Method and apparatus for performing complex fourier transforms

A Fourier transform and complex number technology, applied in the field of performing complex Fourier transform and devices, can solve the problem that the camera can only restore the intensity, and achieve the effect of high precision and high calculation efficiency

Active Publication Date: 2018-10-23
CAMBRIDGE ENTERPRISE LTD
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The camera can on...

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  • Method and apparatus for performing complex fourier transforms
  • Method and apparatus for performing complex fourier transforms
  • Method and apparatus for performing complex fourier transforms

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Embodiment Construction

[0054] Some examples are described in ID. However, it can be readily appreciated that such embodiments extend naturally to 2D.

[0055] phase determination

[0056] The present disclosure can be conveniently understood with reference to an embodiment in which an input function and its Fourier transform are pixelated. That is, in an embodiment, the complex Fourier transform of an input function is a pixelated representation of the complex Fourier transform of said input function comprising a spatial array of elements, where each element comprises an amplitude value and a phase value . In this regard, the complex optical Fourier transform of the input function can be considered to comprise two components: an amplitude function and a phase function. It will be appreciated that the discrete input corresponds to the discrete Fourier transform and the Nyquist-Shannon sampling theorem applies. In an embodiment, the amplitude function of the complex Fourier transform of the inpu...

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Abstract

A method of performing a complex Fourier transform of an input function comprising amplitude and phase information, the method including the steps of: decomposing the input function into a plurality of sub-functions, wherein the Fourier transform of each sub-function comprises an amplitude function and a phase function in which the phase is constrained to a plurality of possible phase values; determining the phase function of the Fourier transform of each sub-function by measuring the amplitude function of an optical Fourier transform of the sub-function and changes in the amplitude function of the optical Fourier transform caused by applying a perturbation function to the sub-function; and combining the determined phase functions and the measured amplitude functions for each sub-functionto form the complex Fourier transform of the input function.

Description

technical field [0001] The present disclosure relates to a method of determining the phase component of a complex optical Fourier transform based on the measurement of the amplitude component of the optical Fourier transform. More specifically, the present disclosure relates to a method of performing a complex Fourier transform of an input function, an apparatus for performing a complex Fourier transform of an input function, and a method of determining a phase value of an element in a spatial array of elements, the The elements are arranged to form a pixelated representation of the complex Fourier transform of the input function. Background technique [0002] The Fourier transform is a useful mathematical operation that is ubiquitous. The Fourier Transform (FT) is used in many different computing applications and is usually implemented by the Fast Fourier Transform (FFT) algorithm. These algorithms scale O(n.logn) with a transform of size n. Performing an FFT is computat...

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Application Information

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IPC IPC(8): G06E3/00
CPCG06E3/003G06F17/14G06E3/005G06F17/141
Inventor 亚历山大·约瑟夫·麦克法登
Owner CAMBRIDGE ENTERPRISE LTD
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