



IBIS Data Analysis

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Acquired Data
On 21 June, we obtained 20 scans of the solar spectrum in the 630.2 nm spectral range. Each scan consisted of images at 250 separate spectral positions in the approximate range 6300.6 to 6302.9 Å. FabryPerot #2 was stepped in constant steps of 2 V, corresponding to 9.2 mÅ, from 461V to +37V. FabryPerot #1 was tuned synchronously with FP #1, predominately in steps of 7 V, though 11 of the 249 steps were only 6 V in order to maintain the alignment of the transmission peaks of the two FabryPerot's. Overall, the average spectral step was 9.18 mÅ and the total spectral range covered was 2287 mÅ.
A region scanned by the present observations. The black line shows the
spectrum from the Jungfrau atlas, while the redline shows the average
spectral profile measured from a single spectral scan.

The series of 20 scans began at 00:05:10 UTC on 22 June, 2003 and completed at 00:29:53 UTC. The time between the start of subsequent exposures was approximately 294 milliseconds, with a 1.1 second pause between each scan. The exposure time was 60 milliseconds. Each image was binned 2x2 to produce a 512 x 512 pixel image with approximately (0.16 x 0.16) arcsec^{2} per pixel. The average counts were approximately 3000 ADU in the continuum, dipping down to close to 1000 ADU in the center of the spectral lines. Assuming 9.5 e per ADU, this implies, for a single measurement, a statistical error due to photon shot noise of approximately 0.006 in the continuum and 0.01 in the line cores. The prefilter transmission in the range used was generally above 90%, except in the extreme redward portion of the scan, where it dropped down to 75%.
The region scanned was located at the center of the solar disk. The telescope was in focus and the image was not moved during the 20 scans, though the seeing was rather poor, blurring out many of the features in the field of view. The contrast was observed to be about 2.5% (RMS intensity fluctuations divided by mean intensity) in the continuum and > 6% in the center of the iron lines.
During the approximately 25 minutes over which the 20 scans were acquired, the average light level fell by approximately 7.5%. This was determined by comparing successive measurements for a given wavelength through all 20 scans, and confirmed by the light levels measured by the DST monitor. This slow decrease in flux implies a reduction of 0.3% in the relative intensity between one scan and the next. A cubic polynomial can be fit to the light level changes to remove the slow drifts. The remaining residual fluctuations, which approximate random flux changes from between single images, have an RMS noise of 0.4%.
The intensty changes observed during the course of the observations
(black line) and the cubic polynomial fit to the curve (orange line).
The image acquisition rate was approximately 200 images/minute.

Data Reduction
The images from each scan were loaded and corrected for the nonlinearity of the CCD camera. The effect of the prefilter transmission profile was also removed using highprecision scan of the profile obtained 12 hours after the observations. No corrections were made for removing, the bias, dark current, or flat field effects on the images. It should be noted that spectrally stable structures in the flatfield (e.g. the relative changes in pixel sensitivity, vignetting) will not alter the shifts in line center positions found on a pointbypoint basis (but will cause variations in the line depth found). It should also be noted that there are spectrally varying structures, particularly at the edges of the filter passband.
The center and edge of the field of view were determined once and applied equally for all images. The determined field center was [x=255.5, y=252], only slightly offset in the vertical direction from the array center, and the effective edge of the field of view was approximately 250 pixels, with some spurious effects becoming visible past 240 pixels from the center.
At each point in the field of view, a entire spectral scan of 250 points was extracted. This scan was interpolated from its semiregular spacing on a 9.2 mÅ grid onto a regularly spaced grid at 2 mÅ intervals using a cubic spline interpolation. For each interpolated spectrum, the position of the line center of each of the four lines was independently determined. This determination was performed by fitting a parabola to a fixed number of points around the position of minimum intensity in the observed spectrum. The number of points used was approximately 11 (uninterpolated) points, or 100 mÅ for the iron lines and 5 points, or 45 mÅ for the atmospheric oxygen lines. These widths are comparable to the FWHM of the spectral lines, and hence the determined line center is governed by the true line center as well as higher portions of the line.
A sample line profile showing the originally sampled line profile in
black, with crosses (+) at each fieldcenter wavelength position, and the cubic sline
interpolated line profile in orange. The blue crosses (X) indicate the
determined line centers for this spectrum.

From the line centers determined for the atmospheric oxygen line at 6302.0 Å, we can determine the magnitude of the radial blueshifts produced by the the classical mounting of the interferometers. Examination of the measured line center positions, it was determined that the optical center of the images was at [x=257.5, y=254]. Using that as the central point, the line center positions of the oxygen line were averaged radially. This curve was then fit with a parabola to determine the observed radial shift. The resulting fit was (0.000257 ± 0.000001) mÅ x r^{2}, where r was the distance, in fullresolution pixels, from the optical center. The same value was determined both as the mean of fits to the shifts measured from each of the 20 scans, and from fitting the shifts averaged over all 20 scans. The residual errors to the fit were approximately ± 0.15 mÅ. Note that the value determined for the above fit is based on the nominal step size of the two interferometers, 1.325 and 4.611 mÅ, which may not be completely accurate values. This shift can also be measured in terms of steps of FabryPerot #1 as 1.954*10^{4} V x r^{2}, where the interferometer is stepped in one volt increments.
The measured radial shift in the line center locations as a function of
distance (fullresolution pixels) from the optical center (black line). The orangle line gives
the parabolic fit to the observed shifts.

This radial trend can be subtracted from the observed line center measurements to produce the corrected map of line center positions. This shows that removing this trend leaves a smooth field of much smaller velocity variations. These variations are mostly random noise or small scale structures (from atmospherically generated changes in the underlying intensity pattern), with residual variations on the order of 0.2 mÅ RMS. By averaging the residual line center positions over all 20 scans, even these small scale fluctuations are removed, leaving only structures due to the lack of flat fielding and small annular artifacts produced by the line center finding algorithm. These artifacts produce about half the observed RMS fluctuations, or 0.13 mÅ RMS.
The residual variation in line center positions of the 6302.8 Å
oxygen line after removing the
measured radial trend. Left: The residuals measured from a
single scan. The predominant features are the small scale fluctuations,
probably due to changes in the underlying intensity structure during
the scan of the line. Right: The residual line center positions
averaged over all twenty spectral scans, showing the horizontal stripes
due to spectral variations in the fringe pattern that are uncorrected
due to the lack of flat fielding.

Error Estimation
The measurements of the positions of the two different oxygen lines in the observed spectra can be used to estimate the magnitude of the errors in the line center determinations. The observed spacing between the cores of the two oxygen lines should remain constant at all points in the field of view. Any bulk atmospheric or instrumental effects should operate equally on the two lines. The variation in the line center positions found for the two lines will give an estimate of the relative accuracy of the line center finding technique. There are also other effects, such as spectrally dependent flat field/fringe variations or temporally varying distortions in the underlying solar structures that will produce changes in the observed line center differences, increasing the magnitude of the error found.
The difference map between the line center positions found for the
6302.0 and 6302.8 Å oxygen lines. The scaling in the image is
± 0.5 mÅ.

The line center positions for the 6302.0 and 6302.8 Å oxygen lines were subtracted to produce a map of line center differences across the field for each scan. The mean difference between the two line centers is 765.1 ± 0.3 mÅ. The average RMS fluctuation in the difference map for a single scan is 0.6 mÅ. These differences can be further seperated into their radial and nonradial components, with the nonradial errors being the dominant factor in the linecenter position fluctuations. The study of these differences shows that for a single spectrum, with approximately 5 spectral points per FWHM, we are able to reliably determine the line center position to better than 0.5 mÅ.
The average line center position difference maps separated into their
radial and nonradial components and scaled between
± 0.5 mÅ Left: The radial component of
the difference, with variations presumably due to errors in locating
the line center position due to sampling effects. Right: The
nonradial component of the difference, again showing the
horizontal stripes due to fluctuations in the (uncorrected) flat
field.

Interferometer Spacing
It is also technically possible to determine the exact interferometer spacings from the measurements of the position of two spectral lines whose separation is known. In the case of IBIS, we can use the two telluric oxygen (O_{2}) lines. These two very similar lines, which are not affected by the solar atmospheric motions, solar rotation, or terrestrial rotation, offer a relatively stable spectral source for this measurement. These two line can be used to determine the separation of the FabryPerot plates in the following manner. The center of each line is determined separately, and the number of steps between the two line centers calculated. Knowing the true wavelengths of the two lines we have the following equations:
d / n = λ_{1}
d + Δd / n = λ_{2}
where λ_{1} and λ_{2} are the known wavelengths, Δd is the measured spacing change between these two wavelengths, and d, the separation between the plates, and n, the order are to be determined. We determine, from measuring the Jungfrau spectral atlas, the wavelengths of the two lines as λ_{1} = 6301.9885 Å and λ_{2} = 6302.7523 Å, for a net separation of Δλ = 0.7648 Å.
We then take the point by point measurements of the line center positions of the two oxygen line and reconvert the wavelength scale into the scale of commanded voltages. We then take the pointwise difference between the line center positions of the two oxygen lines, given in Volts. Then applying the nominal spacing change of interferomter spacing of 4.816, we find the true change in spacing, Δd, between the two lines. From the observations, we find 579.4 voltage steps bweteen the cores of the two lines, corresponding to a true spacing change of 0.2790 Å. From the two equations above, this implies a true interferomter spacing of 2.299 mm and the use of order 3649.
This measurement, however, is a very sensitive one. An error of 0.1 mÅ in the line center measurement will produce an uncertainty of 0.11 V in the voltage difference, corresponding to 0.5 mÅ in the determination of Δd. This in turn generates an error of 4 x 10^{3} Å in the determination of the plate center, and an uncertainty of 0.6 in the order number.
From the error in the line center determination described above, we would expect an error in the difference between the two oxygen line positions to be ~0.7 mÅ. However, by summing up the differences measured in the 180,000 points in the field of view, we would expect to reduce the error in the mean difference by a factor of 100 or more.
Taking the spectral line position difference separately for each of the 20 different scans, however, we observe an RMS variations of 0.3 mÅ. The line center positions determined for each spectral line also show random fluctuations of approimately the same magnitude. The variations in the two different lines are not correlated. This observed jitter is due to true shifts in the mean spectral lines, not merely noise in the position determination. Some of these relative shifts may be caused by rapid variations in intensity during the scan through the spectral line. Such changes could be caused by changes in atmospheric transmission, fluctuations in shutter timing, or small errors in the positioning of the interferomter plates. In any case, such variations prevent the determination of the spacing with significant accuracy to determine the order being used.
Last Updated: 31 August, 2003