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Integrating Spheres Jehona Salaj [email protected] University of Eastern Finland Department of Physics and Mathematics November 6, 2012

Integrating spheres

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Page 1: Integrating spheres

Integrating Spheres

Jehona Salaj

[email protected]

University of Eastern Finland

Department of Physics and Mathematics

November 6, 2012

Page 2: Integrating spheres

Figure : Sculpture of the integrating sphere in the Technical University ofDresden (photo:Kay Korner).

Page 3: Integrating spheres

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

Page 4: Integrating spheres

Outline

1 The Sphere

2 Theory

3 Designing an integrating sphere

4 Measurements

Page 5: Integrating spheres

Outline

1 The Sphere

2 Theory

3 Designing an integrating sphere

4 Measurements

Page 6: Integrating spheres

The sphere

Figure : Scheme of an integrating sphere.

Note!

An integrating sphere spatially integrates the radiant flux.

Page 7: Integrating spheres

Outline

1 The Sphere

2 Theory

3 Designing an integrating sphere

4 Measurements

Page 8: Integrating spheres

Radiation Exchange

Figure : Radiation exchange between dA1 and dA2.

dFd1−d2=

cos θ1 cos θ2

πS2dA2 ⇒ F1−2 =

A2

4πR2=

A2

AS

(1)

Page 9: Integrating spheres

Surface radiance

Figure : Surface radiance LS for the input flux Φi

LS =Φi

πAS

×ρ

1 − ρ(1 − f )(2)

Page 10: Integrating spheres

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)

Page 11: Integrating spheres

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)

Page 12: Integrating spheres

Outline

1 The Sphere

2 Theory

3 Designing an integrating sphere

4 Measurements

Page 13: Integrating spheres

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.

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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.

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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.

Page 16: Integrating spheres

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)

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Fiber in use

Figure : Coupling the light out using an optical fiber.

Φf = LSAf π(NA)2(1 − R) (10)

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Choosing sphere coatings

Two important factors:

Reflectance

Durability

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Sphere coatings

Some usual coatings:

barium sulfate based spray coatings

packed PTFE coatings

Labsphere’s proprietary reflectance materials and coatings:

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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)

Page 21: Integrating spheres

Outline

1 The Sphere

2 Theory

3 Designing an integrating sphere

4 Measurements

Page 22: Integrating spheres

Radiometers and photometers

Figure : Use of integrating sphere as a radiometer or photometer:(a)Sphere Photometer, (b)Laser Power meter, (c)Cosine receptor.

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Reflectance and transmittance

Figure : Measuring reflectance and transmittance.

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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◦).

Page 25: Integrating spheres

Questions or comments?