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# Integrating spheres

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### Integrating spheres

1. 1. Integrating Spheres Jehona Salaj jehonas@student.uef.fi University of Eastern FinlandDepartment of Physics and Mathematics November 6, 2012
2. 2. Figure : Sculpture of the integrating sphere in the Technical University ofDresden (photo:Kay K¨rner). o
3. 3. Uses of Integrating Spheres Alone or as accessory of other devices In radiometry and photometry For measuring transmittance and reﬂectance For measuring the light sources E , I and Φ
4. 4. Outline 1 The Sphere 2 Theory 3 Designing an integrating sphere 4 Measurements
5. 5. Outline 1 The Sphere 2 Theory 3 Designing an integrating sphere 4 Measurements
6. 6. The sphere Figure : Scheme of an integrating sphere. Note! An integrating sphere spatially integrates the radiant ﬂux.
7. 7. Outline 1 The Sphere 2 Theory 3 Designing an integrating sphere 4 Measurements
8. 8. Radiation Exchange Figure : Radiation exchange between dA1 and dA2 . cos θ1 cos θ2 A2 A2 dFd1 −d2 = 2 dA2 ⇒ F1−2 = 2 = (1) πS 4πR AS
9. 9. Surface radiance Figure : Surface radiance LS for the input ﬂux Φi Φi ρ LS = × (2) πAS 1 − ρ(1 − f )
10. 10. The sphere multiplier The second part of equation (2) is the sphere multiplier. Considering the wall reﬂectance as average and the port reﬂectance zero we get: ρ0 M= (3) 1−ρ ¯
11. 11. Spacial and temporal integration Integrating spatially: Φ = Φi ρn (1 − f )n (4) Temporal response is of form e −t/τ (5) where 2 DS 1 τ =− (6) 3 c ln ρ ¯
12. 12. Outline 1 The Sphere 2 Theory 3 Designing an integrating sphere 4 Measurements
13. 13. The Sphere diameter Radiance relates to the sphere diameter: M LS ∝ 2 (7) DS Decreasing port fraction increases M Port fraction ≤ 5% of the sphere surface Note! Best choice: Large sphere diameter and small port size.
14. 14. Use of baﬄes Figure : The use of baﬄes in the integrating sphere. Baﬄes help preventing that the direct incident light enters the ﬁeld-of-view of the photodetector.
15. 15. Use of diﬀusers Figure : The use of an auxiliary or satellite integrating sphere as a diﬀuser. If the sphere is used as a collector for measuring radiant ﬂux, the error increases if the incident ﬂux enters the detector’s ﬁeld-of-view.
16. 16. Detector in use Figure : Use of lens for collecting the light to the active area of the photodetector. Without a lens: Φd = LS Ad π sin2 θ (8) Putting a lens in the system: π Φd = LS Ad ε0 (9) (2f / )2
17. 17. Fiber in use Figure : Coupling the light out using an optical ﬁber. Φf = LS Af π(NA)2 (1 − R) (10)
18. 18. Choosing sphere coatings Two important factors: Reﬂectance Durability
19. 19. Sphere coatings Some usual coatings: barium sulfate based spray coatings packed PTFE coatings Labsphere’s proprietary reﬂectance materials and coatings:
20. 20. Sphere coatings(cont.) Spectralon (over 95% reﬂectance at 250nm to 2500nm; stable even above 350◦ C ; durable over 100h under UV ﬂux exposure.) Spectraﬂect (barium sulfate; 98% at 400nm to 1100nm; durable up to 350◦ C ; not good in humid environment; cheap.) Duraﬂect (94 to 96% reﬂectance over 350nm to 1200nm; good in humid environment; not good for UV range uses; not compatible with some plastic substrates.) Infragold (electrochemically plated; gold metallic reﬂectance coating; 92 to 96% reﬂectance over 1µm to greater than 20µm)
21. 21. Outline 1 The Sphere 2 Theory 3 Designing an integrating sphere 4 Measurements
22. 22. Radiometers and photometers Figure : Use of integrating sphere as a radiometer or photometer: (a)Sphere Photometer, (b)Laser Power meter, (c)Cosine receptor.
23. 23. Reﬂectance and transmittance Figure : Measuring reﬂectance and transmittance.
24. 24. Measurement geometries ”d/0◦ and 0◦ /d” The geometries used when dealing with integrating spheres are indeed d/8◦ and 8◦ /d, but are considered d/0◦ and 0◦ /d (as everything with an angle smaller than 10◦ ).