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Using both analytical and Monte Carlo techniques, beam-pointing errors of planar-phased arrays are analyzed. The obtained simple formulas for rms pointing errors are applicable to uniform planar arrays with both uniform and Gaussian uncorrelated phase-error distributions and for any arbitrary scan angle.
Probabilities of overflow and error in coded phase shift keyed systems with sequential decoding
Detection of earth-like planets around other stars using coronagraphy requires the optical beam into the coronagraph to be extremely uniform in both phase and amplitude. Errors in phase can be corrected using a deformable mirror, and error in amplitude can be corrected using a spatial light modulator, both in the pupil plan,a. These corrections can be combined using a Michelson interferometer. If amplitude corrections of only a few percent range are needed, the required accuracy of 10 (circumflex) -4 can be obtained with spatial light modulators with the modest dynamic range of 8 bits.
There are no author-identified significant results in this report.
The broadband performance of the high-contrast imaging testbed (HCIT) at JPL is investigated through optical modeling and simulations. The analytical tool is an optical simulation algorithm developed by combining the HCIT's optical model with a speckle-nulling algorithm that operates directly on coronagraphic images, an algorithm identical to the one currently being used on the HCIT to actively suppress scattered light via a deformable mirror. It is capable of performing full three-dimensional end-to-end near-field diffraction analysis on the HCIT's optical system. By conducting speckle-nulling optimization, we clarify the HCIT's capability and limitations in terms of its broadband contrast performance under various realistic conditions. Considered cases include non-ideal occulting masks, such as a mask with optical density and wavelength dependent parasitic phase-delay errors (i.e., a not band-limited occulting mask) and the one with an optical-density profile corresponding to a measured, non-standard profile, as well as the independently measured phase errors of all optics. Most of the information gathered on the HCIT's optical components through measurement and characterization over the last several years at JPL has been used in this analysis to make the predictions as accurate as possible. The best contrast values predicted so far by our simulations obtainable on the HCIT illuminated with a broadband light having a bandwidth of 80nm and centered at 800nm wavelength are Cm=1.1x10-8 (mean) and C4=4.9x10-8 (at 4(lamda)/D), respectively. In this paper we report our preliminary findings about the broadband light performance of the HCIT.
A method is presented for calculating the effect of carrier-phase reference error in a receiver phase-locked loop on bit error rates in convolutionally coded data, for the practical design of systems using short-constraint-length convolutional codes. A set of design curves shows the relation between design bit error rate, uplink carrier tracking loop SNR, downlink total SNR, and downlink modulation index. These curves make possible rapid and simple system optimization.
Gregorian, Cassegrain, and single reflector systems were analyzed in configuration studies for communications satellite receive antennas. Parametric design and performance curves were generated. A preliminary design of each reflector/feed system was derived including radiating elements, beam-former network, beamsteering system, and MMIC module architecture. Performance estimates and component requirements were developed for each design. A recommended design was selected for both the scanning beam and the fixed beam case. Detailed design and performance analysis results are presented for the selected Cassegrain configurations. The final design point is characterized in detail and performance measures evaluated in terms of gain, sidelobe level, noise figure, carrier-to-interference ratio, prime power, and beamsteering. The effects of mutual coupling and excitation errors (including phase and amplitude quantization errors) are evaluated. Mechanical assembly drawings are given for the final design point. Thermal design requirements are addressed in the mechanical design.
The WFIRST coronagraph employs two sequential deformable mirrors to compensate for phase and amplitude errors in the coronagraph optical system. In such a system the actuators of the deformable mirrors would be used for two purposes: To flatten the overall wavefront errors at a system pupil, and to create "dark-holes". The actuators have limited stroke ranges. Therefore, if the pupil phase errors are relatively large, flattening them completely could use up a significant portion of the actuator stroke, sometimes leaving insufficient stroke for creating the dark-holes. We have investigated the impact of partially-corrected pupil phase errors on a Hybrid Lyot Coronagraph (HLC) broadband contrast performance. The predicted broadband contrast floor and the contrast chromaticity agree well with those measured on the HLC testbed.
The performance of quantum error correcting (QEC) codes is often studied under the assumption of spatiotemporally uniform error rates. On the other hand, experimental implementations almost always produce heterogeneous error rates, in either space or time, as a result of effects such as imperfect fabrication and/or cosmic rays. It is therefore important to understand if and how their presence can affect the performance of QEC in qualitative ways. Here, in this work, we study the effects of nonuniform error rates in the representative examples of the 1D repetition code and the 2D toric code, focusing on when they have extended spatiotemporal correlations; these may arise, for instance, from rare events (such as cosmic rays) that temporarily elevate error rates over the entire code patch. These effects can be described in the corresponding statistical mechanics models for decoding, where long-range correlations in the error rates lead to extended rare regions of weaker coupling. For the 1D repetition code where the rare regions are linear, we find two distinct decodable phases: a conventional ordered phase in which logical failure rates decay exponentially with the code distance, and a rare-region dominated Griffiths phase in which failure rates are parametrically larger and decay as a stretched exponential. In particular, the latter phase is present when the error rates in the rare regions are above the bulk threshold. For the 2D toric code where the rare regions are planar, we find no decodable Griffiths phase: rare events which boost error rates above the bulk threshold lead to an asymptotic loss of threshold and failure to decode. Unpacking the failure mechanism implies that techniques for suppressing extended sequences of repeated rare events (which, without intervention, will be statistically present with high probability) will be crucial for QEC with the toric code.
Dynamic simulation errors for coupled loop models for digital differential and electronic differential analyzers
An improved method and apparatus have been devised for measuring cyclic errors in the readouts of laser heterodyne interferometers that are configured and operated as displacement gauges. The cyclic errors arise as a consequence of mixing of spurious optical and electrical signals in beam launchers that are subsystems of such interferometers. The conventional approach to measurement of cyclic error involves phase measurements and yields values precise to within about 10 pm over air optical paths at laser wavelengths in the visible and near infrared. The present approach, which involves amplitude measurements instead of phase measurements, yields values precise to about .0.1 microns . about 100 times the precision of the conventional approach. In a displacement gauge of the type of interest here, the laser heterodyne interferometer is used to measure any change in distance along an optical axis between two corner-cube retroreflectors. One of the corner-cube retroreflectors is mounted on a piezoelectric transducer (see figure), which is used to introduce a low-frequency periodic displacement that can be measured by the gauges. The transducer is excited at a frequency of 9 Hz by a triangular waveform to generate a 9-Hz triangular-wave displacement having an amplitude of 25 microns. The displacement gives rise to both amplitude and phase modulation of the heterodyne signals in the gauges. The modulation includes cyclic error components, and the magnitude of the cyclic-error component of the phase modulation is what one needs to measure in order to determine the magnitude of the cyclic displacement error. The precision attainable in the conventional (phase measurement) approach to measuring cyclic error is limited because the phase measurements are af-
A ground-based astronomical telescope with a segmented primary mirror will suffer image-degrading wavefront aberrations from at least two sources: (1) atmospheric turbulence and (2) segment misalignment or figure errors of the mirror itself. This paper describes the derivation of a mirror control feedback matrix that assumes the presence of both types of aberration and is optimum in the sense that it minimizes the mean-squared residual wavefront error. Assumptions of the statistical nature of the wavefront measurement errors, atmospheric phase aberrations, and segment misalignment errors are made in the process of derivation. Examples of the degree of correlation are presented for three different types of wavefront measurement data and compared to results of simple corrections.
A closed loop phase control system using an all-fiber optical configuration has been developed for use in phase-stepping interferometry. This system drives the relative phase of two interfering beams through a sequence of pi/2 rad increments so that the initial relative phase of these beams can be determined. This phase-stepping system uses optical fibers to provide spatially uniform phase steps from a flexible, easily aligned optical configuration. In addition, this system uses phase feedback to eliminate phase modulator errors and to compensate for phase drifts caused by environmental disturbances.
The optimum phase detector is presented for tracking square-wave subcarriers that have been bandwidth limited to a finite number of harmonics. The phase detector is optimum in the sense that the loop signal-to-noise ratio (SNR) is maximized and, hence, the rms phase tracking error is minimized. The optimum phase detector is easy to implement and achieves substantial improvement. Also presented are the optimum weights to combine the signals demodulated from each of the harmonics. The optimum weighting provides SNR improvement of 0.1 to 0.15 dB when the subcarrier loop SNR is low (15 dB) and the number of harmonics is high (8 to 16).
A method for constructing interferograms, schlieren, and shadowgraphs from ideal- and real-gas, two- and three-dimensional computed flowfileds is described. The computational grids can be structured or unstructured, and multiple grids are an option. The constructed images are compared to experimental images for several types of flow, including a ramp, a blunt-body, a nozzle, and a reacting flow. The constructed images simulate the features observed in the experimental images. They are sensitive to errors in the flowfield solutions and can be used to identify solution errors. In addition, techniques for obtaining phase shifts from experimental finite-fringe interferograms and for removing experimentally induced phase-shift errors are discussed. Both the constructed images and calculated phase shifts can be used for validation of computational fluid dynamics (CFD) codes.
A method for constructing interferograms, schlieren, and shadowgraphs from ideal- and real-gas, two- and three-dimensional computed flow fields is described. The computational grids can be structured or unstructured, and multiple grids are an option. The constructed images are compared to experimental images for several types of flow, including a ramp, a blunt-body, a nozzle, and a reacting flow. The constructed images simulate the features observed in the experimental images. They are sensitive to errors in the flow-field solutions and can be used to identify solution errors. In addition, techniques for obtaining phase shifts from experimental finite-fringe interferograms and for removing experimentally induced phase-shift errors are discussed. Both the constructed images and calculated phase shifts can be used for validation of computational fluid dynamics (CFD) codes.
By probing the field on a small subreflector at a minimal number of points, the main reflector surface errors can be obtained and subsequently used to design a phase-correction subreflector that can compensate for main reflector errors. The compensating phase-error profile across the subreflector can be achieved either by a surface deformation or by the use of an array of elements such as patch antennas that can cause a phase shift between the incoming and outgoing fields. The second option is of primary interest here, but the methodology can be applied to either case. The patch array is most easily implemented on a planar surface. Therefore, the example of a flat subreflector and a parabolic main reflector (a Newtonian dual reflector system) is considered in this work. The subreflector is assumed to be a reflector array covered with patch elements. The phase variation on a subreflector can be detected by a small number of receiving patch elements (probes). By probing the phase change at these few selected positions on the subreflector, the phase error over the entire surface can be recovered and used to change the phase of all the patch elements covering the subreflector plane to compensate for main reflector errors. This is accomplished by using a version of sampling theorem on the circular aperture. The sampling is performed on the phase-error function on the circular aperture of the main reflector by a method developed using Zernike polynomials. This method is based upon and extended from a theory previously proposed and applied to reflector aperture integration. This sampling method provides for an exact retrieval of the coefficients of up to certain orders in the expansion of the phase function, from values on a specifically calculated set of points in radial and azimuthal directions in the polar coordinate system, on the circular reflector aperture. The corresponding points on the subreflector are then obtained and, by probing the fields at these points, a set of phase values is determined that is then transferred back to the main reflector aperture for recovering the phase function. Once this function is recovered, the corresponding phase function on the subreflector is calculated and used to compensate for main reflector surface errors. In going back and forth between sub and main reflectors, geometrical (ray) optics is employed, which even though it ignores edge diffraction and other effects, is shown to be accurate for phase recovery.
Timing errors effect on detector output statistics of phase shift keyed /PSK/ communication systems