Optical Tests of Nanoengineered Liquid Mirrors

Optical tests of nanoengineered liquid mirrors

Helene Yockell-Lelievre, Ermanno F. Borra, Anna M. Ritcey, andLande Vieira da Silva, Jr.

We describe a new technology for the fabrication of inexpensive high-quality mirrors. We begin bychemically producing a large number of metallic nanoparticles coated with organic ligands. The par-ticles are then spread on a liquid substrate where they self-assemble to give optical quality reflectivesurfaces. Since liquid surfaces can be modified by a variety of means �e.g., rotation, electromagneticfields�, this opens the possibility of making a new class of versatile and inexpensive optical elements thatcan have complex shapes and that can be modified within short time scales. Interferometric measure-ments show optical quality surfaces. We have obtained reflectivity curves that show 80% peak reflec-tivities. We are confident that we can improve the reflectivity curves because theoretical models predicthigher values. We expect nanoengineered liquid mirrors to be useful for scientific and engineeringapplications. The technology is interesting for large optics, such as large rotating parabolic mirrors,because of its low cost. Furthermore, because the surfaces of ferrofluids can be shaped with magneticfields, one can generate complex, time-varying surfaces that are difficult to make with conventionaltechniques. © 2003 Optical Society of America

OCIS codes: 000.3110, 240.6700, 260.3910, 350.1260.

1. Introduction

Liquid surfaces follow equipotential surfaces so thata reflective liquid makes a mirror that has the shapeof equipotentials. Liquid mirrors therefore offernew possibilities for the fabrication of unique opticalelements. For example, the fact that the surface ofa liquid rotating in a gravitational field takes theshape of a parabola has been used to make largeinexpensive parabolic mirrors. For a given diame-ter, the cost of a diffraction-limited mercury liquidmirror is almost 2 orders of magnitude lower than thecost of a glass mirror, making it competitive for someapplications. The technology is young but its qual-ity and robustness have been documented in the lab-oratory1,2 as well as in observatory settings.3–5

However, liquid metals have several disadvantages�e.g., high density and toxicity� so that it would beadvantageous to replace them with other liquids hav-

All the authors are with the Centre d’Optique, Photonique etLasers, Universite Laval, Quebec G1K 7P4, Canada. H. Yockell-Lelievre �[email protected]� and A. Ritcey �[email protected]� are with the Departement de Chimie; E. F. Borra�[email protected]� and L. Vieira da Silva, Jr. �[email protected]� are with the Departement de Physique, Genie Physiqueet Optique.

Received 4 October 2002; revised manuscript received 13 De-cember 2002.

0003-6935�03�101882-06$15.00�0© 2003 Optical Society of America

1882 APPLIED OPTICS � Vol. 42, No. 10 � 1 April 2003

ing better characteristics. Furthermore, liquid sur-faces can be shaped by means other than rotation.For example, the surfaces of ferrofluids can be shapedwith magnetic fields.6 Unfortunately, mercury andsome gallium alloys7 are the only metals that areliquid at room temperature so that we have a limitedrange of parameters �e.g. magnetic susceptibilities� towork with if restricted to liquid metals.

To extend the range of useful liquids and the rangeof available parameters, such as magnetic suscepti-bility, we have begun a research program that en-deavors to find techniques that allow the depositionof high-reflectivity metallic surfaces on liquids. In arecent paper8 Borra et al. discussed the characteris-tics of metal liquidlike films �MELLFs� trapped at theinterface between two liquids. MELLFs were origi-nally developed by chemists to study the character-istics of the chemicals that coat metallic grains.Realizing their potential use in optical applications,we have started a research program to investigatetheir optical properties and refine the chemical tech-niques for optical applications.

Here we describe the basic technology �Section 2�and discuss the optical characteristics of MELLFsdeposited on the top surface of a liquid �Section 3�.The spreading of the reflecting layer on the top sur-face represents a significant improvement comparedwith our previous mirrors in which the nanoparticleswere assembled on the interface between two liquids.In the present configuration, the reflective nanopar-

ticle coating is the first surface encountered by theincoming electromagnetic wave.

2. Preparation of Silver Particles and Deposition ofReflective Films on Liquids

Stable interfacial suspensions of silver nanoparticleshave been described in the literature and are fre-quently referred to as MELLFs.9,10 These uniquesystems combine the optical properties of metals withthe fluidity of a liquid suspension and are thereforewell adapted to applications in the field of liquid op-tics. The fabrication of a MELLF involves the cre-ation of silver nanoparticles, generally by chemicalreduction of a silver salt in aqueous solution, and thesubsequent coating of the particles with a strongmetal-bonding organic molecule, a ligand. Whencoated, the particles are no longer stable in the aque-ous phase and spontaneously assemble on the water–organic interface.

The MELLFs investigated in this study were pre-pared in the following way: Silver nanoparticleswere first prepared by chemical reduction of silvernitrate with citrate in an aqueous solution followinga known procedure.11 Two different preparationswere considered: in one case the temperature wasmaintained precisely at 100 °C, whereas in the otherthe temperature was less well controlled and slightlylower �around 95 °C�. The silver nitrate solutionwas brought to a boil �100 °C� before addition of thereducing agent. In the case of more precise temper-ature control, the citrate solution was also heated toboiling before its addition, thus permitting the temper-ature to be maintained at 100 °C throughout the re-duction process. In the second preparation method, aroom-temperature citrate solution was added to thesilver nitrate solution, resulting in a temporary drop inthe temperature. The resulting aqueous suspensionof metallic particles was then vigorously shaken for5 min together with a solution of either 1,10-phenanthroline, 2,9-dimethyl-1,10-phenanthroline, or2,2-dipyridyl in 1,2-dichloroethane. This step pro-vokes the spontaneous formation of a concentratedfluid phase of particles at the interface between thetwo liquids. Finally, the concentrated interfacial sus-pension of particles was collected by removal of theexcess aqueous and organic phases, washed, and thenpoured onto a water surface. At this point, the resid-ual 1,2-dichloroethane in the MELLF evaporates, leav-ing a thin dried film of ligand-coated nanoparticles.Although this film is not truly liquidlike, it is able towithstand small deformations without breaking.

It must be noted that, although the results re-ported below refer only to mirrors spread on purewater, certain characteristics of the liquid support�e.g., viscosity or magnetic susceptibility� can be eas-ily varied by introduction of suitable additives intothe water �e.g., water-soluble polymers or colloidalparticles�. Complete details of the chemical prepa-ration and characterization of the MELLFs will ap-pear elsewhere.

The shape and the size of the particles obtainedfrom the two preparations are shown in the trans-

mission electron microscope images in Fig. 1. Keep-ing a constant temperature of 100 °C predominantlyproduces spherical particles having variable diame-ters of a few tens of nanometers. If we reduce thetemperature by a few degrees during chemical reduc-tion, we produce elongated particles of the order of100 nm. We obviously have some measure of controlover the size and the shapes of the particles by con-trolling the temperature during the first few minutesof the chemical reduction that produces them.

3. Optical Tests of Nanoengineered Mirrors

A. Interferometry

The Laval Liquid Mirror Laboratory is currently car-rying out work to develop large rotating parabolicliquid mirrors that use metal-coated liquids as well asmagnetically deformable adaptive mirrors made ofcoated ferrofluids.6 Most of this research is inprogress and will be reported elsewhere in the future.Because our aim here is to introduce the basic conceptand coating technology, we shall discuss only flatwater-based mirrors. We have made and tested sev-eral flat liquid mirrors. We have carried out inter-ferometric tests at a wavelength of 632.8 nm with aFizeau interferometer made by the Zygo Corporation�Model GPI-XP�.

Figure 2�b� shows an interferogram that we ob-

Fig. 1. Transmission electron microscopy images of MELLF sam-ples prepared from a silver colloid reduced to �a� a constant boilingtemperature of 100 °C and �b� a slightly lower temperature of95 °C.

Fig. 2. Interferograms of �a� a clean optically flat mirror and �b� a6.5-cm-diameter MELLF sample dried at the water–air interface.It is readily obvious that the surfaces have comparable qualities.

1 April 2003 � Vol. 42, No. 10 � APPLIED OPTICS 1883

tained by measuring a 6.5-cm-diameter sample of oneof our dried MELLF surfaces. The lateral resolutionon the surface of the liquid was 0.1 cm. We cancompare the fringes with those obtained under thesame conditions by measuring a ��20 glass mirror�Fig. 2�a��. We can readily see that the surfaceshave comparable qualities. This is to be expectedsince the surface of a liquid follows an equipotentialsurface to a high precision, as shown by the study onmercury liquid mirrors in Ref. 1. On the other hand,there are specific problems that can occur with thecoating technology. For example, large surfaces canbe marred by a few bubbles as well as a few scarlikedefects caused by evaporating water drops that leavesolid residue. The fractions of the surfaces affectedare not large �of the order of a few percent�, and weare currently developing techniques to minimizethese defects.

Obviously, interferometry does not provide infor-mation about the surface roughness over distancessmaller than the resolution of the interferometer.Scattered-light measurements will be made to quan-tify the scattering, but results are not available atthis time. Atomic force microscope analyses of sam-ples deposited on glass indicate root-mean-square�rms� surface deviations of the order of 20 nm. Al-though glass mirrors can have smoother surfaces,this value corresponds to approximately ��20 at 500nm and predicts a small amount of scattered light.On the other hand, some scattered light can also becaused by clumps of coalesced particles. As dis-cussed below, our reflectivity and transmissioncurves show that this is a real problem if we use asmall concentration of the protective ligands. Thecurves give some indications of the importance ofscattered light since the lost energy is due to a com-bination of scattered light and absorbed light.

B. Reflectance and Transmittance Curves

We measured the reflectivity and transmissioncurves of several of our samples as a function of wave-length with a spectrophotometer �Varian Cary 500Scan�. We normalized the reflectivity curves bycomparing them with the curves obtained on a sam-ple of clean mercury. Although the reflectivitycurves shown are measured on the reflective liquid,the transmission curves are measured on samplesdeposited on a glass microscope slide. We trans-ferred the sample from the water surface simply bysliding the glass under the surface and then lifting ithorizontally to remove a section of the MELLF. Afreshly deposited dried MELLF rests on top of thethin layer of water that wets the slide. This layerevaporates within a few minutes, leaving a dried filmon the glass. Transmission measurements werecarried out on both water-deposited and glass-deposited samples, and no significant differenceswere found. The reflectivity curves for a typicaldried MELLF is shown in Fig. 3, curve a�. Maxi-mum reflectivities of the order of 80% were obtainednear 700 nm. Lower reflectivity is observed at bothhigher and lower wavelengths. The reflectivity

losses can be attributed to dissipative absorption,scattering, and the fact that the reflective layer isrelatively thin and transmits some of the light. Weused the transmission curves to evaluate the percent-age of light lost to the different factors. The differ-ence between the reflectivity and the transmissioncurves is plotted in Fig. 3, curve �b�, and indicatesthat transmission alone is not responsible for theloss. In addition, there is obviously a combination ofscattering and dissipative absorption. At shorterwavelengths, important losses that are due to thesurface plasmon absorption near 320 nm are evident.Above 700 nm transmission increases with an in-crease in wavelength, varying from approximately10% at 500 nm to 30% at 1200 nm.

The reflectivity curves provide information aboutthe physical characteristics of the reflecting layersand useful indications of what is needed to improvethe optical properties of the films. For example, Fig.4 illustrates the influence of the size and the shape of

Fig. 3. �a� Reflected light and �b� lost light �100 � reflected �transmitted�, corresponding to scattered and absorbed light mea-sured on a dried MELLF sample prepared from a colloid reduced to100 °C.

Fig. 4. Reflected light as a function of wavelength measured ondried MELLF samples prepared from silver colloids reduced to �a�100 °C and �b� 95 °C.


the particles, showing results for samples preparedfrom the two different preparations of colloidal par-ticles, formed by reduction at either the boiling pointor a slightly lower temperature. Although they arequantitatively different, the reflectivity curves ex-hibit similar tendencies. Both show that the lowestreflectivity value is in the plasmon frequency for bulksilver at �320 nm. In the visible region of the spec-trum there is a peak in the reflectivity at �500 nmfollowed by a slight decrease that gives it a hunch-back profile. The values then increase to their high-est value of �800 nm to decrease monotonically withan increase in wavelength. These are the typicalfeatures we see in the spectra of all our MELLFs.

The three ligands that we tested �1,10-phenanthroline, 2,9-dimethyl-1,10-phenanthroline,and 2,2-dipyridyl� had a relatively small effect on theform of the reflectivity curves. However, consider-ing the limited number of ligands tested and theirobvious structural similarities, we cannot make de-finitive statements with regard to the importance ofthe chemical composition of the ligands. We are cur-rently investigating a variety of additional ligands.

We found that reflectivity decreases if we lower theconcentration of ligands. Presumably this increasesthe amount of scattered light since too little ligandcould leave unprotected areas on the silver grainsthat clump together to give large irregularly shapedaggregates that scatter light.

C. Model of Reflectance Properties

To understand the shape of our reflectivity curvesand to try and find ways to improve them, we use thetheoretical framework described in Ref. 12. Farb-man et al. developed a model that they call the Tor-quato Kreybig Fresnel approximation, whichdescribes the optical behavior of composite systemsmade of particles embedded in a dielectric. The TKFapproximation corrects the bulk optical constants of ametal in relation to particle size13 and in relation tothe volume fraction �filling factor� of the particles inthe matrix.14 The approximation uses the correctedvalues with Fresnel equations to calculate the reflec-tivity of the system. Whenever the particle size iscomparable to or smaller than that of the mean-free-path of the conduction electrons in bulk material�linf�, we need to correct the dielectric constants of thesystem. This must be so because the collisions ofthese electrons with the particle surfaces lower theeffective mean-free-path leading to an increase in thecollision frequency. This is the classical approach.The new dielectric constant is then a function of theincident light frequency and of the radius of the par-ticle.13

Let � 3.7 10�14 s be the collision time �relax-ation time� for bulk silver at 273 K. The mean-free-path of the conduction electrons in the bulk materialis then given by linf vf�. One obtains linf 52 nmwith the Fermi velocity vf 1.4 106 m�s. Thevalue for linf is different if the collision bulk fre-quency, which is given by �0 ��1, changes. Ifparticle sizes are comparable to or smaller than linf,

the collision times � change. The new collision timeis a function of the radius of the particle13 and is givenby �corr R�vf. Finally, if the collision time changes,so does the collision frequency, which is then cor-rected for the particle size13 to give �c�R� �0 ��corr�

�1 and �c�R� �0 � �vf�R�. The change in thecollision frequency affects the optical constants. Forsilver, the real part of the optical constant �n� is in-versely proportional to the radius of the particle.The imaginary part �k� remains basically the sameexcept for the plasmon region of the spectra. TheTKF model predicts that reflectivity will decrease fora smaller particle radius in the 400–600-nm region ofthe spectra. Changes in the particle size do notchange the reflectivity from 700 nm on. Note, how-ever, that our experimental curves in Fig. 2 disagreewith this statement. On the other hand, the dis-agreement could partially be due to differences be-tween the model and our samples, as discussed inSubsection 3.D. Further discussion is given in Ref.13.

The correction of the optical constants for varia-tions in the filling factor, defined as the volume ratioof the sum of the metallic particles to the total volumeof the matrix and particles, is taken into account byuse of the expressions given by Torquato.14 He con-siders multipolar electromagnetic interactions be-tween spherical particles, which increase with thehigh filling factor: the higher the filling factor,the higher the electrical conductivity and the higherthe reflectivity. This can be understood by theincrease of clusters of particles15 that result on anincreased electrical conductivity.

Unfortunately, there is an upper limit to the fillingfactor, partly because the particles are wrapped in athin layer of ligand �approximately 1 nm thick� andpartly because of the geometric limit to the packing ofparticles that are not orthorhombic �e.g., boxes�.The filling factor therefore depends on the shapes andthe distributions of the particles. For example, themaximum filling factor value for a random close pack-ing of spheres that have the same diameters would be�63%.16 It might be possible to increase the fillingfactor by mixing spheres of different sizes. Tor-quato14 gives a three-point parameter that varieswith the filling factor for each different spatial ar-rangement such as simple cubic, face-centered-cubicamong others, allowing us to consider these differentpackings in the TKF model calculations.

D. Comparison of Reflectivity Data to Models

Reflectivity curves computed with the TKF modelshow the effect of the sizes of the particles �assumingspheres� as a function of diameters for a filling factorof 55% in Fig. 5. Theory predicts that reflectivityincreases from 1- to 30-nm diameter, whereas there islittle size effect for spherical particles larger than 30nm. However, it is obvious that the experimentalreflectivity curves in Fig. 4 are significantly affectedby the sizes and the shapes of the particles. Thediscrepancy could be due to inadequacies of the TKFtheory or to the fact that the theory assumes smooth


spherical particles all having the same radii, whereasthe electron microscope images show that the parti-cles are not spherical and have different sizes �Fig. 1�.Figure 6 shows reflectivity curves for particles havingdiameters of 20 nm and three different filling factors.We used Torquato’s14 values for randomly distributedspheres. Figure 5 shows that reflectivities longwardof 650 nm can be greatly improved if we increase thefilling factor. It must be noted that hard sphereshaving the same diameter cannot give filling factorshigher than 74%, so that the 95% curve is misleadingfor such a situation. On the other hand, a fillingfactor larger than 75% might be obtained by use of adistribution of diameters, since the smaller sphereswill fill the regions between the larger spheres.

Notwithstanding the disagreements mentioned inthe preceding discussion, the TKF model points theway to improve the reflectivity of our liquids. Figure6 shows that the major improvements can beachieved if we increase the filling factor.

4. Conclusion

We have used a novel chemical technique that coatsthe air–water interface with a reflective layer of self-assembling metallic nanoparticles. We have suc-ceeded in coating the top surface of water with a layerof silver grains coated with a ligand. This is a sig-

nificant improvement over the results presented inRef. 8 in which Borra et al. trapped the reflectinglayer at the interface between two liquids becausenow the reflecting layer coats the first surface seen bylight. Interferometry shows that the coated sur-faces have good optical qualities. Reflectivity mea-surements show peak values of the order of 80%,comparable with the reflectivity of mercury �approx-imately 80%�. Reflectivity is lower than the reflec-tivity of silver or aluminum-coated glass but onemust consider that, in practice, coated glass mirrorsare seldom recoated, hence degrade with time as theyget covered with dust and dirt. This is particularlytrue for telescope mirrors used in astronomy, thespace sciences, and the atmospheric sciences becausethey are exposed to the elements unprotected. Onthe other hand, our reflecting layers are easy to gen-erate and inexpensive so that they could be refreshedoften. The 80% peak reflectivity was obtained ef-fortlessly, and we are confident that reflectivities canbe improved by the additional research currently inprogress.

Experimental and theoretical curves based on theTKF model are in qualitative agreement but disagreein the details. We can probably hand wave the dif-ferences by invoking real-world differences betweenour results and the TKF calculations. The TKFmodel assumes smooth spherical particles having thesame diameters. In our case, the electron micro-scope images �Fig. 1� show that the particles can beelongated, are not smooth, and have different radii.Furthermore, our particles tend to clump together, sothat we do not have any of the idealized distributionsassumed in the computations. Finally there is a lossthat is due to scattering by large aggregates of par-ticles that we cannot evaluate at this time. Still, themodels should be useful to show ways to increasereflectivity. They suggest that we should increasethe filling factor to improve reflectivity.

We expect that nanoengineered liquid mirrorswould be useful for scientific and engineering appli-cations. The technology is interesting for large op-tics, such as large parabolic mirrors, because of itslow cost. Consider that the mirror basically consistsof a 1-mm-thick layer of liquid coated with a 150-nm-thick layer of nanoparticles. A 10-m-diameter mir-ror would thus weigh of the order of 100 kg. Becausethe cost of the mirror and supporting hardware �e.g.,container and bearing� depend on the weight of themirror, it should be quite inexpensive �of the order ofa few tens of thousands of dollars�. The costs of thechemical involved are negligible and the process notoverly demanding of human time. The cost of anastronomical observatory would then be totally dom-inated by the cost of the building and the instrumen-tation. For all essential purposes one would get themirror for free. Note also that, although mercurymirrors cannot be tilted, thus limiting their useful-ness, rotating mirrors that use viscous liquids can betilted.8 Coated ferrofluids6 are especially interest-ing for practical applications because they promise tomake versatile low-cost mirrors. Because the sur-

Fig. 5. Theoretical reflectivity curves calculated with the TKFmodel. The curves show the effect of the sizes of spherical parti-cles �assuming spheres� for a filling factor of 55%.

Fig. 6. Reflectivity curves calculated with the TKF model thatcorrespond to filling factors of 55%, 65%, 75%, and 95% and as-suming spherical silver particles with a 20-nm radius. We usedTorquato’s values for randomly distributed spheres.


faces of these mirrors can be shaped with magneticfields, one can generate complex, time-varying sur-faces that would be difficult to make with conven-tional techniques.

This is a young technology and there is a significantamount of research to be done before it reaches theperformance and robustness expected for practicalapplications. We are currently at work to improveit. Recently, we developed a technique to coat thesurface of oils with MELLFs, which will be reportedelsewhere. We are also investigating the use ofother metals �e.g., gold and aluminum�. The re-search carried out so far has been relatively simple,and we have reached several milestones with relativeease, boding well for the future.

This research has been supported by grants to E.Borra and A. Ritcey from the Natural Sciences andEngineering Research Council of Canada and the Ca-nadian Institute for Photonics Innovation. LandeVieira da Silva, Jr. is financially supported by a schol-arship from the Conselho Nacional de Desenvolvi-mento Cientıfico e Tecnologico, CNPq, Brazil.

References1. L. Girard and E. F. Borra, “Optical tests of a 2.5-m-diameter

liquid mirror: behavior under external perturbations andscattered-light measurements,” Appl. Opt. 36, 6278–6288�1997�.

2. G. Tremblay and E. F. Borra, “Optical tests of a 3.7-m-diameter liquid mirror: behavior under external perturba-tions,” Appl. Opt. 39, 5651–5662 �2000�.

3. R. J. Sica, S. Sargoytchev, P. S. Argall, E. F. Borra, L. Girard,C. T. Sparrow, and S. Flatt, “Lidar measurements taken witha large-aperture liquid mirror. 1. Rayleigh-scatter system,”Appl. Opt. 34, 6925–6936 �1995�.

4. P. Hickson and M. Mulrooney, “University of British

Columbia-NASA Multi-Narrowband Survey. I. Descriptionand photometric properties of the survey,” Astrophys. J. Suppl.115, 35–42 �1998�.

5. R. Cabanac, E. F. Borra, and M. Beauchemin, “A search forpeculiar objects with the NASA orbital debris observatory 3-mliquid mirror telescope,” Astrophys. J. 509, 309–323 �1998�.

6. P. R. Laird, E. F. Borra, A. Ritcey, H. Yockell-Lelievre, N.Robitaille, V. Berube, “Applications of magnetically shapedliquid optical surfaces,” in Applications of Photonic Technology5, R. A. Lessard, G. A. Lampropoulos, and G. W. Schinn, eds.,Proc. SPIE 4833, 451–457 �2003�.

7. E. F. Borra, G. Tremblay, Y. Huot, and J. Gauvin, “Galliumliquid mirrors: basic technology, optical-shop tests and obser-vations,” Publ. Astron. Soc. Pac. 109, 319–325 �1997�.

8. E. F. Borra, A. M. Ritcey, and E. Artigau, “Floating mirrors,”Astrophys. J. Lett. 516, L115–L118 �1999�.

9. D. Yogev and S. Efrima, “Novel silver metal like films,” J. Phys.Chem. 92, 5754–5760 �1988�.

10. K. C. Gordon, J. J. McGarvey, and K. P. Taylor, “Enhanced-Raman scattering from liquid metal films,” J. Phys. Chem. 93,6814–6817 �1989�.

11. P. C. Lee and D. Meisel, “Adsorption and surface-enhancedRaman of dyes on silver and gold sols,” J. Phys. Chem. 86,3391–3395 �1982�.

12. I. W. Farbman, O. Levi, and S. Efrima, “Optical response ofconcentrated colloids of coinage metal in the near-ultraviolet,visible and infrared regions,” J. Chem. Phys. 96, 6477–6485�1992�.

13. U. Kreibig and C. V. Fragstein, “The limitation of electronmean free path in small silver particles,” Z. Phys. 224, 307–323�1969�.

14. S. Torquato, “The electrical conductivity of two-phase disor-dered composite media,” J. Appl. Phys. 58, 3790–3797 �1985�.

15. U. Kreibig, “Optical absorption of small metallic films,” Surf.Sci. 156, 678–700 �1985�.

16. S. Torquato, T. M. Truskett, and P. G. Debenedetti, “Is randomclose packing of spheres well defined?,” Phys. Rev. Lett. 84,2064–2067 �2000�.


Optical Tests of Nanoengineered Liquid Mirrors

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