Introduction

This test evaluates the prospects of creating an artificial psf for the reconstruction. This methods can be used to reconstruct a target without using a compatible calibrator. In addition, an artificial psf can be used as a starting point for a blind deconvolution method.

The setup of the simulation is described in table 1. The input data for the test uses a raw target image with strehl values between 10 and 100 percent. In this experiment a bright psf star is chosen (14 mag), so that the reconstructions made with a conventional Richardson-Lucy method can be used as a reference.

Table 1: Setup for the simulation in J-Band and K-Band, for the common test setup see table 1.
Parameter	Description
Atmosphere/AO	The AO delivers a strehl between 10 and 100 percent for the target and calibrator.
Observation	The brightness of the psf-star is set to 14mag.

The raw data were generated according to the common scheme described in section Overview. In addition 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.). The created psfs were used to create artficial psf which are a combination of a perfect psf and a gaussian AO halo. The AO halo ist defined by a size and an exponent (smaller then 2.0). These parameters are fitted with gnuplot to the simulated psfs.

All simulated input data for the LN DRS pipeline are available as a tar-file (ex10_j_input.tar.gz (???MB) and ex10_k_input.tar.gz (???MB)). The corresponding results are also available as tar files (ex10_j_results.tar.gz (???MB) and ex10_k_results.tar.gz (???MB)).

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.

Calibrator

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 (J-Band) and figure 2 (K-Band) the calibrator for some strehl values are shown.

Figure 1: Central 128x128 pixels of the generated J-Band images of a calibrator at 14 mag and with different strehl (from top left to bottom right: 0.10, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, and 0.90).

Figure 2: Central 128x128 pixels of the generated K-Band images of a calibrator at 14 mag and with different strehl (from top left to bottom right: 0.10, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, and 0.90).

From the simulated psfs the parameters for the artificial psf were calculated using gnuplot. In figure 3 (J-Band) a comparison of the simulated and fitted AO halo is presented.

Figure 3: This plot shows a comparison of the simulated and fitted AO halo in the J-Band (left side) and K-Band (right side).

Raw Frames and Results for an AGN

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 4 (J-Band) and figure 5 (K-Band).

Figure 4: The simulated J-Band raw images for different Strehl (0.10 at top left, to 1.0 at bottom right) and the position angle o180 degree of a AGN including sky background.

Figure 5: The simulated K-Band raw images for different Strehl (0.10 at top left, to 1.0 at bottom right) and the position angle o180 degree of a AGN including sky background.

A comparison of the reconstructions depending on the algorithm and psf creation method is presented in figure 6 and figure 7 (J-Band) and figure 8 and figure 9(K-Band).

Figure 6: AGN: J-Band reconstruction of an AGN. In the left column, the coadded raw image is presented. In the middle column, a reconstruction with Richardson-Lucy and the extracted calibrator PSF is shown. In the right column, the reconstruction with Richardson-Lucy and an artificial PSF is shown. The Strehl for the target and calibrator was 0.1, 0.2, 0.3, 0.4 and 0.5 (from top left to bottom right).

Figure 7: AGN: J-Band reconstruction of an AGN. In the left column, the coadded raw image is presented. In the middle column, a reconstruction with Richardson-Lucy and the extracted calibrator PSF is shown. In the right column, the reconstruction with Richardson-Lucy and an artificial PSF is shown. The Strehl for the target and calibrator was 0.6, 0.7, 0.8, 0.9 and 1.0 (from top left to bottom right).

Figure 8: AGN: K-Band reconstruction of an AGN. In the left column, the coadded raw image is presented. In the middle column, a reconstruction with Richardson-Lucy and the extracted calibrator PSF is shown. In the right column, the reconstruction with Richardson-Lucy and an artificial PSF is shown. The Strehl for the target and calibrator was 0.1, 0.2, 0.3, 0.4 and 0.5 (from top left to bottom right).

Figure 9: AGN: K-Band reconstruction of an AGN. In the left column, the coadded raw image is presented. In the middle column, a reconstruction with Richardson-Lucy and the extracted calibrator PSF is shown. In the right column, the reconstruction with Richardson-Lucy and an artificial PSF is shown. The Strehl for the target and calibrator was 0.6, 0.7, 0.8, 0.9 and 1.0 (from top left to bottom right).

In table 2 (J-Band) and table 3 (K-Band) the errors for the AGN depending on the PSF creation method are presented. In figure 10 the image errors depending on the strehl ratio are shown.

Table 2: AGN: Errors depending on the PSF creation method (J-Band).
Testcase	Richardson-Lucy	RL, artificial PSF	Building-Block
Strehl	Image Error	Image Error	Image Error
0.10	0.034 (0.034)	0.043 (0.043)	0.010 (0.010)
0.20	0.018 (0.018)	0.031 (0.031)	0.005 (0.005)
0.30	0.011 (0.011)	0.025 (0.025)	0.005 (0.005)
0.40	0.008 (0.008)	0.020 (0.019)	0.004 (0.004)
0.50	0.006 (0.006)	0.017 (0.015)	0.004 (0.004)
0.60	0.004 (0.004)	0.016 (0.013)	0.004 (0.004)
0.70	0.004 (0.004)	0.014 (0.010)	0.004 (0.004)
0.80	0.003 (0.003)	0.013 (0.008)	0.004 (0.004)
0.90	0.003 (0.003)	0.012 (0.008)	0.004 (0.004)
1.00	0.002 (0.002)	0.011 (0.007)	0.003 (0.003)

Table 3: AGN: Errors depending on the PSF creation method (K-Band).
Testcase	Richardson-Lucy	RL, artificial PSF	Building-Block
Strehl	Image Error	Image Error	Image Error
0.10	0.055 (0.055)	0.043 (0.043)	0.009 (0.009)
0.20	0.028 (0.028)	0.032 (0.032)	0.007 (0.006)
0.30	0.019 (0.019)	0.033 (0.032)	0.004 (0.004)
0.40	0.012 (0.012)	0.022 (0.022)	0.003 (0.003)
0.50	0.009 (0.009)	0.022 (0.021)	0.003 (0.003)
0.60	0.006 (0.006)	0.014 (0.014)	0.003 (0.003)
0.70	0.005 (0.005)	0.012 (0.012)	0.002 (0.002)
0.80	0.003 (0.003)	0.009 (0.009)	0.003 (0.002)
0.90	0.003 (0.003)	0.008 (0.008)	0.002 (0.002)
1.00	0.002 (0.002)	0.007 (0.007)	0.003 (0.002)

Figure 10: Reconstruction error depending on the strehl ratio (left side: J-Band, right side: K-Band).

In figure 11 (J-Band) and figure 12 (K-Band) a horizontal cut slightly above the intensity maximum of the reconstructions of NHC4151 compared with the ideal reference image is shown.

Figure 11: J-Band: Horizontal profile through the center of the reconstructed galaxy compared to the ideal image (left side: use the extracted PSF, right side: use an artificial PSF). In the bottom row only the central part is shown.

Figure 12: K-Band: Horizontal profile through the center of the reconstructed galaxy compared to the ideal image (left side: use the extracted PSF, right side: use an artificial PSF). In the bottom row only the central part is shown.

Raw Frames and Results for a Star Cluster

The basis of this simulation is a small star cluster (see figure 2). The simulated raw images are shown in figure 13 (J-Band) and figure 14 (K-Band).

Figure 13: The simulated J-Band raw images for different Strehl (0.10 at top left, to 1.0 at bottom right) and the position angle o180 degree of a star cluster including sky background.

Figure 14: The simulated K-Band raw images for different Strehl (0.10 at top left, to 1.0 at bottom right) and the position angle o180 degree of a star cluster including sky background.

A comparison of the reconstructions depending on the algorithm and psf creation method is presented in figure 15 and figure 16 (J-Band) and figure 17 and figure 18(K-Band).

Figure 15: Star cluster: J-Band reconstruction of a star cluster. In the left column, the coadded raw image is presented. In the middle column, a reconstruction with Richardson-Lucy and the extracted calibrator PSF is shown. In the right column, the reconstruction with Richardson-Lucy and an artificial PSF is shown. The Strehl for the target and calibrator was 0.1, 0.2, 0.3, 0.4 and 0.5 (from top left to bottom right).

Figure 16: Star cluster: J-Band reconstruction of a star cluster. In the left column, the coadded raw image is presented. In the middle column, a reconstruction with Richardson-Lucy and the extracted calibrator PSF is shown. In the right column, the reconstruction with Richardson-Lucy and an artificial PSF is shown. The Strehl for the target and calibrator was 0.6, 0.7, 0.8, 0.9 and 1.0 (from top left to bottom right).

Figure 17: Star cluster: K-Band reconstruction of a star cluster. In the left column, the coadded raw image is presented. In the middle column, a reconstruction with Richardson-Lucy and the extracted calibrator PSF is shown. In the right column, the reconstruction with Richardson-Lucy and an artificial PSF is shown. The Strehl for the target and calibrator was 0.1, 0.2, 0.3, 0.4 and 0.5 (from top left to bottom right).

Figure 18: Star cluster: K-Band reconstruction of a star cluster. In the left column, the coadded raw image is presented. In the middle column, a reconstruction with Richardson-Lucy and the extracted calibrator PSF is shown. In the right column, the reconstruction with Richardson-Lucy and an artificial PSF is shown. The Strehl for the target and calibrator was 0.6, 0.7, 0.8, 0.9 and 1.0 (from top left to bottom right).

In table 4 (J-Band) and table 5 (K-Band) the errors for the star cluster depending on the PSF creation method are presented. In figure 19 the image errors depending on the strehl ratio are shown.

Table 4: Star cluster: Errors depending on the PSF creation method (J-Band).
Testcase	Richardson-Lucy		RL, artificial PSF		Building-Block
Strehl	Image Error	Magnitude Error	Image Error	Magnitude Error	Image Error	Magnitude Error
0.10	0.029 (0.029)	0.02, -0.01, 0.09, 0.26, 0.59	0.047 (0.047)	0.04, 0.03, 0.18, 0.17, 0.53	0.023 (0.023)	0.02, -0.01, 0.17, 0.43, 2.15
0.20	0.017 (0.017)	0.02, 0.00, 0.06, -0.03, 0.27	0.035 (0.035)	0.04, 0.03, 0.12, -0.06, 0.37	0.019 (0.019)	0.02, 0.00, 0.15, 0.10, 0.93
0.30	0.012 (0.012)	0.01, 0.00, -0.00, 0.11, 0.22	0.026 (0.026)	0.02, 0.02, 0.05, 0.10, 0.44	0.013 (0.013)	0.01, -0.00, 0.10, 0.24, 0.84
0.40	0.008 (0.008)	0.01, 0.00, -0.00, 0.14, 0.15	0.021 (0.021)	0.02, 0.02, 0.01, 0.13, 0.15	0.011 (0.011)	0.01, -0.00, 0.10, 0.28, 0.58
0.50	0.011 (0.011)	0.01, 0.01, 0.04, 0.00, 0.08	0.023 (0.023)	0.02, 0.02, 0.06, -0.01, 0.11	0.009 (0.009)	0.01, 0.00, 0.11, 0.09, 0.28
0.60	0.008 (0.008)	0.01, 0.01, 0.01, 0.01, 0.13	0.020 (0.020)	0.02, 0.02, 0.02, 0.00, 0.13	0.009 (0.009)	0.01, 0.00, 0.10, 0.10, 0.41
0.70	0.013 (0.013)	0.01, 0.01, 0.01, -0.00, 0.10	0.024 (0.024)	0.02, 0.02, 0.02, -0.00, 0.10	0.010 (0.010)	0.01, 0.01, 0.04, 0.05, 0.20
0.80	0.010 (0.010)	0.01, 0.01, 0.01, 0.03, 0.02	0.021 (0.021)	0.01, 0.01, 0.02, 0.03, 0.03	0.010 (0.010)	0.00, 0.00, 0.04, 0.07, 0.14
0.90	0.009 (0.009)	0.01, 0.01, 0.02, 0.02, 0.02	0.018 (0.018)	0.01, 0.01, 0.02, 0.02, 0.01	0.009 (0.009)	0.00, 0.00, 0.06, 0.07, 0.18
1.00	0.010 (0.010)	0.01, 0.01, 0.03, 0.01, 0.15	0.019 (0.019)	0.01, 0.01, 0.03, 0.01, 0.16	0.011 (0.011)	0.01, 0.01, 0.04, 0.04, 0.24

Table 5: Star cluster: Errors depending on the PSF creation method (K-Band).
Testcase	Richardson-Lucy		RL, artificial PSF		Building-Block
Strehl	Image Error	Magnitude Error	Image Error	Magnitude Error	Image Error	Magnitude Error
0.10	0.151 (0.151)	0.19, 0.04, 0.30, 2.71, 1.99	0.157 (0.157)	0.20, 0.07, 0.40, 2.31, 1.99	0.088 (0.088)	0.17, 0.04, -0.02, 3.41, 1.85
0.20	0.071 (0.071)	0.06, -0.01, 0.67, 0.49, 0.66	0.080 (0.080)	0.08, 0.02, 0.84, 0.44, 1.04	0.048 (0.048)	0.06, -0.00, 0.58, 0.57, 0.62
0.30	0.048 (0.048)	-0.01, 0.02, 0.79, 0.13, 2.09	0.052 (0.052)	-0.00, 0.03, 1.43, -0.07, 2.10	0.038 (0.038)	-0.00, 0.02, 0.84, 0.22, 1.93
0.40	0.041 (0.041)	0.03, 0.04, 0.04, 0.22, 0.27	0.048 (0.048)	0.04, 0.05, 0.11, 0.15, 0.43	0.033 (0.033)	0.03, 0.04, 0.09, 0.26, 0.39
0.50	0.028 (0.028)	0.03, 0.02, 0.30, 0.54, 0.52	0.031 (0.031)	0.04, 0.03, 0.43, 0.47, 0.79	0.023 (0.023)	0.03, 0.02, 0.35, 0.60, 0.68
0.60	0.021 (0.021)	0.02, 0.00, 0.08, 0.27, 0.41	0.025 (0.025)	0.02, 0.01, 0.14, 0.24, 0.53	0.017 (0.017)	0.02, 0.01, 0.11, 0.32, 0.54
0.70	0.019 (0.019)	0.02, -0.01, 0.31, 0.28, 0.82	0.022 (0.022)	0.03, 0.00, 0.36, 0.26, 0.93	0.017 (0.017)	0.03, -0.00, 0.34, 0.30, 0.98
0.80	0.025 (0.025)	0.02, 0.02, 0.12, 0.24, 0.68	0.028 (0.028)	0.02, 0.03, 0.13, 0.23, 0.78	0.025 (0.025)	0.02, 0.03, 0.14, 0.25, 0.76
0.90	0.019 (0.019)	0.02, 0.01, 0.07, 0.03, 0.24	0.024 (0.024)	0.02, 0.02, 0.09, 0.02, 0.27	0.020 (0.020)	0.02, 0.02, 0.09, 0.04, 0.28
1.00	0.018 (0.018)	0.01, -0.01, 0.12, 0.19, 0.92	0.015 (0.015)	0.01, -0.00, 0.09, 0.14, 0.72	0.018 (0.018)	0.02, -0.00, 0.19, 0.28, 1.41

Figure 19: Reconstruction error depending on the strehl ratio (left side: J-Band, right side: K-Band).