Reflectance of the Teflon R for ultraviolet light

Transcription

1 Reflectance of the Teflon R for ultraviolet light Cláudio Silva, José Pinto da Cunha Vitaly Chepel, Américo Pereira Vladimir Solovov, Paulo Mendes M. Isabel Lopes, Francisco Neves Reflectance of the Teflon R for ultraviolet light p.1/24

2 . Reflectance of the Teflon R for ultraviolet light Jornadas do LIP, Braga, 7-9 Janeiro 2010 Reflectance of the Teflon R for ultraviolet light p.2/24

3 The PTFE/Teflon R PTFE (polytetrafluoroethylene) is a common choice for the inner walls of liquid/gaseous xenon experiments Dark matter experiments Zeplin II, Xenon 10, Xenon 100, LUX(Maybe!) Neutrinoless double beta decay EXO, NEXT (gas) A high reflectance ( 99% in the visible spectra) optimize the light collection. Good chemical resistance, low water absorption and low outgassing and resists to low temperatures Reflectance essential for the data analysis, especially for larger detectors Reflectance of the Teflon R for ultraviolet light p.3/24

4 Objectives The reflectance of the PTFE for the xenon scintillation light (λ=175 nm) is currently not known. This material is currently modeled as a perfect diffuser. The measurement of the bidirectional reflectance distributions of various fluoropolymers samples for the xenon scintillation light The modeling of the processes involved. Application to Geant4 simulations. Prediction of the reflectance for the liquid xenon/ptfe interface Reflectance of the Teflon R for ultraviolet light p.4/24

5 cements Different Reflectance Definitions ϱ (θ i, φ i ; θ r φ r ) BIDIRECTIONAL R (θ i, φ i ; 2π) = 2π ϱdω r DIRECTIONAL-HEMISPHERICAL θ i θ r φ i φr DIRECTIONAL-CONICAL Ω r BI-HEMISPHERICAL R (θ i, φ i, Ω r ) = 1 Ω r Ω r ϱdω r R (2π; 2π) = 2π 2π ϱdω rω i Reflectance of the Teflon R for ultraviolet light p.5/24

6 The Reflectance Measurement Proportional The optical system is placed in an air tight chamber filled with argon gas The light of 175 nm is emitted by a xenon proportional counter Counter Xe anode iris diaphragm 50 mm 90.6 mm 80.0 mm +HV Xenon Gas 1 bar e α α 1.3 kv θ i α θ r VUV ˆn c Light Source Quartz Window Pin Hole Surface Sample θ i nc θ r PMT Slit 66.4 mm PMT Reflectance of the Teflon R for ultraviolet light p.6/24

7 Reflectance Components Light Source Photo Sensor PSfrag replacements θ incident ray γ i γ r diffuse lobe θ i n θ r reflecting surface Specular Lobe Specular Spike Reflectance of the Teflon R for ultraviolet light p.7/24

8 lded PTFE Skived PTFE PTFE Reflectance Distribution Directional-Conical Reflectance Factor (sr 1 ) θ i = Skived PTFE θ i = Viewing Angle θ r (deg) Directional-Conical Reflectance Factor (sr 1 ) θ i = Molded PTFE θ i = Viewing Angle θ r (deg) The reflectance distribution shows three different components, specular lobe, specular spike and diffuse lobe Reflectance of the Teflon R for ultraviolet light p.8/

9 The Diffuse Component Caused by light that penetrates below the surface and is scattered by sub-surface inhomogeneities back into the incoming medium PSfrag replacements Assumed to be scattered isotropically in the bulk of Incident the material light The light can be reflected in the interface dielectric-air returning back to the dielectric Air Incident light 1 st 2 nd Reflected order order light Dielectric Internal scattering absorption Reflectance of the Teflon R for ultraviolet light p.9/24

10 The Diffuse Component 0 30 A good approximation of this component for relatively θ i =30 smooth surfaces is given by the Wolff model θ i =30 ϱ D = ρ L π cos θ r { 1 F ( θ i, n 0 n θ i =20 )} { 1 F ( sin 1 [ n 0 n sin θ r ] )}, n/n 0 Dir-Con. Reflectance Factor (sr 1 ) MOLDED PTFE 560 nm θ i = nm pt MOLDED PTFE Viewing Angle θ r (deg) Viewing Angle θ r (deg) Reflectance of the Teflon R for ultraviolet light p.10/24

11 The Slope Distribution Model The surface is described by a collection of small micro-facets each having a local normal n distributed around the global PSfrag normal replacements of the surface n. For planar micro-facets we have P (α, m) = 1 πm 2 cos 4 α exp ( Trowbridge-Reitz Model v) tan2 α m 2 The surface is composed by an ensemble of micro-areas randomly oriented and randomly curved modeled as an ellipsoid of revolution P (α, γ) = γ 2 π(γ 2 cos 2 α+sin 2 α) 2 da i θ i θ i n α n θ r θ r V φ r Reflectance of the Teflon R for ultraviolet light p.11/24

12 -20 The Specular Lobe Corresponds to the fluctuating field, it is distributed around the specular direction ϱ S = (1 Λ (θ i, θ r ; σ h )) F (θ ; n) P (α; γ) G (θ i, θ r, φ; γ) 0 30 θ 1 θ i =20 i =30 45 R (θi, θr) (sr 1 ) P(α) Planar Micro-facets 4 cos θ i 65 Trowbridge-Reitz Viewing Angle θ r (deg) Reflectance of the Teflon R for ultraviolet light p.12/24

13 The Specular Spike ϱc/ (ϱs + ϱc) Λ = exp ( K cos θ i ) P z gaussian» Λ = exp 4πσh cos θ 2 i λ Λ = P z exponential » 1 1+8( πσ h λ cos θ i) 2 cos θ i The usual distributions do not describe the data. Λ = exp ( K cos θ i ) is an empirical function. 2 Reflectance of the Teflon R for ultraviolet light p.13/24

14 The Fits A global fit is applied to results with only three or four parameters. For the different samples we obtain n ρ l γ K Skived PTFE 1.49± ± ± PTFE Expanded 1.56± ± ± PTFE (not polished) 1.51± ± ± Extruded ( ) PTFE 1.50± ± ± ±0.3 Extruded ( ) PTFE 1.46± ± ± ±0.5 Molded PTFE 1.45± ± ± ±0.2 PFA 1.44± ± ± ±0.4 FEP 1.41± ± ± ±0.4 ETFE 1.44± ± ± ±0.2 Reflectance of the Teflon R for ultraviolet light p.14/24

15 The Hemispherical Reflectances R (θi, 2π) Molded PTFE Not Polished Total Reflectance Diffuse Lobe 0.1 Specular Lobe Angle of Incidence θ i Specular Spike Bi-Hemispherical Reflectance Factor Diffuse. S. Lobe S. Spike Total Skived PTFE Molded Polished PFA Reflectance of the Teflon R for ultraviolet light p.15/24

16 The Liquid Xenon Liquid/PTFE R (θi), 2π Gas/PTFE Total Reflectance Diffuse Lobe Specular Spike Specular Lobe Viewing Angle θ r (deg) Gas/PTFE R (θi), 2π Total Reflectance Diffuse Lobe Diffuse Lobe Specular Lobe Specular nptfe Spike Total Ref Gas Liq. Gas Liq. Gas Liq. Gas Liq. ngas Liquid/PTFE Specular Spike Specular Lobe Viewing Angle θ r (deg) Skived PTFE Molded PTFE PFA In the liquid/ptfe interface more than 50% of the reflectance is specular Reflectance of the Teflon R for ultraviolet light p.16/24

17 Conclusion three main reflection components, a diffuse lobe, a specular lobe and a specular spike for the reflectance distribution of the PTFE four free parameters and reproduces fairly well the details of the reflectance distribution measured the specular lobe is reproduced using the Trowbridge-Reitz model the intensity of coherent specular spike vary with the law exp ( K cos θ i ). the reflectance in the liquid xenon is significantly increased (R (2π, 2π) > 0.9) Reflectance of the Teflon R for ultraviolet light p.17/24

18 The Specular Spike 1.0 PSfrag replacements ρs/ (ρs + ρc) 0.50 ETFE 0.20 PTFE 0.10 ET 0.05 EL cos θ i = 0.5 (cos θ i + cos θ r) The same behavior is observed for polished (extruded (EL and ET) and molded (PL) PTFE) and non-polished surfaces. Reflectance of the Teflon R for ultraviolet light p.18/24

19 The Reflectance Measurement Proportional Counter Xe anode iris diaphragm The goniometer measures the reflected intensity (dn/dt) for different angles of incidence θ i and reflectance θ r. The reflectance factor is given by the ratio between the intensity and the incident flux θ i θ r ˆn c +HV 1.3 kv Xenon Gas 1 bar e α α α VUV Light Source 50 mm 90.6 mm 80.0 mm Quartz Window Pin Hole Surface Sample θ i nc θ r PMT Slit 66.4 mm PMT Reflectance of the Teflon R for ultraviolet light p.19/24

20 The Height Distribution Model For the study of the specular components is necessary a representation -0.2 of the roughness of a surface. σ h = 0.06 µm σ h = 0.06 µm h (µm) τ = 0.24 µm τ = 0.72 µm x (µm) 10 h (x, y) corresponds to the height function z = h (x, y) z = h (x, y) =0, P z - height distribution function, usually assumed to be gaussian P z = 1/(2πg) exp ( h (x, y) /2g) with g = 2πσ h cos θ i λ Reflectance of the Teflon R for ultraviolet light p.20/24

21 The Trowbridge-Reitz Model The surface is composed by an ensemble of micro-areas randomly oriented and randomly curved modeled by an average surface irregularity The average irregularity PSfrag replacements proposed is an ellipsoid of α revolution h h 2 a 2 + r2 b 2 = 1 h = ±bγ ( 1 r2 b 2 ) The probability distribution function of the angle α is given by: P (α, γ) = γ 2 π ( γ 2 cos 2 α + sin 2 α ) 2 a b n arctan γ r Reflectance of the Teflon R for ultraviolet light p.21/24

22 The Specular Spike Corresponds to the coherent field yielding a spike right at the direction of the specular reflection θ i = θ r ϱ C = Λ (θ i, θ r ; σ h ) F (θ i ; n) F (θ i ; n) are the Fresnel equations Λ gives the relative strength of the specular spike Λ = exp (in 0 k z h (x, y)) = k z = 2π λ σ h cos θ i dzp z (z) exp (in 0 k z z) Reflectance of the Teflon R for ultraviolet light p.22/24

23 The Liquid Xenon The reflectance obtained in the gas/ptfe is between 60-80%. Values obtained in the liquid are much higher. This difference is caused by the higher index of refraction of the liquid xenon (n 1.69) Reflectance of the Teflon R for ultraviolet light p.23/24

24 The Liquid Xenon Reflectance F(θ i) 1 b 0.5 a c n(ptfe)=1.5 n(gas)=1.0 gas/ptfe n(ptfe)=1.5 n(ptfe)=1.69 PTFE/gas 0.01 liquid/ptfe 0.01 PTFE/liquid Angle of incidence θ i (deg) Angle of incidence θ i (deg) Probability of reflection in PTFE/liquid interface 3 % 60% Reflectance of the Teflon R for ultraviolet light p.24/24