Towards the Ronchi test for gravitational lenses: the gravitoronchigram

Abstract

The aim of this work is to present a Ronchi test for a gravitational lens. To this end, we use the geometrical optics point of view of the Ronchi test and the definition of the exact lens equation without reference to a background space-time to introduce the analog of the ideal ronchigram, which we named the gravitoronchigram. We first present the ideal ronchigram for an axicon lens and then using the space-time perspective of the lensing phenomenon we obtain analytical equations of the ideal gravitoronchigram for the Schwarzschild lens in the thin lens approximation and in an exact way. Finally, because the caustic associated with the deflected light by the axicon and the Schwarzschild lenses is a line along the optical axis we conjecture the generation of a gravitoBessel beam by illuminating the Schwarzschild lens with a point light source analogous to that generated by an axicon lens. That is, a particular example of the so-called non-diffracting light fields.

Approaching all the configurations for the analytical ronchigram in relation to the caustic region for an arbitrary plano-convex lens

“…We remark the importance of the analysis of the new configurations, where both planes (the grating and detection planes) are inside the caustic region. The importance lies in the fact that, while in optics, we can choose the grating position and the detection plane outside the caustic, in gravitational lenses [8] we cannot choose the observer position (the detection plane). Therefore, this work is a didactical model that establishes a foundation for understanding the specific configurations of gravitational lenses.…”

“…Due to its symmetry, this test can be interpreted in a natural way. In addition, we choose the Ronchi test because it has direct experimental applicability in optics [2][3][4][5], astronomy, electron microscopy, and gravitational lenses [6][7][8]. In particular, for gravitational lenses, it is fundamental to be able to analyze all the possible configurations of the optical system.…”

Geometric treatment of the radiation captured by the Large Millimeter Telescope (LMT/GTM) and ronchigrams at the caustic region for a static source

“…Furthermore, since we are interested in computing the ronchigram, we have to study the distribution of the reflected light rays on planes z = constant around the caustic region. Therefore in figure (4) we present the intersection between some reflected light rays with the planes z 0 = 15 m, z 0 = 17.5 m (the focus) and z 0 = 20 m for the antenna of the LMT/GTM with β = 0 and α = π/200. From figure 3(b) it is clear that the dominant aberration of the optical system for these parameters is that of the coma one.…”

“…Since in the Schwarzschild spacetime a part of the caustic associated with the light cone of a point light source is a semi-infinite straight line along the optical axis [4], then, asymptotically the wave describing the radiation of that point light source in the vicinity of the Schwarzschild black hole could be the zero-order Bessel beam. For this reason, in the present work, we assume that the radiation emitted by any point light source in the vicinity of a Kerr black hole is described asymptotically by a nonzero order Bessel beam, which gets its orbital angular moment from the rotation of the Kerr black hole.…”

Classical Characterization of quantum waves: Comparison between the caustic and the zeros of the Madelung-Bohm potential

“…The geometric description of a wavefunction is a practical tool to study wave propagation in quantum mechanics and optics, and even in the general relativity background. The knowledge of the set of rays and geometrical wavefronts associated with the wavefunction enables us to study a series of properties and approximations such as self-reconstruction [1,2], the classical description of the beam [3,4], image formation, lens design and ronchigrams [5,6,7,8], and even an approximation for the field associated with the refraction phenomena [9]. Nowadays, the research on the engineering of structured beams has an astonishing impulse due to its applications [10,11], from nanoparticle manipulation and nanotechnology applications [12,13,14,15,16] to the enhancement of communication systems [17,18,19], high-resolution observation [20,21] and metrology [22,23,24], to name a few.…”