This online article is a supplement to our manuscript in preparation about studying the Solar Gravitational Lens (SGL) at arbitrary distances from the optical axis.
In this paper, we obtained an integral expression that can be used to either model the light field produced by the SGL in its focal region, or the view of an imaging telescope looking back at the SGL from that location.
Combined with the efficient, closed form quartic solution of the SGL with its J2 zonal harmonic, we have a formalism that can efficiently model the SGL in all regions. To demonstrate the power of this formalism, we modeled the view by a spacecraft equipped with a 1-m imaging telescope as it approaches the optical axis while viewing a distant star (uniformly illuminated disk) that corresponds to an image area with a radius of 200 km in the image plane.
Preapproach animations
The first three animations show early approach, as the spacecraft travels from 1,000,000 km from the optical axis to 4,000 km. The Sun is indicated by a thin yellow circle. The image that we see at first (or rather, don't see because it would be obscured by the solar disk initially) is the "secondary" image; the "primary" image (which begins its existence as the unobstructed, unamplified view of the distant star) floats into the viewing area from the right. Both images become brighter as a result of amplification by the SGL, such that by the time we reach 4,000 km, the ring-like Airy pattern, produced by the diffraction-limited optical telescope, becomes dominant.
Telescope distance from the Sun: 550 AU:
Telescope distance from the Sun: 650 AU:
Telescope distance from the Sun: 900 AU:
Final approach animations
The next six animations show final approach. For each of the three distances in question, two animations are available: One shows the telescopic view while the other offers a three-dimensional representation that makes it easier to visually estimate light amplification.
Telescope distance from the Sun: 550 AU:
Telescope distance from the Sun: 650 AU:
Telescope distance from the Sun: 900 AU:
The three parameters shown in the video frames are: 1) Distance (from the optical axis), 2) Total: amount of light relative to the total amount of light we would receive from the unobstructed, unamplified star, 3) Peak: the peak brightness compared to the peak brightness of the unobstructed, unamplified star.
