Biomedical Applications of Terahertz Spectroscopy and Imaging.

Terahertz (THz) science and technology have greatly progressed over the past two decades to a point where the THz region of the electromagnetic spectrum is now a mature research area with many fundamental and practical applications. Furthermore, THz imaging is positioned to play a key role in many industrial applications, as THz technology is steadily shifting from university-grade instrumentation to commercial systems. In this context, the objective of this review is to discuss recent advances in THz imaging with an emphasis on the modalities that could enable real-time high-resolution imaging. To this end, we first discuss several key imaging modalities developed over the years: THz transmission, reflection, and conductivity imaging; THz pulsed imaging; THz computed tomography; and THz near-field imaging. Then, we discuss several enabling technologies for real-time THz imaging within the time-domain spectroscopy paradigm: fast optical delay lines, photoconductive antenna arrays, and electro-optic sampling with cameras. Next, we discuss the advances in THz cameras, particularly THz thermal cameras and THz field-effect transistor cameras. Finally, we overview the most recent techniques that enable fast THz imaging with single-pixel detectors: mechanical beam-steering, compressive sensing, spectral encoding, and fast Fourier optics. We believe that this critical and comprehensive review of enabling hardware, instrumentation, algorithms, and potential applications in real-time high-resolution THz imaging can serve a diverse community of fundamental and applied scientists.

Toward real-time terahertz imaging

The human body absorbs and loses heat largely through infrared radiation centering around a wavelength of 10 micrometers. However, neither our skin nor the textiles that make up clothing are capable of dynamically controlling this optical channel for thermal management. By coating triacetate-cellulose bimorph fibers with a thin layer of carbon nanotubes, we effectively modulated the infrared radiation by more than 35% as the relative humidity of the underlying skin changed. Both experiments and modeling suggest that this dynamic infrared gating effect mainly arises from distance-dependent electromagnetic coupling between neighboring coated fibers in the textile yarns. This effect opens a pathway for developing wearable localized thermal management systems that are autonomous and self-powered, as well as expanding our ability to adapt to demanding environments.

Dynamic gating of infrared radiation in a textile.

Traditional terahertz (THz) equipment faces major obstacles in providing the system cost and compactness necessary for widespread deployment of THz applications. Because of this, the field of THz integrated circuit (THz IC) design in CMOS and SiGe HBT technologies has surged in the last decade. An interplay of advances in silicon process technology, design technique, and microelectronic packaging promises to narrow the gap between the requirements and the reality of system cost and performance of THz components. Furthermore, the scalability, reconfigurability, and signal processing features of silicon technology have initiated research in complex THz ICs that expand the functionality of THz systems; this has enabled new applications, methods, and algorithms. This paper reviews the progress in THz IC research and investigates several realizations of THz imaging and sensing applications with silicon-based components regarding their motivation, system performance, and challenges. THz computed tomography, broadband multicolor imaging, high-resolution FMCW radar imaging, subwavelength resolution near-field imaging, and compressed sensing are presented.

Terahertz Imaging and Sensing Applications With Silicon-Based Technologies

Preface Prologue: The Exponential Function Chapter 1: Abstract Integration Set-theoretic notations and terminology The concept of measurability Simple functions Elementary properties of measures Arithmetic in [0, ] Integration of positive functions Integration of complex functions The role played by sets of measure zero Exercises Chapter 2: Positive Borel Measures Vector spaces Topological preliminaries The Riesz representation theorem Regularity properties of Borel measures Lebesgue measure Continuity properties of measurable functions Exercises Chapter 3: Lp-Spaces Convex functions and inequalities The Lp-spaces Approximation by continuous functions Exercises Chapter 4: Elementary Hilbert Space Theory Inner products and linear functionals Orthonormal sets Trigonometric series Exercises Chapter 5: Examples of Banach Space Techniques Banach spaces Consequences of Baire's theorem Fourier series of continuous functions Fourier coefficients of L1-functions The Hahn-Banach theorem An abstract approach to the Poisson integral Exercises Chapter 6: Complex Measures Total variation Absolute continuity Consequences of the Radon-Nikodym theorem Bounded linear functionals on Lp The Riesz representation theorem Exercises Chapter 7: Differentiation Derivatives of measures The fundamental theorem of Calculus Differentiable transformations Exercises Chapter 8: Integration on Product Spaces Measurability on cartesian products Product measures The Fubini theorem Completion of product measures Convolutions Distribution functions Exercises Chapter 9: Fourier Transforms Formal properties The inversion theorem The Plancherel theorem The Banach algebra L1 Exercises Chapter 10: Elementary Properties of Holomorphic Functions Complex differentiation Integration over paths The local Cauchy theorem The power series representation The open mapping theorem The global Cauchy theorem The calculus of residues Exercises Chapter 11: Harmonic Functions The Cauchy-Riemann equations The Poisson integral The mean value property Boundary behavior of Poisson integrals Representation theorems Exercises Chapter 12: The Maximum Modulus Principle Introduction The Schwarz lemma The Phragmen-Lindelof method An interpolation theorem A converse of the maximum modulus theorem Exercises Chapter 13: Approximation by Rational Functions Preparation Runge's theorem The Mittag-Leffler theorem Simply connected regions Exercises Chapter 14: Conformal Mapping Preservation of angles Linear fractional transformations Normal families The Riemann mapping theorem The class L Continuity at the boundary Conformal mapping of an annulus Exercises Chapter 15: Zeros of Holomorphic Functions Infinite Products The Weierstrass factorization theorem An interpolation problem Jensen's formula Blaschke products The Muntz-Szas theorem Exercises Chapter 16: Analytic Continuation Regular points and singular points Continuation along curves The monodromy theorem Construction of a modular function The Picard theorem Exercises Chapter 17: Hp-Spaces Subharmonic functions The spaces Hp and N The theorem of F. and M. Riesz Factorization theorems The shift operator Conjugate functions Exercises Chapter 18: Elementary Theory of Banach Algebras Introduction The invertible elements Ideals and homomorphisms Applications Exercises Chapter 19: Holomorphic Fourier Transforms Introduction Two theorems of Paley and Wiener Quasi-analytic classes The Denjoy-Carleman theorem Exercises Chapter 20: Uniform Approximation by Polynomials Introduction Some lemmas Mergelyan's theorem Exercises Appendix: Hausdorff's Maximality Theorem Notes and Comments Bibliography List of Special Symbols Index

Real and Complex Analysis. By W. Rudin. Pp. 412. 84s. 1966. (McGraw-Hill, New York.)

Three-dimensional terahertz computed tomography has been used to investigate dried human bones such as a lumbar vertebra, a coxal bone, and a skull, with a direct comparison with standard radiography. In spite of lower spatial resolution compared with x-ray, terahertz imaging clearly discerns a compact bone from a spongy one, with strong terahertz absorption as shown by additional terahertz time-domain transmission spectroscopy.

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Three-dimensional terahertz computed tomography of human bones

A monochromatic millimeter-wave imaging system coupled with an infrared temperature sensor has been used to investigate historic objects preserved at the Museum of Aquitaine (France). In particular, two-dimensional and three-dimensional analyses have been performed in order to reveal the internal structure of nearly 3500-year-old sealed Egyptian jars.

/pdf/terahertz-tomographic-imaging-of-xviiith-dynasty-egyptian-2nn6f85etz.pdf

Terahertz tomographic imaging of XVIIIth Dynasty Egyptian sealed pottery

Recent advances for the measurement of TeraHertz (THz) radiation by using original IR temperature flux sensors are presented. The bolometer principle is used for designing simple thermal converters for THz radiations (measurement of the temperature increase of a sensitive absorber). Most of these sensors are efficient, sensitive and fast enough for quantitative measurement of THz source power as well as for 2D and 3D THz imaging. By combining optical and thermal technologies, we extend and adapt the use of thermal sensors to large THz wavelength till 3 mm (0.1 THz). A large variety of mono- or arrayed- thermal sensors is used and optimized for real-time room temperature THz imaging using adapted IR focal-plane microbolometers array (FPMA) camera. Optimisation and adaptation of such FPMA is discussed and a new arrayed prototype device of THz-Thermal Converter, “TTC”, for full-field real-time THz imaging is presented. This small size, low cost and efficient prototype design is discussed from the thermal poi...

Photothermal converters for quantitative 2D and 3D real-time TeraHertz imaging

https://hal.archives-ouvertes.fr/hal-00731822/document

Advantage of terahertz radiation versus X-ray to detect hidden organic materials in sealed vessels

We retrieve the complex optical index of single-walled carbon nanotube (CNT) films in the 0.6–800 μm spectral range. Results are obtained from a complete set of optical measurements, reflection and transmission, of free-standing CNT films using time domain spectroscopy in the terahertz (THz) and Fourier transform infrared (IR) spectroscopy in the visible–IR. Based on a Drude–Lorentz model, our results reveal a global metallic behavior of the films in the IR, and confirm their high optical index in the THz range.

Bruno Chassagne

Papers

Three-dimensional terahertz computed tomography of human bones

Terahertz tomographic imaging of XVIIIth Dynasty Egyptian sealed pottery

Photothermal converters for quantitative 2D and 3D real-time TeraHertz imaging

Advantage of terahertz radiation versus X-ray to detect hidden organic materials in sealed vessels

Complex optical index of single wall carbon nanotube films from the near-infrared to the terahertz spectral range.