1. ENA measurements of the ring current
Robert DeMajistre

3. Overview Motivation for ENA imaging Measurement mechanism
The HENA instrument
HENA measurements/retrievals
Validation
Results
The next steps

4. In situ measurements Cluster observation of the ring current
Precise measurements
Lack of global context – single trace through a 4 dimensional structure (3 space, time)

5. Global context In situ measurements often alias space and time
Overall morphology is difficult to deduce
Multiple spacecraft help
Statistical models are difficult to assemble
Combination of precise in situ measurements and qualitative morphology very attractive
ENA imaging to the rescue

6. ENA emission from RC

7. ENA imaging

8. IMAGE geometry
(geographic)

9. High Energy Neutral Atom Imager+ -

10. Example HENA Image Earth disk Magnetic field lines Direction to Sun
Clock
Angle
Magnetic field lines
Particle brightness is
represented in false color
Direction to Sun

11. Sample image sequence

12. Retrieval Method
Transform spatial integral into dipole coordinates (L, f, m), expand pitch angle dependence in Legendre polynomials
Use 2-D linear quadrature to convert to linear equations
Use 2-D constrained least squares to solve

13. Tuning scheme

14. Tuning inputs
Simulated image from October 4, 2000

15. Tuning Results
Second difference (H2) provides better quantitative agreement at the peak
Markov provides better overall morphology
In practice, we combine the two

16. Results for actual image

17. Preliminary Validation

18. Selected Results
Ring current peak is often observed at midnight (or later) rather than at the ‘classical’ position at dusk
Dipolarizations and depletions (observed) in time series – clues to how substorms develop

19. ~100-150 keV Oxygen | 40-50 keV Hydrogen
March 31, 2001

20. Next steps TWINS Casini/INCA Dual vantage point Earth looking
Launches in 06 and 07
Casini/INCA
Currently orbiting Saturn
Good data on both Saturn and Titan

21. Conclusion
ENA imaging is giving us a new view into ring current morphology
We’ve improved our insight into the storm time behavior of the magnetosphere
In coordination with the in situ instruments we can make important quantitative statements about how the magnetosphere behaves.

22. Backup

23. Overview Remote sensing – what and why
Mathematical framework for inverse problems
Case studies:
Nighttime electron density inferred from ultraviolet emission measurements (TIMED/GUVI)
Atmospheric composition inferred from Stellar Occultation Measurements (MSX/UVISI)
Ion intensities inferred from Energetic Neutral Atom (ENA) imaging (IMAGE/HENA)
System engineering implications

24. What?
Making measurements where the instrument does not have direct physical access to the object of measurement
Why?
Many problems in space science require measurement of multiple locations nearly simultaneously – costs of sufficient in situ measurements are prohibitive

25. Remote sensing is indirect
y=F[X;P]
Forward model
Inverse model
X=F-1[y;P]

26. Problems with using exact inverse
y=F[X;P]
X=F-1[y;P]
Solution may not exist
Only for an EOM in specific forms
It may not be unique – many x may produce a single y
It may be poorly conditioned – slightly different x may yield different y
Measurement noise is always present
Pose a similar problem that can be solved more easily

27. Example of direct retrieval
I=Kh
Simplified example – similar to recombination problem
Linear problem
Noise added to measurement
Noise amplification very noticeable (poorly conditioned)
Only marginally acceptable results

28. The least squares alternative
Instead of exact solution, search for the values of x that are most consistent with the measurement
Minimize the square (epTSy-1ep) of the prediction error ep=y-F(x;p) weighted by the inverse of Sy (the measurement covariance)
There are standard solutions for linear problems (e.g., Bevington)
Even moderately nonlinear problems can be solved iteratively

29. Adding information
The least squares solution is likely to be just as ill conditioned as is the direct solution
Adding measurements is not very effective (~N-1/2)
Additional physical information must be introduced to stabilize the inversion

30. Constrained inversions
Minimize epTSy-1ep+gxTHx where the matrix H is chosen with the expectation that xTHx should be small. The tuning parameter g modulates the influence of the constraint
Example – if we expect x to be smooth, we could put H=D1TD1, where D1 is the first derivative operator

31. Constraints in perspective
Constraints add information to the problem
Can be formally equivalent to additional measurements
H and g quantify the character of these constraints
(y-Kx)Ts-2 (y-Kx)+gxDTDx

32. Constraints Constraints can dramatically reduce error amplification
They can also introduce significant systematic errors
Prediction error ALWAYS increases
Relying on information in addition to the actual measurements

33. Metrics for tuning constraints
Tune through simulation
cr2=(1/Ny) epTSy-1ep – does the data fit the model
g =(1/Nx)(xm-xs)T Sx-1(xm-xs) – does the retrieval match the input to the simulation
q=(cr2 -1)2+(g-1)2
Minimize q

35. EOM for space based measurements
Many measurement systems can be represented by a common physical model
Though mechanisms vary, the formal similarity is striking
Two essential parts
Instrument equation
Equation of transfer

36. Equation of transfer
Applicable to a wide variety of information carries:
Photons
Massive particles in tenuous media
Transmission from 0 to s
Transmission
from s’ to s s = ò I ( s ; E ) I ( ; E ) T ( s , ; E ) + J ( s ; E ) T ( s , s ; E ) d s
Intensity at s
Intensity at 0
Source at s’

37. Background counts in channel i
Instrument equation
Covers most instrument effects
Non-linearity neglected for now
Assumes instrument measures local intensity of information carriers
Smearing function
Background counts in channel i
Counts in channel i

38. Approach to Solution Replace integrals with discrete quadratures
Cast problem in general form
Replace integrals with discrete quadratures
Linearize the problem (if necessary)
Formulate constraints
Tune the constraints
Validate with independent measurements

39. Case studies
TIMED/GUVI electron density retrievals – one dimensional, single color, single constituent retrieval (limited by SNR)
MSX/UVISI Stellar occultation – one dimensional, multi-spectral, multi constituent retrieval (limited by SNR and size of data set)
IMAGE/HENA ENA imaging – two dimensional retrieval (limited by SNR and viewing geometry)

40. Constraint Matrices
Boundary constraint – force solution to be small at boundaries of L
Cylindrical boundary in f
Smoothness constraint with asymmetry parameter
First difference (force solution to be small)
Second difference (force Laplacian to be small)
Markov constraint – force changes to be small over a correlation length
Optimize smoothness strength, g, boundary strength, l, and either asymmetry or correlation length, a – need a method

41. Impact of ENA measurements
ENA imaging on the IMAGE spacecraft provides the first global view of the inner magnetosphere
The retrievals described here have been used to study global behaviors for the first time
Skewed peak of the ring current density towards midnight
“Dipolarizations” of the ring current during substorms
Growth phase dropouts – “choking off” of the ring current during the growth phase

42. Common Elements of Case Studies
Similar inversion procedures have been successfully applied to disparate data sets
Problems and solutions are formally similar
Common tuning process for constraints are used
Suggests common solutions in measurement system design
Replace integrals with discrete quadratures
Linearize the problem (if necessary)
Formulate constraints
Tune the constraints
Cast problem in general form
Validate with independent measurements
In all cases, retrievals were designed after instrument flight

43. System Engineering
The tools used for developing retrievals and tuning constraints can also be used as part of instrument design
Forward modeling of the Equation of Measurement
Retrieval sensitivity to instrument parameters
System focus on retrieval accuracy rather than radiometric accuracy
Optimize (quantitatively) instrument tradeoffs based on final retrieval accuracy (e.g., should I sacrifice some SNR for better spectral resolution?)

44. Measurement System Design
Develop coupled simulation of radiation mechanism and instrument early
Use it to help with instrument and spacecraft tradeoffs
Keep it current as project develops
Alternate lower fidelity models can be developed and compared
Add data system and inversion modules to be used with optimization of instrument
Use these modules to identify and exploit opportunities for in-flight calibration refinement

45. Calibration and data products
Currently, calibration emphasizes the production of radiances from instrument data (required by NASA)
Shift focus to characterizing full instrument function for use in retrievals.
Shift priority to lower level data products for retrieval team and higher level products for the users (calibrated radiances are almost always of marginal utility)

46. Science Impacts Night-side ionosphere Stellar Occultation ENA
New quiet time maps of the low/midlatitude ionosphere
Basis for studying the quiet time interaction of the thermosphere/ionosphere
Stellar Occultation
Study of ozone behavior during polar night
Study of molecular oxygen and ozone in the mesosphere/thermosphere
ENA
First global quantitative view of the inner magnetosphere
Several storm time phenomena have been observed and studied from a global perspective
Comparisons with models of the inner magnetosphere

47. Next steps Night-side ionosphere Stellar occultation ENA
SSUSI an instrument similar to (but more sensitive than) GUVI is now in orbit, more are planned
Additional instruments are being proposed focusing on nighttime limb observations
Stellar occultation
Instruments to be proposed include extensions to IR for use at Mars
ENA
Doublestar (now flying )TWINS (near launch) to provide multi-position ENA measurements
Cassini/INCA now at Saturn, IBEX now phase B

48. Conclusions
We’ve described a general framework for space based remote sensing
Techniques developed here have been used successfully across a broad range of applications
The products resulting from these techniques are being applied to significant and interesting problems
The techniques also allow for more effective system design of remote sensing systems