integrating spheres
TRANSCRIPT
Integrating Spheres
Jehona Salaj
University of Eastern Finland
Department of Physics and Mathematics
November 6, 2012
Figure : Sculpture of the integrating sphere in the Technical University ofDresden (photo:Kay Korner).
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
Outline
1 The Sphere
2 Theory
3 Designing an integrating sphere
4 Measurements
Outline
1 The Sphere
2 Theory
3 Designing an integrating sphere
4 Measurements
The sphere
Figure : Scheme of an integrating sphere.
Note!
An integrating sphere spatially integrates the radiant flux.
Outline
1 The Sphere
2 Theory
3 Designing an integrating sphere
4 Measurements
Radiation Exchange
Figure : Radiation exchange between dA1 and dA2.
dFd1−d2=
cos θ1 cos θ2
πS2dA2 ⇒ F1−2 =
A2
4πR2=
A2
AS
(1)
Surface radiance
Figure : Surface radiance LS for the input flux Φi
LS =Φi
πAS
×ρ
1 − ρ(1 − f )(2)
The sphere multiplier
The second part of equation (2) is the sphere multiplier.Considering the wall reflectance as average and the portreflectance zero we get:
M =ρ0
1 − ρ(3)
Spacial and temporal integration
Integrating spatially:
Φ = Φi
∑ρn(1 − f )n (4)
Temporal response is of form
e−t/τ (5)
where
τ = −2
3
DS
c
1
ln ρ(6)
Outline
1 The Sphere
2 Theory
3 Designing an integrating sphere
4 Measurements
The Sphere diameter
Radiance relates to the sphere diameter:
LS ∝M
D2S
(7)
Decreasing port fraction increases M
Port fraction ≤ 5% of the sphere surface
Note!
Best choice: Large sphere diameter and small port size.
Use of baffles
Figure : The use of baffles in the integrating sphere.
Baffles help preventing that the direct incident light enters thefield-of-view of the photodetector.
Use of diffusers
Figure : The use of an auxiliary or satellite integrating sphere as adiffuser.
If the sphere is used as a collector for measuring radiant flux, theerror increases if the incident flux enters the detector’sfield-of-view.
Detector in use
Figure : Use of lens for collecting the light to the active area of thephotodetector.
Without a lens:Φd = LSAdπ sin2 θ (8)
Putting a lens in the system:
Φd = LSAd
π
(2f /])2ε0 (9)
Fiber in use
Figure : Coupling the light out using an optical fiber.
Φf = LSAf π(NA)2(1 − R) (10)
Choosing sphere coatings
Two important factors:
Reflectance
Durability
Sphere coatings
Some usual coatings:
barium sulfate based spray coatings
packed PTFE coatings
Labsphere’s proprietary reflectance materials and coatings:
Sphere coatings(cont.)
Spectralon (over 95% reflectance at 250nm to 2500nm; stableeven above 350◦C ; durable over 100h under UV fluxexposure.)
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; notcompatible with some plastic substrates.)
Infragold (electrochemically plated; gold metallic reflectancecoating; 92 to 96% reflectance over 1µm to greater than20µm)
Outline
1 The Sphere
2 Theory
3 Designing an integrating sphere
4 Measurements
Radiometers and photometers
Figure : Use of integrating sphere as a radiometer or photometer:(a)Sphere Photometer, (b)Laser Power meter, (c)Cosine receptor.
Reflectance and transmittance
Figure : Measuring reflectance and transmittance.
Measurement geometries
”d/0◦ and 0◦/d”
The geometries used when dealing with integrating spheres areindeed d/8◦ and 8◦/d , but are considered d/0◦ and 0◦/d (aseverything with an angle smaller than 10◦).
Questions or comments?