This test investigates the dependency of the reconstruction error on overlap errors (flexure). For this test, the beam position error is composed of a fixed offset and a gaussian distributed jitter.

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 calibrator has a magnitude of 14. In addition, the target and psf star PSF are influenced by a beam position error (overlap error).

Each beam position error is described by two values: a fixed offset and a small jitter given in airy disc radii (1.22 λ/D). For the offset error values from 0.0 (no offset) up to 1.0 in steps of 0.2 and for the jitter 0.0 (no jitter), 0.1, and 0.2 are used.

In order to generate a PSF (target and calibrator), for each position angle, a random angle (uniform distribution) is calculated. The first beam is shifted along this angle from the nominal position by the specified offset. The second beam is shifted into the opposite direction. Therefore the total overlap error is doubled. For each phase screen, a small additional jitter is calculated by generating a random angle (uniform distribution) and a random deviation (gaussian distribution with the standard deviation given as jitter). This means, that for a PSF the average beam position is fixed, but for each phase screen a small random deviation is calculated.

The raw data were generated according to the common scheme described in section Overview. In addition the phase screens for the psfs are influenced by a beam position error on both pupils, and the images for the target and psf-star are generated separately which means, that the psf-star image is not influenced by the target (no halo, etc.) and shows a different position error.

All simulated input data for the LN DRS pipeline are available as a tar-file (ex5_j_input.tar.gz (91MB) and ex5_k_input.tar.gz (101MB)). The corresponding results are also available as tar files (ex5_j_results.tar.gz (9.8MB) and ex5_k_results.tar.gz (11MB)).

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 the calibrators for different overlap errors (position angle 108 degree) are shown.

Figure 1: Central 128x128 pixels of the generated J-Band (top row) and K-Band (bottom row) images of a calibrator with overlap errors of 0.0 (no jitter), 0.2 (jitter 0.1), 0.6 (jitter 0.1), and 1.0 (jitter 0.1).

The basis of the simulation is an image of NGC4151 with an overlayed dust torus (see figure 1. The simulated raw images for a position angle of 108 degree are shown in figure 2.

Figure 2: Central 128x128 pixels of the generated J-Band (top row) and K-Band (bottom row) images of NGC4151 with overlap errors of 0.0 (no jitter), 0.2 (jitter 0.1), 0.6 (jitter 0.1), and 1.0 (jitter 0.1).

A comparison of the reconstructions depending on the phase error is presented in figure 3 for the J-Band. For the K-Band the results are presented in figure 4.

Figure 3: The top row shows the central part of the coadded J-Band images of NGC4151 with overlap errors of 0.0 (no jitter), 0.2 (jitter 0.1), 0.6 (jitter 0.1), and 1.0 (jitter 0.1). In the second row, the reconstructions using the Richardson-Lucy algorithm are shown and in the third row, the Building-Block method was used.

Figure 4: The top row shows the central part of the coadded K-Band images of NGC4151 with overlap errors of 0.0 (no jitter), 0.2 (jitter 0.1), 0.6 (jitter 0.1), and 1.0 (jitter 0.1). In the second row, the reconstructions using the Richardson-Lucy algorithm are shown and in the third row, the Building-Block method was used.

In table 2 (J-Band) and table 3 (K-Band) the errors for the star cluster depending on the beam overlap error are presented. In figure 5 the image errors depending on the beam overlap error are shown.

Figure 5: In this figure, the image errors depending on the beam overlap 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 6 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 beam overlap error on the reconstruction error and the optimal iteration number is clearly visible.

Figure 6: Reconstruction error depending on the iteration number for the J-Band (left side) and K-Band (right side). In the first row, Richardson-Lucy was used for the reconstruction. In the second row, the Building-Block method was used.

In figure 7 (J-Band) and figure 8 (K-Band) a horizontal cut slightly above the intensity maximum of the reconstructions of NHC4151 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 right side only the central part is shown. In the first row, Richardson-Lucy was used for the reconstruction. In the second row, the Building-Block method was used.

Figure 8: 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. In the first row, Richardson-Lucy was used for the reconstruction. In the second row, the Building-Block method was used.

The basis of the simulation is an image of a star cluster (see figure 2. The simulated raw images for a position angle of 108 degree are shown in figure 9.

Figure 9: Central 128x128 pixels of the generated J-Band (top row) and K-Band (bottom row) images of the star cluster with overlap errors of 0.0 (no jitter), 0.2 (jitter 0.1), 0.6 (jitter 0.1), and 1.0 (jitter 0.1).

A comparison of the reconstructions depending on the phase error is presented in figure 10 for the J-Band. For the K-Band the results are presented in figure 11.

Figure 10: The top row shows the central part of the coadded J-Band images of the star cluster with overlap errors of 0.0 (no jitter), 0.2 (jitter 0.1), 0.6 (jitter 0.1), and 1.0 (jitter 0.1). In the second row, the reconstructions using the Richardson-Lucy algorithm are shown and in the third row, the Building-Block method was used.

Figure 11: The top row shows the central part of the coadded K-Band images of the star cluster with overlap errors of 0.0 (no jitter), 0.2 (jitter 0.1), 0.6 (jitter 0.1), and 1.0 (jitter 0.1). In the second row, the reconstructions using the Richardson-Lucy algorithm are shown and in the third row, the Building-Block method was used.

In table 4 (J-Band) and table 5 (K-Band) the errors for the star cluster depending on the beam position error are presented. In figure 12 the image errors depending on the beam overlap error are shown.

Figure 12: In this figure, the image errors depending on the beam overlap 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 13 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 beam position error on the reconstruction error and the optimal iteration number is clearly visible.

Figure 13: Reconstruction error depending on the iteration number for the J-Band (left side) and K-Band (right side). In the first row, Richardson-Lucy was used for the reconstruction. In the second row, the Building-Block method was used.

In the figures figure 14, figure 15, figure 16, and figure 17 the image and photometric errors depending on the overlap error and the iteration number is shown. The overall shape is the same, but the optimum number of iterations is difficult to select, because not all photometric errors have their minimum at the same iteration number.

Figure 14: Image and photometric errors depending on the iteration number in the J-Band (left side) and K-Band (right side). The overlap error is 0.0, 0.0. In the first row, Richardson-Lucy was used for the reconstruction. In the second row, the Building-Block method was used.

Figure 15: Image and photometric errors depending on the iteration number in the J-Band (left side) and K-Band (right side). The overlap error is 0.2, 0.1. In the first row, Richardson-Lucy was used for the reconstruction. In the second row, the Building-Block method was used.

Figure 16: Image and photometric errors depending on the iteration number in the J-Band (left side) and K-Band (right side). The overlap error is 0.6, 0.1. In the first row, Richardson-Lucy was used for the reconstruction. In the second 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 overlap error is 1.0, 0.1. In the first row, Richardson-Lucy was used for the reconstruction. In the second row, the Building-Block method was used.