1. Integrating Spheres
Jehona Salaj
jehonas@student.uef.fi
University of Eastern Finland
Department of Physics and Mathematics
November 6, 2012

2. Figure : Sculpture of the integrating sphere in the Technical University of
Dresden (photo:Kay K¨rner).
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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. Outline
1 The Sphere
2 Theory
3 Designing an integrating sphere
4 Measurements

5. Outline
1 The Sphere
2 Theory
3 Designing an integrating sphere
4 Measurements

6. The sphere
Figure : Scheme of an integrating sphere.
Note!
An integrating sphere spatially integrates the radiant flux.

7. Outline
1 The Sphere
2 Theory
3 Designing an integrating sphere
4 Measurements

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. Surface radiance
Figure : Surface radiance LS for the input flux Φi
Φi ρ
LS = × (2)
πAS 1 − ρ(1 − f )

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. 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. Outline
1 The Sphere
2 Theory
3 Designing an integrating sphere
4 Measurements

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. 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. 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. 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. Fiber in use
Figure : Coupling the light out using an optical fiber.
Φf = LS Af π(NA)2 (1 − R) (10)

18. Choosing sphere coatings
Two important factors:
Reflectance
Durability

19. Sphere coatings
Some usual coatings:
barium sulfate based spray coatings
packed PTFE coatings
Labsphere’s proprietary reflectance materials and coatings:

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. Outline
1 The Sphere
2 Theory
3 Designing an integrating sphere
4 Measurements

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. Reflectance and transmittance
Figure : Measuring reflectance and transmittance.

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◦ ).

25. Questions or comments?