Mid-infrared (mid-IR) light scatters much less than shorter wavelengths, allowing greatly enhanced penetration depths for optical imaging techniques such as optical coherence tomography (OCT). However, both detection and broadband sources in the mid-IR are technologically challenging. Interfering entangled photons in a nonlinear interferometer enables sensing with undetected photons, making mid-IR sources and detectors obsolete. Here we implement mid-IR frequency-domain OCT based on ultra-broadband entangled photon pairs spanning from 3.3 to 4.3 µm. We demonstrate 10 µm axial and 20 µm lateral resolution 2D and 3D imaging of strongly scattering ceramic and paint samples. By intrinsically being limited only by shot noise, we observe times more sensitivity per integration time and power of the probe light. Together with the vastly reduced footprint and technical complexity, our technique can outperform conventional approaches with classical mid-IR light sources.

The only quadrature operator of order two on L₂(ℝ²) which covaries with orthogonal transforms, in particular rotations is (up to the sign) the Riesz transform. This property was used for the construction of monogenic wavelets and curvelets. Recently, shearlets were applied for various signal processing tasks. Unfortunately, the Riesz transform does not correspond with the shear operation. In this paper, we propose a novel quadrature operator called linearized Riesz transform which is related to the shear operator. We prove properties of this transform and analyze its performance vs. the usual Riesz transform numerically. Furthermore, we demonstrate the relation between the corresponding optical filters. Based on the linearized Riesz transform we introduce finite discrete quasi-monogenic shearlets and prove that they form a tight frame. Numerical experiments show the good fit of the directional information given by the shearlets and the orientation obtained from the quasi-monogenic shearlet coefficients. Finally, we provide experiments on the directional analysis of textures using our quasi-monogenic shearlets.

Optical coherence tomography (OCT) is a high-resolution three-dimensional imaging technique that enables nondestructive measurements of surface and subsurface microstructures. Recent developments of OCT operating in the mid-infrared (MIR) range (around 4 µm) lifted fundamental scattering limitations and initiated applied material research in formerly inaccessible fields. The MIR spectral region, however, is also of great interest for spectroscopy and hyperspectral imaging, which allow highly selective and sensitive chemical studies of materials. In this contribution, we introduce an OCT system (dual-band, central wavelengths of 2 µm and 4 µm) combined with MIR spectroscopy that is implemented as a raster scanning chemical imaging modality. The fully integrated and cost-effective optical instrument is based on a single supercontinuum laser source (emission spectrum spanning from 1.1 µm to 4.4 µm). Capabilities of the in situ correlative measurements are experimentally demonstrated by obtaining complex multidimensional material data, comprising morphological and chemical information, from a multilayered composite ceramic-polymer specimen.

We report on a technically simple approach to achieve high-resolution and high-sensitivity Fourier-domain optical coherence tomography (OCT) imaging in the mid-infrared (mid-IR) range. The proposed OCT system employs an I n F 3 supercontinuum source. A specially designed dispersive scanning spectrometer based on a single InAsSb point detector is employed for detection. The spectrometer enables structural OCT imaging in the spectral range from 3140 nm to 4190 nm with a characteristic sensitivity of over 80 dB and an axial resolution below 8 µ m . The capabilities of the system are demonstrated for imaging of porous ceramic samples and transition-stage green parts fabricated using an emerging method of lithography-based ceramic manufacturing. Additionally, we demonstrate the performance and flexibility of the system by OCT imaging using an inexpensive low-power (average power of 16 mW above 3 µ m wavelength) mid-IR supercontinuum source.