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He divi[ Planetary rovers : robotic exploration of the solar system. This book on planetary rover development covers all aspects relevant to the design of systems. Sign In. Advanced Search. Article Navigation. Close mobile search navigation Article Navigation. Volume Article Contents. Geometrical optics problem. Diffraction optics and gravitational PSF. Diffraction optics: limiting cases. PSF in the focal plane of a telescope. Discussion and conclusions.
On the role of caustics in solar gravitational lens imaging Igor Loutsenko. E-mail: loutseni crm. Oxford Academic. Google Scholar. Cite Citation. Permissions Icon Permissions. Abstract We consider scattering of electromagnetic waves from a distant point source by the gravitational field of the sun, taking the field oblateness due to the quadrupole moment of the sun into account.
The trajectory of light in the gravitational field of the sun can be found using post-Newtonian approximations for the null geodesics of the post-Minkowski metric element see, e. Here, one can apply the thin-lens approximation, which leads to the following picture see Fig. Open in new tab Download slide. It follows from Eqs. Then, from Eq. On the other hand, from Eqs. The change of polarization angles of light in weak gravitomagnetic fields is of a post-post-Newtonian order and can be neglected see, e.
The intensity magnification, i. For a detailed derivation and justification of the Fresnel—Kirchhoff diffraction integral 18 see, e. In Eq.
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As seen from Fig. As follows from Eq. For an analytic description of the above numerical result we expand the argument of the exponential in Eq. Therefore, provided Eq. Then, provided that the above conditions hold, from Eqs. It follows from Eq. The validity domain of Eq. Taking into account that Eq. Correspondence between the Cartesian and caustic-linked coordinates in the observer plane. After substituting Eq. Therefore see Eq. The integral in Eq.
The domain of validity of Eq. The behavior of the PSF can be easily described in both small and big aperture limits. When the aperture is much smaller than the scale of the diffraction pattern i.
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Here our computations are facilitated due to the fact that one can perform the 2D stationary phase integration in Eq. Then, similarly to the case of the GPSF cf. When the angular separation between the geometrical optics images of a point source is much bigger than the diffraction limit of a telescope, the double sum in the last equation can be dropped.
Completing this section, we would like to mention the influence of the higher multipole moments of the sun on the PSF. We start with the computation of the intensity near a regular point of the caustic. On the other hand, it follows from Eqs. Comparing the above equation with Eq. According to the theory of the uniform caustic expansions see, e. Then with the help of Eq. The solar atmosphere introduces corrections to the gravitational deflection picture. This leads to an underestimate in the corrections to deflections by about three orders of magnitude in comparison with, e.
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The latter are based on a model with a correctly estimated quadrupole moment. As a consequence, the transverse aberration was also underestimated by about three orders of magnitude in Ref. The latter will be introduced further. Such a double stationary phase integration results in Eq. Note, however, that permutation of the solutions only reverses the sign of integral 28 since both solutions parametrize the same curve differently. For reviews, see, e. Search ADS. Google Preview. Issue Section:. Download all figures. View Metrics.