This paper reports on the optical properties, outgassing rate, and cryogenic performance of surface finishing we have adopted for large optical baffles absorbing stray light in KAGRA, an advanced interferometer for detecting gravitational waves. The surface finishing is based on an electroless nickel-phosphorus-tungsten (NiPW) plating, applicable to large surface area up to ~ 800 mm in diameter, and achieves less than 3% total reflectance against a light beam at 1064 nm with a reasonable scattering distribution ~ 0.05/sr. The outgassing rate from the black coating meets our requirements of 3×10−7 Pa · m3 s−1 m−2. The black coating can tolerate low temperature down to 12 K, and can be installed close to cold mirrors indispensable for the future interferometers.
© 2016 Optical Society of America
Stray light in an optical system often creates measurable spurious signals, unless it is sufficiently suppressed. The effect of stray light is also an issue for the gravitational-wave (propagating waves of strain of spacetime) detectors under development like LIGO, Virgo, and KAGRA, which are laser interferometers with several-kilometer arm lengths . Laser interferometry is such a precise technique that it can detect tiny displacements of length (or spacetime) due to gravitational waves ; such weak signals can, however, be easily buried in noise due to stray light generated inside the interferometers [3,4].
In order to improve the ratio of such weak signals with respect to the noise due to the stray light, several kinds of large optical baffles with black surface finishings are designed and installed in the interferometers. Requirements for the baffles are different for each interferometer, so we would like to focus on the case of our project, KAGRA, in this paper, but our report will be also usable for other applications.
Electroless nickel-phosphorus (NiP) plating is a long-established and useful technique for making black surfaces [5–7], although the darkest man-made surfaces today are made of carbon nano tubes (CNTs) . The robust surface of the NiP plating is preferable for reducing the risk of breaking accidentally during the installation of the baffles, which are of large size (~800-mm diameter) and number (~250 pieces), while the CNT forest is generally fragile. The NiP plating is so far more useful for applying to the required large surface area and complicated structures of the baffles rather than the CNT forests.
KAGRA has adopted a kind of nickel-phosphorus-tungsten (NiPW) black coating for the surface finishings of the large optical baffles. Some reports on developing this coating itself (Solblack by Asahi Precision, see Fig. 1) are found in . The black coating should meet several requirements for this purpose. It should have not only low reflectance, but also low scattering of light from the surface, as the baffles should absorb as much stray light as possible. It should be vacuum compatible, as the interferometer will be operated under ultra-high vacuum (~ 10−7 Pa) along with the baffles. It should be usable at cryogenic temperature, as the main mirrors of KAGRA will be cooled down to 20 K, and some baffles will be installed close to the mirrors. Note that the baffles will heat up when they absorb stray light, and become undesirable heat sources near the cooled mirrors.
In this paper, we report the results of the investigation on this black surface finishing including its optical properties, outgassing rates, and cryogenic performances.
2. Overview of the large optical baffles for KAGRA
Before starting detailed discussion on the performance of the black coating, in this section we briefly summarize stray-light noises and the large optical baffles in the advanced interferometers, focusing on the KAGRA case.
2.1. Stray-light noises in the interferometers
The stray light in the interferometer originates from either ghost beams or scattered light generated at optical elements like mirrors when they are illuminated by the input laser light. If the stray light going out of the main (expected) optical path somehow comes back into the path again with unwanted phase modulation, spurious signals (stray-light noise) at the output port of the interferometer will be observed. Note that gravitational waves will also cause tiny phase modulation on the light beams in the interferometer, which are the only signals we actually want to observe. When the spurious signals or noises surpass the actual signals, we miss the gravitational waves.
Most of the optical elements in the interferometer are enclosed in vacuum chambers. Without any optical baffles, those ghost beams or scattering lights could hit the inner walls of the chambers, where some of them would be reflected, and some of the reflected photons would be recombined to the main optical path. As the walls of the chambers shake due to seismic vibrations or air flow around the chambers, the reflected photons suffer phase modulations. Then the effects of stray-light noise in terms of the interferometer signals can be written in a frequency-dependent form as
Installing appropriate optical baffles to reduce the probability of recombining of stray light will reduce the stray-light noise, or in other words, improve the signal-to-noise ratio (the ratio of the gravitational-wave signals with respect to the noise). Moreover, it is also effective to reduce the shaking of the baffles which now hide the chamber walls, and thus those baffles will sometimes be supported by vibration isolators.
2.2. Baffle system of KAGRA
There will be five categories in the optical baffle system for KAGRA: (1) arm-duct baffles, (2) cryo-duct shields, (3) narrow-angle baffles, (4) wide-angle baffles, and (5) others including several kinds of middle- and small-sized baffles or beam dumps. Among these, the ones from (1) to (4) are to be installed in both of the 3-km arms of the interferometer, and all these baffles have large sizes up to ~ 800 mm diameters at maximum, so that they can hide the inner walls of the vacuum enclosure from stray light generated at the main mirrors as in Fig. 2. This means that the surface finishing to be used for these baffles should be applicable on large size (at a reasonable cost). The baffles sometimes have slightly complicated mechanical shapes so that they can catch and absorb as much stray light as possible, so the applicability to such shapes cannot be ignored. The NiPW coating satisfies these requirements.
Obviously, it is desirable for the surface finishings of the optical baffles to be black coatings. It would be good to have as low reflectance as possible to the input laser light used for the interferometer. The wavelength of the light is 1064 nm for KAGRA, and this is the same for other large-scale interferometers like LIGO and Virgo. Not only the low reflectance, but also low scattering of light from the surface is a key feature. With these parameters, optical design of the large baffles has been performed by non-sequential ray tracing.
The interferometer needs to be operated in ultra-high vacuum (~ 10−7 Pa) for avoiding contamination to optics and lowering phase noise of light due to air turbulence, and thus a low outgassing rate from the surface is required. A black surface made of NiPW plating generally has such microstructures that make the net surface area very large (Fig. 1), and would cause high outgassing rate. The surface finishing should be a compromise of these contradictory requirements.
Moreover, KAGRA is the first large-scale cryogenic interferometer, which means, unlike others, it will have cryogenic mirrors. Some of the baffles will be put close to these mirrors, and should tolerate temperatures of 10–70 K [10,11]. In addition, a high emissivity of the surface is preferable for improving the cooling-down time, as the initial phase of cooling is dominated by thermal radiation.
In summary, the surface finishing for the large optical baffles should satisfy these requirements: it should be dark with low outgassing rate, and it should neither break nor have low emissivity at cryogenic temperature. In the following sections, these are assessed for the adopted NiPW black plating.
3. Optical reflectance and scattering
In this section, optical properties of the black surface finishing are discussed. Measurements in this paper will show that the surface finishings or smoothness of substrates under the black coating determine the scattering distributions of light from the resultant black surfaces, even though the NiPW plating is relatively thicker (estimated to be of order 10 µm) than the wavelength of light (1064 nm) to be used in the interferometers; the total thickness of the plating is about 10 µm, within which the depth contributing to the darkness is about 1µm (Fig. 1). We prepared substrates with different surface finishings, and applied the black coating to them to make the samples for our measurements (Table 1).
In order to set requirements on the optical performance for the black coating to be used for the baffles, we need to remember Eq. (1); the stray-light noise is determined by the product of amplitude of the recombined stray light and vibration of the baffles. This means that a baffle surface does not need to be extremely dark if the baffle is sufficiently quiet. Moreover, the baffle is shaped like a cone to trap entering light, and not a simple flat board facing on incident light at 0 degree angle of incidence. Note that the efforts for reducing recombined power of stray light by 100 times correspond to reducing the baffle’s movement by 10 times as shown in Eq. (1). At the same time, the baffles should be manufactured in a realistic industrial way with a reasonable cost. The requirements should be determined taking these conditions into consideration.
In our case, the requirement for the darkness is to be less than 3–4% in the total reflectance with a reasonable distribution of scattered light. Here, the total reflection is defined to consist of specular reflection, which follows the law of reflection (angles of incidence and reflection are the same), and a scattering component. As shown below, all the test pieces with the black coating show similar total reflectance, while the scattering distribution and sharpness of the specular reflection are different. That is why we also set the necessary conditions for the full width at the half maximum of the specular reflection to be less than at least 3–4 degrees, and for the scattering distribution out of the specular profile to have no features (or uniform). In other words, we tolerate an increase in the specular reflectance in order to suppress the scattered light. With suitable shapes of the baffles, the specular reflected light can be got rid of by multiple reflections and absorptions.
3.1. Mathematical expressions of optical scatterings
By way of background, some definitions of and relationships between the key optical properties are shown here. The scattering probability distribution function per unit solid angle of a surface dP/dΩ can be defined as 
The total integrated scattering (TIS) can be theoretically derived by12]:
3.2. Measurements of the optical properties
Some optical properties were measured for test pieces (30–50 mm square), each of which has the substrate material under the black coating made of stainless steel or aluminum alloy, as summarized in Table 1.
If there are no reasons to do otherwise in a specific case, a stainless steel like SUS304 (in Japan Industrial Standard, JIS) will be used as a substrate for the baffle, as one can easily make a smooth surface on the material with a low outgassing rate. One can even purchase off-the-shelf metal sheets made of bright-annealed (BA) stainless steel, which have smooth surfaces like mirrors. It is more expensive to polish surfaces of aluminum alloy to the comparable smoothness.
For the substrates of the cryogenic baffles, aluminum alloy is preferable to stainless steel because of its better thermal conductivity at low temperatures; pure aluminum would be preferable to aluminum alloys from the viewpoint of the thermal conductivity, but pure aluminum is too soft to keep the manufactured shape or structure, and therefore will not be used.
3.2.1. Total reflectances
Total reflectances, which include the scattered light and the specular reflected light, of the black-coated test pieces were measured with a spectrometer, SolidSpec-3700 by Shimadzu (Fig. 3). The spectrometer has an integrating sphere to catch both reflected and scattered light from the surface under test. The incident angle of the probe light to the test piece is 8 degrees.
For all the kinds of test pieces in Table 1, the measurements show that the total reflectances are less than 3% at 1064 nm. Of the black coated test pieces in Fig. 3, Al ECB (electro-chemical buffed aluminum alloy) ones have higher reflectance than the rough Al (unpolished aluminum alloy), while the SUS BA (bright-annealed stainless steel) has the lowest. In terms of smoothness of the substrates, the SUS BA is the smoothest, the Al ECB is next, and the rough Al is the roughest, so it seems the roughness of the substrate does not affect the total reflectance.
3.2.2. Scattering distributions
To design optical baffles, it is important to know not only the total reflectance of the black coating but also the distribution of scattered light from it. The scattering distributions of light were measured for these test pieces (Figs. 4 and 5). In the figures the vertical axis corresponds to dP/dΩ defined in Eq. (2). During the measurements, the incident angle of light (1064 nm with mixed polarizations) to a test piece is selected once for each measurement, and a photodiode rotates automatically around the test piece in the plane of incidence of light; the horizontal axis in these figures are scattered angles θs, but whose positive region corresponds to ϕs = 0 and negative to ϕs = π. The photodiode has a 2-mm diameter, and is located 50 mm away from the test pieces, which corresponds to a 2.2-degree angular resolution (in terms of θs). The rotational resolution of the photodiode around the test piece is first set to 0.1 degree, but each step width is not controlled by a closed loop with an encoder, so the stability of the resolution is not well guaranteed to less than 1 degree. In a certain angular region during each measurement, the photodiode shadows the test piece against the entering light, so the measured data are not correct there; such direct back-scatterings toward the light source will be measurable with another setup, but are not reported here. The incorrect region is plotted with a dotted line for each measurement in Figs. 4 and 5.
The peak features in the figures are considered to be specular reflections, and can be fitted to Lorentzian function as in Table 2. As can be seen in Fig. 5, the finesses of the peaks appear related to the treatments of the substrates under the black coatings, even though the total reflectances are almost the same for these test pieces, and moreover, the roughness of the top layer of the black coating has microstructures in the same manner as shown in Fig. 1. The specular reflections from the black coatings on the bright-annealed stainless steel (SUS BA) and the electro-chemical buffed aluminum alloy (Al ECB) have comparable sharpness in this figure, where the full-width at the half maximum is around 1–1.5 degrees, which is, however, comparable to the angular resolution of this measurement system as described above. According to visual inspections (at visible wavelengths) of the test pieces, the SUS BA can make a sharper image of a light source than the Al ECB. In order to confirm this, a finer resolution would be required.
Apart from the peak features, assuming Lambert scattering, the measurements can be fitted to α0/π ≃ 0.02/sr in terms of Eq. (5) for both of the Al ECB and rough test pieces when the angle of incidence is set to 30 degrees. During the measurements of these Al test pieces, the background of the system is around 0.01/sr, which can also be estimated from the data around −30 degrees in the figure, where the photodiode shadows the test pieces. The blue dashed curve in Fig. 5 is the fitted Lambert scattering with the background. Substituting the estimated value into Eq. (5) gives the corresponding surface roughness, or an “effective roughness” σrms ≃ 0.45 µm assuming the black surface on the Al test pieces has 0.3% of the specular reflectance (estimated from Fig. 6 though that is the case of SUS BA). A Lorentzian function as in Table 2 can fit the diffuse component for the SUS BA cases, and yet a Lambert component would be required to cover all the regions.
Although the surface roughness of the substrates under the black coating is different (about Ra≃ 0.05 µm for the Al ECB, which is the level achieved in a prototype test of a large baffle made of aluminum alloy for a reasonable cost; there are no data for the rough Al, but it can be estimated that Ra> 0.3 µm, where the surface roughness in terms of “Ra” corresponds to about 0.8σrms assuming a random roughness with a Gaussian height distribution), the measurements show the same levels of scattering. The height ratio of the peak features in Fig. 5 suggests the rough Al has a less “specular” reflectance than the Al ECB, so the resultant effective roughness could become larger, but a finer measurements would be required to determine the maximum values of the peaks. In the case of the SUS BA, the same analysis gives an effective roughness of σrms ≃ 0.28 µm from the black coating, while the surface roughness of the substrate is estimated to be σrms ≃ 0.022 µm. These are summarized in Table 3.
With these results, the scattering distribution is seen to be affected by the surface roughness of the substrate under the black coating. As a rule of thumb, one can say the resultant effective roughness of the black surface finishing can become 10 times rougher than the substrate’s surface roughness. The Lambert scattering component from the black coating can be estimated from the effective roughness, but also depends on information about the specular reflectance.
3.2.3. Specular reflectances
The specular reflectance of a test piece whose substrate was made of SUS304 BA was measured against 1064-nm light (Fig. 6). The polarization of the incident light was settable to either S or P by a combination of a polarizing beam splitter and a half-wave plate in front of the test piece.
They were not measured here on the other test pieces listed in Table 1. For both of the Al test pieces (ECB and rough), reflected light beams were surrounded by large diffuse components, and specular reflections could not be identified, although the peak features from the SUS BA and Al ECB test pieces are similar in Fig. 5; finer measurements would be required to resolve these differences as mentioned above.
Unlike usual smooth surfaces like mirrors, the measured data in Fig 6 are not well-fitted to a model given by the simple Fresnel’s law, even though a local minimum for the P-polarized beam (like a Brewster angle) is observed. As shown in Fig. 1, the top layer of the black coating has microstructures, and further investigations would be required to make models explaining this .
The total reflectance 1.9% in Fig. 3 (at 8 degrees) includes the specular reflectance, which was measured to be 0.24% (at 10 degrees). The angles of incidence (AOI) are different among these measurements, but they can be compared, as they will not change rapidly with respect to the AOI in this angular region. This means, even though the substrate is made of SUS BA (the smoothest surface in Table 1), the main component of the reflected light from the black coating on it is scattered light. In order to design the baffles, optical simulations considering the scattered light are indispensable. As the total reflectance is not much affected by the substrate’s surface roughness (Fig. 3), improving the substrate’s surface under the black coating will help in reducing the net amount of the scattered light instead of increasing the specular reflection. When the baffle’s shape is designed so that the specular reflection is trapped with multiple reflections, they can be absorbed.
4. Outgassing rate
The large optical baffles as well as the main optics of the interferometers will be installed in ultra-high vacuum. In the case of KAGRA, of the order of 10−7 Pa is required for avoiding Brownian noise (and squeezed-film damping effects as well) to the mirrors from the residual gases .
A decade ago, diamond-like carbon (DLC) was the primary candidate for the black coating of the large optical baffles, as measurements showed the coating can provide the lowest (and sufficient) outgassing rate in the candidates under test . Some of the prototyping tests were done with the DLC-coated baffles in a mid-size interferometer, TAMA300 . Despite the good outgassing rate, DLC was often bright; the reflectance depends sensitively on the thickness of the DLC layer (and the wavelength of the input light), and it is hard to control the thickness in an industrial manner especially on large and relatively complicated areas like optical baffles for KAGRA.
The low reflectance and the low outgassing rate are incompatible requirements in general. A rough surface tends to have a larger outgassing rate than a smooth one, as the rough surface has the larger surface area. On the other hand, the reason why the NiPW black (and also CNT) surfaces seem dark is that they capture most of the input light into the microstructural valleys existing on their rough surfaces and absorb them before they escape (Fig. 1). We aim to balance both of the requirements.
Outgassing rates of the black-coated test pieces were measured (Fig. 7). The measurements were done by the conductance-modulation method [17,18], and the figure shows outgassing per unit time per unit area of each test piece against elapsed time since the pumping started; note that the product of pressure and volume is proportional to the number of particles in the equation of state of the (ideal) gas. Specifying the pumping speed of the pump (in m3/s), the surface area of the optical baffle, and the volume of the vacuum chamber, the achievable pressure in use can be estimated.
In the case of KAGRA, having an outgassing rate of less than 3 × 10−7 Pa m3s−1m−2 after 50-hour pumping is the requirement for the baffle arrays made of many vanes·in the 3-km arms (category 1 “arm-duct baffles” in Fig. 2), where 125 baffles will be installed per arm, with substrates made of SUS BA. As shown in Fig. 7, after the SUS test piece was baked (in 250°C for 4 hours), the outgassing rate was sufficiently reduced.
As described above, making a smooth surface on aluminum alloy is difficult in general. Probably as a consequence, the aluminum test piece has a larger outgassing rate than the stainless steel, even though they are coated with the same black plating. Note that aluminum alloy will start softening (due to recrystallization) around 150°C and change its performance, so it should be baked at a lower temperature (for example, below 120°C), and will take more time to reach an equivalent outgassing rate to that of stainless steel.
5. Cryogenic performance
The next-generation interferometers for observing gravitational waves like the Einstein Telescope are planned to have cryogenic optics to reduce thermal noise. Even among the current-generation interferometers, KAGRA will also have its main mirrors cooled down to around 20 K .
The first stage of the mirror cooling will be dominated by thermal radiation. Therefore, large optical baffles to be installed close to or surrounding those cooled mirrors should have moderate emissivity (still keeping a “black” surface for 1 micron radiation) for room temperature radiation as well as be robust against large temperature changes. Moderate emissivity will accelerate the cooling speed, and will save debugging time for the interferometers, and eventually also observation time.
The final stage of the cooling will be dominated by thermal conduction. Therefore the baffles for the cold region should be also made of materials with high thermal conductivity at low temperatures. From this viewpoint, aluminum alloy is preferable for the substrates, as it has higher thermal conductivity than stainless steel in low temperature (and a reasonable cost). Pure aluminum would be even better thermally, but it is too soft for shaping the baffles.
In order to investigate the cryogenic performance of the black coating, we started with simple tests. Test pieces made of aluminum alloy with the black coating were sunk into liquid nitrogen several times in air. The black coatings neither cracked nor became fragile after the tests, even though the surfaces were covered by frost due to water vapor in air.
The reflectance of the black coating at 10.6 µm, which is representative of room-temperature radiation, is measured to be around 40%. The reflectance was also measured in a cryostat, and it was experimentally confirmed that it does not change during the cooling. These results have been incorporated in the design of the cryogenic duct shields for KAGRA (category 2 “cryo-duct shields” in Fig. 2), and more details are reported in Ref. .
Following the cooling tests of a half-sized payload and four cryostats for KAGRA described in Ref. , a cooling test of the black coating on aluminum alloy was done. Two dummy baffles made of aluminum alloy, on which the black coating was applied, and the half-sized payload were suspended in an actual cryostat of KAGRA for the cooling test (Fig. 8). The half-sized payload included a dummy mirror made of sapphire, of which the KAGRA’s main mirrors will be made; the baffles are suspended one on each side of the dummy mirror. These dummy baffles correspond to category-4 “wide-angle baffles” in Fig. 2. A dummy baffle has the shape of a pipe with diameter 130 mm and length 500 mm, while the dummy mirror is a cylinder with diameter 100 mm and thickness 60 mm (details on the half-sized payload are reported in Ref. ). For designing the actual wide-angle baffles, a realistic shape for an optical absorber should be considered, but here a simple pipe is used to test the cryogenic tolerance of the black coating. Some heat links were connected to the baffles. The contact points of the heat links avoid the black coating to make the thermal resistance as low as possible.
In Fig. 9, the dummy baffles reached 12 K on around the 8th of August 2013, so the temperature tolerable by the black coating in vacuum is experimentally confirmed down to this temperature. About 10 days later, the dummy mirror reached the goal temperature of 20 K. A part of the field of view from each side of the dummy mirror is covered by the baffle. Due to this, the rate of mirror cooling is slightly reduced during the first stage, where thermal radiation dominates, compared to the estimated cooling time without the baffles. The cooling time with the baffles was also estimated from the assumed emissivity of the black coating , and can explain the measurements.
With these results, the black coating (on aluminum alloy) is applicable to the actual optical baffles to be installed close to KAGRA’s cryogenic main mirrors, and will be useful for designing other cryogenic baffles in the future.
A surface finish for large optical baffles to be installed in advanced interferometers for detecting gravitational waves was assessed against the requirements for KAGRA. The black coating based on an electroless nickel-phosphorus-tungsten (NiPW) plating, Solblack by Asahi Precision, was investigated for optical, vacuum, and cryogenic performance. The total reflectance of the black coating is less than 3% at 1064 nm with reasonable optical scattering distributions, while showing low outgassing rate on the order of 10−7 Pa · m3 s−1 m−2 (after 50 hours of pumping), and also tolerates low temperatures down to 12 K. Even with such a dark surface, the surface roughness of the substrate under the black coating will affect the distribution of scattered light from the surface finish.
Based on the investigations, we have adopted the black coating for some of KAGRA’s large optical baffles. The substrate of each baffle shown in Fig. 2 has been determined as follows. Bright-annealed stainless steel has been selected for the arm-duct baffles because it shows the lowest outgassing rate as well as the better scattering distribution. In particular, the low out-gassing rate is a strong reason, as there are 125 vanes for each arm. Electro-chemical buffed aluminum alloy (Al ECB) has been selected for the cryo-duct shields [10, 11], because these will be used at low temperatures. For the narrow-angle baffles, Al ECB has also been selected for a different reason; the narrow-angle baffle will be used at room temperature, but has a large volume (800-mm diameter and 140-mm thickness), so the light weight material is preferable for the manufacturing and the installation. Prototyping of the wide-angle baffles is still ongoing, but Al ECB is a strong candidate for the substrate for the same reason as for the cryo-duct shields. The surface finish could be also usable for the baffles in future interferometers with cold mirrors.
This work was supported by MEXT, Leading-edge Research Infrastructure Program, JSPS Grant-in-Aid for Specially Promoted Research 26000005, Scientific Research (C) 25420857, and JSPS Core-to-Core Program, A. Advanced Research Networks. The spectrometer used here was prepared by Advanced Technology Center (ATC) in NAOJ. The JASMINE group in NAOJ supported us in measuring the scattering distribution of the test pieces. Asahi Precision, Co., Ltd. made most of the test pieces, and prepared the SEM photographs.
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