This test investigates the dependency of the reconstruction error on the altitude differences between the target and calibrator. This might be the case when no calibrator is in the field of view for the target, This normally results in separate images of a usefull calibrator. These images may be influenced by deviations on the atmospheric dispersion (refraction) due to slightly different altitudes. In addition, a very red target (0.5 mag brighter in the red) and a slightly red calibrator (0.2 mag brighter in the red) were used. For this test, the PSFs are generated using several (41) monochromatic PSFs. 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 41 (with atmospheric dispersion) monochromatic PSFs. The altitude of the calibrator may deviate 5.0, 2.0, 1.0, 0.5, 0.2, 0.1, 0.0 degree from the altitude of the target (in both directions). A positive difference mans that the calibrator has a larger altitude than the target.

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 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.

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 41 monochromatic PSFs.

All simulated input data for the LN DRS pipeline are available as a tar-file (ex9_j_input.tar.gz (?MB) and ex9_k_input.tar.gz (?MB)). The corresponding results are also available as tar files (ex9_j_results.tar.gz (?KB) and ex9_k_results.tar.gz (?KB)).

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 an 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 the most extreme declination of -30 degree is shown. The effects are smaller for higher declinations.

Figure 1: Central 128x128 pixels of the generated J-Band calibrator images at a declination of -30 degree. Each column contains the calibrator images for a specific position angle (from left to right: 144, 180, and 216 degree). Each row contains the calibrator images with a specific altitude difference (from top to bottom: -5.0, -1.0, 0.0, +1.0, +5.0 degree).

Figure 2: Central 128x128 pixels of the generated K-Band calibrator images at a declination of -30 degree. Each column contains the calibrator images for a specific position angle (from left to right: 144, 180, and 216 degree). Each row contains the calibrator images with a specific altitude difference (from top to bottom: -5.0, -1.0, 0.0, +1.0, +5.0 degree).

The basis of this simulation is an image of NGC4151 with an overlayed dust torus (see figure 1). The simulated raw images are shown in figure 3 (J-Band and K-Band).

Figure 3: Central 128x128 pixels of the generated J-Band (top row) and K-Band (bottom row) AGN images at a declination of -30 degree (first column), -20 degree (second column), 0 degree (third column), and +20 degree (fourth column).

A comparison of the reconstructions depending on the altitude difference is presented in figure 4 and figure 5 for the J-Band and K-Band.

Figure 4: Central 128x128 pixels of the 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 target to calibrator differences are -5.0 degree for the first row, -1.0 degree for the second row, no difference for the third row, +1.0 degree for the fourth row, and +5.0 degree for the fifth row.

Figure 5: Central 128x128 pixels of the 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 target to calibrator differences are -5.0 degree for the first row, -1.0 degree for the second row, no difference for the third row, +1.0 degree for the fourth row, and +5.0 degree for the fifth row.

In figure 6 the image error dependend from the altitude difference between target and calibrator is shown. This diagram shows clearly the dependency on the target declination and altitude difference. It seems, that the difference can be larger at higher declination (and therefore altitudes) which is exactly what was expected.

Figure 6: Reconstruction error depending on the target declination and altitude difference for the J-Band (left side) and K-Band (right side).

In figure 7 (J-Band) and figure 8 (K-Band) a horizontal cut slightly above the intensity maximum of the reconstructions of NGC4151 compared with the ideal reference image is shown.

Figure 7: Horizontal profile through the center of the reconstructed galaxy compared to the ideal image (J-Band). On the left side only the central part is shown.

Figure 8: Horizontal profile through the center of the reconstructed galaxy compared to the ideal image (K-Band). On the left side only the central part is shown.

In table 3 (J-Band) and table 4 (K-Band) the errors for the AGN depending on the altitude difference between target and calibrator are presented.

The basis of this simulation is a small star cluster (see figure 2). The simulated raw images are shown in figure 9 (J-Band and K-Band).

Figure 9: Central 128x128 pixels of the generated J-Band (top row) and K-Band (bottom row) star cluster images at a declination of -30 degree (first column), -20 degree (second column), 0 degree (third column), and +20 degree (fourth column).

A comparison of the reconstructions depending on the altitude difference is presented in figure 10 and figure 11 for the J-Band and K-Band.

Figure 10: Central 128x128 pixels of the 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 target to calibrator differences are -5.0 degree for the first row, -1.0 degree for the second row, no difference for the third row, +1.0 degree for the fourth row, and +5.0 degree for the fifth row.

Figure 11: Central 128x128 pixels of the 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 target to calibrator differences are -5.0 degree for the first row, -1.0 degree for the second row, no difference for the third row, +1.0 degree for the fourth row, and +5.0 degree for the fifth row.

In table 5 (J-Band) and table 6 (K-Band) the errors for the star cluster depending on the altitude difference between target and calibrator are presented.

In figure 12 the image error dependend from the altitude difference between target and calibrator is shown. This diagram shows clearly the dependency on the target declination and altitude difference. It seems, that the difference can be larger at higher declination (and therefore altitudes) which is exactly what was expected.

Figure 12: Reconstruction error depending on the target declination and altitude difference for the J-Band (left side) and K-Band (right side).