How can one produce a thin-film filter that reproduces irregular spectral transmittance and reflectance curves for near-normal incident light? How about filters intended for use at oblique angles of incidence? These problems were part of a unique thin-film manufacturing competition at OSA’s Topical Meeting on Optical Interference Coatings.
2001 manufacturing problem: A mountain range in the Canadian Rockies and its reflection in Bow Lake provide the target transmittances TD and reflectances RD for the manufacturing problem.
From time to time, the optical thin film community has organized competitions to test the state of the art in multilayer thin-film design. These design problems have become a tradition at OSA’s Topical Meeting on Optical Interference Coatings (OIC), in addition to round-robin measurements to assess the properties or performance of thin film multilayers or the optical constants of single thin films. Both of these exercises have helped the meeting participants to better understand certain aspects of optical thin-film design, and they have in fact advanced the state of the art.
At the 2001 OIC meeting in Alberta, Canada, the organizing committee decided to add a new twist to the proceedings. They presented a manufacturing problem for the participants’ consideration. Since then, such a problem has been presented at each meeting. This article reviews three such problems from the 2001, 2004 and 2007 OIC meetings and summarizes the solutions offered by participants.
Basic concepts and procedures
The manufacturing problems are intended to test the state of the art in producing multilayers with a specified performance, which is usually defined in terms of a merit function. Before the problems were posed to participants, the organizers carried out extensive calculations to ensure that solutions exist, and that the solutions are based on common coating materials and consist of a reasonable number of layers and overall thicknesses.
Furthermore, the organizers conducted investigations to ensure not only that such solutions existed, but that at least some of them were not excessively sensitive to the values of the construction parameters. This ensured that there was a reasonable chance that they could actually be manufactured. Two random-thickness error perturbation analyses were carried out for each acceptable solution found.
In the first, the average thickness perturbation for each layer was 1 percent of its thickness; this tested the sensitivity of the system to errors in the thicker layers. In the second analysis, the average thickness perturbation for each layer was 1 nm; this gauged the sensitivity of the system to errors in the thinner layers. The problem was not considered to be ready until solutions were found that passed all these criteria.
The participants were free to implement the design that they felt would give them the best chance to meet the specifications experimentally. Thus, it was up to them to choose the number of layers and the coating materials, as well as the overall thickness of the thin-film system and the deposition process. The resulting measured performance of the sample was the only metric that mattered. There were two restrictions: no toxic materials could be used in the system and the size of the substrates had to be as specified in order to facilitate the measurements.
To encourage participation, the manufacturing problem was chosen so that the resulting multilayer did not have any commercial value. The participants did not need to disclose the materials or processes that they used in its manufacture. The organizers promised to measure the transmittance and reflectance only, and not to examine the samples with any other analytical methods. The samples were returned to the participants after the event.
The participants were required to provide the normal incidence spectral transmission measurement of the sample and the data required to plot the refractive index profile of the resulting multilayer system. Transmittance data were compared to similar measurements performed at the measurement laboratories; any serious differences between these measurements indicated that there were problems that needed to be resolved. The refractive index profiles were necessary in order for the organizers to have a meaningful discussion about the results. In the past, these profiles also revealed problems with the samples or the measurements. The optical constants used in these diagrams were specified at a wavelength of 550 nm.
To make the final reports more interesting, the organizers asked the participants to provide information such as the calculated merit function of the system and, whenever possible, details or references to published descriptions of the deposition equipment and process that they used.
The submitted samples were measured at two independent laboratories: Optical Data Associates and the National Institute of Standards and Technology. These organizations were not permitted to participate in the competition. The two laboratories used both commercial and custom-built measurement equipment. The average of the two merit functions obtained by these laboratories was used to grade the submissions.
The first manufacturing problem
Banff, Alberta, Canada, July 16, 2001
The aim of the first manufacturing problem was to investigate the degree to which it is possible to reproduce certain irregular spectral transmittance and reflectance curves. The targets selected were based on a photograph of a mountain range in the Canadian Rockies and its reflection in Bow Lake, located within easy driving distance from the actual conference.
The silhouette of the mountains provided the desired transmittance target TD, and its reflection in the lake, the reflectance target RD. Since one curve is a mirror image of the other about the line T=0.5, it follows that TD+RD=1.0, and that, for the best results, the use of coating materials with finite extinction coefficients would be undesirable. To facilitate the measurement of the spectral reflectance, the organizers arbitrarily specified that both TD and RD were for s-polarized light incident at 7°. The merit function used to determine the performance of the submitted samples was defined at 101 wavelengths λi in the 0.4 to 0.6 µm spectral region by the expression:
Here, TiM, RiM are the measured transmittance and reflectance at the wavelength λi. Because of the perceived relative accuracy of transmission and reflection measurements, different weights were ascribed to the two in the merit function. In this and the two subsequent exercises, the transmittance measured had to include the effect of the second surface of the substrate.
This article is based on an invited talk presented by J.A. Dobrowolski at the optical coatings session of the 2008 Annual Technical Conference of the Society of Vacuum Coaters, in Chicago, Ill., U.S.A., on April 23.
(Top) Participants and results, 2001. (Bottom) Measurements and refractive index profile of the 2001 solution submitted by D. Poitras et al.
Six groups participated in this exercise, submitting a total of 11 samples for measurement. (Only one of the participating groups represented a commercial entity.) The names of the participants, their affiliations and the average measured merit functions of the submitted samples are given in the table. As the table shows, the number of layers and overall metric thicknesses of the samples varied between 8 and 27, and 768 and 4,226 nm, respectively. In all the samples, the layers were on one side of the substrate, and the second side was left uncoated. The table also lists the deposition processes used to produce the layer systems.
The organizers of the first manufacturing problem neglected to ask the participants to specify the measurement area at which the performance was to be tested. It turned out that many of the coatings had significant thickness variations. To overcome this problem, a number of measurements had to be performed on most samples to find the spot with the lowest merit function value.
The normal- and 7° s-polarized light transmission and reflection measurements, and the refractive index profile for the sample with the lowest merit function value MF=0.98 are shown in the figure on the right. This also happens to be the sample that had the greatest overall thickness and the most layers.
A filter having a transmittance curve that corresponds to the silhouette of a mountain range is, of course, of no practical use. However, in telecommunications and some other fields, there is a need for correction or gain flattening filters with irregular spectral transmission features. Given that there is large commercial interest in filters of this kind, perhaps it is not surprising that all but two of the samples submitted had merit function values that were of the order of 1.5 or less.
The second manufacturing problem
Tucson, Ariz., U.S.A., June 2004
The purpose of the second manufacturing problem was to see how precisely one can produce filters that are intended for use at oblique angles of incidence. After doing some preliminary investigations, the participants were asked to produce a plate beam splitter operating with light incident at an angle of 60° in which, at wavelengths λi throughout the 450 to 650 nm spectral region, the target transmittances TTi,p, RTi,s for p- and s-polarized light would have values that were as close as possible to 0.7 and 0.3, respectively. Three types of solutions for this problem were identified in the preliminary calculations. The merit function was defined by the following expression:
(Top) Participants and results, 2004. (Bottom) Measurements and refractive index profiles of the 2004 solutions submitted by Netterfield and Dligatch (a); Ma, Lin and Altmann (b, c); and Zhupanov and Kluev (d).
Here, TMi,p, TMi,s are the measured transmittances at the wavelength λi for p- and s-polarized light incident at 60°. The measurements are made at m-equispaced wavelengths. The solutions needed to take into account the contributions of both surfaces of the beam splitter. Equation 2 did not preclude the use of absorbing layers.
We found the response to this manufacturing problem to be rather disappointing. Only three groups participated, and they contributed a total of six samples for evaluation, of which four were nominally different. This time there was no participation from companies.
As shown in part (a) of the figure on the right, the system consisted of 33 layers of three different dielectric materials that were deposited onto one side of the quartz substrate. The all-dielectric system of (b) was made of 40 layers composed of only two materials, also deposited onto one side of the plate. In the solution depicted in (c), the two sides of the substrate were coated with 4 and 12 dielectric layers, respectively. Because the substrate was thick compared to the wavelength of light, there was no coherent interference between the two sets of layers.
The final system, shown in (d), consists only of three layers, one of which is a very thin nickel layer. The coating is deposited onto one side of the substrate. It illustrates very convincingly the usefulness of thin-metal layers in the solution of some problems.
Despite the small number of teams that participated, this exercise was still interesting because the four solutions differed from each other quite a bit. In fact, they encompassed all three of the types of solutions that the organizers had considered when they designed this experiment. The lowest measured average merit function MF=0.786 was obtained by the system shown in (c). Another conclusion drawn from this exercise was that the measurement of transmittances at oblique angles of incidence is not a trivial matter.
(Top) The 2007 manufacturing problem specs. (Bottom) Refractive index profile, measured spectral transmittance and reflectance curves, and the corresponding CIE parameters for sample JZI.
The third manufacturing problem
Tucson, Ariz., U.S.A., June 2007
The aim of the third problem was to see how closely the participants could meet a performance that had been entirely specified in CIE standard colorimetric terms. This time, the problem was posed in such a way that solutions had to make use of thin absorbing layers. The controlled deposition of the required absorbing layers was deemed to be the main challenge in this problem.
The perceived color of the multilayer coating when illuminated at near-normal incidence by the CIE Standard Illuminant D65 was to be yellow and blue, respectively, in light reflected from its two surfaces A and B, while it was to appear gray when viewed in transmission mode. These three beams were to be of equal luminous reflectance or transmittance. The exact target specifications are shown in the table.
The merit function MF used in the evaluation of the performances of the submitted samples was:
In the above, xTm, yTm, YTm and xm, ym, Ym are the target and experimentally measured CIE x and y chromaticity coordinates and CIE tristimulus values Y, respectively, for the three beams m=1, 2 and 3. A computer program was posted on the OIC conference Web site to assist the participants in these calculations.
As in the previous two problems, the organizers carefully investigated the feasibility of designing and manufacturing a coating that would meet these requirements. In particular, they performed calculations to ensure that various common metallic layers could be used in the design of the solutions. For this application, metal films that are poor reflectors are better than metal films that are good reflectors. Calculations also showed that, as the number of layers in a design increases, the performance of the design converges to a finite limit that is imposed by the reflection of the second surface. This can be avoided by using an antireflection coating on that surface.
Participants and results, 2007.
However, before posing the problem, the organizers assessed the reasons for the poor participation in the 2004 event. They concluded that groups in the commercial sector may need an added incentive to participate. After all, unlike in the design contests, which normally involve only a computer and one person—who is frequently working at home in his or her spare time—the manufacturing problems require the use of a team of skilled people working on expensive deposition and measurement equipment. During the time that the equipment is used for the competition, it will not be available for production, and companies might not be willing to incur these expenses. Moreover, corporate participants probably cannot risk the bad publicity that might result should their contribution have the worst performance.
To address these potential concerns, the organizers decided to change the rules for participation. In the third problem, the names of the participants were again published, but the measured samples were assigned random names and were not linked to their manufacturers in the oral and written reports on the event.
Thus, in effect, the contributions were anonymous. The participants could, of course, recognize their sample from the refractive index profile, and they could see where they ranked with respect to the other participants, but they would not know who produced any of the other samples. In order to safeguard the participants’ anonymity, details that might help identify the manufacturer of a given sample were not included in the write-up of the additional voluntary information provided by the participants.
Possibly because of these measures, 11 groups submitted a total of 18 samples to the 2007 manufacturing problem. At least four of the 11 groups represented commercial companies. In order to emphasize the anonymity of the samples, the participant and sample portions are separated in the summary table on the facing page for this problem.
Performance of a typical sample, 2007. Photographs of the reflected (a), (b) and transmitted (c) beams of a typical sample. (d) Simultaneous view of all three beams.
A number of different types of solutions were submitted. Some were coated on one side of the substrate only and contained either one or two metal layers. Others were coated on both sides and contained either one metal layer only, or a metal layer on each side of the substrate. The solutions were made of three or four different materials and consisted of anywhere between 5 and 24 layers. A wide range of absorbing layers was used in the submitted samples.
The figure at the top of the page shows the refractive index profile, the measured spectral transmittance and reflectance curves, and the corresponding CIE colorimetric parameters for the sample JZI that had the lowest measured merit function value (MF=4.81). Photographs of the two reflected (a, b) and the transmitted (c) beams for another, typical sample are shown in the figure on the right. In the simultaneous photograph (d) of the three beams from the sample 4, the blue reflection is seen with the aid of mirror 2. The yellow beam is desaturated by light from the white background 3 that was needed to illuminate the blue side of the sample, and also to serve as a screen for the transmitted beam.
These three manufacturing problems have provided useful insight into the state-of-the-art for the manufacture of various multilayer coatings. For a more detailed description of this topic, readers are referred to the original reports on the 2001, 2004 and 2007 problems, which were published in Appl. Opt. 41, 3039-52; Appl. Opt. 45, 1303-11; and Appl. Opt. 47, C231-C245, respectively.
Much progress has been made recently in this field. Further advances will be brought about by more accurate in situ measurements of the coatings during their construction, especially if they are combined with etching, to reduce the thicknesses of layers that, during manufacture, exceed the optimum design values. We invite you to participate in developing future manufacturing problems.
J.A. Dobrowolski is with the National Research Council of Canada, Ontario, Canada. Stephen Browning is with Ball Aerospace & Technologies in Boulder, Colo., U.S.A. Michael Jacobson is with Optical Data Associates in Tucson, Ariz., U.S.A. Maria Nadal is with the National Institute of Standards and Technology in Gaithersburg, Md., U.S.A.
References and Resources
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