Optics, Optoelectronics and Photonics

Summary

It can be argued that the earliest example of an optical technology being used for biological applications, in a manner relevant to today's usage, is that of the optical microscope. The word microscope comes from the Greek, wherein micron means small and skopein means to look at or to see. Beyond the simple magnifying glass, compound optical microscopes were first used to observe biological structures invisible to the naked eye in the seventeenth century. The English scientist Robert Hooke [1635–1703] described what he observed with a low-power (∼40×) microscope in a popular book called Micrographia, which provided the first illustrations of a variety of biological objects, including detail of a fly's eye, and (barely resolved) plant cells. It was the Dutch scientist Anton van Leeuwenhoek [1632–1723], however, who made the first compound lenses that were of high enough quality and short enough focal length to lead to a magnification of 270×, powerful enough to be considered a true microscope, rather than a strong magnifying glass. He reported the first observations of bacteria, yeast, blood cells, and various microscopic life forms commonly found in a water droplet. Perhaps surprisingly, it took nearly another 200 years before the French chemist and microbiologist Louis Pasteur [1822–1895] was able to explain the workings of bacteria. It is also interesting to note that the microscopes commonly used today by histopathologists, to examine the cellular structure of tissues for diagnosing disease, do not exhibit dramatically better optical performance than van Leeuwenhoek's early creation.

The general field of optical microscopy is too large to be covered in one chapter, and numerous excellent resources are available to provide ample detail about the optical design and common configurations of “traditional” optical microscopes, including many general textbooks on optics. Some of these are listed under further reading at the end of this chapter. In Section 17.1 we provide an abbreviated review of the basics of traditional microscopy, because these core elements are also found as parts of modern developments in the field, especially those applied to biomedical imaging. Beyond the classical configuration, a variety of more recent inventions in types of microscopy and microscopes offer images with a range of information content and/or resolution beyond the traditional limits. Not all of these are optical microscopes, but many are, and in the subsequent sections of the chapter we introduce some of the important advances in non-traditional optical microscopy.

Summary

When people are in a nightclub with “black light” illumination, one can often observe various articles of clothing that “glow in the dark.” What is happening is that the “black light” is illuminating at near-ultraviolet wavelengths (a broad range around 350 nm), and various dyes in the clothing absorb UV light and remit light (fluoresce) at longer (visible) wavelengths. (This includes dyes from laundry detergent intended to make your clothes “brighter than white”!) Your eyes do not see most of the UV wavelengths, and the nightclub room is otherwise rather dark, so strongly fluorescent dyes, which are often called fluorophores, stand out dramatically. What you cannot see is that people's skin is also fluorescent, albeit much more weakly.

A variety of endogenous (naturally occurring in the body) molecules in tissue exhibit some degree of fluorescence. By spectroscopically measuring, or by imaging, the fluorescence emission from tissue, one can obtain information about the constituents that are present in the tissue, which can serve as valuable diagnostic information. Alternatively, an exogenous (not naturally occurring in the body) fluorophore can be formulated, or conjugated with targeting moieties, such that it will bind preferentially to certain tissue types, or to cells with a specific disease state. In that case, if the fluorophore is administered, it can serve as a tissue-selective “optical reporter.” Of course, for human use such a compound would be treated as a new drug, requiring FDA approval, following extensive testing to demonstrate safety and efficacy.

One of the major advantages of fluorescence measurements is that they are essentially “background-free” measurements, meaning that there is typically no fluorescence emission unless the molecules are illuminated with shorter-wavelength excitation light, which is readily filtered out at detection. This dark-background type of measurement enables sensing of fluorophores at exceedingly small concentrations, as small as femtomolar, or even at a single-molecule level. Although such measurements are always more complicated in living tissue, a variety of sensing and diagnostic applications in biomedical optics are based on fluorescence detection or imaging.

Fluorescence emission relevant to measurements in biological systems

Why is the wavelength of fluorescence emission from biomolecules almost always longer than that of the excitation light?

Summary

In Chapter 11, we considered time-domain methods as one form of time-resolved tissue spectroscopy that is based on pulsed illumination. In this chapter, we consider an alternative type of time-resolved spectroscopy that operates in the frequency space by employing temporally modulated illumination. While these two variations of time-resolved spectroscopy are mathematically equivalent, being related by Fourier transformation, they invoke different concepts, instrumentation, and methods of data collection. The conceptual and theoretical frameworks of frequency-domain spectroscopy are described and developed in this chapter. Experimental and instrumentation aspects of frequency-domain spectroscopy are presented in Chapter 13 (Section 13.4.2).

Basic concepts of frequency-domain tissue spectroscopy

In frequency-domain diffuse spectroscopy of tissue, the optical power incident from the light source is temporally modulated at a sinusoidal angular frequency, and phase-resolved detection yields the amplitude and phase of the resulting fluence rate or flux measured in the scattering medium. The source power, and the fluence rate at any point, are both modulated about an average value. By applying the nomenclature of electrical direct current (DC) and alternating current (AC) to indicate the average value and the amplitude of the modulated component of the optical power, respectively, the modulation depth (or, simply, modulation) (m) is defined as the AC/DC ratio. The modulation is a measure of the amplitude of the oscillations normalized to their average value, and as such is a dimensionless quantity that represents the relative depth of optical oscillations.

This approach can be thought of as analogous to the modulation and carrier frequencies of an amplitude modulation (AM) radio signal, with a difference that the carrier signal is at zero frequency in the case of frequency-domain optical spectroscopy. Given that the optical power and the fluence rate are always positive, the modulation is bounded between 0 and 1 (0 ≤ m ≤ 1). There is, therefore, a fundamental difference between alternating electrical current, which is bipolar, thereby oscillating between positive and negative values, and modulated optical power and fluence rate, which oscillates about an average value, remaining always positive. The average value, or DC component, corresponds to the time-independent optical power and fluence rate considered in Chapter 10 for continuous-wave (CW) spectroscopy. The oscillating optical signal, or AC component, at angular frequency ω is related to the time-domain optical signal of Chapter 11 through a temporal Fourier transform.

Summary

The information content of the optical signals collected with continuous-wave (CW) methods is restricted by the constant intensity. In non-scattering media, the optical properties are fully characterized by one parameter, the absorption coefficient, which can be determined by application of the Beer-Lambert law (Eqs. (2.8) and (10.11)). In scattering media, which are described by two optical coefficients (the absorption and scattering coefficients) and by the scattering phase function, the information content of CW methods (measured at a single location and a single wavelength) is insufficient for a full optical characterization of the material. Even in the diffusion-approximation regime, where the details of the scattering phase function are not relevant, since it is only the average cosine of the scattering angle (g = ⟨cos θ⟩) that matters, and where two parameters (the absorption and the reduced scattering coefficient) fully characterize the medium, a single measured quantity, the constant intensity, provides limited information content. Such information content may be enriched by measuring the continuous-wave intensity under different conditions (e.g., multiple angles in the non-diffusive regime, or multiple distances from a point source, or multiple wavelengths of light, or multiple spatial frequencies of structured illumination, etc.), and this may provide valuable additional information for a more complete optical characterization of the medium.

Time-resolved methods, however, in which the detected optical signal is not constant in time, provide additional information related to the distribution of the optical pathlengths in scattering media, which is not accessible to CW methods. Time-resolved methods are typically implemented either in the time domain, with a pulsed light source and time-resolved detection, or in the frequency domain, with an intensity-modulated light source and phase-sensitive detection. Theoretical and general concepts for time-domain methods are described in this chapter, whereas frequency-domain methods are described in Chapter 12. Experimental and instrumentation aspects of time-domain spectroscopy are presented in Chapter 13 (Section 13.4.1). The reader will note that the index of refraction (n) has not been mentioned above in the description of the optical quantities that characterize a scattering medium. The reason is that for light propagation in scattering media, the index of refraction only plays the role of scaling the speed of light in the medium, since cn = c/n.

Summary

In Chapter 5 we reviewed methods of fluorescence spectroscopy and fluorescence measurements related to bioscience applications that enable monitoring of cellular metabolism, drug distribution, enzymatic processes, etc. In Chapter 6 we covered methods for spectroscopy of vibrational modes, which can yield diagnostic information by identification of the molecular “fingerprints” of biomolecules. These methods are powerful, and they predominantly provide information on the biochemistry of cells and tissue. Nonetheless, when considering potential clinical diagnostic applications, one might ask, “How does a pathologist diagnose cancer, when looking at a histology slide under a microscope?” After all, the pathologist is using an optical detector/camera (the human eye) to examine light coming from a sample of tissue through an optical instrument (the microscope). The term histology (from Greek: histos = tissue; logia = science or study) refers to the study of the microscopic structure of cells and tissue. Thus, the traditional practice of histopathology (the microscopic study of diseased tissue, usually for the purpose of diagnosis), which has been around for more than 120 years, may be regarded as one of the earliest techniques of biomedical optics to be put into practice.

In the common practice of histopathology, a small tissue sample is surgically cut from the organ where disease is suspected in a patient, a procedure called biopsy, and the sample is examined microscopically as part of the clinical diagnosis process. The biopsy sample is first fixed in formalin, which dehydrates it. It is then embedded in paraffin (for mechanical stability), and a very thin (typically 3–10 μm) slice is cut with a microtome and placed on a microscope slide. The thin slice is typically stained, most commonly with hematoxylin and eosin stains (when combined, called H&E stain), which stain for DNA (hence, nuclei) and other dense structures, mostly proteins. It is interesting to note that without such staining, very little cellular structure is visible in conventional bright-field microscopy, due to lack of contrast.

Getting back to the question about what a pathologist looks for when reading a slide and determining a diagnosis for disease (say, cancer), most of the time the pathologist is not performing biochemical assays or conducting genetic analysis: most of the time the pathologist is visually examining the cellular architecture, shapes and structures. Are the nuclei enlarged? What is the ratio of nuclear volume to cell volume? Is the nuclear staining especially dense (hyperchromatic), indicating excessive DNA?

Summary

Measurement techniques based on different physical properties can be combined in a variety of ways to result in multi-modal spectroscopy or imaging methods. One may simply apply them independently and then combine the complementary information content of their results. For example, physicians often combine the information content of X-ray tomography and magnetic resonance imaging (MRI) to provide information about both hard and soft tissues. Alternatively, one may use the results of one technique as prior information to enhance the performance of another technique. Finally, two techniques may be combined at a more fundamental level, yielding a hybrid technology in which both physical mechanisms contribute to the generation of the measured signals. In this chapter, we describe two intimately integrated hybrid imaging methods that combine optical and ultrasound techniques.

In one hybrid implementation, called acousto-optics, light and ultrasound are delivered to the tissue and their interaction results in a modulated optical signal that originates from the ultrasound focal region (which can be scanned). Such a modulated optical signal is detected at the tissue surface. This approach is also called ultrasonic tagging of light (UTL), acousto-optic tomography (AOT), or ultrasound-modulated optical tomography (UOT).

In a second hybrid implementation, short laser pulses are delivered to the tissue to generate opto-acoustic pressure perturbations as a result of the local thermal expansion/relaxation of optical absorbers within the tissue. These pressure perturbations have a frequency content in the ultrasound range (MHz to tens of MHz), which propagate to the tissue surface where they can be detected with ultrasound imaging methods. This approach is also called photoacoustic (PA) imaging (with the variants of PA tomography [PAT] and PA microscopy [PAM]) or laser optoacoustic imaging (implemented by laser optoacoustic imaging systems [LOIS]).

The two approaches, based on acousto-optics and opto-acoustics, are conceptually illustrated in Figure 16.1. This chapter first introduces general concepts of ultrasound imaging, and then describes the theory, methods, and applications of both acousto-optic and opto-acoustic approaches to the combination of light and ultrasound. These two different techniques (one based on light and one on ultrasound) are joined into integrated systems that exploit their synergistic combination at a fundamental level.

Basic concepts of ultrasound imaging

The nature of ultrasound

Sound and ultrasound are pressure waves that propagate through compressible media such as air, water, or biological tissue.

Summary

In a sense, quantitative biomedical optics methods seek to enhance and quantify the visual perception of color and brightness of light transmitted through or reflected by biological tissues. This is especially the case for diffuse optical spectroscopy and imaging, which are based on the spectral dependence, spatial distribution, and temporal characteristics of the detected optical signals.

The “color” of tissue is determined by the spectral features of its absorbing and scattering constituents, with hemoglobin playing an important role, given its abundance and the relationship between its oxygen saturation and its absorption spectrum. For example, human skin color is determined by the amount of melanin in the skin, by the hemoglobin in cutaneous circulation, and by other chromophores, such as β-carotene and bilirubin, that may be indicative of pathological conditions. The dilatation or contraction of skin arterioles (for example as a result of warm or cold environments), and the resulting enhancement or reduction in cutaneous blood flow, affects the color of the skin, which, for fair-skinned people, may tend toward white (pallor: vascular constriction), red (erythema: vascular dilatation), or blue/purple (cyanosis: inadequate blood flow). Of note, the blue appearance of superficial veins is due to a combination of the reduced level of venous blood oxygenation, the scattering properties of the skin and blood constituents, and the visual perception of color contrast (Kienle et al., 1996).

The spatial distribution of light transmission through tissue can be affected by an inhomogeneous distribution of chromophores. For example, tumor angiogenesis or hematomas are associated with a focal increase in the concentration of blood in tissue, which results in a localized increase in light absorption.

Temporal characteristics of the detected optical signal may be directly associated with time-varying and dynamic physiological processes (arterial pulsation, respiration-modulated blood pressure, blood flow, etc.), thus yielding potentially valuable diagnostic information, and can also be used to monitor the evolution of metabolic and physiological conditions or drug delivery to tissues.

This chapter describes a representative sampling of in vivo applications of diffuse tissue spectroscopy and imaging, demonstrating how the quantitative methods described in Chapters 10–14 find practical applications in a number of research and clinical areas.

Summary

In Chapter 17 we noted that conventional microscopes are ineffective at rejecting out-of-focus light, either scattered or emitted as fluorescence, and are consequently limited to imaging thin samples. We also reviewed some methods to achieve optical sectioning in microscopic imaging by spatial gating, which requires the illumination source to be spatially coherent, and, for some methods, may also require phasefront-preserving optics for the detection stage. The other general class of methods that can effect sectional imaging is based on temporal gating of back-reflected light. Conceptually, this is simple: if one can generate a very short pulse of light – a 10-fs pulse, for example, would span ∼3 μm in the axial direction – and measure precisely the arrival time of a back-reflected pulse, a time gate could (theoretically) reject light that reflects from shorter or longer distances. In principle, this is what pulse-echo ultrasound imaging achieves: an ultrasound imaging system determines the depth of imaged objects by timing the arrival of sound pulses that have reflected from discontinuities in the tissue density (or acoustic characteristic impedance) associated with structures in the body (see Section 16.1.2). Since the speed of sound (in water) is ∼1500 m/s, the timing precision needed for, say, 100 μm in axial resolution would be of the order of 100 ns, which is comfortably within the capability of common electronic timing circuitry. In Chapter 16 (Section 16.4.3), we saw that for hybrid photoacoustic imaging, the spatial (lateral) resolution of the ultrasound imaging component can approach microscopic dimensions.

In a purely optical system, however, even though ultrashort laser pulses are available, microscopic axial resolution of, say, 3 μm would require a temporal resolution for detection of the order of 10−14 s, which is far shorter than the response time of any electronic sensor. Optical methods, nonetheless, offer us ways to get around this limitation. Early approaches, in a manner conceptually analogous to the sectioning capability of second-harmonic-generation microscopy (as detailed in Section 17.4.2), invoked time gating by correlating the overlap of the sample signal with a reference signal in a nonlinear medium. For example, Fujimoto et al. (1986) first demonstrated the potential for precision “time-of-flight” ranging of distances in biological structures by use of a nonlinear-optical cross-correlation time-gate based on second-harmonic generation, with the harmonic signal separated angularly between the crossed beams from the sample and reference.

Summary

In Chapter 4 we introduced the concepts of IR-absorption spectroscopy and Raman spectroscopy in general terms. Both are methods that enable study of the vibrational modes of molecules. Here we explore these quantitatively. While IR-absorption spectroscopy is frequently used in the fields of chemistry and biochemistry, Raman spectroscopy has proven more practical for biomedical applications, especially for in vivo measurements, thanks to the absence of interference from water absorption in the visible range, and to the convenience of using fiberoptic components, which are generally not available for the mid-IR wavelengths associated with the vibrational modes that generate IR-absorption bands. (Raman scattering can also result from the interaction of light with the rotational modes of a molecule. This type of scattering, however, is not addressed here because molecular rotation is only significant in the gaseous state, whereas with tissue we are dealing with condensed matter.)

The Raman effect was discovered in 1928 by Indian physicist Sir Chandrasekhara Venkata Raman [1888–1970]. Raman's early experiments (Raman and Krishnan, 1928), conducted long before the development of lasers, utilized sunlight transmitted through a violet spectral filter as a narrowband light source. This narrowband light was directed through a transparent material being studied and then to a spectrograph, where it featured additional spectral lines, slightly red-shifted from the illumination wavelength. Raman presented his explanation of the phenomenon at a scientific conference in Bangalore, India, and received the Nobel Prize in physics, remarkably a mere two years later, in 1930.

Vibrational modes in biological molecules

The number of possible different vibrational modes in a biological molecule is truly large. Each of N atoms in a molecule has three degrees of freedom, which results in 3N possible variations of motion. The number can be reduced slightly for biomolecules in liquid or solid media (condensed matter), where we can ignore translational and rotational degrees of freedom, leading to 3N − 6 possible internal degrees of freedom, or vibrational modes. This translates to a lot of detailed spectral structure for a biological molecule, mostly in the near-IR to IR range, which is why the infrared or Raman spectra of biomolecules are sometimes referred to as spectral “fingerprints.”

A typical protein molecule may have more than 20,000 normal modes of vibration, with many overlapping in frequency. Consequently, one might fear that attempts to decipher vibrational spectra would be futile.

Summary

In the years following the demonstrations of the first working lasers in the early 1960s a flurry of speculation emerged, predicting medical applications of lasers that were both fanciful and unjustifiably optimistic. As the laser industry emerged and grew, a number of the companies opened medical laser divisions, received FDA approval for surgical lasers and began marketing them to hospitals and surgical group practices. These were generally high-power continuous lasers, often Nd:YAG lasers operating in the NIR at 1.06 μm, or their frequency-doubled version at 532 nm. Little in the way of statistically powered research had been carried out to determine whether these “laser scalpels” could actually achieve better patient results than traditional surgical tools. While some laser wavelengths, at appropriate power levels, can indeed achieve improved degrees of hemostasis (stoppage of bleeding), this can also be accomplished with an electrically heated scalpel blade, which cauterizes as it cuts, and at much lower cost. The introduction of a new technology is at its best when it enables a process or procedure that cannot be accomplished by other means, or that accomplishes the objective more efficaciously or at lower cost. This was not always the case in those early days of medical lasers, and within a few years many hospitals had large, expensive laser systems gathering dust in closets.

One example of an application that originally inspired optimism but has fallen out of favor is laser angioplasty: the use of high-power pulsed lasers to ablate atherosclerotic blockages, thereby restoring blood flow in coronary arteries. Initial studies in the 1980s indicated that acute response was promising, with immediately restored blood flow. Restenosis was found to occur within months, however, in almost all cases, often with blockages worse than the pre-procedure condition (Sanborn, 1996). It was eventually determined that the new blockage was a result of the local infiltration (and proliferation) of smooth muscle cells, released due to the absence of the protective endothelium (the layer of cells that line the inner surface of blood vessels), which of course was also ablated while removing the plaque (Köster et al., 2002).

Low-power lasers, however, have facilitated novel methodologies in re-search for cellular biology, with an explosion of applications enabled by the development of optical tweezers, which offer precision manipulation of particle location and measurement of piconewton forces.

Summary

Optical measurements on biological tissues require four major components: a light source, a means to deliver light to and from the investigated tissue, an optical detector, and a method to process the signals generated by the optical detectors. In this chapter, we build upon the general description of spectroscopy instrumentation in Section 4.7, and we add detail about all four components as applicable to systems devoted to diffuse optical measurements on biological tissue. We also depict typical configurations of time-resolved instrumentation in the time domain and frequency domain. Additionally, we address the safe limits of skin exposure to light, which ultimately set the maximum levels of radiant exposure or optical intensity that can be delivered to tissue and still be considered noninvasive for diagnostic applications. (In Chapter 19, we will consider higher exposure levels, which may be encountered with therapeutic applications.)

Light sources

Relevant properties of light sources for diffuse optical spectroscopy

Optical spectroscopy in the diffusion regime does not involve specific requirements for the illumination source in terms of its coherence (except for diffuse correlation spectroscopy, as discussed in Section 8.9.1), polarization, directionality, and bandwidth. In fact, polarization and directionality of the incident light are quickly lost, as multiple scattering events result in a distribution of photon paths, and randomize the photon polarization and direction of propagation. Coherence (to be discussed extensively in Chapter 18) is reduced by virtue of the range of optical pathlengths between the source and a detection point. Additionally, the broad spectral features typically associated with absorption and scattering of biological tissue do not translate into stringent spectral resolution requirements, so that highly monochromatic illumination is usually not required. The relevant properties of light illumination for optical tissue spectroscopy in the diffusion regime are mostly:

Summary

Diffuse optical spectroscopy (DOS) is applied to the local measurement of the optical properties of scattering media, whereas diffuse optical imaging (DOI) and diffuse optical tomography (DOT) are used to characterize or image the spatial distribution of the properties. These methods can be converged into powerful spectral imaging measurements that combine information on the wavelength dependence of the optical properties of the scattering medium (which are relevant for the characterization of its composition and microscopic scattering properties) and on their spatial dependence (which provides localization of regions of interest and indications on large-scale organization). A quantitative description of the volume probed by an interrogating optical signal in a scattering medium is significant for both spectroscopy and imaging measurements. In spectroscopy (localized measurements) it specifies the sampled region, whereas in imaging (spatially resolved measurements) it gives information on the spatial resolution. Such a quantitative description, leading to the definition of a region of sensitivity in the scattering medium, is presented in detail in this chapter.

There are numerous methods for diffuse optical imaging, ranging from straightforward backprojection and optical topography (i.e., 2D projections from diffuse reflectance data) to more complex linear and nonlinear image reconstruction schemes. Some of these methods (for example topography and backprojection) directly translate the measured optical data into an image of the investigated tissue. Other methods (such as linear image reconstruction approaches) translate the imaging problem into an algebraic matrix inversion that can be performed with numerical methods. The most powerful tomographic approaches are nonlinear iterative techniques that make use of forward solvers to calculate the optical signals that correspond to a given spatial distribution of the tissue optical properties. An initial estimate of a spatial distribution is iteratively updated until its associated optical signals match, to within a given tolerance level, the measured optical signals and constitute the desired reconstructed optical image.

These imaging methods have their relative strengths and weaknesses, and are subject to different trade-offs among robustness, simplicity, power, and accuracy. Our goal in this chapter is to describe the basic principles and quantitative methods for diffuse optical imaging techniques that are frequently used in the study of biological tissues.

Summary

Biological tissues are strongly heterogeneous media, with spatial inhomogeneities occurring on length scales ranging from nanometers (structural proteins), to hundreds of nanometers (cellular organelles), to tens of microns (cells), all the way to millimeters and centimeters (at tissue and organ levels). These inhomogeneities are associated with spatial gradients and discontinuities in physical properties that play key roles in determining the optical properties of tissues, which govern how light propagates within tissues. For example, a discontinuity in the refractive index at a plane or interface causes reflection and refraction of light, whereas, as discussed in Chapters 7 and 8, localized optical inhomogeneities associated with particles result in light scattering, with a wavelength dependence and an angular distribution that depend on the shapes and refractive indices of particles and their sizes relative to the wavelength of light. Further, as described in Chapter 2, a number of molecules found in tissues (e.g., aromatic amino acids, melanin, bilirubin, rhodopsin, hemoglobin, cytochrome c, water, etc.) absorb light with spectral extinction coefficients that determine their wavelength-dependent absorption efficiency. Whereas Chapter 7 developed the theories that describe scattering from single particles, and Chapter 8 described treatment of light transport between a source and detector separated by only a few optical mean free paths, this chapter addresses the diffuse field, for which source and detector are separated by a distance large compared to the mean free path for scattering.

When considering the transport of light in bulk turbid media, it is frequently easier, conceptually, to invoke the particle representation rather than the wave nature of light. (See Section 4.7.1.) In the particle-like description of light propagation as a flow of photons, one may describe the effects of spatial heterogeneities and absorbing molecules in terms of deflections and annihilations, respectively, of traveling photons. This means that the tissue can be seen as a collection of scattering and absorbing centers that interact with photons randomly but according to quantitative rules that specify the probability of interaction and the way in which the tissue constituents deflect or absorb the incident photons. This is conceptually no different than a flow of metal balls in a pinball machine with posts (scattering centers) and holes (absorbing centers).

Summary

Many of the concepts and technologies of biomedical optics, as introduced in this text, are intended as novel, and often minimally invasive, diagnostic methods that are capable of measuring or sensing a variety of physiological parameters. To facilitate understanding the value of novel diagnostics, we introduce here some of the statistical concepts that are most commonly used to assess the reliability of a diagnostic test. As such, we are limiting discussion to a narrow range of the statistical issues in medicine. Among a substantial number of other classes of statistical analysis are: verification that one treatment is superior to another (or to placebo); determining dosage equivalence of two treatments; estimating the mean value of a physiological parameter in a population; measuring the prevalence of a disease in a sample population (for example, to determine whether the disease prevalence is growing); estimating the prevalence of a condition in the general population based on measurements in a sample of the population. All of these require determinations of statistical significance, often invoking measures such as paired and unpaired “t-tests” and “p-values,” and each type of assessment has different criteria, but those considerations are outside the scope of this chapter.

When developing a new diagnostic method or medical test it is always necessary to determine how well the method works by statistical methods. Why? Let us pose a very simple, non-medical problem (and not related to diagnosis). Imagine you have a friend who lives in a small town that recently installed its first traffic light at a central intersection, which was previously controlled by four-way stop signs. After two years the mayor announces that the accident rate at that intersection was lower in 2013 than it had been in 2012. Consequently, the mayor's office is asking the Town Council to raise taxes so that they can install five more traffic lights at other intersections. At a Town Council meeting a concerned citizen asks for the numbers: how many accidents have there been in those two years? The mayor, who wants to take credit for the improvement, is quick to respond that there were 42 accidents in 2012 and “only” 37 in 2013, a 12% drop. He claims that this is “significant” and that he expects the improvement to continue. Economic times are tough, however, so installation of more lights is delayed a couple of years.

Summary

In Chapter 9 (Section 9.5), we derived the diffusion equation for spatially uniform turbid media (Eq. (9.38)). If one is interested in measuring an average tissue property (say, the average hemoglobin concentration in muscle tissue, or the average hemoglobin saturation over a certain cerebral cortical volume), then Eq. (9.38) may provide a suitable analytical approach, within the limits of the assumption that the investigated tissue is spatially homogeneous. Of course, strictly speaking, this assumption is not correct, since biological tissues are not spatially homogeneous. At a microscopic level, it is the very presence of molecular species, intracellular organelles, and cellular structures that ultimately accounts for the absorption and scattering of light in tissues. However, these tissue inhomogeneities occur over spatial scales of microns (cellular structures), sub-microns (cellular organelles), and nanometers (structural proteins, organelle ultrastructure, biological macromolecules, etc.) that are not directly relevant to the macroscopic treatment of the absorption coefficient, diffusion coefficient, and optical energy density distribution that are considered by diffusion theory. By contrast, the presence of a macroscopic spatial heterogeneity in tissues, associated, say, with the skin and subcutaneous layers, bones, larger blood vessels, tendons, and multiple tissue types within the optically probed volume, may raise questions about the applicability of a model that assumes the spatial homogeneity of tissue.

In this chapter, we identify the length scale that is relevant in diffusion theory; in other words, the typical diffusion length that one should consider in comparison with the length scale over which the tissue optical properties vary. This chapter also derives expressions for the continuous-wave diffuse reflectance under a variety of conditions, and examines its dependence on the optical properties of the medium. Diffuse optical spectroscopy (principles described in Chapters 10–12 and experimental methods in Chapter 13) places an emphasis on the overall optical properties of the examined biological tissue, from which some relevant physiological or diagnostic parameters can be extracted. Diffuse optical imaging (described in Chapter 14), instead, places an emphasis on the spatial distribution of the optical properties of tissue at a macroscopic scale and is relevant in the detection of localized abnormalities (tumors, hemorrhagic or ischemic lesions, fluid-filled cysts, etc.) or focal events (targeted brain activation, localized hemodynamic responses, etc.). This chapter is devoted to continuous-wave methods for tissue spectroscopy, where the emission of the light source is constant; i.e., it is not time-varying.

Summary

Is a rose a rose? To crudely paraphrase Shakespeare, “What's in a name?” Can the same flower be described and characterized differently when viewed from different perspectives? Different scientific and technical fields tend to develop variations of the nomenclature for the same physical quantities. Within each field there is generally a degree of consistency, but interdisciplinary topics that bring together scientists, engineers, and practitioners from disparate fields often face inconsistencies in the symbols, units, and terminology utilized for quantitative analysis. The field of biomedical optics has not been immune to this problem, and publications in the field have invoked a variety of terms and symbols. In some cases, the same terms and symbols, as used in different fields, carry subtle but crucial differences in their meanings. An important example is the different meaning of the term intensity in physics (power per unit area), in radiometry (power per unit solid angle), and in heat transfer (power per unit area, per unit solid angle). Another example is that of the molar extinction coefficient for optical absorption of hemoglobin, which is typically defined using the logarithm to base-10 in chemistry and biology, or to base-e in physics, and may refer to one functional heme group or to the full molecule (four heme groups), depending on the specific physiological or biochemical characterizations. This may lead to a mismatch by as much as a factor of 9.2 (i.e., 4 × ln (10)) among the numerical values reported for the molar extinction coefficient of hemoglobin according to different conventions. For a long time, the three fields that most commonly make use of and describe (and teach) the methods of quantitative optical measurements have been physics, astronomy, and electrical engineering (or its subfield, optical engineering), although chemistry and biology also make use of optical characterization techniques. Because biomedical optics is a broad interdisciplinary field, which is based on contributions from researchers in a variety of specialty areas, it is important that a common language be used to describe and characterize its key quantitative parameters.

In this chapter, we define the nomenclature used in this book for the quantities that describe the optical radiation field and its interaction with biological tissue.

Optics, Optoelectronics and Photonics

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