Abstract: A method for measuring a physical function forms a symmetric composite function by combining the physical function with a reference function. The method obtains a Fourier transform of the symmetric composite function. The method calculates an inverse Fourier transform of the obtained Fourier transform, wherein the calculated inverse Fourier transform provides information regarding the physical function. The physical function can be a nonlinearity profile of a sample with at least one sample surface. The physical function can alternatively by a sample temporal waveform of a sample optical pulse.

Abstract: A method determines a nonlinearity profile of a material. The method includes providing a magnitude of a Fourier transform of a measured nonlinearity profile measured from the material. The method further includes providing an estimated phase term of the Fourier transform of the measured nonlinearity profile. The method further includes multiplying the magnitude and the estimated phase term to generate an estimated Fourier transform. The method further includes calculating an inverse Fourier transform of the estimated Fourier transform. The method further includes calculating a real component of the inverse Fourier transform to generate an estimated nonlinearity profile.

Abstract: Exemplary apparatus and method for obtaining information associated with at least one image of at least one portion of a sample can be provided. For example, at least one first electro-magnetic radiation can be provided from the at least one portion (e.g., using a first electro-magnetic radiation guiding arrangement which is configured to provide). A plurality of spatial frequency bands of the image associated with the first electro-magnetic radiation can be generated. Further, at least one second electro-magnetic radiation which is associated with the spatial frequency bands of the image can be received (e.g., using a second arrangement), and the image can be reconstructed based on the spatial frequency bands.

Abstract: A method for measuring a physical function forms a symmetric composite function by combining the physical function with a reference function. The method obtains a Fourier transform of the symmetric composite function. The method calculates an inverse Fourier transform of the obtained Fourier transform, wherein the calculated inverse Fourier transform provides information regarding the physical function. The physical function can be a nonlinearity profile of a sample with at least one sample surface. The physical function can alternatively by a sample temporal waveform of a sample optical pulse.

Abstract: A method for measuring a physical function forms a symmetric composite function by combining the physical function with a reference function. The method obtains a Fourier transform of the symmetric composite function. The method calculates an inverse Fourier transform of the obtained Fourier transform, wherein the calculated inverse Fourier transform provides information regarding the physical function. The physical function can be a nonlinearity profile of a sample with at least one sample surface. The physical function can alternatively by a sample temporal waveform of a sample optical pulse.

Abstract: A method determines a complex electric field temporal profile of an optical pulse. The method includes providing a measured magnitude of the Fourier transform of a complex electric field temporal profile of a pulse sequence comprising the optical pulse and a dummy pulse. The method further includes providing an estimated phase term of the Fourier transform of the complex electric field temporal profile of the pulse sequence. The method further includes multiplying the measured magnitude and the estimated phase term to generate an estimated Fourier transform of the complex electric field temporal profile of the pulse sequence. The method further includes calculating an inverse Fourier transform of the estimated Fourier transform, wherein the inverse Fourier transform is a function of time. The method further includes calculating an estimated complex electric field temporal profile of the pulse sequence by applying at least one constraint to the inverse Fourier transform.

Abstract: A method determines the complex scattering function of a portion of a sample under analysis. The method includes providing a magnitude spectrum of a complex spatial Fourier transform of a complex intermediate function. The complex intermediate function is dependent on the complex scattering function of the portion of the sample under analysis. The magnitude spectrum is obtained from power spectrum data of frequency-domain optical coherence tomography of the portion of the sample under analysis. The method further includes providing an estimated phase term of the complex spatial Fourier transform. The method further includes multiplying the magnitude spectrum and the estimated phase term together to generate an estimated complex spatial Fourier transform. The method further includes calculating an inverse Fourier transform of the estimated complex spatial Fourier transform. The inverse Fourier transform of the estimated complex spatial Fourier transform is a spatial function.

Abstract: A method determines a complex reflection impulse response of a fiber Bragg grating. The method includes providing a measured amplitude of a complex reflection spectrum of the fiber Bragg grating. The method further includes providing an estimated phase term of the complex reflection spectrum. The method further includes multiplying the measured amplitude and the estimated phase term to generate an estimated complex reflection spectrum. The method further includes calculating an inverse Fourier transform of the estimated complex reflection spectrum, wherein the inverse Fourier transform is a function of time. The method further includes calculating an estimated complex reflection impulse response by applying at least one constraint to the inverse Fourier transform of the estimated complex reflection spectrum.

Abstract: A method processes an optical image. The method includes providing a measured magnitude of the Fourier transform of a two-dimensional complex transmission function. The method further includes providing an estimated phase term of the Fourier transform of the two-dimensional complex transmission function. The method further includes multiplying the measured magnitude and the estimated phase term to generate an estimated Fourier transform of the two-dimensional complex transmission function. The method further includes calculating an inverse Fourier transform of the estimated Fourier transform, wherein the inverse Fourier transform is a spatial function. The method further includes calculating an estimated two-dimensional complex transmission function by applying at least one constraint to the inverse Fourier transform.

Abstract: A method determines a transient response of a sample. The method includes providing a measured magnitude of the Fourier transform of a complex electric field temporal profile of a pulse sequence comprising a probe pulse and a dummy pulse, wherein the probe pulse is indicative of the transient response of the sample. The method further includes providing an estimated phase term of the Fourier transform of the complex electric field temporal profile of the pulse sequence. The method further includes multiplying the measured magnitude and the estimated phase term to generate an estimated Fourier transform of the complex electric field temporal profile of the pulse sequence. The method further includes calculating an inverse Fourier transform of the estimated Fourier transform, wherein the inverse Fourier transform is a function of time.

Abstract: A method measures a physical function, such as a second-order optical nonlinearity profile, or a temporal waveform of a laser pulse. The method includes forming a symmetric composite function by superimposing the physical function with a substantially identical physical function. The method further includes obtaining a Fourier transform of the symmetric composite function. The method further includes calculating an inverse Fourier transform of the obtained Fourier transform. The calculated inverse Fourier transform provides information regarding the physical function.

Abstract: A method for measuring a physical function forms a symmetric composite function by combining the physical function with a reference function. The method obtains a Fourier transform of the symmetric composite function. The method calculates an inverse Fourier transform of the obtained Fourier transform, wherein the calculated inverse Fourier transform provides information regarding the physical function. The physical function can be a nonlinearity profile of a sample with at least one sample surface. The physical function can alternatively by a sample temporal waveform of a sample optical pulse.

Abstract: A method for measuring a physical function forms a symmetric composite function by combining the physical function with a reference function. The method obtains a Fourier transform of the symmetric composite function. The method calculates an inverse Fourier transform of the obtained Fourier transform, wherein the calculated inverse Fourier transform provides information regarding the physical function. The physical function can be a nonlinearity profile of a sample with at least one sample surface. The physical function can alternatively by a sample temporal waveform of a sample optical pulse.

Abstract: A method for measuring a physical function forms a symmetric composite function by combining the physical function with a reference function. The method obtains a Fourier transform of the symmetric composite function. The method calculates an inverse Fourier transform of the obtained Fourier transform, wherein the calculated inverse Fourier transform provides information regarding the physical function. The physical function can be a nonlinearity profile of a sample with at least one sample surface. The physical function can alternatively by a sample temporal waveform of a sample optical pulse.

Abstract: A method determines a nonlinearity profile of a material. The method includes providing a magnitude of a Fourier transform of a measured nonlinearity profile measured from the material. The method further includes providing an estimated phase term of the Fourier transform of the measured nonlinearity profile. The method further includes multiplying the magnitude and the estimated phase term to generate an estimated Fourier transform. The method further includes calculating an inverse Fourier transform of the estimated Fourier transform. The method further includes calculating a real component of the inverse Fourier transform to generate an estimated nonlinearity profile.

Abstract: A method measures a nolinearity profile of a sample with at least one sample surface and having a sample nonlinearity profile along a sample line through a predetermined point on the sample surface. The sample line is oriented perpendicularly to the sample surface. The method includes measuring a Fourier transform of the sample nonlinearity profile and obtaining a reference nonlinearity profile from a reference material. The method includes forming a first composite sample having a first composite nonlinearity profile and forming a second composite sample having a second composite nonlinearity profile inequivalent to the first composite nonlinearity profile. The method further includes measuring a Fourier transform of the first composite nonlinearity profile and measuring a Fourier transform of the second composite nonlinearity profile.

Abstract: A method for measuring a physical function forms a symmetric composite function by combining the physical function with a reference function. The method obtains a Fourier transform of the symmetric composite function. The method calculates an inverse Fourier transform of the obtained Fourier transform, wherein the calculated inverse Fourier transform provides information regarding the physical function. The physical function can be a nonlinearity profile of a sample with at least one sample surface. The physical function can alternatively by a sample temporal waveform of a sample optical pulse.

Abstract: A method measures a nolinearity profile of a sample with at least one sample surface and having a sample nonlinearity profile along a sample line through a predetermined point on the sample surface. The sample line is oriented perpendicularly to the sample surface. The method includes measuring a Fourier transform of the sample nonlinearity profile and obtaining a reference nonlinearity profile from a reference material. The method includes forming a first composite sample having a first composite nonlinearity profile and forming a second composite sample having a second composite nonlinearity profile inequivalent to the first composite nonlinearity profile. The method further includes measuring a Fourier transform of the first composite nonlinearity profile and measuring a Fourier transform of the second composite nonlinearity profile.

Abstract: A method measures a physical function, such as a second-order optical nonlinearity profile, or a temporal waveform of a laser pulse. The method includes forming a symmetric composite function by superimposing the physical function with a substantially identical physical function. The method further includes obtaining a Fourier transform of the symmetric composite function. The method further includes calculating an inverse Fourier transform of the obtained Fourier transform. The calculated inverse Fourier transform provides information regarding the physical function.