REU Training
Solar Irradiance/Radiometry
Jerry Harder
jerry.harder@lasp.colorado.edu
303 492 1891
Things to remember about the Sun
695,510 km (109  radii)
1.989 x 1030 kg (332,946 ’s)
1.412 x 1027 m3 (1.3 million  ‘s)
151,300 kg/m3 (center)
1,409 kg/m3 (mean)
Temperature 15,557,000° K (center)
5,780° K (photosphere)
2 - 3×106 ° K (corona)
1 AU
1.49495×108 km
TSI (@1 AU) 1,361 W/m2
Composition 92.1% hydrogen
7.8% helium
0.1% argon
Radius
Mass
Volume
Density
Wavelength Dependence of Sun Images
Yohkoh Soft X-ray
Telescope (SXT)
Ca II K
spectroheliograms
NSO
Sacramento Peak
Extreme Ultraviolet
Imaging Telescope
(EIT)
Fe XII 195 Å
He I 10830 Å
spectroheliograms
NSO Kitt Peak
Radiometric Terminology
Name
Radiant Energy
Radiant Power (flux)
Radiant Intensity
Radiance
Irradiance
Symbol
Description
U
Rate of transfer of energy
P
Power per solid angle from source
J
Power per solid angle per unit area
N
from a source
Power per unit area incident on a
H
surface
Units
J
W (or J s-1)
W ster-1
W ster-1cm-2
W m-2
Physical Constants
Planck’s Constant
Boltzman’s Constant
Speed of Light
Solid angle subtended by the
Sun at 1 AU
Symbol
h
k
c

Value
0.66262×10-33
1.3806×10-23
2.997925×108
6.79994×10-5
Advice: PAY ATTENTION TO YOUR UNITS!!!
Units
J sec
J deg-1
m sec-1
steradians
Definition of Solid Angle (  )
• Solid angle subtended by sphere (from an
‘interior’point):
=4
• For an area seen from a point of observation:
dA
 2
s
• Approximation for a distant point ( small):
  2 1  cos 
The inverse square law: Intensity
• Consider a point source of energy radiating
isotropically
– If the emission rate is P watts, it will have a radiant
intensity (J) of:
P
J
(W ster -1 )
4
– If a surface is S cm from the source and of area x cm2, the
surface subtends x2/S2 steradians.
– The irradiance (H) on this surface is the incident radiant
power per unit area:
x2
P
-2
HJ 2 
(W
cm
)
2
S
4 S
Point source illuminating a plane
HJ
x 2 cos
 S 


 cos 
x2
Ho  J 2
S
2
 H o cos3 
Extended sources must be treated differently
than point sources
• Radiance (N): power per unit solid angle per
unit area
• Has units of W m-2 ster-1
• Lambert’s Law: J  = Jo cos 
• Surface that obeys Lambert’s is known as a
Lambertian surface
Brightness independent of angle for a
Lambertian surface
Lambertian source radiating into a
hemisphere
Source has radiance N (W ster -1 cm-2 ) and area A
At some angle  , the intensity is :
J  J 0 cos   NA cos  (W ster -1 )
The incremental ring area on the hemisphere :
da  2 R sin  d
and subtends a solid angle :
2 R sin  d
 2 sin  d
R2
The radiation intercepted by this ring is then :
d 
dP  J 0 2 sin  d  2 NA sin  cos  d
Integrate over hemisphere :
P
 /2
0
 /2
 sin 2  
2 NA sin  cos  d  2 NA 

 2 0
  NA (watts)
{P/A is ½ of what you would expect from a point source}
History of Absolute Radiometry
• Ferdinand Kurlbaum (1857-1927)
– Radiometric developments for the
measurement and verification of the
Stefan-Boltzmann radiation law.
• Knut Ångström (1857-1910)
– Observations of the ‘Solar
Constant’ and atmospheric
absorption
Absolute Radiometry
Basic process for electrical substitution
radiometry
Remember:
Joule Heating:
P = I2R = V2/R
Implementation for SORCE (SIM)
Total Irradiance Monitor (TIM)
Goals
• Measure TSI for >5 yrs
• Report 4 TSI measurements per day
• Absolute accuracy<100 ppm (1 s)
• Relative accuracy 10 ppm/yr (1 s)
• Sensitivity
1 ppm (1 s)
Major Advances
• Phase sensitive detection at the
shutter fundamental frequency
eliminates DC calibrations
• Nickel-Phosphide (NiP) black
absorber provides high absorptivity
and radiation stability
Radiometer Cones
Glory Prototype Cone
Post-Soldered Cone
Glory Prototype
Cone Interior
TIM Baffle Design
Glint FOV
46.6 degrees
Vacuum Door
Base Plate
Shutter
Cone
Precision
Aperture
Shutter
Housing
Baffle 1,2,3
FOV
Baffle
Cone
Housing
Rear Housing
TSI Record
Planck’s equation
Planck's distribution law for the density of radiation
in a cavity :
First radiation const = 2 hc 2 = 3.7418e-016 (mks)



2 hc 2 
1


W 
5 
 hc  
hc
Second radiation const =
 0.014388 (mks)
 exp   kT   1 

 

k
(radiation emitted into a hemisphere)
Two important limits :
Wein's approximation
hc
2 hc 2
 hc 
When
? 5 then W 
exp


 kT
5
  kT 
Rayleigh - Jeans approximation
When
hc
2 c kT
= 1 then W 
 kT
4
Properties of the Planck distribution
On differentiation of the Planck equation and setting
 
=0

an equation for the peak wavelength can be found :
hc
maxT 
 2897.8 (micron - degree)
4.965 k
Peak power at max :
Wmax  1.288 1015 T 5
The equation of Stefan - Boltzmann relates the total thermal
radiation density with temperature

WTotal   W d    T 4 (W m -2 )
0
2 5 k 4
8


5.6697

10
{the Stefan - Boltzmann Constant mks}
2 3
15c h
Spectral Irradiance Monitor SIM
•
•
•
•
•
•
Measure 2 absolute solar irradiance spectra
per day
Broad spectral coverage
– 200-2400 nm
High measurement accuracy
– Goal of 0.1% (1)
High measurement precision
– SNR 500 @ 300 nm
– SNR  20000 @ 800 nm
High wavelength precision
– 1.3 m knowledge in the focal plane
– (or  < 150 ppm)
In-flight re-calibration
– Prism transmission calibration
– Duty cycling 2 independent
spectrometers
SORCE SIM: ESR-based spectral radiometry
SIM Measures the Full Solar Spectrum
Solar Stellar Irradiance Comparison Experiment (SOLSTICE)
Science Objectives:
• Measure solar irradiance from 115
to 320 nm with 0.1 nm spectral
resolution and 5% or better
accuracy.
• Monitor solar irradiance variation
with 0.5% per year accuracy
during the SORCE mission.
• Establish the ratio of solar
irradiance to the average flux from
an ensemble of bright early-type
stars with 0.5% accuracy for
future studies of long-term solar
variability.
SOLSTICE: Experiment Concept
Solar Observation: Modified Monk-Gilleison Spectrometer
Solar Exit Slit
Camera Mirror
Photomultiplier Detector
Interference Filter In
Diffraction
Grating
Entrance Slit
Stellar Observation: Objective Grating Spectrometer
Stellar Exit Slit
Camera Mirror
Photomultiplier Detector
Interference Filter Out
Diffraction
Grating
Entrance Aperture
•The optical configuration matches illumination areas on the detector
•Interchanging entrance slits and exit slits provides ~ 2x105 dynamic range
•Different stellar/solar integration times provide ~ 103 dynamic range
•A optical attenuator (neutral density filter), which can be measured in flight,
provides additional ~ 102 dynamic range in the MUV wavelength range for
>220 nm
SORCE SOLSTICE FUV & MUV Spectra
The Sun as a blackbody
Brightness Temperature
Tbrightness


h 
1

k   2h 4 1
 ln  2
  c  I1au



 
  1 
 
Sources of opacity in the solar atmosphere
Solar Emissions (VAL, 1992)
SIM Time Series at Fixed Wavelengths
27 Day Variability Depends on the Formation Region
Model Solar Atmosphere (FAL99)
10000
8000
6000
4000
-500
0
500
1000
Height (km)
1500
2000
2500
Wavelength Dependence of Sun Images #2
Identification of solar active regions
Solar Radiation Physical Model (SRPM) employs solar images from HAO's PSPT (left panel) to
identify and locate 7 solar activity features (R=sunspot penumbra; S=sunspot umbra;
P,H=facula and plage; F=active network; E,C=quiet sun) to produce a mask image of the
solar features (center panel). The SRPM combines solar feature information with physicsbased solar atmospheric spectral models at high spectral resolution to compute the emergent
intensity spectrum.
Recent quiet and active solar scenes
11 Feb 2006
15 Jan 2005
27 Oct 2004
Instantaneous Heating Rates
References
• “Modern Optical Engineering”, Warren J.
Smith, McGraw Hill, 1990.
• ‘Quantitative Molecular Spectroscopy and Gas
Emissivities”, S. S. Penner, Addison-Wesley,
1959.
• “Statistical Mechanics”, J. E. Mayer and M. G.
Mayer, Wiley & Sons, 1940.
• “Absolute Radiometry”, F. Hengstberger,
Academic Press, 1989.