Diffuse reflecting material for integrating cavity spectroscopy, including ring-down spectroscopy Michael T. Cone,1 Joseph A. Musser,2 Eleonora Figueroa,1 John D. Mason,1 and Edward S. Fry1,* 1
Department of Physics and Astronomy, Texas A&M Univerisity, 4242 TAMU, College Station, Texas 77843, USA
2
Department of Physics and Astronomy, Stephen F. Austin State University, 1901 Raguet St North, Box 13044, Nacogdoches, Texas 75962, USA *Corresponding author:
[email protected] Received 15 August 2014; revised 14 November 2014; accepted 17 November 2014; posted 19 November 2014 (Doc. ID 221055); published 9 January 2015
We report the development of a diffuse reflecting material with measured reflectivity values as high as 0.99919 at 532 nm and 0.99686 at 266 nm. This material is a high-purity fumed silica, or quartz powder, with particle sizes on the order of 40 nm. We demonstrate that this material can be used to produce surfaces with nearly Lambertian behavior, which in turn can be used to form the inner walls of highreflectivity integrating cavities. Light reflecting off such a surface penetrates into the material. This means there will be an effective “wall time” for each reflection off the walls in an integrating cavity. We measure this wall time and show that it can be on the order of several picoseconds. Finally, we introduce a technique for absorption spectroscopy in an integrating cavity based on cavity ring-down spectroscopy. We call this technique integrating cavity ring-down spectroscopy. © 2015 Optical Society of America OCIS codes: (160.0160) Materials; (160.4670) Optical materials; (300.1030) Absorption; (120.4640) Optical instruments. http://dx.doi.org/10.1364/AO.54.000334
1. Introduction
Since their development by Sumpner and Ulbricht, integrating cavities have become an indispensable tool in optical laboratories [1]. Their ability to collect and spatially integrate the radiant flux emitted from a source facilitates a wide variety of applications. Common uses include measuring the total radiant flux from sources such as lamps and lasers, measuring the reflectance and transmittance of scattering materials, and creating uniform sources of light [2]. Integrating cavities have also been shown to have tremendous value in the area of absorption spectroscopy [3–7]. The high diffuse reflectivity of the cavity wall allows for the measurement of weak 1559-128X/15/020334-13$15.00/0 © 2015 Optical Society of America 334
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absorption signals, even in the presence of strong scattering effects. More recently, integrating cavities have been used to enhance the detection of extremely low concentrations of biological waste products in water supplies [8]. 2. Diffuse Reflecting Materials
The primary constituent of an integrating cavity is the diffuse reflecting material that makes up its inner surface. Specular reflecting surfaces, such as metallic mirrors, reflect incoming light from a single direction into a single outgoing direction, as described by the law of reflection. By contrast, diffuse reflecting surfaces reflect the incoming light in many directions [9]. An important special case is that of a Lambertian reflector for which the incoming light from a single direction is reflected such that the outgoing radiant
power per unit solid angle per unit projected area of the surface, or radiance L W∕sr · m2 , is the same in all directions. This is equivalent to saying that the outgoing radiant power per unit solid angle, or radiant intensity I (W/sr), varies with the cosine of the angle θ between the receiver and the surface normal of the reflecting surface (i.e., I I 0 cos θ) [10]. A.
Properties of Diffuse Reflectors
Diffuse reflecting materials are typically characterized by two parameters: (i) the reflectance and (ii) the bidirectional reflectance distribution function (BRDF) [11]. The reflectance is simply the ratio of the reflected radiant power to the incident radiant power [12]. The BRDF of a surface, as proposed by Nicodemus et al., is defined as the ratio of the outgoing radiance to the incoming irradiance, for a given direction of incidence θi ; ϕi , and direction of scattering θs ; ϕs [13]. The geometry for this is represented pictorially in Fig. 1. The BRDF can be expressed in terms of the incoming radiant power Pi and the scattered radiant power Ps as follows: radianceθs ; ϕs Ps ∕A cos θs dΩ irradiance Pi ∕A Ps ; (1) Pi cos θs dΩ
BRDFθs ; ϕs ≡
where A is the area of the sample. The scattered power is directed into a solid angle dΩ with a direcˆ Although the tion designated by the unit vector Ω. BRDF is a function of both θs and ϕs , symmetry typically allows the azimuthal dependence to be neglected. Since the scattered radiant intensity for a Lambertian reflector is proportional to the cosine of the scattering angle θs , Eq. (1) reduces to ρPi cos θs ∕Pi cos θs dΩ ρ∕dΩ (where ρ is the reflectivity of the sample). In other words, the BRDF for an ideal Lambertian reflector is a constant value. By contrast, an ideal specular reflection is represented by a delta function in the BRDF.
Fig. 1. Geometry for BRDF.
B. Examples of Diffuse Reflecting Materials
There are a large variety of high-quality diffuse reflectance materials available for use in integrating cavities. Barium sulfate-based powders and coatings, such as Eastman Kodak 6080, have been in use for several decades [14,15]. These coatings can easily be applied to many surfaces, making them simple to implement for integrating cavities. A modern example, the barium sulfate-based material Spectraflect, provides a reflectance over 97% throughout the visible (vis) and near-IR (NIR) portion of the spectrum [11]. However, the reflectance of all these barium sulfate materials drops considerably in the UV, with Spectraflect’s reflectance at 250 nm being only 94%. Spectralon, produced by Labsphere, Inc., is recognized as the industry standard in diffuse reflectance over the UV–vis–NIR portion of the spectrum [11]. The material is composed of a powder of polytetrafluoroethylene (PTFE) that is pressed and sintered into machinable blocks. Spectralon has a reflectance of 99.0%–99.2% across the visible spectrum, but much like Spectraflect, this value goes down in the UV, being only 95.0% at 250 nm [11]. Spectralon is also susceptible to photolytic degradation if it is allowed to come into contact with contaminants from water, tubing plasticizers, epoxy components, or other sources [16]. In addition to this, Gibbs and coworkers have shown the degradation of Spectralon samples under long-term exposure to high and low levels of UV irradiation without the presence of these contaminants [17,18]. However, there have been studies that show that this degradation can be mitigated, or even eliminated by a vacuum bake-out procedure [19,20]. Other sintered PTFE products, such as Fluorilon-99 W, produced by Avian Technologies, LLC, exhibit similar diffuse reflectance values to Spectralon throughout the UV–vis–NIR [21]. 3. Simple Model of a Highly Reflecting Wall
By considering the light reflecting off a simple air– glass interface we can gain some insight as to how one might construct a high-efficiency diffuse reflecting wall. Figure 2 shows a set of N glass plates separated by air gaps in front of a back surface with reflectivity η. The reflectivity for normal incidence at the air–glass interface is ρ, and the absorption/ scattering in the glass is assumed to be negligible. For simplicity, we neglect all interference effects and consider only reflectivities. Let in be the intensity of light in the nth location, where the location order and direction are as shown in Fig. 2. Thus the intensity leaving the Nth plate is i4N , and the intensity of light incident from above on the Nth plate is i4N1 , etc. With the initial incident intensity given as i0 , it is straightforward to show that the total reflected light R i1 ∕i0 for the entire stack of N plates is given by R
i1 η 2Nρ − 2N 1ηρ : i0 1 2N − 1ρ − 2Nηρ
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stack of 12,000 glass plates, but micrometer-sized particles, or powders could easily allow one to achieve this number of interfaces for a wall of modest thickness. 4. Diffuse Reflecting Material
Fig. 2. Geometry for calculating the reflectivity of N plates of glass.
In the limiting case of no back surface reflector (η 0), Eq. (2) reduces to R
i1 2Nρ : i0 1 2N − 1ρ
(3)
It should be noted that a similar result was obtained by Stokes 150 years ago [22]. Some additional insight can be gained by considering some special test cases of Eq. (2). If N 0 (i.e., 0 glass plates), the reflectivity is simply η or the reflectivity of the back surface. If ρ 0 the reflectivity is once again η. Finally, if either ρ or η 1 the reflectivity goes to 1. These limiting case results are in agreement with the expectations for such a setup. The more interesting case is when N grows large for a fixed value of ρ. From Eq. (2), it is easy to show that as N grows large, η has little effect on the reflectivity of the stack. If we set η 0 and ρ 0.04, then the reflectivity of the stack reaches 0.999 with an N of approximately 12,000 (see Fig. 3). Thus, very high reflectivities can be reached with a system made up only of interfaces of relatively low reflectivity. Of course, it is completely impractical to build a
We have developed a diffuse reflecting material for use in integrating cavity applications in the UV, visible, and near-IR portions of the spectrum. The material is a fumed silica, or quartz powder and is based on the line of hydrophilic Aerosil products produced by Evonik Industries in Essen, Germany. Several products from this line have been tested, including Aerosil 380, Aerosil 90, and Aerosil EG50. The number attached to each name indicates the specific surface area m2 ∕g for the particular material. Average particle sizes for the various powders range from approximately 20 to 40 nm, but these individual particles are not found alone. Instead the material forms aggregates of partially fused particles, and these can then form larger agglomerate particles that can be several micrometers across [23,24]. In order to see this small-scale structure of the fumed silica we imaged samples of the powder in a JEOL JSM-7500 field emission scanning electron microscope (SEM). The samples were prepared by taking a very small portion of the loose powder (about the size of a pinhead) and dispersing it in several milliliters of isopropyl alcohol. This suspension was then sonicated and applied to the surface of a transmission electron microscopy (TEM) grid, which was then allowed to dry. The TEM grid served to hold the loose powder in place during the imaging process and to reduce any charging effects from the electron beam on the quartz sample. Figure 4(a) shows an SEM image of several aggregate particles, as well as some of the individual spherical base particles that were separated by the sonication process. Figure 4(b) shows a larger agglomerate particle. Based on the results in the previous section, a high-reflectivity surface can be produced by a stack of air–glass interfaces. A group of these fumed silica particles is an excellent candidate to provide such air–glass interfaces. The micrometer size scale of the agglomerate particles means that the required
1.00 0.99
Reflectivity,
0.98 0.97 0.96 0.95 0.94 0.93 0.92
0
2000
4000
6000
8000
10 000
12 000
Number of Layers, N Fig. 3. Plot showing the total reflectivity of a stack of glass plates versus the number of plates in the stack for an air–glass interface of reflectivity ρ 0.04, with background reflectivity η 0. 336
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Fig. 4. SEM images of (a) fumed silica base particles and aggregates of those base particles (the light gray spots) and (b) a larger agglomerate particle. The scale for each image is indicated by the white bar, which represents 1 μm for both images. The darker webbing structure in the background is conductive tape used to hold the TEM grid in place.
24,000 interfaces for a reflectivity of 0.999 could be reached with a wall thickness of only a few cm. Of course, a wall made up of such particles would not produce the type of retroreflections depicted in Fig. 2. The light would instead be diffusely scattered at the various air-quartz interfaces due to the random orientation of the individual particles. This means that we should expect a wall made of this quartz powder to be a good diffuse reflector. A.
Relative Reflectance Measurements
Early investigations into the reflectance of these powders involved making simple comparison measurements between samples of the various powders and a Spectralon reference. Figure 5 shows the basic setup used in these experiments. The individual samples were rotated under a port in an integrating cavity. A 532 nm cw laser was directed through a second port onto the sample at an angle of 8° from the surface normal. The irradiance on one of the cavity walls was sampled with a Hamamatsu 1P21 photomultiplier tube through a third port that was shielded from direct reflections by a baffle. Figure 6 shows the results from one of these tests. The small peaks on each side of the data for the powder samples are the result of the specular reflections from the metal ring that held those samples. The data show that both the Aerosil 90 and the Aerosil EG50 fumed silica powders perform at least as well as the Spectralon sample [25]. All the fumed silica powders used in this work have a very large surface area per unit mass, and therefore they can readily absorb moisture and other volatiles. Remember that in our model for a highly reflecting wall it was assumed that the absorption in the glass was negligible. If this were not so, each time the light passed through one of the plates a small amount would be absorbed, making high reflectivities impossible. In addition, anything that reduces the number of air–glass interfaces (i.e., large amounts of trapped moisture) will also hinder the reflectivity (see Fig. 3). Therefore, some of the powder samples were baked at a temperature of ∼200°C in order to mitigate possible contamination. Figure 7 shows the relative reflectivities for all the samples
Fig. 5. Diagram showing the basic setup for the relative reflectance tests.
Fig. 6. Plot of the oscilloscope output showing the results of the relative reflectance tests.
tested. The reflectivity of the Spectralon sample used as the reference was set to unity. Note that the baked samples outperformed the unbaked samples, with the baked Aerosil EG50 being the best overall. The sample labeled Pegasus in Fig. 7 is another type of pure silica powder produced by Pegasus Glassworks Incorporated in Sturbridge, Massachusetts. B. BRDF Measurements
Recall that the two primary characteristics for a diffuse reflector are its reflectivity and its BRDF. Spectralon has a nearly constant BRDF, and thus exhibits excellent Lambertian behavior [11]. BRDF measurements for both Spectralon and Aerosil 90 were carried out at 404, 532, and 633 nm. Incident light was directed at an angle of 30° from the surface normal, with polarization perpendicular to the plane of incidence. The detector was set to measure 8° out of the plane of incidence and at scattering angles from −90° to 90° with respect to the surface normal. The aperture for the detector was 1.3 cm in diameter and was 56 cm from the sample. Figure 8 shows the results from these measurements for the three wavelengths. Nearly identical results were seen with the incident polarization set parallel to the plane of incidence, as well as when the angle of incidence was changed to 60° for both perpendicular and parallel polarization [25]. These results demonstrate
Fig. 7. Relative reflectances for various fumed silica powders. The plot is scaled such that Spectralon has a reflectance of unity. 10 January 2015 / Vol. 54, No. 2 / APPLIED OPTICS
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Fig. 8. BRDF for incident light at 30° with polarization perpendicular to the plane of incidence.
that the fumed silica is an excellent Lambertian reflector. It should be noted that when measuring the BRDF several complications typically arise. One deals with the finite size of the detector. For example, even when the detector is at 90°, the scattered power will not drop to zero (as it should in the case of an ideal Lambertian surface). To visualize this imagine a circular detecting surface with its center at 90° from the surface normal of the material being illuminated. Half of the surface area of the detector will still be at an angle less than 90° and thus will be able to receive some scattered light; the other half sees no scattered light. This effect was taken into account in the measurements described above and has been described by Musser [25]. Secondary scattering off the measuring apparatus can also be an issue. This is often dealt with by measuring the BRDF for a traceable standard. The difference between the measured signal for the standard and the sample is then added to the standard’s known BRDF. These issues and others are discussed at length by Nicodemus et al. [13] and by Stover [26]. However, for this study we only compared the BRDF of the quartz powder to Spectralon; absolute numbers were not needed.
with a hydraulic press into a semi-solid material that can be used to make the cavity walls. The semi-solid nature of the compressed powder is a consequence of the interlocking of the irregular-shaped quartz powder particles. Previous work comparing packing pressure to transmission of incident light for sample disks of the powder demonstrated that transmission was minimized for a pressure range of 30–1000 psi [25]. In fact, at very high pressures, the pressed powder starts to become transparent as the individual fumed silica particles begin to make optical contact. The cavities themselves are constructed in a variety of different ways. One method involves using a mold that the powder can be packed into to form the desired cavity shape. These molded cavities are usually made in separate halves that are then stacked together to form the complete cavity. In order to avoid contamination, high-purity quartz glass is always used to form the various pieces of the cavity mold. The semi-solid nature of the compressed powder makes it amenable (with care) to standard machining procedures. Based on this, a second method for making cavities involves packing solid cylinders of the quartz powder and then machining out the inner cavity region with a lathe or mill. As an example, typical cutting speeds for a 3∕400 -diameter titanium nitride coated end mill range from ∼150 to 320 surface feet per minute. This method also requires the cavity to be made in halves. Figure 9 shows an example of a cavity made using this machining method. Many of the potential applications for cavities made of this material involve introducing a liquid or gaseous sample into the integrating cavity. In these cases, it is necessary to isolate the porous fumed silica that constitutes the cavity wall from the sample being tested. This is typically done by using a fused silica (quartz glass) sample cell to form the inner cavity wall. The quartz powder is then packed around this sample cell to form the diffuse reflecting wall.
C. Preparation and Design of Fumed Silica Integrating Cavities
In the previous sections the measurements were carried out on small samples of packed fumed silica. Much of what follows involves the use of actual integrating cavities made of the fumed silica. Therefore, some discussion about how such cavities are designed and manufactured is appropriate. It was previously mentioned that, due to its hydrophilic nature, the powder must be baked to achieve the best results. This was done in a Fischer Scientific Isotemp Vacuum Oven that is coupled to a liquid nitrogen sorption pump. The system allows the powder to be baked at a temperature of ∼280°C at a pressure of ∼1 Torr. The oven also has a purge line that allows for backfilling with ultra-high-purity argon as the material is cooling. This prebaked powder is packed 338
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Fig. 9. Picture of the two halves of a machined fumed silica cylindrical integrating cavity.
Because of the intrinsic hardness of the material (quartz has a value of 7 on the Mohs scale), the powder will often “bite” into the surfaces of the mold pieces during packing. This can make it difficult to remove the finished pieces from the mold without significant damage. In addition, the powder can pick up a significant static charge during the packing process, which exacerbates this issue. Both of these issues can be alleviated by “prepacking” the powder before making the final pieces. This involves packing the fumed silica to a given pressure (typically lower than the final packing pressure) in a quartz mold and then crushing this packed material back into a course powder form. During this entire process, only high-purity fused silica pieces are allowed to come into contact with the material to prevent any potential contamination. This prepacked powder exhibits far less static and biting effects during the final packing process, making it significantly easier to produce high quality pieces. D.
Absolute Reflectivity Measurements
The relative reflectance experiments demonstrate that the Aerosil 90 and Aerosil EG50 fumed silica products exhibit a reflectance higher than an equivalent Spectralon sample. However, these measurements do not allow one to get a meaningful value for the absolute reflectivity of the compressed powders. Anderson and co-workers developed a technique for measuring the reflectivity of mirrors via the decay time of an optical cavity formed by the mirrors [27,28]. This can be thought of as a special case of another technique known as cavity ring-down spectroscopy (CRDS) developed by O’Keefe and Deacon [29]. In CRDS a temporally short pulse of light is coupled into a high-finesse two-mirror cavity and is allowed to decay, or “ring down.” The exponential decay in the cavity can be monitored by placing a detector behind one of the mirrors to sample the intensity of the light leaving the cavity. The decay constant τ for a pulse in such a cavity can be expressed as τ
l ; c− ln ρ al
(4)
where c is the speed of light in the cavity, ρ is the mirror reflectivity, a is the absorption coefficient of any absorbing medium placed within the cavity, and l is the length of the cavity [30,31]. For an empty cavity, a 0, the cavity will ring down with a decay constant τe . If that same cavity is filled with an absorber, the intensity will ring down faster, giving a decay constant of τa. These two decay constants can then be used, with Eq. (4), to solve for the absorption coefficient. In addition, if the cavity dimensions (i.e., l) are known, one can also use the empty cavity decay time to determine the absolute reflectivity of the cavity mirrors. In the case of an empty integrating cavity, Eq. (4) reduces to
τ−
1 d¯ ; ln ρ c
(5)
where l has been replaced with the average distance ¯ This is identical to between reflections in the cavity d. the well-known result for the decay of radiation inside an empty integrating cavity [2,32]. Additionally, Fry et al. showed that d¯ for a cavity of arbitrary shape is given by [32] V d¯ 4 ; S
(6)
where V is the cavity volume and S is the cavity surface area. Thus for an integrating cavity of known dimensions, measurement of the empty cavity decay constant τe allows one to measure the absolute reflectivity for the cavity. Ring-down measurements were made for fumed silica integrating cavities at 532 and 266 nm using the second and fourth harmonic outputs from a Continuum Powerlite 9010 ND:YAG laser. The laser had a rep rate of 10 Hz and was not injection seeded for the measurements described in this work. The basic setup is shown in Fig. 10. The input pulse, typically 10-15 ns, was coupled into the cavity via a 200 μm core multimode fiber. Another 200 μm core multimode fiber samples the decay, or ring-down, of the irradiance on the cavity wall. This signal was detected via a Hamamatsu 1P21 photomultiplier tube (PMT) with a rise time of 2.2 ns. The input pulse was also measured with a second 1P21 PMT by taking a reflection off of a glass filter. The data were collected using a Hewlett Packard Infinium oscilloscope. The ring-down signal for single shots can be recorded, but typically the data sets were averaged over 1024 shots. In order to determine the decay constant for the cavity, the output pulse is fitted to an exponential function. This can be done in a variety of ways including fitting only the tail of the output decay curve to an exponential decay, convolving the actual input pulse with an exponential decay and fitting that to the output decay curve, or fitting the decay curve to the convolution of a Gaussian (representing the input pulse) and an exponential decay. All of these methods have been used and give essentially the
Fig. 10. Typical experimental setup for measuring cavity reflectivity via the ring-down signal. 10 January 2015 / Vol. 54, No. 2 / APPLIED OPTICS
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same results. The results shown here are fitted using the third method. The form of the convolution function is given by w2 t − ts − τ 2τ2 2 w − τt − ts p ; × 1 − erf 2wτ
Fitt A exp
(7)
where A is an amplitude coefficient, w is the width of the Gaussian function, ts is a time shift from t 0, erf(…) is the error function, and τ is the decay constant for the exponential function. The absolute reflectivity tests were done on cavities made with the Aerosil EG50 powder. These cavities were manufactured in two halves using the machining method described in the previous section. The cavity used for the 532 nm test was a right-circular cylinder with a diameter of 3.81 cm and a height of 6.47 cm. Figure 11 shows the input laser pulse (in blue), the output ring-down decay curve (in red), and a fit to the decay curve (black dashed line). Both the input and output curves have been normalized for this plot. The fit to the decay curve gives a decay constant of τ 120.5 0.2 ns. Combining this with Eqs. (5) and (6) gives a reflectivity ρ 0.99919 0.00002 for the cavity. The 266 nm absolute reflectivity test was done with a cylindrical cavity with 5.00 cm height and diameter. Figure 12 shows the input laser pulse, the ring-down decay curve, and a fit to the decay curve for the 266 nm test. Again, both the input and output pulses were normalized for the plot. The fit to the decay curve gives a decay constant of τ 35.3 0.2 ns, which yields a cavity reflectivity ρ 0.99686 0.00006 [25]. This value, along with the value of 0.99919 at 532 nm, are, to the best knowledge of the authors, the highest diffuse reflectivity values ever produced. Recall that Spectralon has reflectance values as high as 0.992 in the visible but drops to 0.950 at 250 nm [11]. The values for our fumed silica diffuse
Fig. 11. Plot showing the 532 nm input pulse (in blue), the ringdown decay curve for the fumed silica cavity (in red), and a fit to the decay curve (black dashed line). 340
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Fig. 12. Plot showing the 266 nm input pulse (in blue), the ringdown decay curve for the fumed silica cavity (in red), and a fit to the decay curve (black dashed line).
reflector are considerably higher in both regions. This difference is perhaps better appreciated if we consider the total effective path length Leff for a photon inside the cavity. The average number of reflections n for a photon inside the cavity is given by [32] n−
1 : ln ρ
(8)
Leff should simply be this n multiplied by the average ¯ Thus, distance between reflections in the cavity d. we have Leff −
1 ¯ 1 ¯ 4 V d≈ d ; ln ρ 1 − ρ 1 − ρ S
(9)
where we have used Eq. (6) and exploited the fact that −1∕ ln ρ ≈ 1∕1 − ρ for ρ ≈ 1. Using Eq. (9) for an empty spherical cavity with a diameter of 5 cm, we find total effective path lengths of Leff 4.167 m and Leff 41.15 m for cavity reflectivities of 0.992 and 0.99919, respectively. It should be noted that the measured decay time and resulting absolute reflectivity value represents the average reflectivity of the cavity and not the reflectivity for the diffuse reflecting cavity wall. In general, the measured result for a cavity will be less than or equal to the actual reflectivity (or reflectance) of the fumed silica wall. The reason is that the measured cavity reflectivity intrinsically includes any loss effects due to ports or imperfections in the cavity wall. For instance, the two cavities used in these measurements each had two fibers: one to deliver the input pulse and one to measure the output pulse. These are essentially ports in the cavity wall through which light escapes. Thus, they lower the overall cavity reflectivity from that of an ideal cavity made from the same material. Of course, these port losses will scale as the fraction of the total cavity surface area that the ports comprise. For the 200 μm core (500 μm total diameter) fibers used in these experiments, this
port fraction is less than 0.01% of the total cavity surface area. E.
Sintering Effects and SEM Measurements
The cavity used for the 532 nm reflectivity measurements was made of the same material and was of similar size as that used for the 266 nm test. However, it was subjected to an additional hightemperature bakeout prior to the ring-down measurement. This bakeout was done in a lab furnace at a temperature of ∼1000°C and was in addition to the prebake process described Section 4.C. This baking process resulted in a higher cavity reflectivity than the previous best for the fumed silica at 532 nm; a value of 0.998 [25]. In order to verify the benefit of this additional step, a single cavity was prepared and tested both before and after the bakeout. The two cavity halves were made using the quartz glass mold process described in Section 4.C. This resulted in a spherical cavity with a diameter of 52 mm. A ring-down test at 532 nm was performed immediately after the cavity was completed. The piece was then baked at ∼1000°C for several hours and tested again. Fits to these two ring-down curves yielded decay constants of 13.9 ns (before bakeout) and 83.8 ns (after bakeout). These decay constants correspond to cavity reflectivities of 0.9934 and 0.9985, respectively. Obviously this second reflectivity value is lower than the value from the measurement presented in the previous section (i.e., 0.9985 versus 0.99919). This is because this was a molded piece, as opposed to a pressed and machined piece. The molded cavities tend to have a lower reflectivity than the machined cavities due to the lower packing pressures that are used to avoid damaging the quartz glass mold. It is evident from these reflectivity values that the bakeout has a significant effect on the cavity. Additionally, the material seems slightly more durable and machinable after the bakeout. Of course, one would like to know what, if any, effect this bakeout is actually having on the material at the microscopic level. The basics of the methods used to make these cavities are essentially identical to the process for sintering powders. Sintering typically involves a high-purity metal or ceramic powder that is pressed into a mold and then baked at a high-temperature under the material’s melting point. The result is to turn the powdered material into a solid via atomic diffusion. However, existing work with quartz ceramic powders suggests that no true sintering effects occur for temperatures of less than 1100°C [33]. Another possibility is that this bakeout is simply removing volatile contaminants trapped in the powder. As mentioned before, these fumed silica powders are hydrophilic, so water is a likely contaminant. The prebake procedure described in Section 4.C is done to remove any trapped water. Nevertheless, the second bake after final packing could be removing residual trapped water, or any water vapor that was absorbed during the manufacturing process.
In an effort to determine whether the benefits of the bakeout are due to an actual change in the microscopic characteristics of the material, several samples were imaged with an SEM. The samples were all 2.5 mm thick 12 mm diameter disks of prebaked packed Aerosil EG50. The disks were held in quartz glass rings with a outer diameter of 16 mm and a thickness of 2.5 mm. All of the samples were initially prepared the same way but two of the three samples were given an additional high-temperature bakeout at temperatures of 930°C and 1085°C. These two temperatures were chosen based on previous experience. Pieces baked at ∼1085°C have a tendency to shrink, while pieces baked at ≤1000°C seem to maintain their original volume. These three samples were imaged using a JEOL JSM-7500 field emission SEM. SEM imaging for insulating materials like quartz is complicated by the fact that the quartz sample tends to pick up charge from the electron beam, which then produces a repulsive effect on the beam. This results in a jittering of the beam that limits the SEM’s ability to focus. To alleviate this issue, the quartz samples were placed in a set of brass sample holders. These holders were machined with recesses to accommodate the height and diameter of the quartz glass rings that encompassed the quartz powder sample disks. In addition to this, the top surface of each sample was sputtered with a 5 nm platinumpalladium coating. These two steps were effective in reducing the surface charging effects and allowing for higher magnification imaging. Figure 13 shows SEM images at a magnification of 50; 000× for the unbaked sample (a) and the sample baked at 930°C (b). The slight blur in the images is due to the surface charging effects mentioned above. The two images look strikingly similar and do not show any of the obvious changes in microscopic structure that are seen in the sintering of other types of powders [34]. This suggests that if any true sintering effects are taking place, they are minimal. The images for the sample baked at 1085°C also showed no significant differences when compared to the unbaked samples [35]. 5. Cavity Ring-Down Spectroscopy
When discussing the absolute reflectivity measurements in Section 4.D, the CRDS technique was
Fig. 13. SEM images of packed fumed silica samples (a) without and (b) with the additional high-temperature bakeout at 930°. Each image is at 50; 000× magnification. 10 January 2015 / Vol. 54, No. 2 / APPLIED OPTICS
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briefly mentioned. Consider it now in a bit more detail. Figure 14 shows the basic setup for a conventional CRDS measurement. A temporally short laser pulse is introduced into a high-finesse cavity and allowed to decay. This decay is measured by observing the intensity of light leaving one of the cavity mirrors over time. If an absorber is present in the cavity, the decay constant will be reduced in accordance with Eq. (4). Thus, the absorption coefficient for a sample placed in this cavity can be deduced by comparing the empty cavity decay constant τempty to the decay constant with the sample in the cavity τsample. Using Eq. (4), it is trivial to show that the absorption coefficient asample is given by asample
1 1 1 − ; c τsample τempty
(10)
where we have assumed that the sample uniformly fills the entire cavity length l [29–31]. In CRDS it is the temporal behavior of light inside the cavity that is being measured, so there is an inherent insensitivity to fluctuations in source intensity. However, in order to ensure exponential decay inside the cavity, it is important that the source has a linewidth narrower than the width of the absorption features being measured. The minimum absorbance detectable by CRDS, as given by Zalicki and Zare [30], is Δτ ; als 1 − ρ τ
(11)
where a is the absorption coefficient, ls is the length of the sample inside the cavity, and Δτ is the decrease in the decay constant when the sample is placed in the cavity. They also give an estimate for the best possible accuracy, Δτ∕τmin , that can be expected in a measurement of the ring-down time τ for a single shot (i.e., single ring-down) [30,36,37]. With Δτ∕τmin ≈ 3 × 10−3 , and mirror reflectivities as high as 0.9999 (in the visible), Eq. (11) gives a minimum detectable absorbance of 3 × 10−7, although even higher sensitivity can be attained by averaging over many cavity decays [38]. Thus, the CRDS technique provides an exceptional method for measuring extremely low absorption by a sample. The high sensitivity of CRDS makes it an excellent technique for absorption spectroscopy, but there is a very important complication that must be considered. That problem is that CRDS actually provides a direct measurement of the extinction coefficient
Fig. 14. Diagram of a generic CRDS cavity. 342
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(i.e., scattering plus absorption). In the case where the scattering is negligible this will indeed give a good direct measurement of the absorption coefficient. However, when scattering is significant, the a in Eq. (4) must be replaced with the extinction coefficient, and the scattering must be independently measured or determined to obtain a. A. Integrating Cavity Ring-Down Spectroscopy
As a result of the high reflectivites obtained with the quartz powder, we have the opportunity to introduce a new version of CRDS called integrating cavity ringdown spectroscopy (ICRDS). It eliminates both of the complications discussed at the end of the previous section. Figure 15 shows a cross section of a generic ICRDS cavity. The input pulse is delivered to the integrating cavity via a fiber. A second fiber samples the ring-down of the irradiance on the cavity wall. The issue of scattering is solved because after several reflections of the input pulse the light field inside the integrating cavity is essentially isotropic. Thus, the effects due to any scattering present in the sample are negligible. This means that ICRDS provides a true direct measurement of the absorption coefficient, even in the presence of strong scattering. It should also be noted that integrating cavities (owing to the disordered makeup of the diffuse reflecting wall structure) have no preferred modes. In principle, an ICRDS cavity can be used continuously over the entire wavelength range for which the wall reflectivity is sufficiently high. For samples with negligible scattering, traditional CRDS will be able to outperform ICRDS whenever the cavity mirror reflectivity exceeds the diffuse reflectivity for the integrating cavity wall. This is the case in the visible spectrum, where mirror reflectivities can easily exceed 0.9999. However, mirror reflectivities drop off considerably in the UV. Below 355 nm, the best mirrors have reflectivities of 0.995 [39], which is less than the 0.99686 diffuse reflectivity measured for the fumed silica cavity in Section 4.D. Therefore, ICRDS could potentially
Fig. 15. Diagram of a generic ICRDS cavity.
outperform CRDS in the UV, even when scattering effects are negligible [37]. For the case of significant scattering ICRDS will always outperform CRDS for measuring the absorption coefficient provided that the cavity reflectivity is sufficiently high. And, ICRDS will also actually measure the absorption of the scattering particulates themselves. In order to illustrate the importance of our new diffuse reflector for ICRDS, let us consider the decay of a 10 ns FWHM Gaussian input pulse inside a 5 cm diameter spherical integrating cavity. Figure 16 shows the calculated ring-down decay curves for cavity reflectivities of ρ 0.992 (Spectralon at 532 nm) and ρ 0.99919 (Fumed Silica at 532 nm). The dramatic difference between these curves demonstrates the significance of the increased reflectivity. We can also consider the effect on the ring-down curve when the cavity is filled with an absorbing sample. For the same 5 cm cavity with ρ 0.99919, Fig. 17 shows the calculated ring-down decay curves for absorption coefficients of a 0 cm−1, 5 × 10−5 cm−1 , 1 × 10−4 cm−1 , and 5 × 10−4 cm−1 . This demonstrates the high sensitivity of the ICRDS technique. For example, the Δτ between the empty cavity and the a 5 × 10−5 cm−1 lines in Fig. 17 is 23.4 ns. Between the empty cavity and a 5 × 10−4 cm−1 lines this value is 92.3 ns. If we consider the same absorption coefficients for a cavity reflectivity ρ 0.992 (Spectralon), the corresponding Δτ values for the a 5 × 10−5 cm−1 and 5 × 10−4 cm−1 lines are only 0.3 and 2.4 ns, respectively. Clearly the fumed silica diffuse reflector offers a substantial increase in sensitivity for ICRDS and makes this a viable technique. Additionally, we can use Eq. (11) from the previous section to estimate the minimum detectable absorption coefficient for ICRDS. Using the single-shot value Δτ∕τmin ≈ 3 × 10−3 reported for traditional CRDS, replacing ls with the d¯ for our 5 cm cavity (i.e., 3.33 cm) and using a reflectivity of ρ 0.99919 (fumed silica at 532 nm), we find a minimum detectable absorption coefficient of 1.7 × 10−6 cm−1.
Fig. 17. Plot modeling the decay of a 10 ns pulse in a 5 cm diameter spherical cavity (ρ 0.99919) filled with an absorbing sample with a 0 cm−1 , 5 × 10−5 cm−1 , 1 × 10−4 cm−1 , and 5 × 10−4 cm−1 , respectively.
Of course, this minimum can be made even smaller with a larger cavity. It is also important to consider the stability of the measured τ for a given cavity over time. To examine this we prepared a cylindrical cavity with a 5.72 cm height and diameter. The ring-down decay curve for the cavity was measured at 532 nm using the same setup described in Section 4.D, but the averaging on the oscilloscope was reduced to only 64 shots. The measurement was repeated 16 times, and each decay curve was fit using Eq. (7) to find the corresponding decay constant τ. The average and standard deviation for these results was τavg 101 1 ns, with the largest deviation being less than 2 ns. This yields a cavity reflectivity of ρ 0.99874 0.00003. Based on this, it is clear that for this particular cavity in the experimental setup, the minimum detectable absorption coefficient would be closer to 9 × 10−6 cm−1 or roughly a factor of 5 higher than the hypothetical minimum calculated above. However, since the reflectivity of this cavity is lower than our highest measured cavity reflectivity (ρ 0.99919 at 532 nm), the reduced sensitivity seen here is not unexpected. B. Measuring the Cavity Wall Time
Fig. 16. Plot modeling the decay of a 10 ns FWHM Gaussian pulse in a 5 cm diameter spherical integrating cavity. The black curve is the input pulse and the red and green curves are the ring-down curves for cavity reflectivities ρ of 0.992 and 0.99919, respectively.
For a typical specular reflection the incoming light is reflected off the surface of the reflector. However, for a diffuse reflector the light actually penetrates into the cavity wall. Individual photons will, in general, scatter off of many particles before finding their way out of the wall. The difference between these two processes is illustrated in Fig. 18. It is clear that the light spends some time in the cavity wall, and thus any measurement of the decay time for a cavity with diffuse reflecting walls will include this contribution. To account for this “wall time,” Eq. (5) can be modified as follows: ¯ d 1 δt ; τ − ln ρ c 10 January 2015 / Vol. 54, No. 2 / APPLIED OPTICS
(12)
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Fig. 18. Diagram illustrating the difference between (a) specular reflections off a surface and (b) diffuse reflections off a surface for light incident from a single direction.
where δt is the average amount of time the light spends in the wall for each reflection. This modified equation also suggests a method to measure δt. Rearranging Eq. (12) as follows, d¯ − ln ρτ − δt mτ b; c
(13)
we have a linear equation in terms of τ, where the slope is given by m − ln ρ and the y intercept is given by b −δt. Thus we can make several cavities ¯ versus τ for the entire of increasing size and plot d∕c set. A linear fit to this data provides a determination of δt and ρ for the cavities. In practice, it is difficult to reproduce exactly the same reflectivity for multiple cavities, even when they are made the same way. To deal with this issue a single cylindrical cavity was used for the entire experiment. The increases in cavity size were achieved by machining out ever larger cavities after each measurement. The outer diameter of the cylindrical cavity was made large to minimize any effects due to changes in cavity wall thickness. For the data presented here the total wall thickness was never less than 25 mm. The cavity halves were prepared by taking prebaked Aerosil EG50 powder and pressing it into solid cylindrical pieces at a pressure of ∼85 psi. These two cylindrical halves were then baked at 1000°C for 10 h. The interior cavity size was machined out using a mill, with an increasing diameter for each successive measurement. The setup for the experiment was essentially identical to Fig. 10. The input pulse was the 532 nm frequency doubled output from a Continuum Powerlite 9010 Nd:YAG. A pair of 200 μm core multimode fibers were used to couple the input pulse into the cavity and sample the output ring-down signal. The output signal was measured using a 1P21 PMT. Each cavity size produced its own ring-down curve that was fit with the convolution fit function given in Eq. (7) to calculate its decay constant τ. The average distance between reflections d¯ for each cavity is divided by c and shown as a function of the measured τ in Fig. 19. The geometry of each cavity size was a right-circular cylinder with D H, so Eq. (6) yields d¯ 2∕3D. The linear least squares fit to the data gives a slope of m 9.61 0.25 × 10−4 ns and a y intercept of b −3.5 2.6 × 10−3 ns. Comparing these values with the equivalent terms in Eq. (13) leads to a cavity 344
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¯ versus the cavity decay constant τ for a Fig. 19. Plot showing d∕c single fumed silica cavity that has been machined with an increasing inner diameter. A linear fit to the data is also shown.
wall time of δt 3.5 2.6 ps and an average cavity reflectivity of ρ 0.99904 0.00003. A second measurement of this wall time involved filling the cavity with solutions of increasing (but known) absorption coefficient. The wall time can then be calculated by considering a plot of the inverse of the cavity decay time versus the absorption coefficient of the various samples. This method also suggested a wall time on the order of several picoseconds but the uncertainty in the measurement due to the presence of the quartz glass sample holder could not be fully ascertained [35]. Therefore, those results are not presented here. Recall that δt is the average amount of time light spends in the cavity wall for each reflection. If we consider a cavity with reflectivity ρ 0.999, then, via Eq. (8), the average number of reflections for a photon in the cavity is ∼1000. Thus, photons can end up spending several nanoseconds inside the cavity wall over the course of the entire ring-down process. That being said, this wall time will typically be only a small percentage of the total time an average photon spends inside the cavity. For example, photons in a cavity with d¯ 3 cm have an average transit time between reflections of ∼100 ps, compared to the average wall time of several picoseconds for each reflection. If the cavity size is increased, the contribution of the wall time becomes even less significant. Thus, we see that while the cavity wall time is important, it is not a major consideration for ICRDS measurements, particularly when the cavity size is large. We can also consider the effect of the wall time on the reflectivity for a cavity. Table 1 shows the measured decay constant τ and the reflectivity ρ as calculated by Eq. (5) (i.e., without δt), for the various cavity sizes used in the wall-time measurements presented above. Comparison of these reflectivity values with the average cavity reflectivity with δt, ρ 0.99904 0.00003, indicates that the wall time has little effect on the reflectivity. It should also be noted that we have not made any assumptions about the distribution of the wall times
Table 1. Table of the Measured Decay Constant τ and Reflectivity ρ (with δt Neglected) for Various Cavity Sizes d
d¯ (mm)
Decay Const., τ (ns)
Reflectivity, ρ
46.9 61.3 76.9 94.9 105.9 120.6 138.9 146.6
0.99910 0.99908 0.99908 0.99911 0.99907 0.99906 0.99909 0.99904
12.7 16.9 21.2 25.4 29.6 33.9 38.1 42.3
where V is the cavity volume and S is the cavity surface area. This gives a relative uncertainty of 7% for the d¯ of the smallest cavity size, and only 2% for the largest size. The uncertainty in the wall time δt was calculated from a linear least squares fit to the data in Fig. 19. This gave relative uncertainties of 2.6% for the slope and 75% for the y intercept. These values lead to relative uncertainties of 75% for δt and 0.003% for the average reflectivity of the cavity ρ. 7. Conclusions and Future Work
for individual photons inside the cavity. This measurement only serves to give an estimate of the average δt for each reflection. For instance, if the distribution for the wall time has a long nonexponential tail, this could artificially inflate any measurement of the decay constant for the cavity. However, for any ICRDS measurements of absorption, the empty cavity τ would always be measured and used as a baseline. Thus, these effects should effectively cancel out of the final measurement. 6. Error Analyses A.
Reflectivity Measurements
There are two sources of error for the absolute reflectivity measurements presented in Section 4.D: error in the cavity dimensions and error in the decay constant. Any error in the cavity dimensions manifests ¯ The machining process for the cylindrical itself in d. cavities had an accuracy of 0.3 mm for the height and 0.3 mm for the radius. This leads to relative uncertainties of 2.2% and 1.8% for the d¯ of the 532 and 266 nm test cavities, respectively. The uncertainty in the decay constant τ was determined using the standard error values for the convolution fit function given in Eq. (7). These were calculated using the nonlinear fitting parameter confidence options in Mathematica. The relative uncertainty for τ is less than 1% for both of the tests. Using Eq. (5), and basic error propagation, we find the uncertainty in the cavity reflectivity ρ is less than 1 × 10−4 for both the 532 and 266 nm tests. B.
Cavity Wall-Time Measurements
In Section 5.B the cavity wall time was determined by measuring the decay constant for increasing cav¯ The various cavity sizes were achieved by ity size d. machining out ever larger cavities from two cylindrical cavity halves. The accuracy for this machining process was the same as for the reflectivity measurements described above. All cavities were rightcircular cylinders with D H. Based on Eq. (6), the resulting relative uncertainty in the cavity d¯ is given by the expression δd¯ d¯
s 2 2 δV δS ; V S
(14)
We have demonstrated that high-purity fumed silica powders can be used to make ultrahigh reflectivity diffuse reflecting surfaces. Using this material we have recorded reflectivity values as high as 0.99919 at 532 nm and 0.99686 at 266 nm. These values are, to the best knowledge of the authors, the highest diffuse reflectivity values ever produced at those wavelengths [11]. We also introduced a new spectroscopic technique that we call ICRDS. It is based on traditional CRDS, but the mirrored cavity is replaced with an integrating cavity. ICRDS offers a significant benefit over traditional CRDS because it provides a direct measurement of the absorption (as opposed to the extinction) of the sample. In other words, ICRDS, unlike CRDS, is insensitive to scattering in the sample. Finally, we discussed the idea that light propagating inside an integrating cavity will spend a small amount of time in the cavity wall during each reflection. We demonstrated this cavity wall time by measuring it for a set of cavities with increasing diameter. The results suggest that the wall time is on the order of several picoseconds in magnitude. Thus, it is of marginal importance for applications involving the temporal response of an integrating cavity. The fumed silica has proven to be an excellent choice for the visible and UV, but many of the ideas presented in this work are not specific to any one material. If one recalls the model described in Section 3, it was only required that the plates had negligible absorption. Thus by finding a material with the appropriate optical properties, one could easily extend this work into other regions of the spectrum. We gratefully acknowledge support from the Robert A. Welch Foundation under Grant A-1218 and the George P. Mitchell Chair in Experimental Physics. We also thank Bill Merka and Yordanos Bisrat for their assistance and advice. References and Notes 1. J. Palmer and B. Grant, The Art of Radiometry (SPIE, 2010). 2. J. Beaulieu, “A guide to integrating sphere theory and applications,” Tech. Rep. (Labsphere Inc., 1999). 3. P. Elterman, “Integrating cavity spectroscopy,” Appl. Opt. 9, 2140–2142 (1970). 4. E. S. Fry, G. W. Kattawar, and R. M. Pope, “Integrating cavity absorption meter,” Appl. Opt. 31, 2055–2065 (1992). 5. R. M. Pope and E. S. Fry, “Absorption spectrum (380–700 nm) of pure water. ii. Integrating cavity measurements,” Appl. Opt. 36, 8710–8723 (1997). 10 January 2015 / Vol. 54, No. 2 / APPLIED OPTICS
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