has a thickness (distance t) of 1020±10 µm, and exhibited alignment accuracy within ±15 µm. Sample B has a thickness of 1080±10 µm and showed alignment accuracy within ±25 µm. The thickness was measured with a micrometer screw. The target thickness of 1000 µm was almost reached for sample A. Sample B was made thicker so that the focal length of the lenses did not equal the thickness. The alignment accuracy refers to the lens-mirror alignment, and this was measured in a light optical microscope. The lens and mirror aperture diameter and radii of curvature is described in Section 3.3.
shows how the measured coefficient of retroreflection for the two samples at observation angle 0.2° is varying with entrance angle. The observation angle is the angle between the illumination axis and the observation axis. At entrance angles close to zero a peak in the spectra arises as a result of the specular reflection. The difference in reflection between the two samples is due to the variation in thickness between the two samples. However, what is most striking about the two curves is the peak, located for sample A at 15° and for sample B at 20°, and the following drop in brilliancy as the entrance angle increases. Since the paraxial rays are of terminal importance for the retroreflection at small observation angles, a small change in lens and mirror radius of curvature would cause the brilliancy to change considerably. Our explanation of this phenomenon is as follows:
As described in Sec. 3.3, the lens and mirror geometry at the outer, marginal rim is different from the geometry at the vertex. It is the marginal parts of the lenses and the mirrors that refracts and reflects the paraxial rays at large entrance angles. As a consequence, at the entrance angle where the peaks occur, the geometrical conditions for paraxial retroreflection is obviously more favorable. An element ideal in geometry and with corresponding design would retroreflect the paraxial rays independent of entrance angle and is only limited by the maximum entrance angle for retroreflection. It is apparent from Fig. 10
that the maximum entrance angle for retroreflection, approximately 31° in the figure, do not seem to coincide with the theoretical values, which for samples A and B are 28° and 26°, respectively. The aspherical shape of the lenses and the mirrors changes the ideal optical situation and allows retroreflection to occur at higher angles. The misalignment of the lenses and the mirrors could also cause the maximum angle for retroreflection to differ from the theoretically calculated value. At entrance angles larger than the maximum one for retroreflection, only stray light is registered.
Fig. 10. Experimental coefficient of retroreflection RA
for two different samples as a function of entrance angle β (in degrees). Sample A is ~1020 µm thick and sample B is ~1080 µm thick. The observation angle α is 0.2°.
show, for sample A and B, how the brilliancy is varying with the observation angle for a set of entrance angles. The difference in between the two samples is large, a fact that can be attributed mainly to the difference in thickness (and to lesser extent the alignment accuracy). Considering sample A in Fig. 10
, there is a tendency for the brilliancy to decrease with increasing observation angles. This is not true for sample B shown in Fig. 12
. For entrance angles 5° and 10° the brilliancy does not seem to fall off as the observation angle increases. This is a natural effect from the displacement of the paraxial focus admitted by the larger distance t
in sample B. The divergence is larger in an element with the geometry of sample B than for one of A type.
No attempt was made to simulate the actual lens/mirror system and derive a “theoretical” performance that could be compared to the actual measurements results. The reason for this was the limitations found in the ray trace software used.
Benchmarking with tabulated data, the obtained retroreflecting properties of our example sheet are indeed comparable with commercial sheetings, for example 3M Scotchlite™
Reflective Engineer Grade and High Intensity Grade [18
Product Catalog for Traffic Control Materials (3M Traffic Control Materials Division, St. Paul, MN, 2003), http://www.3M.com/tcm.
]. However, since we did not have the opportunity to benchmark these materials in the same measurement set-up, we have to rely on tabulated data. For example, 3M Scotchlite Reflective Engineer Grade is stated, for an observation angle of 0.2°, to have 70 cd/lux,m2 at 4° incidence angle, and 30 cd/lux,m2
at 30° incidence angle. Corresponding values for observation angle 0.5°, 30 cd/lux,m2
at 4° incidence angle and 15 cd/lux,m2
at 30° incidence angle. For 3M Scotchlite High Intensity Grade one has for a observation angle of 0.2°, 250 cd/lux,m2
at 4° incidence angle, and 175 cd/lux,m2
at 30° incidence angle. For observation angle 0.5°, 95 cd/lux,m2
at 4° incidence angle and 70 cd/lux,m2
at 30° incidence angle. Finally, at observation angle 1.0°, 10 cd/lux,m2
at 4° incidence angle and 9.5 cd/lux,m2
at 30° incidence angle. Still, our main objective was not to optimize the performance for these applications but rather to explore the design possibilities.
Fig. 11. Experimental coefficient of retroreflection RA
as a function of observation angle α (in degrees) for a set of entrance angles β (5°, 10°, 20°, 30°) for sample A where t ~1020 µm.
Fig. 12. Experimental coefficient of retroreflection RA
as a function of observation angle α (in degrees) for a set of entrance angles β (5°, 10°, 20°, 30°) for sample B where t ~1080 µm.
Chromaticity measurements (a two-dimensional Cartesian plot that depicts perceived colors) were also performed on sample A [19
Publication CIE 15.2-1986, Colorimetry, 2nd Edition, ISBN 3 900 734 00 3 (Commission Internationale de L’Eclairage, 1986).
]. Two different observation angles were used in combination with incidence angle 0°. For observation angle 0.33° we obtained chromaticity coordinates x=0.452 and y=0.412 (corresponding temperature 2830 K), and at 2° we achieved x=0.499 and y=0.423 (corresponding temperature 2317 K). This verifies the behavior seen in Fig. 6
(at larger observation angles more green light is present compared to blue light), and we should expect less blue at larger observation angles. The coordinate x is the normalized relative intensity of a defined red (increasingly red with increased x-value) and the coordinate y is the normalized relative intensity of a defined green (increasingly green with increased y-value). The normalized relative intensity of a defined blue is obtained by 1-x-y.
The attenuation of the retroreflectance in absolute numbers in a real situation is attributed mainly to absorption and reflection losses. The level is depending on the dielectric properties of the materials used. Attenuation occurs also due to unwanted reflections and scattering, e.g. internal reflections, reflections from the area beside the lenses, scattering due to surface roughness, and scattering due to voids in the epoxy. The fill-factor, i.e. the ratio of area covered by an array of retroreflective elements and the total area, has a theoretical maximum of 0.9 for mirrors and lenses with a circular aperture. A use of hexagonal lenses would increase the fill-factor. Another source of attenuation is geometrical defects such as alignment errors and errors in curvature of the two spherical surfaces.
The accuracy of the thickness and the alignment accuracy of the lens-mirror were given by the manufacturing method. One obvious way to lessen its impact is to make the diameter d
larger. Recent industrial advances in double-sided replication now allows alignment accuracies down to a few micrometers [20
M. Rossi and I. Kallioniemi, “Micro-optical modules fabricated by high-precision replication processes”, in Diffractive Optics and Micro-Optics, Vol. 75 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 2002), pp. 108–110.
]. We therefore believe that our type of retroreflector is suitable for mass production by methods such as embossing or even injection molding. In the latter case the alignment between the two sides will prove a true challenge.
The main objective of this investigation was to study a type of micromachined retroreflector of cat’s eye type. By varying the ratio of distance t between a primary spherical lens and a secondary spherical mirror and the aperture diameter d (i.e. t/d) we have shown that the brilliancy, divergence and angularity can be steered over a wide range. By simply adjusting the distance t we demonstrate how the brilliancy distribution can be chosen to vary in angularity and intensity.
We have also shown that the design permits wavelength selective properties, which gives the possibility to bring out one color (wavelength) while suppressing another at certain observation angles. The effect is greater for a more dispersive substrate material, and for a design reducing any spherical aberration. This is particularly important when making blue colored traffic signs, since traditional methods of applying a blue colored filter over a white reflecting surface also drastically reduces the brilliancy. However, such a wavelength selective design does not accept large entrance angles.
To verify the theoretical model an epoxy sheet sample was fabricated and evaluated. The applied fabrication process is based on double sided replication by casting, but in principle the method is transferable into mass production processes such as injection molding or roll embossing. From an environmental point of view the thermosetting and thermoplastic materials are to be favored, since the high refractive index (metal doped) materials used by some competing technologies are more hazardous.