Understanding Focal Length and Field of View - define focal distance

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Figure 15. Birefringent materials, such as the common mineral calcite, split unpolarized beams of light into two. The ordinary ray behaves as expected, but the extraordinary ray does not obey Snell’s law.

Raman spectroscopyprinciple

(a) 2D-CARS single-shot spectra recorded in pure N2 at room temperature. In the second row of 2D spectra, the center structure of the mask is removed to provide a defined 2D imaging field. (b) Recorded spectra in pure N2 and N2 in a mixture with O2 (Air), detected with a larger dispersion, are shown to indicate the potential for separately analyzing the 2D spatial field in mixtures of species. A vector diagram is used to orientate each spatial location of the measured 2D field. The image consists of ∼125 × 120 pixels which give about 15 000 spectra provided by a single-laser-shot.

Find Polaroid sunglasses and rotate one while holding the other still and look at different surfaces and objects. Explain your observations. What is the difference in angle from when you see a maximum intensity to when you see a minimum intensity? Find a reflective glass surface and do the same. At what angle does the glass need to be oriented to give minimum glare?

Figure 13. Optical activity is the ability of some substances to rotate the plane of polarization of light passing through them. The rotation is detected with a polarizing filter or analyzer.

Many crystals and solutions rotate the plane of polarization of light passing through them. Such substances are said to be optically active. Examples include sugar water, insulin, and collagen (see Figure 13). In addition to depending on the type of substance, the amount and direction of rotation depends on a number of factors. Among these is the concentration of the substance, the distance the light travels through it, and the wavelength of light. Optical activity is due to the asymmetric shape of molecules in the substance, such as being helical. Measurements of the rotation of polarized light passing through substances can thus be used to measure concentrations, a standard technique for sugars. It can also give information on the shapes of molecules, such as proteins, and factors that affect their shapes, such as temperature and pH.

Anti stokes raman spectroscopyprinciple

Figure 10. Artist’s conception of an electron in a long molecule oscillating parallel to the molecule. The oscillation of the electron absorbs energy and reduces the intensity of the component of the EM wave that is parallel to the molecule.

Single-shot 2D-CARS signals from pure N2 at 295 K in the 40-mm2 probed field, recorded with and without a mask inserted in the probe beam path, are displayed in Fig. 2(a). Note that a frequency scale is not suitable in the employed representation, instead the individual rotational Raman S-branch transitions (J → J + 2) are being indicated with rotational quantum number J. The characteristic features of the rotational spectrum of N2 are evident: equidistant lines separated by ∼4B (=8 cm−1) and the characteristic 4:1 intensity alternation between the odd and even transitions, which is related to the nuclear spin degeneracy for N2. The image quality, quantified in terms of a horizontal and vertical line-spread function, was evaluated to be ∼3.5 pixels full-width at half maximum (fwhm) in the horizontal dimension (∼56 μm) and ∼2 pixels fwhm in the vertical dimension (∼32 μm), respectively, and the total image consists of ∼125 × 120 pixels which provides about 15 000 spectra generated in a single-laser-shot. The vertical extent of the imaged field here is limited only by the choice of mask, as most of the probe beam was reflected away by the mask, and a vertical size 3 to 4 times larger is achievable with the current laser setup. The extra pixel in the width of the horizontal line-spread function is because of the convolution of the image in this dimension with the rotational spectrum. In Fig. 2(b), a mixture of 21% O2 and 79% N2 (air) at 295 K is probed, and a vector diagram is illustrated to demonstrate the principle for extracting spectral information corresponding to a spatial location in the two-dimensional field. The presented spectra have been detected with larger dispersion, achieved by increasing the focal length of the “effective” lens in the detection system, from 0.75 m to 2 m. This is an important tuning ability of the technique, as the experimenter can tune the dispersion higher if needed to separate lines from multiple species in a mixture. Further, a larger dispersion may be used to allow for a larger 2D field to be imaged to the CCD if desired. For example, O2 spectral contributions are being indicated from a 2D-CARS spectrum recorded in air. With the presented dispersion, many of the O2 and N2 lines do not overlap, providing for simple data extraction.

Because the presented 2D-CARS technique is a coherent wave-mixing technique, allowing for the selection of wavelengths far from absorption, the beams are not significantly attenuated, and can be reflected back to the probe volume along a slightly displaced 2D imaging plane, and the 2D signal sent to a second CCD. By repeating this process a few 2D planes could be measured in a single laser shot, effectively creating a 3D-CARS measurement over a large field, and the instantaneous thermal field and relative species concentrations could be evaluated in 3D.

Light is one type of electromagnetic (EM) wave. As noted earlier, EM waves are transverse waves consisting of varying electric and magnetic fields that oscillate perpendicular to the direction of propagation (see Figure 2). There are specific directions for the oscillations of the electric and magnetic fields. Polarization is the attribute that a wave’s oscillations have a definite direction relative to the direction of propagation of the wave. (This is not the same type of polarization as that discussed for the separation of charges.) Waves having such a direction are said to be polarized. For an EM wave, we define the direction of polarization to be the direction parallel to the electric field. Thus we can think of the electric field arrows as showing the direction of polarization, as in Figure 2.

Figure 1 displays the experimental setup for the 2D-CARS measurements reported here and the 2D imaging spectrometer developed. We implemented the hybrid fs-pump/ps-probe CARS scheme15 to probe the rotational manifold population distribution of the ground vibrational state of gas-phase N2 and O2. A nearly transform-limited 45 fs pump/Stokes beam at 800 nm is formed into a sheet by focusing it to the probe volume with a f = 1000 mm cylindrical lens. The 532 nm probe beam remains collimated, and intersects the pump/Stokes sheet at an angle of 6°. The probe beam was 90-ps in duration, providing high spectral resolution (∼0.25 cm−1) in the rotational CARS spectrum. The generated coherent 2D signal was relay imaged through a diffraction grating (3600 lines/mm), to the CCD.28 The diffraction grating was placed after the image collimating lens, and the diffracted light was sent back at Littrow's angle to the lens to suppress image distortions as seen in Fig. 1. The signal was then reflected to the CCD. The signal generation plane is thus relay imaged to the face of the CCD. Each of the rotational transitions probed get mapped to a different, isolated, position on the CCD. To assess the effect of the grating on the imaging quality a mask was placed in the probe beam to provide structured illumination. As seen in Fig. 1, the probe light passing through this mask was imaged to the beam crossing, and the signal from an individual rotational transition of N2, J = 8, is shown in blue. Qualitatively, it is clear from looking at the image scattered from a single rotational coherence that the image is well-maintained through the detection system. The structured illumination serves as a resolution target for evaluating the imaging quality and any distortions to the J-specific images. The 4-mm mask is down-collimated in the imaging optics 2:1 to the beam crossing. Given the crossing angle of 6°, this arrangement probes a 2D spatial field of ∼2 mm × 20 mm.

Each of the rotational-level-specific images in Fig. 2(a) was vectorized, and the data from a single height in the image (a single pixel row slice) are presented in Fig. 3. The rotational CARS intensity spectra30 were simulated using a time-domain CARS code similar to that used previously31,32 and the theoretical spectrum for the average evaluated temperature is shown in red. A library of theoretical rotational CARS spectra, generated over a range of temperatures, was fitted to the experimentally extracted signal intensities using a quick-fitting nonlinear interpolating procedure.33 The resulting average evaluated temperature was 299 K, an error in accuracy of 1.5%, and the standard deviation in temperature evaluation across the spectra was 1.4%.

The development of 2D-CARS will open many new directions for research in the field of combustion diagnostics and pollutant formation. Thermal boundary layers near burner or bluff body surfaces are critical to the understanding of flame stabilization mechanisms, and also provide critical input parameters for the boundary conditions for the numerical simulation of combustors. Current methods for single-shot thermal field measurement, such as 2D Rayleigh scattering measurements, are very sensitive to light scattering and, in general, cannot be employed near surfaces. Detailed comparisons of turbulent heated flows can be compared to computational fluid dynamics (CFD) models for model validation and refinement with the high-precision and accuracy of single-shot CARS thermometry. Combined particle-imaging-velocimetry (PIV) measurements34 and 2D-CARS thermometry may provide simultaneous mapping of the flow- and temperature field. 2D thermal field measurements will be vitally important in the development and refinement of dynamical soot formation models,35,36 and to the understanding of energy dissipation following plasma formation.

Figure 1. These two photographs of a river show the effect of a polarizing filter in reducing glare in light reflected from the surface of water. Part (b) of this Figure was taken with a polarizing filter and part (a) was not. As a result, the reflection of clouds and sky observed in part (a) is not observed in part (b). Polarizing sunglasses are particularly useful on snow and water. (credit: Amithshs, Wikimedia Commons)

Figure 4. The slender arrow represents a ray of unpolarized light. The bold arrows represent the direction of polarization of the individual waves composing the ray. Since the light is unpolarized, the arrows point in all directions.

Figure 9. Long molecules are aligned perpendicular to the axis of a polarizing filter. The component of the electric field in an EM wave perpendicular to these molecules passes through the filter, while the component parallel to the molecules is absorbed.

All we need to solve these problems are the indices of refraction. Air has n1 = 1.00, water has n2 = 1.333, and crown glass has n′2=1.520. The equation [latex]\tan\theta_{\text{b}}=\frac{n_2}{n_1}\\[/latex] can be directly applied to find θb in each case.

Anti stokes raman spectroscopyformula

Coherent anti-Stokes Raman spectroscopy (CARS) has been widely used as a powerful tool for chemical sensing, molecular dynamics measurements, and rovibrational spectroscopy since its development over 30 years ago, finding use in fields of study as diverse as combustion diagnostics, cell biology, plasma physics, and the standoff detection of explosives. The capability for acquiring resolved CARS spectra in multiple spatial dimensions within a single laser shot has been a long-standing goal for the study of dynamical processes, but has proven elusive because of both phase-matching and detection considerations. Here, by combining new phase matching and detection schemes with the high efficiency of femtosecond excitation of Raman coherences, we introduce a technique for single-shot two-dimensional (2D) spatial measurements of gas phase CARS spectra. We demonstrate a spectrometer enabling both 2D plane imaging and spectroscopy simultaneously, and present the instantaneous measurement of 15 000 spatially correlated rotational CARS spectra in N2 and air over a 2D field of 40 mm2.

Figure 10 illustrates how the component of the electric field parallel to the long molecules is absorbed. An electromagnetic wave is composed of oscillating electric and magnetic fields. The electric field is strong compared with the magnetic field and is more effective in exerting force on charges in the molecules. The most affected charged particles are the electrons in the molecules, since electron masses are small. If the electron is forced to oscillate, it can absorb energy from the EM wave. This reduces the fields in the wave and, hence, reduces its intensity. In long molecules, electrons can more easily oscillate parallel to the molecule than in the perpendicular direction. The electrons are bound to the molecule and are more restricted in their movement perpendicular to the molecule. Thus, the electrons can absorb EM waves that have a component of their electric field parallel to the molecule. The electrons are much less responsive to electric fields perpendicular to the molecule and will allow those fields to pass. Thus the axis of the polarizing filter is perpendicular to the length of the molecule.

Funding provided by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Figure 11. Polarization by scattering. Unpolarized light scattering from air molecules shakes their electrons perpendicular to the direction of the original ray. The scattered light therefore has a polarization perpendicular to the original direction and none parallel to the original direction.

Extracted rotational CARS spectra taken from a single height (Y) in the image from Fig. 2(a). The spectra originate from a specific height in the probed 2D plane and cover 20 mm (X) of space at this height. From the intensity spectra, the average temperature was evaluated to be 299 K with a standard deviation of 1.4%, this yields an accuracy error of 1.5%. There are 125 such pixel rows in the single laser shot 2D-CARS image, which each provide another set of data like that presented in this figure.

coherent anti-stokesramanscattering microscopy

Figure 14. Optical stress analysis of a plastic lens placed between crossed polarizers. (credit: Infopro, Wikimedia Commons)

Figure 6. The effect of rotating two polarizing filters, where the first polarizes the light. (a) All of the polarized light is passed by the second polarizing filter, because its axis is parallel to the first. (b) As the second is rotated, only part of the light is passed. (c) When the second is perpendicular to the first, no light is passed. (d) In this photograph, a polarizing filter is placed above two others. Its axis is perpendicular to the filter on the right (dark area) and parallel to the filter on the left (lighter area). (credit: P.P. Urone)

In the pursuit of a multiplex 2D-CARS signal in a single laser shot, two significant hurdles are encountered. The first challenge is the generation of a spatially resolved 2D signal. In the conventional crossed-beam CARS phase-matching scheme for gas phase CARS measurements,25 there is no arrangement of pump, Stokes, and probe which follows the phase-matching condition that allows for the generation and probing of a 2D-CARS signal in a well spatially resolved manner. In this work, we first address the generation of a 2D-CARS signal by implementing a newly developed phase-matching scheme in which only two beams are required to generate a CARS signal as opposed to the three beams (pump/Stokes/probe) in the conventional gas-phase CARS arrangement. Crossed-beam CARS using only a single pump/Stokes coherence preparation beam and a probe beam has been recently discovered.26,27 In this scheme, both pump and Stokes photons used to drive the Raman coherence are obtained from the same broadband laser pulse. At low probe crossing angle, this two-beam nonlinear interaction is phase-matched over a large range of transition frequencies, enabling two-beam CARS measurements over a transition frequency range limited primarily only by the bandwidth of the excitation laser. For instance, at a two-beam crossing angle of 4°, the phase-mismatch induced CARS signal intensity reduction is less than 50% for Raman transitions up to 3000 cm−1 covering the fundamental vibrational and rotational transitions of most all molecules.28

The second challenge associated with 2D-CARS is the spectrally resolved detection of the 2D image within a single laser shot. Here, we describe a spectrometer which allows for spectrally resolved 2D imaging of the isolated Raman transitions in a single laser shot. The spectrometer is conceptually similar to the tomographic hyperspectral imaging spectrometer,29 with the exception that we probe narrow, well-isolated spectral lines, significantly simplifying the data analysis. For instance, for the S-branch rotational transitions of N2 molecules, the Raman linewidth is <0.1 cm−1 at 1 bar, and the spacing of the rotational transitions is 8 cm−1.

Polarizing filters have a polarization axis that acts as a slit. This slit passes electromagnetic waves (often visible light) that have an electric field parallel to the axis. This is accomplished with long molecules aligned perpendicular to the axis as shown in Figure 9.

What angle is needed between the direction of polarized light and the axis of a polarizing filter to reduce its intensity by 90.0%?

The Sun and many other light sources produce waves that are randomly polarized (see Figure 4). Such light is said to be unpolarized because it is composed of many waves with all possible directions of polarization. Polaroid materials, invented by the founder of Polaroid Corporation, Edwin Land, act as a polarizing slit for light, allowing only polarization in one direction to pass through. Polarizing filters are composed of long molecules aligned in one direction. Thinking of the molecules as many slits, analogous to those for the oscillating ropes, we can understand why only light with a specific polarization can get through. The axis of a polarizing filter is the direction along which the filter passes the electric field of an EM wave (see Figure 5).

Brewster’s angle: [latex]{\theta }_{\text{b}}={\tan}^{-1}\left(\frac{{n}_{2}}{{n}_{1}}\right)\\[/latex], where n2 is the index of refraction of the medium from which the light is reflected and n1 is the index of refraction of the medium in which the reflected light travels

If you hold your Polaroid sunglasses in front of you and rotate them while looking at blue sky, you will see the sky get bright and dim. This is a clear indication that light scattered by air is partially polarized. Figure 11 helps illustrate how this happens. Since light is a transverse EM wave, it vibrates the electrons of air molecules perpendicular to the direction it is traveling. The electrons then radiate like small antennae. Since they are oscillating perpendicular to the direction of the light ray, they produce EM radiation that is polarized perpendicular to the direction of the ray. When viewing the light along a line perpendicular to the original ray, as in Figure 11, there can be no polarization in the scattered light parallel to the original ray, because that would require the original ray to be a longitudinal wave. Along other directions, a component of the other polarization can be projected along the line of sight, and the scattered light will only be partially polarized. Furthermore, multiple scattering can bring light to your eyes from other directions and can contain different polarizations.

what is coherent anti-stokesraman spectroscopy

When the intensity is reduced by 90.0%, it is 10.0% or 0.100 times its original value. That is, I = 0.100I0. Using this information, the equation I = I0 cos2 θ can be used to solve for the needed angle.

Figure 7. A polarizing filter transmits only the component of the wave parallel to its axis, , reducing the intensity of any light not polarized parallel to its axis.

polarization: the attribute that wave oscillations have a definite direction relative to the direction of propagation of the wave

Anti stokes raman spectroscopywikipedia

To examine this further, consider the transverse waves in the ropes shown in Figure 3. The oscillations in one rope are in a vertical plane and are said to be vertically polarized. Those in the other rope are in a horizontal plane and are horizontally polarized. If a vertical slit is placed on the first rope, the waves pass through. However, a vertical slit blocks the horizontally polarized waves. For EM waves, the direction of the electric field is analogous to the disturbances on the ropes.

17. (a) 2.07 × 10−2 °C/s; (b) Yes, the polarizing filters get hot because they absorb some of the lost energy from the sunlight.

Figure 2. An EM wave, such as light, is a transverse wave. The electric and magnetic fields are perpendicular to the direction of propagation.

Figure 3. The transverse oscillations in one rope are in a vertical plane, and those in the other rope are in a horizontal plane. The first is said to be vertically polarized, and the other is said to be horizontally polarized. Vertical slits pass vertically polarized waves and block horizontally polarized waves.

A fairly large angle between the direction of polarization and the filter axis is needed to reduce the intensity to 10.0% of its original value. This seems reasonable based on experimenting with polarizing films. It is interesting that, at an angle of 45º, the intensity is reduced to 50% of its original value (as you will show in this section’s Problems & Exercises). Note that 71.6º is 18.4º from reducing the intensity to zero, and that at an angle of 18.4º the intensity is reduced to 90.0% of its original value (as you will also show in Problems & Exercises), giving evidence of symmetry.

While you are undoubtedly aware of liquid crystal displays (LCDs) found in watches, calculators, computer screens, cellphones, flat screen televisions, and other myriad places, you may not be aware that they are based on polarization. Liquid crystals are so named because their molecules can be aligned even though they are in a liquid. Liquid crystals have the property that they can rotate the polarization of light passing through them by 90º. Furthermore, this property can be turned off by the application of a voltage, as illustrated in Figure 12. It is possible to manipulate this characteristic quickly and in small well-defined regions to create the contrast patterns we see in so many LCD devices.

coherent anti-stokesraman spectroscopyof single and multi-layer graphene

Figure 5. A polarizing filter has a polarization axis that acts as a slit passing through electric fields parallel to its direction. The direction of polarization of an EM wave is defined to be the direction of its electric field.

Figure 8. Polarization by reflection. Unpolarized light has equal amounts of vertical and horizontal polarization. After interaction with a surface, the vertical components are preferentially absorbed or refracted, leaving the reflected light more horizontally polarized. This is akin to arrows striking on their sides bouncing off, whereas arrows striking on their tips go into the surface.

Light reflected at these angles could be completely blocked by a good polarizing filter held with its axis vertical. Brewster’s angle for water and air are similar to those for glass and air, so that sunglasses are equally effective for light reflected from either water or glass under similar circumstances. Light not reflected is refracted into these media. So at an incident angle equal to Brewster’s angle, the refracted light will be slightly polarized vertically. It will not be completely polarized vertically, because only a small fraction of the incident light is reflected, and so a significant amount of horizontally polarized light is refracted.

By now you can probably guess that Polaroid sunglasses cut the glare in reflected light because that light is polarized. You can check this for yourself by holding Polaroid sunglasses in front of you and rotating them while looking at light reflected from water or glass. As you rotate the sunglasses, you will notice the light gets bright and dim, but not completely black. This implies the reflected light is partially polarized and cannot be completely blocked by a polarizing filter.

Alexis Bohlin, Christopher J. Kliewer; Communication: Two-dimensional gas-phase coherent anti-Stokes Raman spectroscopy (2D-CARS): Simultaneous planar imaging and multiplex spectroscopy in a single laser shot. J. Chem. Phys. 14 June 2013; 138 (22): 221101. https://doi.org/10.1063/1.4810876

Brewster’s law: [latex]\tan\theta_{\text{b}}=\frac{{n}_{2}}{{n}_{1}}\\[/latex], where n1 is the medium in which the incident and reflected light travel and n2 is the index of refraction of the medium that forms the interface that reflects the light

Figure 8 illustrates what happens when unpolarized light is reflected from a surface. Vertically polarized light is preferentially refracted at the surface, so that the reflected light is left more horizontally polarized. The reasons for this phenomenon are beyond the scope of this text, but a convenient mnemonic for remembering this is to imagine the polarization direction to be like an arrow. Vertical polarization would be like an arrow perpendicular to the surface and would be more likely to stick and not be reflected. Horizontal polarization is like an arrow bouncing on its side and would be more likely to be reflected. Sunglasses with vertical axes would then block more reflected light than unpolarized light from other sources.

Polaroid sunglasses are familiar to most of us. They have a special ability to cut the glare of light reflected from water or glass (see Figure 1). Polaroids have this ability because of a wave characteristic of light called polarization. What is polarization? How is it produced? What are some of its uses? The answers to these questions are related to the wave character of light.

The experimental setup for the 2D-CARS measurements displaying the 2D imaging spectrometer system and the alignment of the laser beams. The details of the time-synchronized fs and ps laser systems employed are described in the supplementary material.28 The structured probe beam is formed by passing the probe beam through a mask (4 mm × 4 mm) which is relay imaged to the crossing of the pump/Stokes beam with a 2:1 magnification to increase the probe pulse irradiance. In light blue is the 2D-CARS image from the resolved J = 8 rotational transition. The optical detection system consists of a single “effective” lens used in combination with a diffraction grating to disperse the 2D-CARS light. L1, L2, and L3 – spherical lenses with f1 = 1 m, f2 = 0.5 m, f3 = 0.75 m, respectively. M – mirror, HWP – half wave plate, CL – cylindrical lens (f = 1 m / 0.3 m), BD – beam dump, PBS – polarizing beam splitter cube, SP – short wave pass filter, G – grating (3600 l/mm), CCD – charge coupled device camera, RF – 100 MHz radio frequency source to which both the fs and ps seed lasers are phase-locked.

Only the component of the EM wave parallel to the axis of a filter is passed. Let us call the angle between the direction of polarization and the axis of a filter θ. If the electric field has an amplitude E, then the transmitted part of the wave has an amplitude E cos θ (see Figure 7). Since the intensity of a wave is proportional to its amplitude squared, the intensity I of the transmitted wave is related to the incident wave by I = I0 cos2 θ, where I0 is the intensity of the polarized wave before passing through the filter. (The above equation is known as Malus’s law.)

Anti stokes raman spectroscopynotes

In flat screen LCD televisions, there is a large light at the back of the TV. The light travels to the front screen through millions of tiny units called pixels (picture elements). One of these is shown in Figure 12 (a) and (b). Each unit has three cells, with red, blue, or green filters, each controlled independently. When the voltage across a liquid crystal is switched off, the liquid crystal passes the light through the particular filter. One can vary the picture contrast by varying the strength of the voltage applied to the liquid crystal.

Photographs of the sky can be darkened by polarizing filters, a trick used by many photographers to make clouds brighter by contrast. Scattering from other particles, such as smoke or dust, can also polarize light. Detecting polarization in scattered EM waves can be a useful analytical tool in determining the scattering source.

Figure 12. (a) Polarized light is rotated 90º by a liquid crystal and then passed by a polarizing filter that has its axis perpendicular to the original polarization direction. (b) When a voltage is applied to the liquid crystal, the polarized light is not rotated and is blocked by the filter, making the region dark in comparison with its surroundings. (c) LCDs can be made color specific, small, and fast enough to use in laptop computers and TVs. (credit: Jon Sullivan)

Coherent anti-Stokes Raman spectroscopy (CARS) yields laser-like signals that are chemically selective, temperature sensitive, and spatially resolved. Due to the uniqueness of molecular rotational and vibrational Raman spectra, CARS has often been used as a chemical sensing tool. In this context, CARS techniques have been developed for species identification in the microscopic imaging of biological tissues,1,2 the standoff detection of explosives,3 and species concentration measurements in combustion.4,5 While some of the early work in gas-phase CARS required tuning the frequency of one of the beams to generate a CARS spectrum,6,7 multiplex CARS utilizing broadband preparation pulses has been implemented7–9 to measure the population distribution within the rotational and vibrational energy levels of the probed molecules within a single laser shot, making CARS an exquisite probe of the local instantaneous temperature,10 a scalar of vital importance to the probing of reacting flows.11 Chemical effects, such as reaction rate constants, and physical effects, such as gas expansion and heat transfer, are directly linked to the instantaneous thermal field,12 and CARS is often held as the gold standard for nonintrusive gas-phase measurements of thermometry. CARS signals are emitted as a coherent laser-like beam, yielding high collection efficiencies even at large distances away from the probed volume, making the technique ideally suited for probing in highly luminous or scattering environments, such as those often encountered in the study of combustion, plasmas, and particle-laden flows. Ultrafast, time-resolved, spectroscopy techniques have greatly extended the utility of CARS measurements recently. The use of transform limited femtosecond (fs) pulses in the preparation of Raman coherences has been shown to be extremely efficient13 as many pairs of photons within the bandwidth of the pump/Stokes pulse envelopes combine in phase to amplify the CARS signal. Hybrid CARS utilizes transform limited fs pulses to efficiently drive the Raman coherences, and a tailored probe pulse, often in the picosecond (ps) regime, to yield spectrally resolved signals in a single-laser shot.14,15 The applicability of the CARS technique has been extended using time-resolved probing to map the dephasing mechanisms for a number of molecules following coherent excitation.16–21 In rotational CARS, mixtures of multiple species yielding a complex spectrum can be simplified as the coherence from the small molecules is significantly longer-lived; thus, an appropriate probe delay can yield simplified spectra.22,23

Another interesting phenomenon associated with polarized light is the ability of some crystals to split an unpolarized beam of light into two. Such crystals are said to be birefringent (see Figure 15). Each of the separated rays has a specific polarization. One behaves normally and is called the ordinary ray, whereas the other does not obey Snell’s law and is called the extraordinary ray. Birefringent crystals can be used to produce polarized beams from unpolarized light. Some birefringent materials preferentially absorb one of the polarizations. These materials are called dichroic and can produce polarization by this preferential absorption. This is fundamentally how polarizing filters and other polarizers work. The interested reader is invited to further pursue the numerous properties of materials related to polarization.

Figure 6 shows the effect of two polarizing filters on originally unpolarized light. The first filter polarizes the light along its axis. When the axes of the first and second filters are aligned (parallel), then all of the polarized light passed by the first filter is also passed by the second. If the second polarizing filter is rotated, only the component of the light parallel to the second filter’s axis is passed. When the axes are perpendicular, no light is passed by the second.

[latex]\tan\theta_{\text{b}}=\frac{n_2}{n_1}\\[/latex] gives [latex]\tan\theta_{\text{b}}=\frac{n_2}{n_1}=\frac{1.333}{1.00}=1.333\\[/latex].

One of the long-standing goals in CARS measurements has been the capability to obtain CARS spectra in multiple spatial dimensions simultaneously. Such single shot two-dimensional (2D) measurements would significantly add to the information available for the rigorous comparison between numerical simulations of complex dynamical systems and experiments for model validation and development. However, up to now, if a 2D image of CARS spectra was desired, sample- or laser-scanning techniques have been used to collect 2D data across many laser shots, thus forfeiting time-resolution altogether in favor of more complete spatial information. But in the probing of rapidly fluctuating systems, which are often encountered in turbulent combustion and fluid dynamics measurements, for instance, single-laser-shot data are needed to probe the system instantaneously. Single shot 2D measurements can potentially overcome many of the particular difficulties in comparing measurement results with the results a model provides, such as in the modeling of combusting flows,24 and fundamentally increase the ongoing progress of comparisons between numerical simulations of multidimensional phenomena and experiments.

There is a range of optical effects used in sunglasses. Besides being Polaroid, other sunglasses have colored pigments embedded in them, while others use non-reflective or even reflective coatings. A recent development is photochromic lenses, which darken in the sunlight and become clear indoors. Photochromic lenses are embedded with organic microcrystalline molecules that change their properties when exposed to UV in sunlight, but become clear in artificial lighting with no UV.

Since the part of the light that is not reflected is refracted, the amount of polarization depends on the indices of refraction of the media involved. It can be shown that reflected light is completely polarized at a angle of reflection θb, given by [latex]\tan\theta_{\text{b}}=\frac{n_2}{n_1}\\[/latex], where n1 is the medium in which the incident and reflected light travel and n2 is the index of refraction of the medium that forms the interface that reflects the light. This equation is known as Brewster’s law, and θb is known as Brewster’s angle, named after the 19th-century Scottish physicist who discovered them.

Glass and plastic become optically active when stressed; the greater the stress, the greater the effect. Optical stress analysis on complicated shapes can be performed by making plastic models of them and observing them through crossed filters, as seen in Figure 14. It is apparent that the effect depends on wavelength as well as stress. The wavelength dependence is sometimes also used for artistic purposes.