REU TrainingSolar Irradiance/Radiometry

Jerry Harderjerry.harder@lasp.colorado.edu

303 492 1891

Things to remember about the Sun

Radius 695,510 km (109 radii)Mass 1.989 x 1030 kg (332,946 ’s) Volume 1.412 x 1027 m3 (1.3 million ‘s)Density 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 kmTSI (@1 AU) 1,361 W/m2 Composition 92.1% hydrogen

7.8% helium 0.1% argon

Wavelength Dependence of Sun Images

Yohkoh Soft X-rayTelescope (SXT)

Extreme UltravioletImaging Telescope(EIT)Fe XII 195 Å

Ca II KspectroheliogramsNSOSacramento Peak

He I 10830 Åspectroheliograms NSO Kitt Peak

Radiometric Terminology

Name Symbol Description Units Radiant Energy U J Radiant Power (flux) P Rate of transfer of energy W (or J s-1) Radiant Intensity J Power per solid angle from source W ster-1

Radiance N Power per solid angle per unit area from a source

W ster-1cm-2

Irradiance H Power per unit area incident on a surface

W m-2

Physical Constants Symbol Value Units Planck’s Constant h 0.66262×10-33 J sec Boltzman’s Constant k 1.3806×10-23 J deg-1

Speed of Light c 2.997925×108 m sec-1

Solid angle subtended by the Sun at 1 AU

6.79994×10-5 steradians

Advice: PAY ATTENTION TO YOUR UNITS!!!

Definition of Solid Angle ( )

Solid angle subtended by sphere (from an ‘interior’point):

=4• For an area seen from a point of observation:

• Approximation for a distant point ( small):

2

dA

s

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:

– 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:

-1(W ster )4

PJ

2-2

2 2 (W cm )

4

x PH J

S S

Point source illuminating a plane

23

2

coscos

cos

o

xH J H

S

2

2o

xH J

S

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

-1 -2

-10

Source has radiance (W ster cm ) and area

At some angle , the intensity is :

cos cos (W ster )

The incremental ring area on the hemisphere :

2 sin

and subtends a solid angle :

2 sin

N A

J J NA

da R d

R dd

2

0

/ 22/ 2

00

2 sin

The radiation intercepted by this ring is then :

2 sin 2 sin cos

Integrate over hemisphere :

sin2 sin cos 2 (watts)

2

dR

dP J d NA d

P NA d NA NA

{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)

Major Advances• Phase sensitive detection at the shutter fundamental

frequency eliminates DC calibrations• Nickel-Phosphide (NiP) black absorber provides

high absorptivity and radiation stability

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)

Radiometer Cones

Glory Prototype Cone Interior

Glory Prototype Cone

Post-Soldered Cone

TIM Baffle DesignGlint FOV46.6 degrees

Vacuum DoorBase Plate

Shutter

PrecisionAperture

ShutterHousing

Baffle 1,2,3 FOV Baffle

ConeHousing

Rear Housing

Cone

TSI Record

Planck’s equation

2

2

5

Planck's distribution law for the density of radiation

in a cavity :

First radiation const = 2 = 3.7418e-016 (mks)2 1

hcexp 1 Second radiation const = 0.014388 (k

hchc

WhckT

2

5

4

mks)

(radiation emitted into a hemisphere)

Two important limits :

Wein's approximation

2When 5 then exp

Rayleigh - Jeans approximation

2When 1 then

hc hc hcW

kT kT

hc c kTW

kT

?

=

Properties of the Planck distribution

max

max

max

15 5

On differentiation of the Planck equation and setting = 0

an equation for the peak wavelength can be found :

2897.8 (micron - degree)4.965

Peak power at :

1.288 10

The equation

hcT

k

W T

4 -2Total 0

5 48

2 3

of Stefan - Boltzmann relates the total thermal

radiation density with temperature

W (W m )

25.6697 10 {the Stefan - Boltzmann Constant mks}

15

W d T

k

c 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.

•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

SOLSTICE: Experiment Concept

Photomultiplier Detector

Interference Filter Out DiffractionGrating

Photomultiplier Detector

Interference Filter In DiffractionGrating

Camera Mirror

Camera Mirror

Stellar Observation: Objective Grating Spectrometer

Solar Observation: Modified Monk-Gilleison Spectrometer

Solar Exit Slit

Stellar Exit Slit

Entrance Aperture

Entrance Slit

SORCE SOLSTICE FUV & MUV Spectra

The Sun as a blackbody

Brightness Temperature

4

21

1

2 1ln 1

brightness

au

hT

k hc I

Sources of opacity in the solar atmosphere

Solar Emissions (VAL, 1992)

SIM Time Series at Fixed Wavelengths

Model Solar Atmosphere (FAL99)

-500 0 500 1000 1500 2000 2500Height (km)

4000

6000

8000

10000

27 Day Variability Depends on the Formation Region

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 physics-based solar atmospheric spectral models at high spectral resolution to compute the emergent intensity spectrum.

Recent quiet and active solar scenes

11 Feb 2006 27 Oct 200415 Jan 2005

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.