This test investigates the dependency of the reconstruction error on the atmospheric dispersion (refraction). For this test, the PSFs are generated using several (11 or 41) monochromatic PSFs. For the target and calbrator a constant spectrum was assumed. This simulation only tests the difficult cases where the target has a declination between -30 and +20 degree. For each target, three parallactic angles were used which corresponds to the largest angle which can be achieved going down to 75 degree zenith angle.

The setup of the simulation is described in table 1. The input data for the test uses a strehl value of 0.30 for target and calibrator. The psf star has a magnitude of 14. In addition, the target and psf star PSF are generated by using 11 (no atmospheric dispersion) or 41 (with atmospheric dispersion) monochromatic PSFs.

The multi-monochromatic PSFs are created by generating a monochromatic OPD screen for the shortest wavelength λ₀. The OPD values are then rescaled for a given wavelength λ (we used 11 or 41 discrete wavelength to sample a spectral band) by λ₀/λ. The result was put into an array which was enlarged by λ/λ₀. Then the atmospheric dispersion was simulated by moving the center of the psf according to the assumed zenith angle and a model atmosphere. A PSF for a specific wavelength was then calculated by |FFT^-1|², weighted by the spectral intensity and all summed up to the final multi-monochromatic PSF.

In table 2 all combinations of declination, culmination, smallest altitude, and parallactic angles are shown. In addition, each test case was also created without atmospheric dispersion.

The raw data were generated according to the common scheme described in section Overview. In addition, the target and psf star PSF are generated by using 10 monochromatic PSFs.

All simulated input data for the LN DRS pipeline are available as a tar-file (ex7_j_input.tar.gz (3.9MB) and ex7_k_input.tar.gz (4.3MB)). The corresponding results are also available as tar files (ex7_j_results.tar.gz (552KB) and ex7_k_results.tar.gz (546KB)).

The generated calibrator raw images are shown in section Calibrator. The raw images and deconvolution results are shown in section Raw Frames and Results for an AGN for the AGN and section Raw Frames and Results for a Star Cluster for the star cluster.

The simulated raw LBT interferograms used for the deconvolution are ideal images, they are not influenced by detector effects like different pixel gain or bad pixels. In figure 1 and figure 2 the raw calibrator for different declination with dispersion is shown.

Figure 1: Central 128x128 pixels of the generated J-Band calibrator images at a declination of -30 degree (first column), -20 degree (second column), 0 degree (third column), and +20 degree (fourth column). The first row contains the calibrator images where the position angle is smaller than 180 degree and the altitude is 15.6 degree, 16.5 degree, 15.1 degree, and 55.7 degree. The second row contain the calibrator images at culmination (altitudes 27.3 degree, 37.3 degree, 57.3 degree, and 77.3 degree).

Figure 2: Central 128x128 pixels of the generated K-Band calibrator images at a declination of -30 degree (first column), -20 degree (second column), 0 degree (third column), and +20 degree (fourth column). The first row contains the calibrator images where the position angle is smaller than 180 degree and the altitude is 15.6 degree, 16.5 degree, 15.1 degree, and 55.7 degree. The second row contain the calibrator images at culmination (altitudes 27.3 degree, 37.3 degree, 57.3 degree, and 77.3 degree).

The basis of the simulation is an image of NGC4151 with an overlayed dust torus (see figure 1. The simulated raw images for the smallest altitude with atmospheric dispersion and without atmospheric dispersion are shown in figure 3 for the J-Band and in figure 4 for the K-Band.

Figure 3: Central 128x128 pixels of the generated J-Band NGC4151 images at a declination of -30 degree (first column), -20 degree (second column), 0 degree (third column), and +20 degree (fourth column). The first row contains the calibrator images where the position angle is smaller than 180 degree and the altitude is 15.6 degree, 16.5 degree, 15.1 degree, and 55.7 degree. The second row contain the AGN images at culmination (altitudes 27.3 degree, 37.3 degree, 57.3 degree, and 77.3 degree).

Figure 4: Central 128x128 pixels of the generated K-Band NGC4151 images at a declination of -30 degree (first column), -20 degree (second column), 0 degree (third column), and +20 degree (fourth column). The first row contains the calibrator images where the position angle is smaller than 180 degree and the altitude is 15.6 degree, 16.5 degree, 15.1 degree, and 55.7 degree. The second row contain the AGN images at culmination (altitudes 27.3 degree, 37.3 degree, 57.3 degree, and 77.3 degree).

A comparison of the reconstructions depending on the atmospheric dispersion is presented in figure 5 for the J-Band. For the K-Band the results are presented in figure 6.

Figure 5: Central 128x128 pixels of the coadded and reconstructed J-Band NGC4151 images at a declination of -30 degree (first column), -20 degree (second column), 0 degree (third column), and +20 degree (fourth column). The first row contains the coadded raw target images. The second row contain the reconstructions created with the Richardson-Lucy algorithm. For the third row, the Building-Block method was used.

Figure 6: Central 128x128 pixels of the coadded and reconstructed K-Band NGC4151 images at a declination of -30 degree (first column), -20 degree (second column), 0 degree (third column), and +20 degree (fourth column). The first row contains the coadded raw target images. The second row contain the reconstructions created with the Richardson-Lucy algorithm. For the third row, the Building-Block method was used.

In table 3 (J-Band) and table 4 (K-Band) the errors for the star cluster depending on the atmospheric dispersion are presented. In figure 7 the image errors depending on the atmospheric dispersion are shown.

Figure 7: In this figure, the image errors depending on the atmospheric dispersion are shown. The left column shows the J-Band values and in the right column, the K-Band values are shown. In the first row, Richardson-Lucy was used for the reconstruction. In the second row, the Building-Block method was used.

In figure 8 the image error describing the difference between the reconstruction and the reference image is shown for each iteration (in steps of 100 iterations). The effect of the atmospheric dispersion on the reconstruction error and the optimal iteration number is clearly visible.

Figure 8: Reconstruction error depending on the iteration number for the J-Band (left side) and K-Band (right side). The first row contain the reconstructions created with the Richardson-Lucy algorithm. For the second row, the Building-Block method was used.

In figure 9 (J-Band) and figure 10 (K-Band) a horizontal cut slightly above the intensity maximum of the reconstructions of NHC4151 compared with the ideal reference image is shown.

Figure 9: Horizontal profile through the center of the reconstructed galaxy compared to the ideal image (J-Band). On the right side only the central part is shown. The first row contain the reconstructions created with the Richardson-Lucy algorithm. For the second row, the Building-Block method was used.

Figure 10: Horizontal profile through the center of the reconstructed galaxy compared to the ideal image (K-Band). On the right side only the central part is shown. The first row contain the reconstructions created with the Richardson-Lucy algorithm. For the second row, the Building-Block method was used.

The basis of the simulation is an image of a starcluster (see figure 2. The simulated raw images for the smallest altitude with atmospheric dispersion and without atmospheric dispersion are shown in figure 11 for the J-Band and in figure 12 for the K-Band.

Figure 11: Central 128x128 pixels of the generated J-Band star cluster images at a declination of -30 degree (first column), -20 degree (second column), 0 degree (third column), and +20 degree (fourth column). The first row contains the calibrator images where the position angle is smaller than 180 degree and the altitude is 15.6 degree, 16.5 degree, 15.1 degree, and 55.7 degree. The second row contain the star cluster images at culmination (altitudes 27.3 degree, 37.3 degree, 57.3 degree, and 77.3 degree).

Figure 12: Central 128x128 pixels of the generated K-Band star cluster images at a declination of -30 degree (first column), -20 degree (second column), 0 degree (third column), and +20 degree (fourth column). The first row contains the calibrator images where the position angle is smaller than 180 degree and the altitude is 15.6 degree, 16.5 degree, 15.1 degree, and 55.7 degree. The second row contain the star cluster images at culmination (altitudes 27.3 degree, 37.3 degree, 57.3 degree, and 77.3 degree).

A comparison of the reconstructions depending on the atmospheric dispersion is presented in figure 13 for the J-Band. For the K-Band the results are presented in figure 14.

Figure 13: Central 128x128 pixels of the coadded and reconstructed J-Band star cluster images at a declination of -30 degree (first column), -20 degree (second column), 0 degree (third column), and +20 degree (fourth column). The first row contains the coadded raw target images. The second row contain the reconstructions created with the Richardson-Lucy algorithm. For the third row, the Building-Block method was used.

Figure 14: Central 128x128 pixels of the coadded and reconstructed K-Band star cluster images at a declination of -30 degree (first column), -20 degree (second column), 0 degree (third column), and +20 degree (fourth column). The first row contains the coadded raw target images. The second row contain the reconstructions created with the Richardson-Lucy algorithm. For the third row, the Building-Block method was used.

In figure 15 the image error describing the difference between the reconstruction and the reference image is shown for each iteration (in steps of 100 iterations). The effect of the atmospheric dispersion on the reconstruction error and the optimal iteration number is clearly visible.

Figure 15: Reconstruction error depending on the iteration number for the J-Band (left side) and K-Band (right side). The first row contain the reconstructions created with the Richardson-Lucy algorithm. For the second row, the Building-Block method was used.

In the figures figure 16, figure 17, figure 18, and figure 19 the image and photometric errors depending on the atmospheric dispersion and the iteration number is shown.

Figure 16: Image and photometric errors depending on the iteration number in the J-Band (left side) and K-Band (right side). The declination is -30 degree, the top row shows the results using the Richardson-Lucy algorithm, in the bottom row the Building-Block method was used.

Figure 17: Image and photometric errors depending on the iteration number in the J-Band (left side) and K-Band (right side). The declination is -20 degree, the top row shows the results using the Richardson-Lucy algorithm, in the bottom row the Building-Block method was used.

Figure 18: Image and photometric errors depending on the iteration number in the J-Band (left side) and K-Band (right side). The declination is 0 degree, the top row shows the results using the Richardson-Lucy algorithm, in the bottom row the Building-Block method was used.

Figure 19: Image and photometric errors depending on the iteration number in the J-Band (left side) and K-Band (right side). The declination is +20 degree, the top row shows the results using the Richardson-Lucy algorithm, in the bottom row the Building-Block method was used.

In table 5 (J-Band) and table 6 (K-Band) the errors for the star cluster depending on the atmospheric dispersion are presented.