Partially Transparent Petaled Mask/Occulter for Visible-Range Spectrum

The presence of the Poisson Spot, also known as the spot of Arago, has been known since the 18th century. This spot is the consequence of constructive interference of light diffracted by the edge of the obstacle where the central position can be determined by symmetry of the object. More recently, many NASA missions require the suppression of this spot in the visible range. For instance, the exoplanetary missions involving space telescopes require telescopes to image the planetary bodies orbiting central stars. For this purpose, the starlight needs to be suppressed by several orders of magnitude in order to image the reflected light from the orbiting planet. For the Earth-like planets, this suppression needs to be at least ten orders of magnitude. One of the common methods of suppression involves sharp binary petaled occulters envisioned to be placed many thousands of miles away from the telescope blocking the starlight. The suppression of the Poisson Spot by binary sharp petal tips can be problematic when the thickness of the tips becomes smaller than the wavelength of the incident beam. First they are difficult to manufacture and also it invalidates the laws of physical optics. The proposed partially transparent petaled masks/occulters compensate for this sharpness with transparency along the surface of the petals. Depending on the geometry of the problem, this transparency can be customized such that only a small region of the petal is transparent and the remaining of the surface is opaque. This feature allows easy fabrication of this type of occultation device either as a mask or occulter. A partially transparent petaled mask/ occulter has been designed for the visible spectrum range. The mask/occulter can suppress the intensity along the optical axis up to ten orders of magnitude. The design process can tailor the mask shape, number of petals, and transparency level to the near-field and farfield diffraction region. The mask/occulter can be used in space astronomy, ground-based telescope, and high-energy laser systems, and optical lithography to eliminate the Poisson Spot

Limits on Achievable Intensity Reduction with an Optical Occulter

Deep shadowing of a normally incident plane wave by an opaque circular disk is partially negated by the formation of a region of strong intensity surrounding the axis passing normally through the disk center. This local intensity enhancement, historically referred to as the Poisson Spot (also known as the Spot of Arago), has been the principal source of difficulties in applications where a significant reduction of the incident intensity is essential. In particular, the NASA Terrestrial Planet Finder's (TPF) mission requires suppression of direct starlight by at least 10 orders of magnitude over the entire visible spectral range. One technique that has been proposed for blocking the direct starlight is to use a rotationally symmetric disk with petallike segments along its boundary. We find that, even though such configurations could, indeed, theoretically provide the desired intensity reduction, they would require unreasonably small radii of curvature at the petals' tips (in the range of micrometers). When the radii of curvature are increased to 3 mm, the intensity reduction drops to a modest 5 to 6 orders of magnitude. Given that for the NASA's TPF mission the proposed occulter radius would be on the order of 25 m, even the 3 mm radius of curvature would be too small for any practical implementation. Further increases of the radius of curvature result in progressively poorer intensity suppression. As an alternative solution we propose an apodized circular disk. We show that with an optimized apodization function, intensity reductions of at least 10 orders of magnitude can be achieved over the entire visible spectral range. Numerical results are presented for parameters appropriate to the NASA TPF mission

Image frequency suppression in frequency-scanned direction-of-arrival estimation systems

Abstract: A novel signal processing approach to the problem of image frequency suppression in wide-band frequency-scanned radio frequency (RF) receiving arrays that employ digital signal processing (DSP) techniques to estimate the direction of arrival (DOA) of incoming radiation has been presented. The conventional approach to image rejection in RF receivers is to employ a front-end RF tuner before downconversion to the intermediate frequency. As DOA processing employs a separate receiver channel for each array element, an RF tuner would be needed behind each element. Clearly for scanned systems at microwave frequencies, this is not a viable option where the tuners would generally have to be implemented in RF hardware. The need for RF tuners can be eliminated by downconversion down to baseband and employing I&Q mixers, which provide an intrinsic image rejection capability. Unfortunately, such a solution requires two analog-to-digital (A/D) converters per array element. An alternative approach is to use image rejection mixers in which case only one A/D converter per array element is needed. The approach also requires only one A/D per array element but achieves the image rejection through a DSP implementation. As a result, use of relatively expensive image rejection mixers is avoided without sacrificing performance. Experimental results are presented that validate the theoretical predictions

Signals and transforms in linear systems analysis

Signals and Transforms in Linear Systems Analysis covers the subject of signals and transforms, particularly in the context of linear systems theory. Chapter 2 provides the theoretical background for the remainder of the text. Chapter 3 treats Fourier series and integrals. Particular attention is paid to convergence properties at step discontinuities. This includes the Gibbs phenomenon and its amelioration via the Fejer summation techniques. Special topics include modulation and analytic signal representation, Fourier transforms and analytic function theory, time-frequency analysis and frequency dispersion. Fundamentals of linear system theory for LTI analogue systems, with a brief account of time-varying systems, are covered in Chapter 4 . Discrete systems are covered in Chapters 6 and 7.  The Laplace transform treatment in Chapter 5 relies heavily on analytic function theory as does Chapter 8 on Z -transforms. The necessary background on complex variables is provided in Appendix A. This book is intended to serve as a text on signals and transforms for a first year one semester graduate course, primarily for electrical engineers