Abstract: An apparatus is provided for measuring a frequency-domain optical coherence tomography power spectrum from a sample. The apparatus includes a broadband light source, an optical spectrum analyzer, and a partially reflective element optically coupled to the light source, to the optical spectrum analyzer, and to the sample. A first portion of light from the light source is reflected by the partially reflective element and propagates to the optical spectrum analyzer. A second portion of light from the light source propagating through the partially reflective element, impinging the sample, reflecting from the sample, and propagating to the optical spectrum analyzer.

Abstract: An optical device and methods of using an optical device are provided. The optical device includes a hollow-core fiber including a first portion and a second portion. The first portion includes a hollow core having a first diameter. The second portion includes a hollow core having a second diameter smaller than the first diameter. The difference between the first diameter and the second diameter is less than 10% of the first diameter.

Abstract: An optical device and methods of using an optical device are provided. The optical device includes a hollow-core fiber including a first portion and a second portion. The first portion includes a hollow core having a first diameter. The second portion includes a hollow core having a second diameter smaller than the first diameter. The difference between the first diameter and the second diameter is less than 10% of the first diameter.

Abstract: An apparatus characterizes at least one fiber Bragg grating. The apparatus includes a laser pulse source, an optical spectrum analyzer, and multiple optical paths. A first optical path includes a pulse stretcher and an attenuator. A second optical path optically coupled to the first optical path includes a mirror. A third optical path optically coupled to the first optical path includes a first fiber Bragg grating. A fourth optical path is optically coupled to the second optical path, the third optical path, and the optical spectrum analyzer. A fifth optical path optically coupled to the laser pulse source and the optical spectrum analyzer includes a delay line.

Abstract: An optical filter and methods of filtering are provided. The optical filter includes a hollow-core fiber including a first portion and a second portion. The first portion includes a hollow core having a first diameter and a cladding having a second diameter. The second portion includes a hollow core having a third diameter smaller than the first diameter and a cladding having a fourth diameter smaller than the second diameter.

Abstract: A method utilizes an optical image processing system. The method includes providing a measured magnitude of the Fourier transform of a complex transmission function of an object or optical image. The method further includes providing an estimated phase term of the Fourier transform of the complex transmission function. The method further includes multiplying the measured magnitude and the estimated phase term to generate an estimated Fourier transform of the 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 complex transmission function by applying at least one constraint to the inverse Fourier transform.

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: An apparatus is provided for measuring a frequency-domain optical coherence tomography power spectrum from a sample. The apparatus includes a broadband light source, an optical spectrum analyzer, and a partially reflective element optically coupled to the light source, to the optical spectrum analyzer, and to the sample. A first portion of light from the light source is reflected by the partially reflective element and propagates to the optical spectrum analyzer. A second portion of light from the light source propagating through the partially reflective element, impinging the sample, reflecting from the sample, and propagating to the optical spectrum analyzer.

Abstract: An apparatus characterizes at least one fiber Bragg grating. The apparatus includes a laser pulse source, an optical spectrum analyzer, and multiple optical paths. A first optical path includes a pulse stretcher and an attenuator. A second optical path optically coupled to the first optical path includes a mirror. A third optical path optically coupled to the first optical path includes a first fiber Bragg grating. A fourth optical path is optically coupled to the second optical path, the third optical path, and the optical spectrum analyzer. A fifth optical path optically coupled to the laser pulse source and the optical spectrum analyzer includes a delay line.

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 sample. The magnitude spectrum is obtained from power spectrum data of frequency-domain optical coherence tomography of the sample. 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 method further includes calculating an estimated intermediate function by applying at least one constraint to the inverse Fourier transform of the estimated complex spatial Fourier transform.

Abstract: An apparatus characterizes at least one fiber Bragg grating. The apparatus includes a laser pulse source, an optical spectrum analyzer, and multiple optical paths. A first optical path includes a pulse stretcher and an attenuator. A second optical path optically coupled to the first optical path includes a mirror. A third optical path optically coupled to the first optical path includes a first fiber Bragg grating. A fourth optical path is optically coupled to the second optical path, the third optical path, and the optical spectrum analyzer. A fifth optical path optically coupled to the laser pulse source and the optical spectrum analyzer includes a delay line.

Abstract: An apparatus characterizes at least one fiber Bragg grating. The apparatus includes a laser pulse source, an optical spectrum analyzer, and multiple optical paths. A first optical path includes a pulse stretcher and an attenuator. A second optical path optically coupled to the first optical path includes a mirror. A third optical path optically coupled to the first optical path includes a first fiber Bragg grating. A fourth optical path is optically coupled to the second optical path, the third optical path, and the optical spectrum analyzer. A fifth optical path optically coupled to the laser pulse source and the optical spectrum analyzer includes a delay line.

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

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 first pulse indicative of the transient response of the sample and a second 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 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 determining a transient response 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 a 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 and 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, and 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 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: An optical filter and methods of filtering are provided. The optical filter includes a hollow-core fiber including a first portion and a second portion. The first portion includes a hollow core having a first diameter and a cladding having a second diameter. The second portion includes a hollow core having a third diameter smaller than the first diameter and a cladding having a fourth diameter smaller than the second diameter.

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