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18 Janvier 2021
Dielectric mirrors utilize Fresnel reflections at multiple optical interfaces, often with constructive interference of such reflections. Fresnel reflections are essential for the operation principle of birefringent tuners. Figure 1: Effective reflectivity at an air gap between two optical fibers vs. The reflectivity can vanish due to.
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Newly developed tools integrated with commercial illumination software quickly create freeform reflective and refractive surfaces.
JAKE JACOBSEN and WILLIAM CASSARLY
The use of freeform optical elements in illumination applications has received a great deal of attention in recent years. For applications with specific target requirements and relatively compact sources, freeform optics offer the ability to precisely tailor the resulting illumination pattern to meet system requirements, enhance the visual appeal, and improve energy efficiency.
Calculation techniques and the resulting design software have been available for years.1 However, it was only recently that the capability to design freeform surfaces was effectively integrated into a fully capable illumination-design software package. Because of this integration, the design and use of reflective and refractive freeform optical elements has become a practical endeavor for a wide range of illumination applications and designers. The inclusion of a freeform design capability in an illumination-design software package allows the designer to integrate freeform elements with other optical components to build more complex systems, add real sources, and use automated tools to analyze the resulting illumination pattern.
As part of its LightTools illumination design software, Synopsys recently introduced the Freeform Designer as an integrated capability in the software's Advanced Design Module. The Freeform Designer can be used to calculate freeform reflective and refractive surfaces based on an illuminance or intensity target distribution, source collection angle and distribution, and several other geometrical settings. The following examples highlight some practical considerations when designing freeform illumination optics.
The calculation of the shape of a freeform surface is based on a mapping of a known source angular distribution to a desired target distribution. That target distribution can be angular or spatial, depending on the need. If we know the distribution of light on the freeform surface as a function of position on the surface and incoming angle, then we can tailor that surface so that the outgoing light meets the desired target distribution either on a specified surface, or in angle space (see Fig. 1).
| FIGURE 1. Conceptual mapping from a point source to a freeform surface (P) to a set of target points (yn). The surface normals (Pn) are set to send the incident rays to their corresponding target points. The surface is then created using a B-spline surface interpolation.2 |
While this is conceptually simple, implementing it in the general case—where symmetries cannot be assumed—can be complex. Watermelon man 1970. Nevertheless, the problem is tractable, and surfaces can be computed for both simple and complex targets (see Fig. 2).
| FIGURE 2. A freeform lens is designed to project a complex target onto a nearby plane. This is an example of a complex target. |
Inherent in the approach is a one-to-one mapping. Rays incident on a given point of the freeform surface are assumed to have the same angle of incidence. This implies a point source or, alternatively, a collimated source. Rays emitted by an extended source will strike a given point on the freeform surface at different angles and thus will strike the target at slightly different locations (or slightly different angles for intensity targets), causing a blur in the target pattern. The extent of this effect is dependent on the angular size of the source as seen from the freeform surface. Because of this, smaller sources such as LEDs and discharge sources tend to produce less blur.
Since the angular size of the source as seen from the freeform surface directly affects the extent of the blur, a good method for reducing the blur size is simply to place the freeform surface farther away from the source. This reduces the apparent source angular extent, which reduces the target blur. Of course, the tradeoff is that the optic will increase in size.
The mapping method described above is, by its nature, discrete rather than continuous. The surface and target must be broken down into sections so that the resulting surface point grid can be fit with a B-spline surface. The number of points used to describe the freeform surface can have an impact on the fidelity with which the target can be reproduced. We have found that targets without small-scale contrast variations can usually be represented with about 25 × 25 points across the surface. Examples of such targets are uniform and Gaussian distributions (see Fig. 3). In contrast to this, targets with significant high-contrast structure can require a significantly larger number of surface points. Figure 2 shows such a target-for its surface, we used an 85 × 51 grid of points.
| FIGURE 3. A freeform lens with an LED source is designed to produce a wide-angle, elliptical Gaussian distribution. Here, a 25 × 25 grid of points describes the surface, with a calculation time of a few seconds. The resulting intensity distribution is shown on the right. |
While increasing the number of grid points on the surface does increase target resolution, it can substantially increase the amount of time needed to calculate the freeform surface—from much less than a minute in many simple cases to many minutes for complex cases. The times cited here are for a midrange laptop where the calculation algorithm uses a single CPU.
With nearly all illumination systems, one goal is to maximize the throughput of the system. Since most sources emit into a wide distribution, this usually means increasing the size of the freeform surface to increase the collection angle and gather more light. This is an effective approach, but it can have drawbacks.
For a reflective system, increasing the collection angle often causes the returning light to be blocked by the source itself and its support structure. While this may be tolerable with segmented reflectors, the one-to-one mapping used with freeforms will lead to hard shadows in the target pattern. To avoid this, reflective systems are usually designed to be off-axis, sending the returning light past the source on one side. This technique alone may not be sufficient for situations with wide target distributions, where the returning light bundle is diverging, or for wide collection angles, where the returning beam bundle is simply too large. In these cases, the reflector can be configured to cross the rays so that the rays on one side of the reflector are sent to the opposite side of the target. This creates an intermediate focus region. While this usually creates a deeper reflective optic, it also creates more clearance for the source (see Fig. 4).
| FIGURE 4. A rectangular freeform reflector transfers light from an LED to a circular lightpipe. The reflector is designed to cross the rays on the way to the target at the front face of the lightpipe, creating an intermediate focus and allowing the rays to clear the source. |
For refractive surfaces, the collection issue is somewhat different. As with reflective elements, increasing the collection angle increases the size of the optic, but also increases the collected energy. The limitations come when the incident angles at the edge of the optic approach the critical angle. At this point, increasing the collection angle further will cause rays at the edge of the optic to undergo total internal reflection. Even for rays approaching the critical angle but still refracting, the Fresnel losses become significant and require active compensation.
To avoid these problems, but still collect as much light as possible, we can use both the first and second surfaces of the lens. One approach to accomplish this uses a Cartesian oval profile for the first surface and tailors the second surface. Cartesian oval refractive surfaces can perfectly focus light from one point to another point or, in this case, from a point to a virtual focus. With this technique, what we can do is move the source forward from its initial position to a point closer to the freeform surface. We then construct a Cartesian oval surface that causes rays from the new source location to bend, creating a virtual focus at the original source location. In this way, the refracted rays that are then incident on the freeform surface appear to have the same collection angle as before, emanating from the original source location, while the actual collection angle is much higher. To put it another way, we collect more light by making the Cartesian oval surface do some of the work (see Fig. 5).
| FIGURE 5. This image compares two freeform lenses with the same intensity target specification. For both lenses, the rays (in red) at the edge are near the critical angle, indicating that the freeform surface is near the limit of collection. In the left image, the source (shown as a blue sphere) is at the nominal position and has a full collection angle of 100°. In the right image, the first lens surface is a Cartesian oval, and the source has been moved toward the lens, increasing the full collection angle to 140° and enabling the collection of substantially more light. |
The integration of a capability that quickly and easily calculates freeform surfaces in the LightTools design software environment will allow for greater use of freeform optics in illumination by facilitating their design and analysis.
1. R. Wester and A. Bäuerle, Adv. Opt. Technol., 2, 4, 301–311 (2013).
2. L. Piegl and W. Tiller, The NURBS Book, Springer Science & Business Media, Berlin, Germany (2012).
Jake Jacobsen is technical marketing manager and William Cassarly is a scientist at Synopsys, Mountain View, CA; e-mail: jake.jacobsen@synopsys.com; https://optics.synopsys.com.
| http://people.csail.mit.edu/jaffer/FreeSnell | ||||||
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FreeSnell is a program to compute optical properties of multilayer thin-film coatings.
FreeSnell is an application of the SCM Scheme implementation and the WB B-tree database package.
FreeSnell-1c3 is a minor release. Details at http://cvs.savannah.gnu.org/viewvc/*checkout*/freesnell/freesnell/ChangeLog
FreeSnell generates (encapsulated) PostScript graphs for output. If you have ImageMagick and GhostScript installed, then FreeSnell will use the ImageMagick convert program to translate these .eps files to other graphics formats:
You can view the PostScript .eps files with GhostView (Unix gv) or GSview (MS-Windows).
To run FreeSnell in MS-Windows from the C:Program FilesFreeSnell diretory, click on the FreeSnell desktop icon. In Unix, from the FreeSnell directory run scm.
You can then type expressions to the SCM interpreter. To run FreeSnell's regression suites type:
To exit SCM type (exit).
The validation source files are a good source for design examples.
| Refractive Index Spectra. |
| Validation suite of dielectric filters; generated from 'dielectric.scm'. |
| Validation of metallic films; generated from 'metallic.scm'. |
| Validation of granular films; generated from 'granular.scm'. |
| How thick films work in FreeSnell; generated from 'coherence.scm'. |
| Characterizing Polyethylene; generated from 'polyethylene.scm'. |
FreeSnell and SimRoof were originally writtento supportRadiative Cooling in Hot Humid Climates,which employs infrared-transparent cold mirror roof panels.
Another Free-Software thin-film program is OpenFilters:
OpenFilters offers multiple tools for the design and optimization of optical interference coatings, including refinement, the needle method, the step method, the Fourier transform method and multiband rugates. It has the ability to optimize a stack to match a target response.
| I am a guest and not a member of the MIT Computer Science and Artificial Intelligence Laboratory. My actions and comments do not reflect in any way on MIT. | ||
| SCM for Engineering | ||
| agj @ alum.mit.edu | Go Figure! | |
Optical Return Loss (ORL) or Back Reflection may affect fiber optic systems with one or more characteristics:
It is the % of power reflected back in relation to forward power at a particular point in a light path.
Optical Return Loss Meters and Back-reflection Meters make the same measurements.
Scientifically, optical return loss (ORL) is the inverse of reflectance, and has the opposite sign, e.g. -50dB reflectance is 50dB return loss. However, there is a widely conflicting common usage of these and related terms, so unfortunately there is no safe assumption about which is what, so it's best to look for context.
Our definition of return loss is the accumulated % of power reflected back in relation to total forward power at onepoint, typically at an ORL test instrument!
This is usually not exactly the sum of all the individual reflections, due to attenuation in both directions along the light path.
For example if a point somewhere along a fiber link has a reflection of -20 dB, and the fiber attenuation to that point is 10 dB, then the measured return loss contribution due to that point will be -40 dB. (eg the back reflection + 2 x the attenuation)
Back reflection from a particular point and measured return loss may be similar if there is negligible loss between the loss point and ORL meter, and if this loss point is the dominant source of reflected light.
Reflection related system issues can be quite baffling, since loss & power levels check out OK, but data transmission shows excessive errors or degradation.
Sensitivity to reflection often varies widely from transmission unit to unit, which is frustrating. So in a line with poor or average ORL performance, just swapping equipment around may fix the problem. This is actually a genuine practical fix, however it may need recording and tagging.
This also gives a clue: the relationship between ORL and system performance can be vague. It may be good to follow up with an optical margin & BER test.
By convention, test instruments usually display a negative dB ORL number. 0 dB return loss implies a perfectly reflective system. A large negative number implies little reflected power.
The Fresnel formula for a simplified reflection where the incident angle is normal, is (dB units) R =10 x log(((n1-n2)/(n1+n2))2)
The most common glass/air interface is a connector end or inside an opto-electric device. In the case of a mated flat-polish connector with a small air gap, there are two glass / air interfaces, resulting in roughly twice the reflection, eg approximately 11 dB. We have seen systems with high connector density, where the return loss was about 6 dB, which was sufficient to disrupt transmission from a simple 1 MHz analogue signal produced by a LED.
The effect of joining fibers depend on the splicing method. Fusion splicing tends to produce negligible reflections. However mechanical splices can result in high reflection levels, depending on the exact splicing and method used. This is one of many reasons why a fusion splicer is the preferred method of jointing.
Intrinsic fiber back-reflection due to Rayleigh scattering is approximately:
| Link length | Return loss due to Rayleigh Backscatter |
| 1 meter | 70 dB |
| 10 meters | 60 dB |
| 100 meters | 50 dB |
| 1Km | 40 dB |
| Infinite | 32 dB |
This limits the sensitivity of a typical return loss test set-up depending on the length of attached fiber.
For example, to use a return loss meter to -70 dB sensitivity would require a total fiber length of less than 1 meter, or 10 meters if the instrument has a 'zero offset' function.
Another problem with very sensitive measurements, is that low levels of stray ambient light can leak in and create a false reading.
Single mode fiber applications are traditionally associated with ORL sensitivity problems, since they have always used lasers, are typically higher data rates, and may have longer links with little performance margin.
In contrast, old multimode applications used LED sources (which are insensitive to ORL issues), lower data rates and typically relatively short links. However in recent years, multimode systems have transitioned to VCSEL lasers, high data rates, and may be operating much closer to their length limit, so ORL has become an issue. Typically, to reduce the sensitivity of these lasers to reflections, the output laser-to-fiber coupling ratio is kept very inefficient, however there are still an increasing number of occasions were ORL contributes to a performance problem.
Technically, the overall causes of reflections in both types of fiber are similar, however connector ORL performance is different.
Single mode Physical Contact PC polish (blue colour) connectors have very variable Optical Return Loss performance. It is largely for this reason that Angled Physical Contact APC polish (green colour) connectors have become preferred in many situations.
PC connector performance varies dramatically between mated and un-mated states, and is also critically dependent on tiny amounts of dirt, which can stop the two fiber ends from contacting each other, although the optical loss is still quite small. Various qualities of PC polish connector can achieve between typically -50 dB to -30 dB when mated nicely, -14.3 dB when un-mated, and as poor as -11.3 dB when poorly mated.
The performance of APC connectors is overall much better, with an un-mated or mated return loss of better than -60 dB. the return loss does improve when mated properly.
Multi mode connectors (beige) are usualy PC polish, and do not have very good ORL performance in comparison to single mode connectors. Use of APC connectors on multimode systems is rare. The problem with these connectors is that the physical contact zone may not cover the entire connector core, so good mated ORL performance may be around -20 dB. Un-mated or poorly mated performance is similar to SMF, eg -14.3 or -11.3 dB.
Note that there are many styles of connector. The above figures apply to commonly available types with a ceramic ferrule. ORL performance may also be lower depending on the exact polishing procedure
It is convenient to measure return loss with an optical return loss meter (or ORL meter or back-reflection meter or optical continuous wave reflectometer or OCWR).
Back reflections of individual components can sometimes be measured with an OTDR, however this is generally of limited accuracy, and in some situations the back reflections may cause saturation of the instrument input amplifier, making measurement impossible. So return loss meters are commonly used for for acceptance work.
Some ORL meters can use automation to work as a pair, and measure return loss each end of a system while simultaneously performing a two-way attenuation measurement, which achieves a total analysis with no extra effort.
Better ORL meters have a couple of standard features which are both very helpful:
Connector return loss measurement challenges commonly depend on the connector end polish. A PC polish connector with a performance of around -40 dB is a lot easier to measure than an APC connector, which is normally un-measurably low.
A tight mandrel (a rod of around 5 mm diameter) can be a very useful ORL testing accessory, used to create a temporary extra loss / isolation to determine where a reflection is coming from.
To reduce back reflections:
Anyone using an ORL meter will probably need to be able to fault-find ORL issues.
Kingfisher International are specialist designers and manufacturers of handheld fiber optic test equipment.
Our equipment is used in all phases of fiber optic manufacture, installation and maintenance. Our comprehensive documentation and resources help you get started easily.
Kingfisher Products are Australian made, with a global distribution & support network spanning over 70 countries.
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