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eSDO 1121: DEM Computation

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Deliverable eSDO-1121: DEM Computation
V. Graffagnino, A. Fludra
08 Sep 2005


Although the AIA is an imaging and not a spectroscopic instrument, the fact that images will be produced in 7 narrowband EUV filters introduces a means of obtaining information concerning the thermal structures via the production of a Differential Emission Measure (DEM) distribution – a measure of the amount of plasma at a given temperature T. A comparison of a number of algorithms used to model the differential emission measure has previously been produced and presented in the report RAL-91-092, “Intensity Integral Inversion Techniques: a Study in Preparation for the SOHO Mission,” edited by Richard Harrison and Alan Thompson in December 1991. The report’s conclusions, all methods have three commonalities: 1) the intensity integral is discretised, 2) a form of smoothing is applied, and 3) the degree of smoothing must be chosen carefully.

Whether a DEM is produced for each pixel is of course dependent on how computationally intensive the chosen algorithms are. The use of parallel computing techniques and / or genetic algorithms may be of use here to improve computation time.

A number of packages are currently employed by the Solar community, but for the purpose of eSDO it is suggested that the Arcetri method (Landi and Landini, 1997), available though the Chianti package, should provide the main general purpose algorithms due to the ease of availability, whether as a standalone program or as part of the SolarSoft package. Two other options are an adaptive smoothing (Thompson, 1990), currently used in the ADAS package, and an iterative multiplicative method (Withbroe 1975; Sylwester et al. 1980).


  • AIA images in 7 EUV narrowband filters – These can be FDLR images for the case of the global DEM or HDHR images for the user wishing to obtain more specific DEMs.


  • DEM curve for each pixel
  • DEM curve for each local area of interest selected by user
  • Global DEM – useful for studies of the Sun as a star as has been done by Reale et al (1998)

The required DEMs would be outputted as FITs files, with the multiple DEMs being contained within a datacube format.

Test data

  • TRACE and / or SOHO EIT images in multiple wavelengths

Tool Interface

  • commandline:
    1. AstroGrid CEA web service: this algorithm will be deployed as a CEA service hosted in the UK that users can call to process datasets on the grid. Due to computation intensity, this service may be restricted to recognized solar community users registered with AstroGrid.
    2. SolarSoft routine: if computational intensity is not too high, the C module will be wrapped in IDL and distributed through the MSSL SolarSoft gateway. Users will access to a SolarSoft installation can call the routine from the commandline or GUI to process locally held data.
    3. JSOC module: the C module will be installed in the JSOC pipeline. Users can access the routine through pipeline execution to operate on data local to the JSOC data centre.

Science Use Case

The user would like to obtain the differential emission measure distribution derived from the AIA images taken at the 7 EUV filter wavelengths. The differential emission measure is defined as the squared density integrated over the column depth along the line of sight for any given temperature:

Φ(T) dT = Ne2 dh

In general, this distribution is derived using a wide range of EUV/X-ray line intensities. For AIA, the spectral line intensities, I, are substituted with filter intensities, and line emissivities G(T) are substituted with the temperature response of each filter. The intensity observed in each filter can be calculated from the integral:

I = ∫ G(T) Φ(T) dT [photons cm-2 s-1 st-1]

The filter responses G(T) are in units of electrons per pixel per second as a function of plasma temperature for unit emission measure. They are calculated by convolving the effective area of each telescope as a function of wavelength with the theoretical EUV spectrum calculated for the entire range of expected coronal temperatures. The calculation of G(T) can be done prior to the DEM analysis, or it can be recalculated each time the DEM algorithm is executed with the user-defined atomic data and elemental abundances.

The following description is for the case where the user selects an area of interest and wants to obtain a DEM for that region. The methodology will be similar for the automated process of obtaining a DEM for each of the whole image pixels.

The procedure involves the following:

  1. The user identifies the local region of interest for which a DEM is required
  2. The user inputs the flatfielded AIA images (one for each filter) – the intensities are calculated for each filter.
  3. Pre-calculated G(T) functions are read
  4. Optional: The user inputs his choice of elemental abundances and ionisation equilibrium data.
  5. Optional: The appropriate atomic data (whether from Chianti or ADAS) is chosen by the user
  6. Optional: The G(T) function, which is dependent on the temperatures and densities is then calculated.
  7. The DEM is calculated.
  8. A Fits output file is produced.

Technical Use Case

The DEM C code should be available both as standalone and also wrapped as an IDL application which can then be distributed through the SolarSoft gateway at MSSL. The technical aspects of the procedure involves the following:

  • The intensities of the pixels in region of interest are summed for each filter.
  • A number of algorithms have been investigated as reported in the RAL report, whose conclusions showed that all the methods were capable of satisfactorily deriving DEMs. Each method employed integral discretisation, together with some form of smoothing applied. In a few methods positivity constraints were also imposed. The following algorithms are recommended for eSDO:

Log-T Expansion Method (Arcetri Code)

  1. Integral discretisation – trapezoidal method
  2. Iterative correction of DEM using a correction factor based on the first term of a power series expansion as a function of log(T)
  3. Goodness-of-fit criterion: chi-squared

Adaptive Smoothing Method (Glasgow Code)

  1. Integral discretisation – product integration.
  2. Smoothing – regularisation
  3. Degree of smoothing controlled by a smoothing parameter

Iterative Multiplicative Algorithm (Wroclaw Code):

  1. Integral discretisation – 3rd order spline interpolation
  2. Smoothing – iterative processing from flat to final solution in a pre-set number of iterations (maintains positivity).
  3. Goodness-of-fit criteria – chi-squared and a parameter ‘sigma’

In particular the Arcetri code algorithm is now employed within the Chianti package and thus has been regularly used and tested by the Solar community. In the case of a fully automated DEM extraction code for each of the 4096x4096 pixels, a check on the DEM being derived should be incorporated to make sure that these values are consistent with the region being examined (e.g. whether the pixels are from an active region etc.)

The DEM algorithm design will be revised following the DEM workshop with AIA collaborators to be held in February 2006.

Quicklook Products

  • none

Support Information

  1. ADAS - http://adas.phys.strath.ac.uk/
  2. CHIANTI atomic database - http://www.damtp.cam.ac.uk/user/astro/chianti/chianti.html
  3. DEM Computation with AIA - http://lasp.colorado.edu/sdo/meetings/session_1_2_3/presentations/session1/1_05_Golub.pdf
  4. Intensity integral inversion techniques: A Study in preparation for the SOHO mission, Editors: R A Harrison, A M Thompson. RAL internal report - Please see DemComputationRalReport
  5. Coronal Thermal Structure from a Differential Emission Measure Map of the Sun. J.W.Cook, J.S.Newmark, and J.D.Moses. 8th SOHO Workshop: Plasma Dynamics and Diagnostics in the Solar Transition Region and Corona. Proceedings of the Conference held 22-25 June 1999
  6. EIT User's Guide http://umbra.nascom.nasa.gov/eit/eit_guide/
  7. A. Fludra, J.T. Schmelz, 1995, Astrophys. J., 447, 936.
  8. M.Gudel, E.F.Guinan, R.Mewe, J.S.Kaastra, and S.L.Skinner. Astrophysical Journal. 479, 416-426 (1997).
  9. J.S.Kaastra, R.Mewe, D.A.Liedahl, K.P.Singh, N.E.White, and S.A.Drake. Astron. Astrophys. 314, 547-557 (1996).
  10. V.Kashyap and J.J.Drake. Astrophysical Journal. 503, 450-466 (1998).
  11. E. Landi and M. Landini, 1997, A&A, 327, 1230
  12. Sylwester, J., Schrijver, J., and Mewe, R., 1980, Sol. Phys., 67, 285
  13. A.M. Thompson, 1990, A&A, 240, 209
  14. Withbroe, G., 1975, Sol. Phys., 45, 301

-- ElizabethAuden - 29 Jun 2005

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Topic revision: r6 - 2005-09-30 - ElizabethAuden
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