Zero Path Difference Research Articles

Fourier Spectroscopy: A Bayesian Way

The concepts of standard analysis techniques applied in the field of Fourier spectroscopy treat fundamental aspects insufficiently. For example, the spectra to be inferred are influenced by the noise contribution to the interferometric data, by nonprobed spatial domains which are linked to Fourier coefficients above a certain order, by the spectral limits which are in general not given by the Nyquist assumptions, and by additional parameters of the problem at hand like the zero-path difference. To consider these fundamentals, a probabilistic approach based on Bayes’ theorem is introduced which exploits multivariate normal distributions. For the example application, we model the spectra by the Gaussian process of a Brownian bridge stated by a prior covariance. The spectra themselves are represented by a number of parameters which map linearly to the data domain. The posterior for these linear parameters is analytically obtained, and the marginalisation over these parameters is trivial. This allows the straightforward investigation of the posterior for the involved nonlinear parameters, like the zero-path difference location and the spectral limits, and hyperparameters, like the scaling of the Gaussian process. With respect to the linear problem, this can be interpreted as an implementation of Ockham’s razor principle.

High-precision broadband measurement of refractive index by picosecond real-time interferometry.

The refractive index is one of the most important quantities that characterize a material's optical properties. However, it is hard to measure this value over a wide range of wavelengths. Here, we demonstrate a new technique to achieve a spectrally broad refractive index measurement. When a broadband pulse passes through a sample, different wavelengths experience different delays. By comparing the delayed pulse to a reference pulse, the zero path difference position for each wavelength can be obtained and the material's dispersion can be retrieved. Our technique is highly robust and accurate, and can be miniaturized in a straightforward manner.

Calibration algorithm for Fourier transform spectrometer with thermal instabilities

Complex domain calibration is an efficient method to correct the amplitude and phase of a spectrum obtained from a Fourier transform spectrometer. This method is, however, not directly applicable in the occurrence of a zero path difference (ZPD) shift between a scene interferogram and calibration blackbody interferograms. This situation is likely to happen for a system with thermal instabilities. It is found that a ZPD shift smaller than 1 sampling point can cause a large disagreement between the spectra evaluated from the two interferometer sweep directions. We have developed an algorithm for a complex calibration in the presence of ZPD shifts. The restricting aspect of the real-time capability is taken into account.

Reflectivity and optical surface height requirements in a broadband coronagraph 1Contrast floor due to controllable spatial frequencies

We derive the broadband contrast floor in a coronagraphic telescope having nonideal optical surfaces. We consider only fundamental spatial frequencies within the control bandwidth of the coronagraph's deformable mirror. Cross terms arising from the beating of spatial frequencies beyond the deformable mirror control bandwidth will be considered in a second paper. Two wavefront control systems are analyzed:a zero-path difference Michelson interferometer with two deformable mirrors at a pupil image, and a sequential pair of deformable mirrors with one placed at a pupil image. We derive requirements on optical surface figure and reflectivity uniformity for both cases.

Determining large step heights using zero-order interference fringe identification and an external cavity diode laser

Zero-order interference fringe identification is a powerful tool for measuring large step heights. In contrast to white light scanning interferometry, this study utilizes an external cavity diode laser as the light source. The zero-path difference point can be accurately identified by combining wavelength scanning interferometry, in which the laser wavelength is continuously changed, with single wavelength interferometry, in which the laser wavelength is fixed. The experimental apparatus is a two-arm interferometer containing the sample in the measurement arm. The step height denotes the distance between two locations of a zero-order interference fringe, which are obtained by continuously varying the length of the reference arm. The accuracy of a sample of 10mm step height was found to be 0.33μm.