United States of America As Represented by the Administrator of Nasa

Bruce H Dean

David L Aronstein

Jeffrey Scott Smith

Lee Daniel Feinberg

Tristram Tupper Hyde

An image-based phase retrieval technique has been developed that can be used on board a space based iterative transformation system. Image-based wavefront sensing is computationally demanding due to the floating-point nature of the process. The discrete Fourier transform (DFT) calculation is presented in 'diagonal' form. By diagonal we mean that a transformation of basis is introduced by an application of the similarity transform of linear algebra. The current method exploits the diagonal structure of the DFT in a special way, particularly when parts of the calculation do not have to be repeated at each iteration to converge to an acceptable solution in order to focus an image.

Discrete fourier transform in a complex vector space

A rebinning device includes a rebinning engine that transforms signal data from a first format to a second format with vectorized binning. Moreover, a data storage operably coupled to the rebinning engine stores the signal data in the second format. The rebinning device may optionally includes a capturing engine that captures the signal data in the first format and a rendering engine that renders the signal data in the second format.

Vectorized rebinning for fast data down-sampling

Padding or adding data to a data signal can increase the speed with which a signal processor can process the data. Methods are provided herein that can accurately predict the optimal pad size of a two dimensional array of data, which can be used to increase the processing speed of a signal processor by optimizing run-time for a two-dimensional (2-D) fast Fourier transform (FFT) operation.

Optimal padding for the two-dimensional fast fourier transform

Disclosed herein are systems, methods, and non-transitory computer-readable storage media for radio phase retrieval. A system practicing the method gathers first data from radio waves associated with an object observed via a first aperture, gathers second data from radio waves associated with the object observed via an introduced second aperture associated with the first aperture, generates reduced noise data by incoherently subtracting the second data from the first data, and performs phase retrieval for the radio waves by modeling the reduced noise data using a single Fourier transform. The first and second apertures are at different positions, such as side by side. This approach can include determining a value Q which represents a ratio of wavelength times a focal ratio divided by pixel spacing. This information can be used to accurately measure and correct alignment errors or other optical system flaws in the apertures.

System and method for phase retrieval for radio telescope and antenna control

According to various embodiments, a method is provided for improving data and a system is provided that is configured to perform the method. The method can comprise processing a data signal by using an optical system comprising a signal processor. The method can comprise collecting data generated by the optical system, wherein the data comprises non-uniformly sampled data. The method can comprise performing an interpolation operation on the non-uniformly sampled data using the signal processor, to generate interpolated data. Further, the method can comprise adjusting the data with the interpolated data using the signal processor, to generate improved data. The improved data can be output to a user, for example, by displaying the improved data on a display unit, or by printing out the improved data. According to various embodiments, the data can comprise any desired data, for example, image data. The method can comprise improving the image resolution, improving the image brightness, improving the image contrast, and/or improving the image focus.

Method and system for signal procesing non-uniformly sampled data

According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.

Discrete fourier transform (DFT) analysis for applications using iterative transform methods

Disclosed herein are systems, methods, and non-transitory computer-readable storage media for simulating propagation of an electromagnetic field, performing phase retrieval, or sampling a band-limited function. A system practicing the method generates transformed data using a discrete Fourier transform which samples a band-limited function f(x) without interpolating or modifying received data associated with the function f(x), wherein an interval between repeated copies in a periodic extension of the function f(x) obtained from the discrete Fourier transform is associated with a sampling ratio Q, defined as a ratio of a sampling frequency to a band-limited frequency, and wherein Q is assigned a value between 1 and 2 such that substantially no aliasing occurs in the transformed data, and retrieves a phase in the received data based on the transformed data, wherein the phase is used as feedback to an optical system.

Method for utilizing properties of the sinc(x) function for phase retrieval on nyquist-under-sampled data

According to various embodiments, provided herein is an optical system and method that can be configured to perform image analysis. The optical system can comprise a telescope assembly and one or more hybrid instruments. The one or more hybrid instruments can be configured to receive image data from the telescope assembly and perform a fine guidance operation and a wavefront sensing operation, simultaneously, on the image data received from the telescope assembly.

Hybrid architecture active wavefront sensing and control system, and method

A method of recovering unknown aberrations in an optical system includes collecting intensity data produced by the optical system, generating an initial estimate of a phase of the optical system, iteratively performing a phase retrieval on the intensity data to generate a phase estimate using an initial diversity function corresponding to the intensity data, generating a phase map from the phase retrieval phase estimate, decomposing the phase map to generate a decomposition vector, generating an updated diversity function by combining the initial diversity function with the decomposition vector, generating an updated estimate of the phase of the optical system by removing the initial diversity function from the phase map. The method may further include repeating the process beginning with iteratively performing a phase retrieval on the intensity data using the updated estimate of the phase of the optical system in place of the initial estimate of the phase of the optical system, and using the updated diversity function in place of the initial diversity function, until a predetermined convergence is achieved.

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New Market, MD, United States of America

Bruce H Dean