Disclosed is a method for determining an phase spectrum θ(ω) of the complex spectral transfer function H(ω) of a medium. In some embodiments, the method is applied for detecting or imaging an object screened by scattering medium or for determining a refractive index spectrum of a material.

Methods and devices for analyzing material properties and detecting objects in scattering media

The Kramers-Kronig (KK) algorithm, useful for retrieving the phase of a spectrum based on the known spectral amplitude, is applied to reconstruct the impulse response of a diffusive medium. It is demonstrated by a simulation of a 1D scattering medium with realistic parameters that its impulse response can be generated from the KK method with high accuracy.

Reconstructing the impulse response of a diffusive medium with the Kramers-Kronig relations

Phase retrieval is one of the classical problems in various fields of physics including x-ray crystallography, astronomy and spectroscopy It arises when only an amplitude measurement on electric field can be made while both amplitude and phase of the field are needed for obtaining the desired material properties In optical and terahertz spectroscopies, in particular, phase retrieval is a one-dimensional problem, which is considered as unsolvable in general Nevertheless, an approach utilizing the maximum entropy principle has proven to be a feasible tool in various applications of optical, both linear and nonlinear, as well as in terahertz spectroscopies, where the one-dimensional phase retrieval problem arises In this review, we focus on phase retrieval using the maximum entropy method in various spectroscopic applications We review the theory behind the method and illustrate through examples why and how the method works, as well as discuss its limitations

https://iopscience.iop.org/article/10.1088/0034-4885/76/6/066401/pdf

Optical and terahertz spectra analysis by the maximum entropy method.

We measure the sub-picosecond optical impulse response of a system consisting of a varying 1D diffusive medium and a stationary hidden object. It is shown that by averaging the temporal optical field response of a diffusive medium (as opposed to the optical intensity response) the signal-to-noise ratio of the object’s reflection can be improved considerably. The Spectral-Ballistic-Imaging technique is used to reconstruct the optical-field impulse response with a 200fs temporal resolution.

Quasi-ballistic imaging through a dynamic scattering medium with optical-field averaging using Spectral-Ballistic-Imaging

Optical impulse-response characterization of diffusive media can be of importance in various applications, among them optical imaging in the security and medical fields. We present results of an experimental technique that we developed for acquiring the impulse response, based upon the Kramers–Kronig algorithm, and have been applied for optical imaging of objects hidden behind clothing. We demonstrate three-dimensional imaging with 5mm depth resolution between diffusive layers.

/pdf/optical-imaging-of-hidden-objects-behind-clothing-363hfb0m1w.pdf

Optical imaging of hidden objects behind clothing

We use the spectral ballistic imaging technique to measure the impulse response of a Fabry–Perot etalon with less than 0.2 ps temporal resolution. The results show excellent agreement with the theoretical predictions and negligible noise. Comparison to the Kramers–Kronig method along with its limitations is also presented.

200 femtosecond impulse response of a Fabry–Pérot etalon with the spectral ballistic imaging technique

We apply the multiply subtractive Kramers-Kronig (MSKK) method to the derivative of a medium's optical transfer function. That is, the phase “difference” or derivative Δθ (instead of the phase) can be evaluated from the measurements of the relative derivative of the intensity Δln[I(ω)]=ΔI(ω)/I(ω) with the aid of a few Δθ measurements. As a result, we obtain a method that integrates two different techniques, MSKK and spectral ballistic imaging. We show that the transfer function can be evaluated with great accuracy without the need to measure the phases at all but rather its derivative, which is a much simpler process.

Differential multiply subtractive Kramers-Kronig relations

The differential multiply subtractive Kramers-Kronig (DMSKK) method is utilized for deriving the optical spectral response of a 1D scattering medium The technique is based on the multiply subtractive Kramers-Kronig technique, where the phase spectrum is reconstructed from the amplitude spectrum in a finite spectral range with the aid of one or more phase-anchoring values We employ a new phase-anchoring technique in the DMSKK method to partially mitigate the finite-range effects This method incorporates spectral ballistic imaging to anchor the phase difference (instead of the phase directly) at one or more reference wavelengths The simplicity of phase derivative measurements and its utilization in the DMSKK method are emphasized by a simple experiment

Yossi Ben-Aderet

Papers

200 femtosecond impulse response of a Fabry–Pérot etalon with the spectral ballistic imaging technique

Quasi-ballistic imaging through a dynamic scattering medium with optical-field averaging using Spectral-Ballistic-Imaging

Optical imaging of hidden objects behind clothing

Differential multiply subtractive Kramers-Kronig relations

Spectral analysis of a one-dimensional scattering medium with the differential multiply subtractive Kramers-Kronig method