Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: A phase retrieval optical metrology system that can be used for evaluating a variety of optical surface errors is provided. The optical metrology system can comprise an optical element defining an optical axis and a focal plane, a fiber coupler coupled to the laser, a fiber connected to the fiber coupler for transmitting light received from the fiber coupler, a collimator for receiving the light received from the fiber and substantially collimating the light to generate a narrowed input light beam, and a defocus element disposed between the optical element and the focal plane.

Abstract: Disclosed herein are systems, methods, and non-transitory computer-readable storage media for determining phase of an optical system. A system practicing the method performs an analysis of image data of a distant object, wherein the image data is received via an optical system. The system derives at least one parameter of the optical system based on the analysis, and retrieves a phase of the optical system based on the at least one parameter. The parameter can be a ratio Q representing a ration of wavelength times a focal ratio divided by pixel spacing. The image data can be a series of still images. The analysis of the image data can be based on a user input indicating, for example, a position and/or a region in the image data. The image data can be in focus and/or out of focus. In one aspect, slightly out of focus image data is more informative.

Abstract: Disclosed herein are systems, methods, and non-transitory computer-readable storage media for reconstructing an image. A system practicing the method receives a corrupted image, such as a blurred image or a still frame from a video, to reconstruct, isolates a set of spatial frequencies in the corrupted image using a wavelet transform, generates restored spatial frequency information for the set of spatial frequencies, and generates a reconstructed image based on the restored spatial frequency information and the corrupted image. Generating the reconstructed image can occur in parallel or in a specific order. The set of spatial frequencies can correspond to different zoom levels. The system can further process the corrupted image and set of spatial frequencies until convergence is reached.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: A variable sample mapping algorithm supplements an iterative transform algorithm stored on a computer readable medium. The variable sample mapping algorithm employs data-to-model mapping comprising: modeling a measured data point; modeling estimated additional data corresponding to the measured data point; and adjusting the estimated additional data to include the corresponding measured data point.