This test investigates the dependency of the reconstruction error on the spectra of the target and calibrator. For this test, the PSFs are generated using several (10) monochromatic PSFs. For the target and calbrator a linear spectrum was assumed. The simple case of a constant target and calibrator spectrum was used as a comparison to the monochromatic case (see section Dependency on the strehl deviation). In addition, a very red target (0.5 mag brighter in the red) and a few slightly red calibrators (0.1 mag and 0.2 mag brighter in the red) were used.

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 10 monochromatic PSFs.

The multi-monochromatic PSFs are created by generating a monochromatic OPD screen for the shortest wavelength λ₀. The OPD values are rescaled for a given wavelength λ (we used 10 discrete wavelength to sample a spectral band) by λ₀/λ. The result was put into an array which was enlarged by λ/λ₀. 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.

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 (ex6_j_input.tar.gz (3.9MB) and ex6_k_input.tar.gz (4.3MB)). The corresponding results are also available as tar files (ex6_j_results.tar.gz (552KB) and ex6_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 the raw calibrator for different spectra are shown.

Figure 1: Central 128x128 pixels of the generated J-Band (top row) and K-Band (bottom row) images of a calibrator with constant spectrum (left column), 0.1 mag brighter in the red (middle column), and 0.2 mag brighter in the red (right column).

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: The simulated J-Band (top row) ad K-Band (bottom row) raw images for a position angle of 108 degree of NGC4151 at 10.1mag including sky background. In the left column, a constant spectrum was used, in the right panel, the target was 0.5 mag brighter in the red.

A comparison of the reconstructions depending on the spectra is presented in figure 3 (J-Band) in figure 4 (K-Band).

Figure 3: NGC4151: In the first row, the coadded raw J-Band images are shown. For the reconstructions in the second row, the Richardson-Lucy algorithm was used and for the third row the Building-Block method was used. the target in the first two columns shows a constant spectrum, whereas for the last two columns, the target is 0.5 mag brighter in the red. In the first and third column, the calibrator shows a constant spectrum and in the second and fourth column, the calibrator is 0.2 mag brighter in the red.

Figure 4: NGC4151: In the first row, the coadded raw K-Band images are shown. For the reconstructions in the second row, the Richardson-Lucy algorithm was used and for the third row the Building-Block method was used. the target in the first two columns shows a constant spectrum, whereas for the last two columns, the target is 0.5 mag brighter in the red. In the first and third column, the calibrator shows a constant spectrum and in the second and fourth column, the calibrator is 0.2 mag brighter in the red.

In figure 5 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 target and calibrator spectrum on the reconstruction error and the optimal iteration number is clearly visible.

Figure 5: Reconstruction error depending on the iteration number for the J-Band (left side) and K-Band (right side). For the first row, the Richardson-Lucy algorithm was used for the reconstruction. In the second row, the Building-Block method was used.

In figure 6 (J-Band) and figure 7 (K-Band) a horizontal cut slightly above the intensity maximum of the reconstructions of NHC4151 compared with the ideal reference image is shown.

Figure 6: 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. For the first row, the Richardson-Lucy algorithm was used for the reconstruction. In the second row, the Building-Block method was used.

Figure 7: 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. For the first row, the Richardson-Lucy algorithm was used for the reconstruction. In the second 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 target and calibrator spectrum are presented.

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

Figure 8: The simulated J-Band (top row) ad K-Band (bottom row) raw images for a position angle of 108 degree of a starcluster at 10.1mag including sky background. In the left column, a constant spectrum was used, in the right panel, the target was 0.5 mag brighter in the red.

A comparison of the reconstructions depending on the spectra is presented in figure 9 (J-Band) in figure 10 (K-Band).

Figure 9: Star cluster: In the first row, the coadded raw J-Band images are shown. For the reconstructions in the second row, the Richardson-Lucy algorithm was used and for the third row the Building-Block method was used. the target in the first two columns shows a constant spectrum, whereas for the last two columns, the target is 0.5 mag brighter in the red. In the first and third column, the calibrator shows a constant spectrum and in the second and fourth column, the calibrator is 0.2 mag brighter in the red.

Figure 10: Star cluster: In the first row, the coadded raw K-Band images are shown. For the reconstructions in the second row, the Richardson-Lucy algorithm was used and for the third row the Building-Block method was used. the target in the first two columns shows a constant spectrum, whereas for the last two columns, the target is 0.5 mag brighter in the red. In the first and third column, the calibrator shows a constant spectrum and in the second and fourth column, the calibrator is 0.2 mag brighter in the red.

In figure 11 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 target and calibrator spectrum on the reconstruction error and the optimal iteration number is clearly visible.

Figure 11: Reconstruction error depending on the iteration number for the J-Band (left side) and K-Band (right side). For the first row, the Richardson-Lucy algorithm was used for the reconstruction. In the second row, the Building-Block method was used.

In the figures figure 12, figure 13, figure 14, and figure 15 the image and photometric errors depending on the spectra and the iteration number is shown.

Figure 12: Image and photometric errors depending on the iteration number in the J-Band (left side) and K-Band (right side). Target and calibrator have a constant spectrum. For the first row, the Richardson-Lucy algorithm was used for the reconstruction. In the second row, the Building-Block method was used.

Figure 13: Image and photometric errors depending on the iteration number in the J-Band (left side) and K-Band (right side). The Target has a constant spectrum and the calibrator is 0.2 mag brighter in the red. For the first row, the Richardson-Lucy algorithm was used for the reconstruction. In the second row, the Building-Block method was used.

Figure 14: Image and photometric errors depending on the iteration number in the J-Band (left side) and K-Band (right side). The target is 0.5 mag brighter in the red and the calibrator has a constant spectrum. For the first row, the Richardson-Lucy algorithm 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 Target is 0.5 mag brighter in the red and the calibrator is 0.2 mag brighter in the red. For the first row, the Richardson-Lucy algorithm was used for the reconstruction. In the second 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 target and calibrator spectrum are presented.