A possible variant of the direct observation of Earth-like planets with the help of a hypertelescope containing circular and/or annular collecting mirrors is considered. Analytical expressions describing the imaging in the focal plane are presented. They give the opportunity to estimate the influence of the photodetector pixel exposure time and accuracy parameters of the mirror control/stabilization system on the quality of the image in the plane of the photodetector and to evaluate a signal-to-noise ratio (SNR) at its output. Numerical results obtained for the hypertelescope containing 126 (for detection) and 1164 (for recognition) identical annular mirrors of diameter 1 m illustrate an opportunity of detecting an Earth-like exo-planet moving around a Sun-like star at a distance of 1 au and recognizing its surface area at a distance of 1 pc on conditions that some technique blocking out the radiation from the exo-planet’s star is used. Some dependencies of the corresponding SNR values on the pixel exposure time and the accuracy parameters of the mirror stabilization system are shown. Several typical aperture configurations are investigated for the case of recognition and the most appropriate configuration is defined.
Analytical expressions for an instantaneous spectral point spread function (PSF) and an instantaneous spectral optical transfer function of a misaligned hypertelescope without delay lines, and containing circular and/or annular collecting mirrors, are presented. The formulas are deduced on the basis of the Fresnel approach to the Kirchhoff diffraction theory. Numerical results obtained for the system containing 60 identical annular mirrors, illustrate the pupil densification properties of the hypertelescope and the influence of random spatial and angular positioning errors of the optical elements on the average PSF (APSF), and on the average modulation transfer function (AMTF) calculated for the errors obeying specified probability distributions. The APSF and the AMTF give the opportunity to estimate the influence of the alignment errors on the resulting image quality in the hypertelescope image plane. This estimation can be used to produce the necessary requirements to the accuracy of the mirror control system and to the accuracy of the optical element alignment in dependence on the values of the exit pupil densification and the desirable resolution capability of the hypertelescope. The notion of the PSF and the modulation transfer function for off-axis beams can be useful for evaluation of a hypertelescope field of view.
KEYWORDS: LIDAR, Vegetation, 3D modeling, Solar radiation models, Instrument modeling, Transmittance, Atmospheric propagation, Optical filters, Sensors, Signal to noise ratio
Structural and biophysical parameters of vegetation canopies, such as tree heights, biomass, vertical and horizontal
heterogeneity are important factors affecting flows of energy, water, carbon and trace gases through terrestrial systems.
Knowing such parameters is required to model processes associated with photosynthesis, energy transfer, and
evapotranspiration at local and global scales. Monitoring vegetation canopies has long been one of the main tasks of
several proposed and launched space missions. Lidar instruments have demonstrated the best potential to provide
estimates of vegetation height, cover, and canopy vertical structural profiles. A spaceborne lidar would deliver such data
on global scale producing the total land biomass value with the accuracy demanded by carbon-cycle and global-change
modelers.
This paper presents the preliminary results of a numerical model simulating signal returns of a spaceborne lidar for the
assessment of land-vegetation canopy biomass. It is a part of work with the overall purpose to develop a trade-off
analysis tool for a spaceborne lidar system as a payload of a land-vegetation observation space mission. An end-to-end
propagation of a spaceborne lidar sensing pulse through vegetation canopies is considered by the model. It consists of
the modules characterizing the laser and the receiver optical systems, satellite's orbit, atmosphere, vegetation canopies,
optical filtering, and detectors. This tool can be used to evaluate the effects of instrument configurations on the retrieval
of vegetation structures, and to carry out trade-off studies in the instrument design.
The presence of a beam combination system that forms a united image in a common focal plane is one of the features of systems with an optical sparse array. Any control system of a beam combiner has a limited accuracy and, as a result, introduces some optical errors that influence the quality of the united image. This especially concerns systems with a dynamic aperture reconfiguration during an active process of observation. We present analytical expressions for the instantaneous spectral optical transfer function (OTF) of the optical sparse array consisting of N circular and annular subapertures depending on the residual random image alignment and optical path difference errors, and the average OTF for the Gaussian probability distributions depending on the statistical parameters of the last. The formulas are deduced on the basis of the Fraunhofer approach to the Kirchhoff diffraction theory. The results can be used for both space and earth sciences applications.
One feature of systems with sparse optical aperture is the possible existence of zero-value regions of the optical transfer function. In using fast-convergent gradient methods for nonlinear constrained optimization with criteria based on the optical transfer function or the modulation transfer function, the gradient of the minimized function can also contain zero-value regions. Such situations can result in a suspension of the calculation if an intermediate solution falls into such a region. We show that, using gradient methods, it is possible to avoid this calculation problem if we redefine the subaperture step pupil functions—in particular, approximate them by continuously differentiable functions having no zero-value regions. This is demonstrated on examples of apertures consisting of circular and annular subapertures. This approach can be used for both types of multiaperture optical telescopes, the Michelson and Fizeau, and for both space and earth science missions.
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