1. Emittance & Absorptance for Cryo Testing
Goal: To better understand emittance and absorptance and how they vary at cryo temperatures
Sample problem
Emittance & absorptance of non-conductors
Effects of wavelength (spectral dependencies and trends)
Effects of low temperatures
Effects of thickness (paints and films)
Honeycomb enhancements

2. Example: SIRTF Thermal Testing
SIRTF Cryo Telescope Assembly
On orbit, CTA passively cooled to 40 K by radiation to space
40 K well below typical LN2-cooled thermal-vac chambers at 80 K
Initial plans for thermal balance test
Simulate space environment
Add helium-cooled shroud inside existing LN2-cooled thermal-vac chamber
Helium-cooled shroud at 4 K
Painted honeycomb on shroud for absorptance close to 1.0
Concerns about test
Validity (see next chart)
Feasibility
Cost
Time
SIRTF CTA (40 K)
Helium-cooled shroud (4 K)
(painted honeycomb)
Nitrogen-cooled coldwall (80 K)
Vacuum chamber walls (293 K)

3. Example: Basis for Conclusion
Emittance of paint at 4 K hard to predict
At 40 K, epaint = 0.70 ± 0.15 uncertainty (Goddard data)
No data at 4 K, but emittance much lower (at 0 K, emittance  0.00)
Even with painted honeycomb shroud, emittance at 4 K could be < 0.50
Test vs space: too different
Tsink = 4 K vs 2.7 K (OK)
esink = 0.48 vs 1.0 (not OK)
Heat reflected back to CTA
CTA won’t get cold enough
Gradients won’t be realistic
Heat balance unpredictable
Thermal balance in 4 K shroud not meaningful
Omit 4 K shroud
Cool CTA with direct liquid helium lines
Make do with questionable thermal balance
Goddard Paint Data
Extrapolated
From model
What’s wrong with this picture?

4. Example: Revised Solution
Helium-cooled shroud gives meaningful test
Absorptivity of the paint is relative to 40 K, not 4 K
Paint’s absorptivity depends on wavelength distribution of incident radiation
Paint’s absorptivity at a given wavelength is independent of paint’s temperature
Effective absorptance = emittance of paint at 40 K = 0.70
At 40 K, absorptance of painted honeycomb can be > 0.90
Some variation with paint thickness and paint process
Some variation with cell size and honeycomb thickness
Use specular paint
Calorimeter uncertainties increase at cryo temperatures
Helium-cooled shroud could mimic space to within 1%
Grow shroud from 2X to 10X the area of SIRTF CTA
Additional cost for liquid helium to cool larger shroud
Concentric spheres: RadK12 = A1/[1/e1 + (A1/A2)(1/e2 – 1)
98%
99.5%
1/2
1/10

5. Spectral Intensity of a Blackbody
Planck’s Radiation Law
I(l,T) = (2phc2/l5)/(ehc/lkT – 1)
Flux (Qbb) = area under curve
Qbb,T = sT4
s = X 10-8 W/m2-K4
Curves have similar shapes
Imax is proportional to T5
lmax is proportional to 1/T
0.004 inches
lmax & Imax

6. Spectral Intensity: Log Plot
lT = 1148m-K
lmaxT = 2897m-K
lT = 22917m-K
Everything shifts proportional to 1/T
Max power occurs at longer wavelengths at lower temperatures
Curve for a lower temperature is less than curve for a higher temperature at all wavelengths
At low temperatures, power spreads over wider range of wavelengths
98% of power

7. Absorptance = Emittance: Kirchhoff’s Law
Absorptance = emittance, if the same…
Surface
Temperature
Wavelength
Angle of incidence
al,T,q,f= el,T,q,f (rest of presentation omits effects of angle of incidence)
Total absorptance = total emittance at the same temperature
Emittance
Total hemispherical emittance
Surface at the given temperature
Absorptance
Surface is at the given temperature
Surface is surrounded by blackbody at the same temperature
Must be true, else violates the 2nd Law of Thermodynamics
a + r + t = 1
a + r = 1 (opaque)

8. Conclusions So Far Emittance varies with wavelength for real surfaces
Some surfaces have a fairly constant emittance over a range of wavelengths
Emittance at a given wavelength can also change with temperature
The blackbody intensity changes non-linearly with temperature
Increases with temperature to the 4th power
At lower temperatures, the distribution shifts towards longer wavelengths
At lower temperatures, the power spreads out more
Therefore, effective emittance changes with temperature, if…
Emittance varies with wavelength, or if…
Emittance at a given wavelength changes with temperature
For the range of wavelengths of importance at the given temperature

9. Emittance of Non-Conductors
For non-metals, el and al is essentially independent of temperature
2-step absorption process
Surface reflectance depends on index of refraction
Reflectance = [( - 1)/( + 1)]2 (normal)
 = index of refraction = 1/relative light speed ≈ [dielectric constant]½
Volumetric absorptance sometimes limited by thickness
Dielectrics are partially transparent
Absorptance within material increases with thickness: a = 1 – e-kx
Free-standing film, or backed by metal layer
No significant difference beyond certain thickness (1 to 10 mils typically)
At low temperatures, emittance of paints and films decreases
Energy shifts to longer wavelengths
When wavelengths exceed thickness, paint or film becomes more transparent
No decrease for non-conductive substrate—if thick enough
Surfaces becomes more specular at low temperatures
As more wavelengths exceed roughness of surface and substrate 1 2

10. Spectral Emittance of a Paint
Emittance/absorptance at a given wavelength doesn’t vary with temperature
Total emittance may vary with temperature as the range of wavelengths shifts
Changing temperature of emitting source may shift the absorptance of an absorbing surface
Changing temperature of absorbing surface does not change its absorptance

11. Emittance of Non-Conductors: Films
For non-conductors, radiation transfer is more of a volumetric phenomenon
Many thin films are partially transparent
Absorptance (and emittance) varies exponentially vs thickness
Films are volume-limited
At low temperatures, wavelengths are longer and films are more transparent
Different paints or films show a decrease in emittance at different temperatures
Emittance of FEP Teflon films drops off at higher temperatures than most films or paints
Paints or OSRs are better on cryo radiators
Painted honeycomb gives highest emittance
If material is thick enough, emittance stays constant to much lower temperature
Emittance of 35-mil fused silica constant from 25 K to 300 K

12. Honeycomb Blackbodies
Open, painted honeycomb cells increase emittance or absorptance
Cavity offers several chances for absorptance
Each cavity approximates a blackbody
Absorptance still equals emittance
Not too sensitive to honeycomb geometry
Aspect ratio: cell width versus cell height
Aluminum honeycomb minimizes DT to base
At cryo temperatures, DT not a factor
Obtaining uniform paint may be driver
Recommend larger cell honeycomb
Allows thicker paint
Paint process less critical
Specular paint increases effective emittance
Diffuse paint: K, K
Specular paint: K, K
Multiple bounces in a honeycomb hex cell
Simplified model
Same hemispherical emittance
100% diffuse vs 100% specular

13. Percent Power vs Wavelength for Cryo
40 mils
1% of power at l less than 1448/T
Maximum power at l of 2897/T
Also 25%/75% split
50% of power either side of l of 7393/T
99% of power at l less than 22,917/T
4 mils
Typical paint thickness = 2 to 8 mils
Paint have reduced emittance when wavelengths exceed thickness
¼” (honeycomb cell) = 6,350 microns
Cell size well beyond significant wavelength effects

14. Conclusions / Recommendations
For radiation between hot and cold surfaces, the hot surface dominates
Temperature of hot emitter determines cold non-conductor’s absorptance
Absorptance depends on distribution of incident wavelengths
Most of the incident radiation originates at the hot surface
For non-conductors, al does not vary with temperature
Total emittance varies with temperature if …
Emittance varies with wavelength
For paints and films, emittance drops off at longer wavelengths (cryo temperatures)
Thicker substrates of non-conductors will not show this effect
Emittance at a given wavelength varies with temperature
Typical non-conductors do not show such an effect
Thicker paint has higher absorptance at low temperatures
Use specular paints for honeycomb or multi-bounce blackbodies