flt: Flat Field Intensity Corrected Image
nbc: Narrow Band Calibration Image
wlm: Wideband Calibrated Image


flt is the flat field intensity correction image, nbc is the narrow-band calibration image and wlm is the wide-band calibration image (also referred to as spurious modulation) needed by VMBICAL to calibrate the solar images. These images all calculated during VMBICAL processing stage from the east- and west-limb calibration measurements, taken daily at each site with the instrument in calibration mode.

wlm and nbc

In calibration mode, the optics produce light at the final focal plane that would, in the absence of instrumental effects, have uniform phase across the camera image. The instrument pupil isolates a circular piece of the solar image. Two separate Doppler images are obtained in this way, one near the east limb and one near the west limb. In the absence of spurious modulation, the two images should be nearly identical except for a phase shift resulting from solar rotation. The calibration images must first be dark- and clamp-corrected to correct for camera effects. After converting the three-band intensity images into phase velocity, modulation amplitude, and average intensity triplets, the signal at each pixel can be represented by a vector, where the phase corresponds to the angle and the modulation amplitude is represented by the vector length. The east/west limb vector is the sum of the spurious modulation vector and the solar signal from the east/west limb. If the phase separation (the mean velocity difference) and the relative amplitude of the two solar observations are known, then the spurious vector component can be deduced. Let Ex,Ey represent the east limb measurement, in rectangular coordinates (after dark/clamp camera corrections have been applied). Similarly, let Wx,Wy represent the dark/clamp-corrected west limb measurement. The wide-band vector, in rectangular coordinates, can then be expressed as

and m is the relative amplitude of the east and west limb signals. The parameter alpha is called the "balance angle" and allows the relative amplitude of east and west vectors to be changed while holding the difference in average velocity between the two measurements, phi, constant.

Image vectors are also corrected for interferometer field effects, the dominant source being path difference variation with angle, by applying a narrow-band correction (nbc) image. The nbc image is calculated by correcting a camera-corrected calibration image (east or west limb measurement) for spurious modulation. The phase of the resultant image is the phase variation and the modulation is the modulation efficiency of the interferometer.

In practice, the phase angle phi and the balance angle alpha are not known to sufficient precision. Pointing errors result in an uncertainty in the phase angle phi; whereas pointing errors and the distribution of solar active regions combine to cause significant variations in the modulation amplitudes of the two observations which translates into an uncertainty in the value of the balance angle, alpha. Therefore, these two parameters, phi and alpha, must be determined in a self-consistent way from each east-west pair of calibration images. The criterion for determining the correct values of these parameters is the symmetry of the final, corrected solar modulation image. Since a properly calibrated modulation image is a map of the equivalent width of the solar absorption line being used, the modulation image should be, on average, symmetric about the center of the sun; isopleths of equal modulation strength should be concentric with the limb of the sun. The effect of an incorrect value for phi is to distort the contours (either flattening or elongating along the sun's north-south line) into ellipses. The effect of an error in the balance angle, alpha, is to cause the centers of the circular contours to shift along an east-west line on the sun. In other words, the correct values of phi and alpha are those that minimize crosstalk between velocity and modulation.

In practice, the root-mean-square (rms) deviation of the modulation from the mean value within a narrow annular ring on the sun's image is a sensitive indicator of symmetry. The rms goes through a distinct minimum over the range of possible phi, alpha pairs. The optimum values of these two parameters are found by minimizing the rms deviation of the modulation in an annulus which is 90-98% of the sun's radius, using a downhill simplex method.

flt

The flat field intensity correction image, flt, is obtained by averaging the intensity bands of the dark/clamp-corrected east and west limb calibration images and is used by the GEOMPIPE section of VMBICAL.


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