Many Tiny Satellites Can Create Image of a Giant Space Telescope
Nanosatellites the size of milk cartons arranged in a spherical (annular) configuration were able to capture images that match the resolution of the full-frame, lens-based or concave mirror systems used on today’s telescopes.
They created a miniature model with a circular-shaped display of sub-apertures to test an image’s resolution. The researchers then contrasted these images to those produced by direct imaging systems, which have similar dimensions of the whole aperture and are based on a layout of annular sub-apertures.
“Several previous assumptions about long-range photography were incorrect,” Bulbul said. “We found that you only need a small part of a telescope lens to obtain quality images.”
Researchers were able to capture high-resolution images using only a tiny fraction of a full lens on each nano-satellite model.
Abstract – Superresolution far-field imaging by coded phase reflectors distributed only along the boundary of synthetic apertures
The resolution of imaging by space and earth-based telescopes is often limited by the finite aperture of the optical systems. We propose a novel synthetic aperture-based imaging system with two physical subapertures distributed only along the perimeter of the synthetic aperture. The minimum demonstrated two-subaperture area is only 0.43% of a total full synthetic aperture area. The proposed optical configuration is inspired by a setup in which two synchronized satellites move only along the boundary of the synthetic aperture and capture a few light patterns from the observed scene. The light reflected from the two satellites interferes with an image sensor located in a third satellite. The sum of the entire interfering patterns is processed to yield the image of the scene with a quality comparable to an image obtained from the complete synthetic aperture. The proposed system is based on the incoherent coded aperture holography technique in which the light diffracted from an object is modulated by a pseudorandom coded phase mask. The modulated light is recorded and digitally processed to yield the 3D image of the object. A laboratory model of imaging with two synchronized subapertures distributed only along the border of the aperture is demonstrated. Experimental results validate that sampling along the boundary of the synthetic aperture is enough to yield an image with the resolving power obtained from the complete synthetic aperture. Unlike other schemes of synthetic aperture, there is no need to sample any other part of the aperture beside its border. Hence, a significant saving of time and/or devices are expected in the process of data acquisition.
We have proposed a novel incoherent synthetic aperture technique with a pair of subapertures having an area as low as 0.43% of total synthetic aperture area. The subaperture pair moves only along the perimeter of the complete synthetic aperture. As a preliminary test, we investigated the combinations of subaperture pairs located on a grid of two to eight equally separated points along the annular perimeter of the complete aperture. Although the synthetic aperture is sampled only along its margin, at least in cases where each subaperture is wide enough, the resolution and the SNR are comparable to the image obtained by the complete aperture. By the proposed method, the image is obtained as a cross-correlation between the system response to the object and the system impulse response. Three impulse intensity responses are recorded for each of the three independent CPMs and for each of the entire subaperture permutations distributed on a grid of 𝑁 equally separated points. The three impulse intensity responses are superposed with different phase constants into complex-valued holograms. A similar recording process is repeated for the observed object. Finally, images of the different planes of the object are reconstructed by cross-correlating the object hologram with the corresponding complex-valued impulse responses. Although the pair of subapertures has 0.43% of the total synthetic aperture area, the aperture ratio can be decreased further by increasing the number of camera shots acquired with different CPMs and averaging over the obtained images. Probably in the future, the aperture ratio will be further reduced by improving the algorithms of synthesizing the CPMs. Analysis of the system limitations is also a task that will be investigated in the future.
The results of SMART are compared to those of direct imaging and of PAIS, both with the same system aperture. The results of SMART are found to be always better than those of PAIS reconstruction and much better than those of conventional direct imaging with the same apertures. In direct imaging, when the subapertures are distributed along the perimeter of the complete aperture, the PSF has relatively high sidelobes that blur the image. In the spatial spectrum, the effect is of using narrow low-pass filtering. SMART and PAIS do not suffer from this problem because both these techniques are indirect imaging methods, and consequently, the image is not obtained as a result of direct convolution between the object and a PSF dictated by the system aperture. From the spectral perspective, the input images of PAIS and SMART are not filtered by the low-pass filter of the direct imaging. Instead, their MTF is chaotic pseudorandomly distributed, and their transmission is distributed over the entire spectral domain more uniformly than the direct imaging with the same aperture, resulting in superresolution for the case of SMART and PAIS.
In addition to the superiority of SMART over other techniques of the synthetic aperture in terms of the aperture coverage, SMART is also an inherent 3D imaging technique. The imaging quality can be further simply improved by using more than eight points in the position grid and by averaging over many independent imaging results. In summary, we have shown in  that a full clear aperture of a conventional imaging system can be replaced by an annular aperture without losing image resolution of the original full aperture system. But for practical purposes, in the present study of SMART and PAIS, we obtained two new findings: first, the annular aperture can be sampled in space or can be replaced by several isolated subapertures. Second, the annular aperture can be sampled in time by a pair of subapertures. In both options, the image resolution of the full clear aperture can be maintained utilizing minimal subaperture area. We believe that the demonstrated idea of SMART with minimal marginal subaperture ratios can be adapted for implementation in space-based and ground-based telescopes over conventional telescopes. The preliminary results shown here using a laboratory model are highly promising and might be a significant contribution to the field of imaging in general and astronomical telescopes in particular. However, further challenges such as atmospheric turbulence, scattering by aerosol, lower light intensity, and finding a stable satellite orbit are anticipated upon scaling up the system for satellite telescope applications, and are topics of future research.