Arcetri Solar Physics Group

IBIS Data Analysis
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Flat Fielding - Introduction

The images obtained by IBIS will have intensity variations across the field of view that are not due to the solar image, but rather caused by instrumental effects that alter the observed intensity in each point of the field of view. Some of the possible causes for the variations in instrument response are:

  • inhomogoneities in the CCD response in each pixel, including noticeably hot or cold pixels;
  • optical vignetting across the imaged area;
  • fringes produced by the various optical elements in the path;
  • ghost images or spurious reflections;
  • electrical interference;

These effects are, especially considering the rather fixed illumination pattern seen by the instrument, generally considered to all be multiplicative effects on a pixelwise basis. Therefore, for each pixel, we can determine a single value, equal to the product of all the above effects (or other unknown variations), which defines that pixel's response relative to all other pixels. By applying these corrections to each pixel, we produce images with a uniform response, whose values at each point are directly comparable with all other points in the array.

One means by which to measure the relative response at each point is to observe a field whose flux is perfectly uniform in all points. In solar physics, the only source bright enough to be observed is never completely uniform. However, by adding a series of images obtained at different locations on the sun, the inherent contrast of the solar surface is reduced (by a factor of N1/2, where N is the number of independent fields observed), resulting in a essentially uniform field. Image motion during the exposure (i.e. rapid telescope slewing) or defocussing of the image can further reduce the contrast in the field of view and result in a more uniform image.

There is the additional complication when observing spectral lines that there in an additional variation in the recorded data cube given by the variation in flux at different points in the spectral line. In addition, with IBIS there is the radially dependent blueshift in the field of view that produces additional spatially dependent intensity modulation.

IBIS Flat Fielding Techniques

A series of repeated spectral scans can be obtained with IBIS, as described above, with multiple fields at different locations on the solar surface. The multiple scans can be summed to produce a mean spectral scan. To within the errors governed by the number of different points combined, every point in the field of the mean scan can be assumed to have observed the same mean solar structure. Therefore, the spectrum observed at each point should be the same as the mean spectrum averaged over all points in the field. Any deviations from this mean spectrum can be assumed to be variations in instrument response. These variations can then be used to construct a flat field at each point and for each wavelength.

As an example, on 21 June, 2003, from 19:51-20:28 UTC, we obtained 75 spectral scans of the solar Fe I line at 6301.5 Å and the telluric O2 line at 6302.0 Å. Each scan included 64 points, with an average spectral step size of 18 mÅ, for a total scan coverage of 1.15 Å The exposure time for each image was 150 msec, and the images were obtained at the full resolution of (0.08 x 0.08) arcsec2 per pixel. The imaes were obtained while the telescope was in "random walk" mode wandering around N07, E07 on the solar disk.

IBIS Raw Flat Field Scan

The 75 images obtained at each wavelength were, after correction for CCD non-linearity effects and the transmission curve of the prefilter, averaged to create a single "average" image at each of the 64 wavelengths. No correction was done to correct for varying light-levels during the successive scans, though the observations were obtained near local noon and the light level was nearly-constant at 5.5. A single, averaged scan was thus obtained, the sum of all 75 individual scans.

The instrumental blueshift from the center to the edge of the field of view, as previously determined, was used to calculated the expected shifts in this averaged scan. There will also be a variable shift across the field caused by the solar rotation. This shift will obviously only apply to the solar lines, and not those produced in the Earth's atmosphere. This trend of the observed shift across the field of view will be constant for any field centered at a point on the solar equator. The absolute offset will vary between 0 mÅ at disk center to approximately 40 mÅ at the limb, but since we do not have an absolute reference, these bulk shifts can be ignored. Observations along the equator will have a relative shift of 3.3 mÅ between the extreme easternmost and extreme westernmost points in the field of view. Points away from the equator will have larger relative shifts with more complicated patterns. Actually, since the average spectrum is derived from the average of multiple images at different locations, the actual shift of the mean profile will be some weighted average of the shifts at the different positions in which the average image was obtained. This is a secondary effect, however, and can be neglected at the present time. The profile of a spectral line may also change its appearance between observations of the atmosphere normal to the line of sight and at higher inclinations towards the limb. Therefore, it is desirable to obtain the flat field measurements center on a point along the equator near the heliographic center of the solar disk.

IBIS Raw Flat Field Scan

Using the averaged scan, the spectrum at each point in the field of view was shifted by the theoretically calculated shift for that point (presently, only the instrumental blueshifts have been taken into account, while the effects of solar rotation have been ignored). In this manner, a single average profile for the the entire field of view is calculated. Then, a new arrays is generated by applying once again the same theoretical shifts at each point in order to shift this overall average spectrum into its assumed position at every point in the field. This array gives the expected data array for observations of a homogeneous field by a system with perfectly uniform response. This can then be compared to the observed averaged spectral scan, with the differences indicating variations of the system response at that physical location and wavelength.

IBIS Calculated Blueshifts Field Scan
IBIS Raw Flat Field Scan

IBIS Calculated Blueshifts Field Scan
IBIS Raw Flat Field Scan

IBIS Calculated Blueshifts Field Scan

Last Updated: 31 August, 2003