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3. Results of the LBT interferometry simulations

3.1. Laboratory simulation of LBT interferometry

 

In our laboratory experiment the LBT interferograms were generated in the laboratory setup shown in Fig. 4 (click here). Atmospheric turbulence was generated by a heater. Small variations of the air temperature cause variations of the refractive index and therefore random wavefront degradations and speckle interferograms in the image plane. A mask simulating the LBT pupil function was inserted in front of a telescope lens. The speckle interferograms of various objects were recorded with a CCD camera in the focal plane.

Figure 5 (click here) shows the results of the LBT laboratory experiment. The details of the speckle masking interferometry image processing theory are described in Sect. 2 (click here). Fig. 5 (click here)a is the LBT pupil function. The geographic latitude tex2html_wrap_inline1548 of the LBT site, an object declination of tex2html_wrap_inline1550 and data recording at four different rotation angles of the earth during 12 hours were simulated (aperture synthesis by earth rotation). The uv-coverage of the experiment is shown in Fig. 5 (click here)b. Figs. 5 (click here)c and  5 (click here)d show the laboratory object. The brightness of the stars is 1.0, 0.59, 0.39, and 0.13. Fig. 5 (click here)e is one of only 200 recorded point source interferograms with simulated seeing corresponding to a Fried parameter tex2html_wrap_inline1554 = 2 m. For each of four chosen earth rotation angles, 50 point source interferograms and 100 object interferograms were recorded. Fig. 5 (click here)f is one of 400 recorded interferograms of the star cluster (degraded by speckle noise and CCD noise). Figs. 5 (click here)g and 5 (click here)h show the diffraction-limited image reconstructed from the 400 interferograms by speckle masking and the building block method.

  figure351
Figure 5: Laboratory simulation of interferometric speckle masking imaging with the LBT: a) LBT pupil function, b) uv-coverage of the laboratory simulation (geographic latitude tex2html_wrap_inline1558; object declination tex2html_wrap_inline1560; 12-hour aperture synthesis time; data recording at four different earth rotation angles), c), d) object (star cluster), e) one of the 200 point source interferograms (required for calibrating the speckle transfer function) with simulated seeing corresponding to a Fried parameter tex2html_wrap_inline1562 = 2 m, f) one of the 400 LBT interferograms of the star cluster, g) and h) diffraction-limited image reconstructed from 400 interferograms by speckle masking and the building block method (1000 iterations)

  figure374
Figure 6: Computer simulation of speckle masking interferometry with the LBT at optical wavelengths (Fried parameter tex2html_wrap_inline1564 cm, corresponding to 0.35 arcsec seeing): a) LBT pupil function, b, c) object (star cluster), d) one of the 200000 generated point source interferograms (for the calibration of the speckle transfer function) with simulated seeing corresponding to a Fried parameter tex2html_wrap_inline1566 cm, e) one of the 200000 generated object interferograms before simulation of photon noise, f) one of the 200000 generated LBT speckle interferograms of the star cluster after injection of photon noise corresponding to a mean count number of 500 photoevents per frame, g, h) diffraction-limited image reconstructed from the 200000 photon noise-degraded interferograms by speckle masking and the building block method (500 photoevents/interferogram; 5000 iterations of the building block method; star separation tex2html_wrap_inline1568 milli-arcsec for tex2html_wrap_inline1570 Å and LBT diameter 22 m), and i) diffraction-limited image reconstructed from the 200000 interferograms degraded by photon noise corresponding to a mean count number of only 200 photoevents/interferogram.
The uv-coverage of the computer experiment (geographic latitude tex2html_wrap_inline1574; object declination tex2html_wrap_inline1576; 12-hour aperture synthesis; data recording at 71 different rotation angles of the earth) is shown in Fig. 8 (click here)b

3.2. Results of LBT computer simulations

  Figures 6 (click here) and 8 (click here) show the results of our LBT computer experiments with a star cluster and an extended object. The image processing theory is described in Sect. 2 (click here). The reconstructions have exact diffraction-limited resolution, for example 6.1 milli-arcsec resolution for tex2html_wrap_inline1580 Å and 22 m interferometer diameter.

3.2.1. Star cluster simulation

  Figure 6 (click here) shows a computer simulation of interferometric LBT imaging of a star cluster. Fig. 6 (click here)a is the LBT pupil function of the experiment. In this experiment an object declination of +60tex2html_wrap_inline1582, a geographic latitude of the LBT site of +tex2html_wrap_inline1584, and data recording at 71 different rotation angles of the earth during a time period of 12 hours were simulated (aperture synthesis by earth rotation). Figs. 6 (click here)b and  6 (click here)c are the object. The brightness of the stars from left to right is 1.0, 0.53, 0.92, and 0.72. The smallest simulated separation is tex2html_wrap_inline1586 mas (for tex2html_wrap_inline1588 = 550 nm and 22 m baseline). Fig. 6 (click here)d is one of the 200000 generated point source LBT interferograms with simulated seeing corresponding to a Fried parameter tex2html_wrap_inline1590 cm, corresponding to 0.35 arcsec seeing. For each of the 71 chosen earth rotation angles, 2817 interferograms were computed.

 
 table413

Table 1: Parameters of the computer experiments shown in Figs. 6 (click here) and 8 (click here). A frame rate of 50 frames/sec was assumed for the calculation of the data recording times. The field of view of the interferograms and the reconstructions is tex2html_wrap_inline1594 pixels (pixel size tex2html_wrap_inline1596arcsec)

Fig. 6 (click here)e is one of the 200000 generated LBT interferograms of the star cluster. Fig. 6 (click here)f shows the same object interferogram after injection of photon noise corresponding to a mean count number of 500 photoevents per frame. Figs. 6 (click here)g and 6 (click here)h show the diffraction-limited image reconstructed from the 200000 noise-degraded interferograms consisting of 500 photoevents/interferogram by speckle masking and the building block method. Fig. 6 (click here)i is the diffraction-limited image reconstructed from 200000 noise-degraded interferograms consisting of 200 photoevents/interferogram. 200000 interferograms correspond to only 1.1 hours of data recording time for a frame rate of 50 frames per second. Table 1 (click here) summarizes the parameters of the star cluster experiment and the photometric error of the reconstructions.

200 photoevents per interferogram correspond to a total magnitude tex2html_wrap_inline161614.3 for two 8 m telescopes, 20 msec exposure time per interferogram, 5 nm filter bandwidth, and 10% quantum efficiency of detector plus optics (see Fig. 7 (click here)). With the above-mentioned intensity ratios of the four stars we obtain for the individual four stars the simulated magnitudes of 15.6, 15.8, 16.4, and 17.1.

  figure437
Figure 7: Number of photons detected in LBT interferograms plotted against V-magnitude of a G0 star for 20 msec exposure time/frame, 5 nm spectral bandwidth (FWHM; use of only one spectral channel), and 10% quantum efficiency of optics and detector. The flux of a G0-type star was taken from Allen (1973)

3.2.2. Simulations of an extended object

 

Figure 8 (click here) shows the results of a computer simulation with an extended object. In this experiment each photon noise-degraded object interferogram consisted of 2000 photoevents. All other experimental parameters were identical as in the star cluster experiment. The experimental parameters are summarized in Table 1 (click here). The average photometric error of the reconstruction (Fig. 8 (click here)i) is about 20%. 2000 photoevents correspond to a total magnitude of 11.3 for two 8 m telescopes, 20 msec exposure time per interferogram, 5 nm filter bandwidth, and 10% quantum efficiency of detector plus optics. Since the object consists of about 10 diffraction-limited resolution elements of similar brightness, we obtain for the brightness of the brightest resolution element (nucleus) about magnitude 13 and for the faintest about magnitude 14. Much fainter objects can be reconstructed if observing time is longer than 1.1 hours, if seeing can be improved by partial adaptive optics, or if data can simultaneously be recorded in, for example, 10 to 100 spectral channels of 5 nm bandwidths.

  figure449
Figure 8: Computer simulation of speckle masking interferometry of an extended object (Fried parameter tex2html_wrap_inline1620 cm, corresponding to 0.35 arcsec seeing): a) LBT pupil function, b) uv-coverage of the computer experiment (geographic latitude tex2html_wrap_inline1624; object declination tex2html_wrap_inline1626; 12-hour aperture synthesis; data recording at 71 different rotation angles of the earth), c, d) object (galaxy), e) one of the generated LBT point source speckle interferograms, f) one of the 200000 generated object interferograms before simulation of photon noise, g) one of the generated 200000 LBT speckle interferograms of the object after injection of photon noise corresponding to a mean count number of 2000 photoevents per interferogram, and h, i) the diffraction-limited image reconstructed from the 200000 photon noise-degraded interferograms by speckle masking and the building block method (2000 photoevents/interferogram; 6000 iterations of the building block method; galaxy diameter tex2html_wrap_inline1628 milli-arcsec for tex2html_wrap_inline1630 Å and LBT diameter 22 m). The contour levels are 15, 20, 30, 40, 50, 60, 70, 80, and 90% of the peak intensity (in order to show greater detail, Figs. d and i have been enlarged)


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