The method applied to the images acquired with the PSPT in order to make an instrument calibration of the detector’s answer to uniform lightening, as proposed by Kuhn et al. (1991), allows us to calculate the flat-field image corresponding to a series of simulated images of the Sun with an accuracy higher than 10-4. However, we know that the numerical application of this method requires the images to confirm some hypotheses. That is why the photometric accuracy obtained by applying the method to the various series of acquired images can be lower than the one indicated above.
We have therefore examined the sample of selected images in order to highlight the possible presence of faults due to the application of the method.
In particular, we know that the CCD camera used in the telescope employs four amplifiers for a four-quadrant quick reading of the images. Because of the differences in the answer of the amplifiers, by evenly lightening the detector, we can notice that each quadrant of the image shows a different average intensity.
The presence of these systematic gain differences in the four amplifiers enables us to evaluate the efficiency of our flat-field correction. This evaluation can be made, for instance, by measuring the differences of average intensity in the four quadrants of calibrated images.
We have therefore analyzed the average intensity along thin rings centered upon the solar disk in the sample images, and we have measured the average values of intensity for each quadrant. The position and dimension of the selected rings have been chosen so as to prevent active regions from “falling” into them.
In Figure 8.1 (bottom) we have charted the variations of intensity and the average intensity for each quadrant inside the selected ring, for one of the sample images. In particular, we have compared the values obtained from the original image and from the corresponding calibrated image (corrected for darkness flow and flat-field answer) obtained in the continuous red on November 2, 2001.
The application of calibration procedures reduces differences among average values of relative intensities, due to the usage of the four amplifiers, up to values <0.2% for images in the continuous red, whereas for images acquired in the continuous blue and in the CaII K line, the largest differences are respectively of the order of 0.2% and 0.8%. It should be noticed that the differences of average intensities in the images untouched for flat-field are of the order of 4%; therefore, a correction for flat-field reduces these differences by a factor above 20.
The same analysis has been made on a sample of imagines acquired with the telescope operating in Mauna Loa, and has given wholly comparable results, as summed up in Table 2.
Table 2: Results of the analysis of the largest differences in the values of average intensity (%) measured for each quadrant of the detector.
FIGURE 8.1: Top: image acquired in the continuous red, uncalibrates for flat-field; values of average intensity of pixels in the image untouched for flat-field inside the selected ring, for each of the four quadrants of the CCD detector (a different symbol is used for each single quadrant); corresponding calibrated image with a superimposed ring inside which average intensities have been measured; values of average intensities in pixels in the corresponding image, corrected for flat-field, inside the same ring. The horizontal superimposed lines indicate average values.
The photometric accuracy of acquired images has been confirmed by the analysis of the level of photometric noise in some images obtained through an holographic diffuser produced by the Physical Optical Corporation. In particular, in the months of October and November 2001, after the end of the daily observing procedures, we have acquired series of 2048×2048 images by placing the diffuser in front of the objective lens (Figure 8.2). These images have been acquired in order to gather useful data for an assessment of the accuracy of alternative calibration methods for flat-field as well as to check the photometric accuracy of acquired data.
To this aim, we have acquired a total of 15 series of 18 images for the three filters, in the course of five of observating days.
The exposure times for the acquisition of these images are much higher (1000 ms) than those employed for normal observations of the solar disk. We have ascertained that the fluctuations of intensity inside sub-arrays of various dimensions (from 10×10 to 512×512 pixels) are of the order of about +1.4%, with a rms value of about 0.03%, for images in the continuous red, whereas for images in the continuous blue and at the CaII K radiation, these values were respectively of 1.1% and 0.9%, with rms values of 0.02%.
The same analysis was made upon images acquired with the telescope operating in Mauna Loa with the same diffuser in the continuous red (Rast et al. 2001), and gave comparable values (1.5 ± 0.12%). The results thus obtained are summed up in Table 3.
Table 3: Results of the analysis of average intensity values (%) measured in sub-arrays of acquired images with a diffuser. “na” stands for results which are not available.
|CaII K||0.9 ± 0.02||na|
|B||1.1 ± 0.02||na|
|R||1.4 ± 0.03||1.5 ± 0.12|
Finally, let us sum up the results obtained by an analysis made before acquiring images with the diffuser. In that case, we had estimated the overall level of noise in the calibrated images of the Sun, by measuring the standard deviation of the average intensity of the sky in small areas (10×10 pixels) beyond the solar edge.
The relative fluctuations resulted lower than 0.0015±0.002% of the average intensity at the center of the disk for images in the continuous and 0.04±0.01% for the CaII K images. The standardized deviation in a small quiet region at the center of the disk (10×10 pixels) also resulted generally <0.1%.
These results allow us to say that photometric accuracy for pixels in the analyzed images is of the order of 0.1%.