Two technical papers recognized as significant early contributions in the discussion of the limitations of analytical accuracy and uncertainty include those by Horwitz of the U.S. FDA (1,2). For this next series of articles, we will be discussing both the topic and the approaches to this topic taken by the classic papers just referenced. The determination and understanding of analytical error is often approached using interlaboratory collaborative studies. We have previously delved into that subject in "Chemometrics in Spectroscopy" with a multipart column series (3–8). 

 A-pages paper (1), inserting the statement made by John Mandel, "the basic objective of conducting interlaboratory tests is not to detect the known statistically significant differences among laboratories: 'The real aim is to achieve the practical interchangeability of test results.' Interlaboratory tests are conducted to determine how much allowance must be made for variability among laboratories in order to make the values interchangeable." 

Horwitz also points out the universal recognition of irreproducible differences in supposedly identical method results between laboratories. It has even been determined that when the same analyst is moved between laboratories, the variability of results obtained by that analyst increases. One government laboratory study concluded that variability in results could be minimized only if one was to "conduct all analyses in a single laboratory . . . by the same analyst." So if we must always have interlaboratory variability, how much allowance in results should be regarded as valid — or legally permissible — as indicating "identical" results? What are the practical limits of acceptable variability between methods of analysis, especially for regulatory purposes? 

 which has been defined previously as "the precision between laboratories." It also has been defined as "total between-laboratory precision." This is a measure of the ability of different laboratories to evaluate each other. Reproducibility includes all the measurement errors or variances, including the within-laboratory error. Other terms include 

 defined as "the closeness of agreement between independent test results obtained under stipulated conditions" (9); and 

 or "the precision for the same analyst within the same laboratory, or within-laboratory precision." Note that for none of these definitions do we require the "true value for an analytical sample." In practice, we do not know the true analyte value unless we have created the sample, and then it is only known to a given certainty (that is, within a determined uncertainty). 

 The bias is the constant value difference between a measured value (or set of values) and a consensus value (or true value if known). 

 is the analytical property of a method or technique to be insensitive to interferences and to yield a signal relative to the analyte of interest only. 

. The MDL is the minimum amount of analyte present that can be detected with known certainty. 

 represents the precision of a laboratory method. A statistical definition is given in the following paragraph. The SEL can be determined by using one or more samples properly aliquoted and analyzed in replicate by one or more laboratories. The average analytical value for the replicates on a single sample is determined as  

 index represents different samples and the 

 index different measurements on the same sample. 

Any analytical method inherently carries with it limitations in terms of speed, allowable uncertainty (as MDL), and specificity. These characteristics of a method (or analytical technique) determine where and how the method can be used. Table I shows a template to relate purpose of analytical methods to the speed of analysis and error types permitted. 

Table I:  Characteristics and allowable uncertainty for different analytical methods			

Bias is allowed between laboratories when constant and deterministic. For any method optimization, we must consider the requirements for precision and bias, specificity, and MDL. 

Horwitz claims that irrespective of the complexity found within various analytical methods, the limits of analytical variability can be expressed or summarized by "plotting the calculated mean coefficient of variation (CV), expressed as powers of two [ordinate], against the analyte level measured, expressed as powers of 10 [abscissa]." In an analysis of 150 independent Association of Official Analytical Chemists (AOAC) interlaboratory collaborative studies covering numerous methods such as chromatography, atomic absorption, molecular absorption spectroscopy, spectrophotometry, and bioassay, it appears that the relationship describing the CV of an analytical method and the absolute analyte concentration is independent of the analyte type or the method used for detection. 

Moving ahead to describe the details of this claim, we need to develop a few basic review concepts. The standard deviation of measurements is determined by first calculating the mean, then taking the difference of each control result from the mean, squaring that difference, dividing by 

 – 1, then taking the square root. All of these operations are implied in the following equation:

Articles

Chemometrics in Spectroscopy

September 2006. In the first part of this two-part series, columnists Jerome Workman, Jr. and Howard Mark discuss the limitations of analytical accuracy and uncertainty.

Limitations in Analytical Accuracy, Part I: Horwitz's Trumpet

There is a form of spectroscopy known as 

. As with many forms of spectroscopy, its name is descriptive. The prefix "photo" makes sense for a form of spectroscopy, but "acoustic"? Doesn't that mean "relating to sound"? Is there really a form of spectroscopy that uses sound? 

In 1880–1881, Alexander Graham Bell (1–3) found that when a thin disk was exposed to mechanically chopped sunlight, sound was emitted. In addition, he noted a similar effect when infrared or ultraviolet light was used. A plot of the loudness of the sound versus, for example, the wavelength of the light used, is called a 

. According to Haisch and Niessner (4), this effect essentially  was forgotten until researchers led by Allen Rosencwaig (ironically) at Bell Labs rediscovered the behavior and provided a theoretical basis (5). To indicate the growth of the field, Figure 1 shows the number of publications listed by the Chemical Abstracts Service under the subject "photoacoustic spectroscopy". 

Figure 1: Number of articles published using the key phrase "photoacoustic spectroscopy" since the early 1970s.			

Photoacoustic spectroscopy is part of a class of photothermal techniques, in which an impinging light beam is absorbed and alters the thermal state of the sample. This "thermal state" can manifest itself as a change in temperature, density, or other measurable property of the sample. One method of detection is to experimentally measure the temperature or density of the absorbing material. This is referred to as thermometric detection. 

However, if the incoming light is modulated, the absorbing sample warms and cools in a cycle. If the cycle is so fast that the sample does not have time to expand and contract in response to the modulated light, a change in pressure develops. This pressure "wave" can lead to the production of a sound wave. These sound waves can be detected by a sensitive microphone, piezoelectric devices, or optical methods (for example, deflection of highly collimated light reflecting from the surface). These techniques are more properly called photoacoustic techniques. It has been argued that photo-acoustic spectroscopy is as much a type of calorimetry as it is spectroscopy (5). 

One advantage to photoacoustic spectroscopy is that it can be performed on all phases of matter. Figure 2 shows a general setup for the photoacoustic spectroscopy of a gas sample. When a species absorbs some of the incoming light, one of several mechanisms of de-excitation is intermolecular colliding, which ultimately leads to increases in translation energy of the gas particles — that is, heating. According to the various gas laws, an increase in the temperature of the gas leads to an increase in the pressure of an isochoric (constant-volume) sample. If the incoming light is modulated — modulation frequencies can vary from single to several thousand hertz — the gas pressure increases and decreases accordingly, creating sound. Varying the wavelength of the incoming light will change the amount of light absorbed, the amount of pressure changes occurring, and the amount of sound produced, and a spectrum of loudness versus wavelength can be produced. 

Figure 2: General experimental setup for performing photoacoustic spectroscopy on a gas.			

One useful aspect of photoacoustic spectroscopy of gases is that very bright light sources — lasers — can be used to detect very tiny concentrations of a particular gas, on the order of parts per 

. This makes photoacoustic spectroscopy very useful in following the concentrations of trace gases in mixtures, like soot in diesel exhaust or NO

 in the atmosphere. Photoacoustic spectroscopy can also be limited because laser light is not very broad in bandwidth; the analyte molecule must absorb some light from the source in order to be detectable. Saturation effects can also cause problems (6). 

Photoacoustic Spectroscopy: Condensed Phases 

The mechanism of the photoacoustic effect in condensed samples is not as straightforward as it is for gas samples. For example, in 1973, Parker (7) noticed a photoacoustic signal apparently coming from the windows of the sample cell, which should have been transparent to the incoming radiation. Further (and this might be unique to this particular form of spectroscopy), the exact mechanism of spectrum production depends on the type of detector used. The commonly accepted mechanism for the photoacoustic effect is called RG theory, after its developers Rosencwaig and Gersho (8,9). The main source of the acoustic wave is the repetitive heat flow from the absorbing condensed-phase sample to the surrounding gas, followed by propagation of the acoustic wave through the gas column to microphone-based detector. 

However, a photoacoustic signal also can be detected piezoelectrically. Instead of being dissipated as heat, the absorbed radiant energy also can be transferred through the solid-state vibrational modes, or phonon modes, of the sample. The motions of these phonon modes are nondissipative (unlike heating), limited only by the size of the sample. A piezoelectric detector physically connected to the sample can detect absorbed energy in this manner. Although piezoelectric detection is about 100 times less sensitive than microphone detectors, it can be preferable for large samples or for samples that do not efficiently convert absorbed light to heat. 

One advantage of photoacoustic spectroscopy is that it is nondestructive to the sample; the sample does not have to be dissolved in some solvent or embedded in a solid-state matrix. Samples can be used "as is." Another advantage is the potential for performing depth profiles of analytes in optically transparent media. Figure 3 shows how this is possible: essentially, the slower the modulation rate, the farther the heat can diffuse before the incoming light is cut off. Figure 4 shows examples of infrared photoacoustic spectra of poly(vinylidene chloride) films using different modulations, showing differences in the spectra due to differences in penetration depth. 

Figure 3: How photoacoustic spectroscopy can perform depth profiling.			

Photoacoustic spectroscopy is not only used for depth profiling. As indicated earlier, it can be used to measure pollutants such as NO

 or soot in the atmosphere or in automobile exhaust. Haisch and Niessner (4) also list the analysis of textile dyes as another practical application of photoacoustic spectroscopy. Photoacoustic spectroscopy is particularly useful for samples that are powdered (like catalysts), amorphous, or otherwise not conducive to reflective or transmission forms of optical spectroscopy. The photoacoustic effect is used to study biological samples such as blood, skin, eye lenses, tumors, and drug-laced tissues. Several studies are available in which photoacoustic spectroscopy has been used to identify different types of bacteria. Interested readers are urged to consult the literature to see if this fascinating form of spectroscopy might be right for them. 

Figure 4: Fourier transformâinfrared photoacoustic spectra of poly(vinylidene chloride) films at four modulations. Spectrum 1: 50 Hz; spectrum 2: 100 Hz; spectrum 3: 400 Hz; spectrum 4: 1000 Hz. (Reprinted with permission from reference 10. Copyright 2004 American Chemical Society.)			

 is a professor of chemistry at Cleveland State University in Ohio. Many of his "Baseline" columns have been reprinted in book form by SPIE Press as 

 available through the SPIE Web Bookstore at 

 (published in May 2006), is available from SPIE Press. He can be reached at 

(3) An article describing the work in the journal 

(7), 156–158 (1881) is available online through Cornell University at http://

cdl.library.cornell.edu/cgi-bin/moa/moa-cgi?notisid=ABS1821-0013-416

Photoacoustics and Photoacoustic Spectroscopy

 (R.E. Krieger Publishing Company, Malabar, Florida, 1980). 

 (R.E. Krieger Publishing Company, Malabar, Florida, 1980), p. 69. 

The Baseline

September 2006. An unusual form of spectroscopy uses light and sound to probe the behavior of materials. Here is a brief introduction to photoacoustic spectroscopy.

Photoacoustic Spectroscopy

The 33rd Annual Meeting of the Federation of Analytical Chemistry and Spectroscopy Societies (FACSS) will be held at 

 Lake Buena Vista, Florida, from September 24 to September 28, 2006. Taking advantage of the unique entertainment opportunities available at the Walt Disney World Resort, the FACSS will hold its Wednesday evening event at the Adventurers Club at Walt Disney World's Pleasure Island. In addition, conferees can purchase specially priced Disney Meeting and Convention tickets for the theme parks when they register. 

Harry McSween, Professor at the University of Tennessee, Knoxville, Tennessee, and a co-investigator for the Mars Exploration Rovers, will open the program with his presentation, 

Spectroscopy on the Red Planet: More than Meets the Eye.

 Professor Alan Marshall of Florida State University, Tallahassee, Florida, will present the closing plenary lecture for the conference, 

Ultrahigh-Resolution Mass Spectrometry for Separation and Identification of Complex Analytical, Biological, and Environmental Organic Mixtures. 

Each daily plenary lecture will be followed by poster sessions and oral presentations from all areas of analytical chemistry and spectroscopy.  

Morning, afternoon, and full-day workshops and short courses covering a wide range of topics in analytical chemistry and spectroscopy will be conducted by leading experts in their respective fields. A complete list of all workshops being held at this year's conference is available at 

https://facss.org/facss/workshops_list.php

For the first time, the Anachem Award, presented annually since 1953, will be given posthumously. Being recognized with this honor is the late Richard D. Sacks, Professor of Chemistry at the University of Michigan, Ann Arbor, Michigan. 

The 2006 Recipient of the Charles Mann Award for Applied Raman Spectroscopy is Michael Morris, Professor of Chemistry at the University of Michigan.  

The Lester W. Strock Award will be presented to Paul Farnsworth. 

 William F. Meggers Award are the authors of the outstanding paper appearing in 

 They are Pavel Matousek, Ian Clark, Edward Draper, Michael Morris, Allen Goodship, Neil Everall, Mike Towrie, William F. Finney, and Anthony Parker.  The recipient of the 2006 Ellis R. Lippincott Award will be announced at the conference. 

The 2006 Tomas A. Hirschfeld Award will be presented to Andrea Rae Tao, University of California, Berkeley, California, and Tim M. Brewer, Clemson University, Clemson, South Carolina. 

Daniel B. Bassil, University of Missouri, Columbia, Missouri, is the 2006 Recipient of the FACSS Student Award. 

Finally, 2006 FACSS Student Award Honorable Mentions will be given to Marion Lawrence-Snyder, University of South Carolina, Columbia, South Carolina, and Maria F. Mora, University of Texas at San Antonio. 

Instrument exhibition is one of the focal points of FACSS. It is always exciting to see how the research discussed during FACSS symposia becomes modern, innovative instrumentation, software, and supplies. One of the exhibit features is the "What's Hot" Vendor Symposium, which will be held Monday, September 25, beginning at 1:30 PM. Exhibitors can share brief PowerPoint presentations on the latest news or products from their companies. 

				Monday: Exhibit opening reception 4:00–6:00 PM 

Tuesday and Wednesday: 9:00 AM–5:00 PM 

For more information and to register on-line, see the FACCS web page at http://

Feature

September 2006. Spectroscopy previews the 33rd Annual Meeting of the FACSS, to be held September 24-28 in Lake Buena Vista, Florida.

33rd Annual FACSS Meeting

Double-beam UV–Vis spectrophotometers include the most advanced instruments in the UV–Vis market today.  They allow more rapid and greatly simplified UV–Vis analyses for users. The market for double-beam UV–Vis instruments is dominated by the major diversified scientific instrument manufacturers. 

In older single-beam spectrophotometers, a reference blank must first be inserted for the instrument to establish a P

 value with which to compare the sample spectrum. In double-beam systems, the light is typically split or alternatively directed in two directions after it has passed through the monochromator, with one path directed through the sample and the other through the reference blank. This eliminates the need to manually switch cuvettes between zeroing the instrument and running the sample, and reduces the total analysis time, as well as eliminating the possibility of lamp drift and other slow fluctuations affecting the measurement. For the most part, all double-beam UV–Vis instruments are scanning systems, which are relatively slow, but many are now capable of performing faster fixed wavelength measurements as well.  

The combined worldwide market for laboratory double-beam UV–Vis and UV–Vis-NIR initial systems in 2005 was nearly $180 million, which represented well over a third of UV–Vis-NIR initial system sales. The majority of scanning UV–Vis system sales and nearly all UV–Vis-NIR system sales by the major vendors are of the double-beam configuration. Demand for dual-beam UV–Vis instruments should see consistently moderate single digit growth for the foreseeable future. 

The foregoing data were extracted from SDi's market analysis and perspectives report entitled 

Edition Global Assessment Report, 9th Edition: The Laboratory Life Science and Analytical Instrument Industry, 

August 2006. For more information, contact Stuart Press, Senior Consultant, Strategic Directions International, Inc., 6242 Westchester Parkway, Suite 100, Los Angeles, CA 90045, (310) 641-4982, fax: (310) 641-8851, 

Departments

Double-beam UV–Vis spectrophotometers include the most advanced instruments in the UV–Vis market today. They allow more rapid and greatly simplified UV–Vis analyses for users. The market for double-beam UV–Vis instruments is dominated by the major diversified scientific instrument manufacturers.

Market Profile: Double-Beam UV-Vis Spectrophotometers

Recently, there has been great interest in a variety of novel ultrafast coherent anti-Stokes Raman scattering (CARS) methods that utilize broadband lasers (1–3), often involving narrowband probe pulses (4–6), chirped pulses (7,8), or fiber-broadened pulses (9–11) to obtain broadband vibrational information from molecules. With the variation of single-pulse, broadband, multiplex CARS microscopy discussed here, broad bandwidth spectra are acquired rapidly during the microscope scan and the spatially variant compositions of samples composed of multiple components are readily determined.  

The essential feature of this method is the use of a single, ultra-broadband femtosecond (fs) pulsed-laser oscillator, which simultaneously provides all of the photons for the CARS scattering. By a combination of phase and polarization control of the 10-fs laser pulses, complete broadband spectral images are acquired in the vibrational fingerprint regime.  An important advantage of this method is that full chemical composition analysis is obtained in a single microscope scan, rather than the multiple scans that are necessary with narrowband CARS microscopy (12–17). There are, however, tradeoffs necessary to gain this spectral width. With narrowband CARS, the signal sensitivity and signal acquisition rate can be much greater, but with broadband CARS, the spatial locations of multiple species can be obtained in a single scan. In the discussion that follows, the techniques of broadband CARS are discussed and illustrated with examples of multicomponent chemical imaging. 

In general, various fluorescence microscopy techniques have become popular for highly sensitive imaging, but most methods require the introduction of fluorescent probes that can perturb the system of interest, and are often limited by photobleaching. On the other hand, infrared (IR) and Raman spectroscopy are excellent tools for identifying the chemical properties and physical environments of molecules within a condensed phase sample based upon intrinsic molecular vibrations. However, there are significant limitations to utilizing these techniques for microscopy. The long wavelengths required for IR absorption result in low spatial resolution, and spontaneous Raman scattering has a characteristically small cross-section. Also, sample fluorescence often overlaps the Stokes lines typically used in spontaneous Raman scattering spectroscopy. CARS has the potential to become a powerful spectroscopic tool due to the stronger signal levels of vibrational spectral information and three-dimensional sectioning capability (18).  

The vibrational fingerprint region extends from about 800 cm

  (19). Therefore, acquiring a full vibrational spectrum with ~1000 cm

  of bandwidth in this spectral region at each spatial location in a sample would enable discrimination of many sample components simultaneously, even those with similar spectral features (9). Furthermore, it is desirable to obtain this full spectrum in single-pulse mode, without scanning over each frequency region individually. 

				With the goal of imaging complex samples in mind, several groups have developed highly refined methods to increase the sensitivity of broadband CARS spectroscopy to combine it with microscopy as a label-free, chemically selective imaging technique (1–4,6–11). However, due to the time it typically takes to collect the full spectrum, to our knowledge, only a few groups have constructed microscope images with a CARS spectrum at each pixel (6,9,11).			

Many applications would benefit from a sensitive imaging technique that provides chemical selectivity for multiple components simultaneously. For example, it would be valuable to obtain the spatial distribution of specific molecules throughout living biological cells and tissues. In particular, the segregation of lipids into distinct domains within the outermost cell membrane is an area of active investigation with implications for an understanding of protein sorting, cell–cell interactions, and signaling processes (20). Recently, narrowband and multiplex CARS microscopy has been used to image the distribution of two different lipids in model lipid membranes by tuning to a single vibrational band or spectral region of interest (6,14). By increasing the spectral bandwidth, it may be possible to determine the precise chemical composition of such domains without extrinsic chemical markers, which are usually necessary to discriminate between different species in a sample. Recent work in narrowband CARS imaging of living cells (11,16,17) makes the prospect of sensitive broadband CARS for imaging biological systems also potentially exciting. 

Another area of great interest for chemically selective imaging is that of chemically amplified polymer photoresists, used in the manufacturing of patterned semiconductor chips for electronics and computing. These photoresists are composed of two similar polymers in a pattern with few hundred nanometer spatial domains of each component. It would be advantageous to have a technique that could analyze these patterned photoresists quickly and easily for quality control purposes. Narrowband CARS microscopy has been used successfully to image single spectral peaks across model polymer photoresists (15), but to quantify multiple materials within the resist at the same time, a broader vibrational spectrum is desirable at each point in the microscope image.  

CARS is a three-photon scattering process in which two intense laser fields, called the pump and Stokes fields, interact with sample molecules to induce coherent vibrations, and subsequent interaction with a probe pulse then results in the emission of a coherent fourth field at a higher frequency. This signal is strongly enhanced when the energy difference between the pump and Stokes pulses matches the energy of an intrinsic molecular vibrational level. Typically, the pump and probe pulses and the Stokes pulse are provided by two separate, synchronized picosecond lasers or two beams produced by a single laser. Single vibrational resonances can be probed one at a time with narrowband CARS microscopy if the difference between the pump and Stokes beams from the picosecond (narrowband) lasers is tuned to match these vibrational frequencies (18).  

By incorporating a broadband laser into this scheme, such that the broadband laser provides multiple Stokes frequencies simultaneously and a narrowband laser provides the pump and probe beams, a broad spectrum can be acquired simultaneously (multiplex CARS) without tuning over the individual resonances (Figure 1) (4,6,18). However, due to the high peak-power laser field applied to the sample, in addition to this vibrationally resonant CARS signal, purely electronic third-order frequency mixing processes in the sample also lead to a large nonresonant background across the entire spectrum (2,18,21). Because this nonresonant background results from the interaction of the laser field with the sample of interest, creative manipulations are necessary for suppression or elimination of this nonresonant background so that the much smaller intensity resonant spectrum can be obtained (1,3,4,13). 

 Figure 1: Energy level diagram of the multiplex CARS process using broadband pump and Stokes fields with a narrowband probe field.			

With phase and polarization pulse-shaping techniques, multiplex CARS spectroscopy can be accomplished with a single laser beam from an ultrafast laser, eliminating complications associated with tuning, timing, and alignment between two separate beams, and significantly reducing or eliminating the nonresonant background (1). The whole array of pump and Stokes frequencies is provided simultaneously by the broadband pulse, and the resulting coherent molecular vibrations are probed by a narrow spectral part of the total bandwidth within the same laser pulse. The probe part of the beam is differentiated by shifting the phase and polarization of that narrow spectral region of the laser pulse. Fingerprint-region CARS spectra with up to 700 cm

  of bandwidth have been obtained previously using single-pulse methods (1,3). With a variation of a pulse-shaping and signal-acquisition scheme developed recently in our laboratory (21), sensitivity improvements have been achieved that allow spectral images to be obtained in a shorter acquisition time with up to 1000 cm

The new spectral interferometry method allows the real-time subtraction of the nonresonant background, after it has been utilized to amplify the resonant CARS signal, thus increasing the sensitivity of the single-pulse CARS spectroscopy (21). This allows rapid acquisition of spectra so that images of the chemical distribution in a sample can be constructed based on the spectrum at each point in the sample (22). In this adaptation, the phase and polarization of the narrow probe part of the laser bandwidth are shifted with respect to the rest of the laser spectrum (Figure 2), and two spectra are recorded simultaneously in two different polarization directions. By taking the difference of the two, the desired background-subtracted Raman-equivalent spectrum is obtained directly. 

Figure 2: The intensity profile of the laser used in this experiment is shown in red, and the phase and polarization profile is shown in blue. Note that both the polarization and phase of a narrow spectral region (~2 nm) are offset by 90Â° with respect to the rest of the spectrum to serve as a narrowband probe.			

Figure 3 shows the experimental system used for the broadband CARS instrument. A Ti:sapphire oscillator with 10-fs pulses, operating at a 90 MHz repetition rate, provides pulses with ~120 nm of bandwidth. The beam is expanded and then passes through an all-reflective 4f geometry pulse shaper. To shape the phase and polarization of the pulses, the light is first dispersed with a 600-grooves/mm diffraction grating and then passed through a spatial light modulator using a curved mirror. The spatial light modulator consists of two banks of 128 liquid crystal pixels whose birefringence is controlled by changing the applied voltage to the individual pixels. 

Figure 3: Experimental system: OSC = oscillator, CM = curved mirror, GR = grating, POL = polarizer, SLM = spatial light modulator, SLT = slit, OBJ = microscope objective, S = sample, FR = Fresnel rhomb (achromatic half-wave plate), WP = Wollaston prism, SWP = sharp-edge short-wave pass filter, SPEC = imaging spectrometer, CCD = two-dimensional charge-coupled device.			

After phase and polarization shaping, the pulse is again collimated and the light is focused through a 1.2-NA water-immersion microscope objective into a condensed-phase sample on an 

 piezoelectric translation stage parallel to the experimental table. After interaction with the sample, the light is collected through a 1.0-NA water-immersion objective and the laser frequencies are filtered out with a sharp-edge short-wave pass filter. The polarization of the light is rotated by 45° by an achromatic half-wave plate, and the signal is split spatially into two separate directions using a Wollaston prism. Both signal traces are focused into a spectrometer and the resulting spectra are imaged onto a two-dimensional CCD detector. 

 are the resonant and nonresonant transient polarizations, respectively, which give the CARS signal. The nonresonant contribution is entirely real, but the resonant part of the signal contains both real and imaginary parts. Also, the purely resonant part of the total signal 

is the smallest term, while the nonresonant part 

 is the largest term. The cross-term is linear in the nonresonant contribution, but also contains the real and imaginary parts of the resonant contribution. The technique used here detects this larger cross-term, in which the nonresonant signal effectively amplifies the resonant signal (21). 

The nonresonant background and resonant CARS signals are coherent, and while the resonant signal depends upon the phase of the probe part of the pulse, most of the nonresonant signal is produced by the broadband part of the pulse, which has a different phase. Thus, it is possible to implement interferometry between the resonant and nonresonant parts of the signal by controlling the phase difference between them. Inducing different phase shifts in the probe part of the pulse with respect to the broadband part results in different interference patterns between the resonant and nonresonant signals that are acquired simultaneously (21).  

To directly obtain the resonant CARS spectrum using broadband pulses, the nonresonant background must be eliminated. By rotating the polarization of the probe part of the pulse, the signal can be separated into two traces based upon the differences in polarization between different signal components (Figure 4a). After passing through the sample, the signals at both of these polarizations contain the same nonresonant background, but by inducing a phase offset of –90° in the probe, an equal but opposite interference results between the resonant and nonresonant signal in the two spectra (

) at the vibrational resonances, which is shown in Figure 4b for toluene. Note that these two spectra are acquired simultaneously. By subtracting one spectrum from the other, most of the nonresonant signal is subtracted in real time and only the imaginary part of the resonant CARS spectrum remains (Figure 4c). This method is called double quadrature spectral interferometry (DQSI) CARS (21). Note that the nonresonant signal from the sample itself serves as the local oscillator here, which amplifies the resonant signal significantly, providing a sensitivity improvement over previous CARS spectroscopy techniques in which the nonresonant signal is suppressed before detection (2,3,13). DQSI was first developed by Lepetit and colleagues (23) and has been used for CARS previously, but usually by acquiring two spectra under separate conditions (5,12,24). The major benefit here is that there is no need for an interferometer, because the interferometry takes place within the single beam. 

Figure 4: (a) Polarization directions of pump/Stokes (x) and probe (y) fields and two-spectrum detection scheme. (b) Spectra i and j for a probe phase of â90Â°. The relative intensity of the resonant signal to the nonresonant background is evident in this figure. (c) Difference between spectrum i and spectrum j, which gives the Raman-equivalent (imaginary) part of the resonant CARS spectrum. 			

Figure 5 shows DQSI CARS spectra of several common solvents, including toluene, acetone, methanol, ethanol, and isopropanol. The acquisition time for each spectrum is 10 ms. For each sample, the excitation volume is estimated to be about 40 aL (attoliters). The spectral resolution is about 35 cm

  , which is slightly worse than the limit of 30 cm

  imposed by the use of two pixels of the dual 128 pixel SLM. All spectra acquired spanned from 400 cm

, although only the spectral window of interest is displayed in Figures 5–7. 

Figure 5: Spectra of some common laboratory solvents obtained with double-quadrature spectral interferometry CARS.			

-dimethylformamide (DMF) was placed on top of the patterned polymer polydimethylsiloxane (PDMS), and the sample was sandwiched between two glass coverslips for imaging. Thin-films of polymethylmethacrylate (PMMA) and polystyrene (PS), which are known to phase separate (25), also were prepared by dissolving 1:1 PMMA–PS in chloroform and spin-casting the solution into a film approximately 2–5 μm thick (thickness verified with atomic force microscopy [AFM], data not shown).  

The samples are placed perpendicular to the laser beam (parallel to the table) and scanned through the laser focus in the 

 directions with the piezoelectric translation stage. A spectrum is obtained in 10 ms for each pixel in the images. Each image is 100 X 100 pixels, containing a total of 10,000 separate spectra. For the PDMS–DMF sample, the total image size is 30 X 30 μm, and the PS–PMMA  image is 20 X 20 μm. The total time for data acquisition and processing is about 3.5 min for each of the images shown. With current state-of-the-art spontaneous Raman microscopy systems, it typically takes about 1 s to acquire each spectrum, which would result in a total imaging time of 3 h for a scan of similar size and resolution (26). 

Spectra of PDMS and DMF are shown in Figures 6a and 6b. The PDMS exhibits a strong band at 460 cm

  while the DMF exhibits a peak at 830 cm

. Because each of these peaks is only present in the spectrum of one molecular species, the 460-cm

  peak specifically identifies the location of PDMS, and the 830-cm

  peak only appears where there is DMF. Figure 6c shows the analysis of the distribution of these two spectral peaks across the sample. It is clear from the spectral data that the two components are separated spatially into distinct domains and do not overlap in the sample. 

Figure 6: (a) CARS spectrum of pure PDMS. (b) CARS spectrum of pure DMF. (c) Image constructed by taking the spectrum at each point across a patterned sample of PDMS and DMF. Only the 460 cmâ1 (red, corresponds to PDMS) and 830 cmâ1 (blue, corresponds to DMF) peak intensities are plotted in this image.			

Figure 7 shows the results for the PS–PMMA spin-cast film sample. Again, the spectra for the individual components are shown (Figures 7a and 7b). However, because the spectra for the two polymers have similar features around both 1000 cm

, we analyzed the ratio of the these peak intensities for each pixel in the image. The contrast scale for the image in Figure 7c is shown. It is a false-color image in which the bright red corresponds to 1000 cm

  = 4, which is the ratio of the spectral peaks in the pure PS spectrum, and the dark blue is 1000 cm

Figure 7: (a) CARS spectrum of pure PS. (b) CARS spectrum of pure PMMA. (c) Image constructed by taking the spectrum at each point across a spin-cast mixture of PS and PMMA. The image contrast is based on the 1000/800 cmâ1 peak ratio. Note that a ratio of 0.5 corresponds to the PMMA spectrum (blue) and a ratio of 4 signifies that mostly PS is present (red). Here, one can also see the relative amounts of both components in the regions where they are mixed. 			

The spatial resolution in Figure 6 and Figure 7 is about 400 nm, which is less than ideal. For 800-nm light, the best spatial resolution observed to date is 230 nm due to the high numerical aperture of the focusing objective (1.2 NA) and the third-order nonlinearity of the CARS signal, which gives an enhancement of the spatial resolution over a one-photon process (27). The degradation of the spatial resolution is most likely the result of chromatic and achromatic aberrations and misalignment through the focusing objective, which can be significant due to the exceptionally broad bandwidth of the spectrum. Due to the increased demand for near-IR applications in microscopy, newer microscope objectives have improved aberration compensation capabilities in the region of interest to us (28). This should allow for significant improvements in the future. 

In addition to imaging multiple species simultaneously, there are two main advantages to taking a spectrum at each pixel and doing a peak ratio analysis for chemical contrast. First, as seen with the PS and PMMA sample, in mixed samples there are often overlapping peaks in the spectra of the molecules of interest. By looking at peaks individually, such as in the first example of PDMS and DMF, true chemical selectivity cannot be achieved for samples whose components have the same or similar spectral features. Second, components in a sample are not always separated into spatially distinct domains, but often are mixed. Using a peak ratio contrast mechanism gives information about the relative proportions of all components simultaneously at each pixel in the image. For example, in Figure 7c, the red regions are pure PS, and the dark blue regions are pure PMMA, but the light yellow and light blue regions in this figure correspond to mixtures of the two polymers. It is evident that the polymers separate into domains tens to hundreds of micrometers in size, but with smaller islands of pure and mixed composition interspersed within these larger domains. AFM images of these spin-cast PS–PMMA films (not shown) indicate that separate regions also differ in thickness from 50 nm to 700 nm, depending upon the initial concentrations of the polymers in solution. For more complex samples, one can utilize the entire spectrum rather than fitting just two distinct peaks, as was done here. 

This type of separation is especially prevalent in the outer lipid bilayer membrane of biological cells, where it is hypothesized that different types of lipids segregate into chemically and physically distinct domains. Questions remain as to the size and nature of these domains, but no direct chemical verification of their composition has yet been achieved in living cells, although there is considerable indirect evidence of their properties (20,29). Single-frequency (narrowband) and relatively narrow bandwidth multiplex CARS methods have been used to image the distribution of two specific lipids in model lipid membrane systems simultaneously (6,14). 

Sample damage due to three-photon absorption and subsequent local heating is a limiting factor in several of the samples that we imaged. Samples in solution or surrounded by water show increased resilience to photodegradation, but further sensitivity improvements still are necessary to obtain spectral images of polymer photoresists and vesicles of lipid bilayers without causing sample damage. The images shown above were taken with polymer samples that were several micrometers thick, while some polymer photoresists are less than 1 μm thick, and the cell membrane is only 5–10 nm thick. We estimate that two orders of magnitude greater sensitivity is required before this technique will be capable of acquiring a distinct spectrum in just 10 ms from a model membrane composed of a single lipid bilayer, and currently we are incorporating improvements to achieve this. In addition, we are implementing a higher resolution SLM and a laser with increased bandwidth that will extend the accessible spectral range to about 4000 cm

. This will allow us to see characteristic Raman bands, such as the carbonyl stretch (~1700 cm

) (19), which are prevalent in biological samples, at a higher spectral resolution than previously possible. 

CARS microscopy already has paved the way for new types of studies, whereby direct chemical information is obtained on interesting and relevant time and length scales without the need for labeling or molecular markers. Although this technique alone will not be able to achieve single-molecule sensitivity, the direct chemical selectivity of broadband CARS for molecules at higher concentrations will be a great complement to the single-molecule sensitivity of fluorescence resonance energy transfer (FRET) spectroscopy (30), fluorescence correlation spectroscopy (FCS) (31), two-photon fluorescence microscopy (29), and other fluorescence techniques, because broadband CARS spectra and fluorescence spectra can be obtained simultaneously. This could be useful, for example, in determining how a certain protein (at low concentrations) co-localizes within domains of different lipid composition. Phase changes of lipids and lipid-like molecules also can be studied via both CARS and fluorescence (6,29), and such changes are expected to play a key role in lipid microdomain formation and function (20). 

Single-pulse, interferometric CARS microscopy is a sensitive, chemically selective two-dimensional imaging technique. Using a single laser beam significantly simplifies the technique by eliminating many of the instabilities associated with using two separate, synchronized laser beams. By acquiring the broad fingerprint-region vibrational spectrum from 400 cm

  obtained at each pixel in the sample, analysis based upon several spectral features can be used to construct detailed images of the sample's chemical composition, even for sample components with peaks at the same frequencies. Three-dimensional imaging also can be performed with the current experimental system by depth profiling the spatial focus. This label-free imaging is an exciting new tool for the direct visualization of segregated chemical domains in polymer photoresists and in biological cells, where direct imaging has proven to be very challenging. While necessary sensitivity improvements are currently underway to achieve chemically selective, label-free, rapid imaging of single lipid bilayers, preliminary results have been extremely promising.  

The authors gratefully acknowledge the Department of Energy, contract DE-AC02-05CH11231 for funding of the instrumentation and the National Science Foundation for support of personnel. A.G. Caster acknowledges a National Science Foundation Graduate Research Fellowship for support. O. Nicolet acknowledges the support of the Swiss National Science Foundation. 

are with the Departments of Chemistry and Physics, University of California, Berkeley, and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California. 

is assistant professor with the Department of Chemistry and Biochemistry, University of Texas, Austin. 

September 2006. The authors rapidly acquire complete vibrational spectra in the fingerprint region using a single femtosecond laser for broadband coherent anti-Stokes Raman scattering (CARS) microscopy to image spatially variant compositions of condensed-phase samples.

Chemically Selective Imaging with Broadband CARS Microscopy

Over the past 30 years, X-ray fluorescence (XRF) has become the elemental technique of choice for the determination of parts-per-million to percentage concentration levels in many solid materials including metals, ores, rocks, glasses, powders, plastics, ceramics, and foodstuffs (1). The principles of XRF spectrometry are well-documented in the literature (2). A sample is irradiated with a beam of high-energy X-rays. As the excited electrons in the sample fall back to a ground state, they emit X-rays that are characteristic of those elements present in the sample. The individual X-ray wavelengths are then separated and measured via a system of crystals, optics, and detectors. Elemental concentrations in unknown samples are quantified by comparing the X-ray intensities against known calibration standards. The major benefit of XRF over arc or spark emission techniques is that it can analyze both conducting and nonconducting materials as well as inorganic and organic matrices with minimal sample preparation (3,4).  

The technique is available in two separate configurations — energy-dispersive (ED) and wavelength-dispersive (WD) XRF. The ED approach measures the intensity of the photon energy of the individual X-rays generated, whereas in WD spectrometry, the polychromatic beam emerging from a sample surface is dispersed into its monochromatic components or wavelengths with an analyzing crystal. A specific wavelength is then calculated from knowledge of the crystal and the diffraction angle (5).  

It is generally recognized that WDXRF has several advantages over EDXRF, including better spectral resolution (up to 10 times better for some elements), superior performance for light elements (B to Cl), and the ability to determine major concentrations of elements without risking saturation of the detectors. Figure 1 shows the periodic table, indicating all the elements that can be determined by WDXRF.  

 Figure 1: Elements that can be determined by WDXRF.			

The quality of the accuracy and precision of the data generated by WDXRF can very well be compared with that of traditional wet chemical methods, but with the clear advantage of faster analysis times. This translates into a significant reduction in the overall cost of analysis, as no complex, labor-intensive wet chemistry procedures are required. The other major benefit of the WDXRF technique is that in addition to conventional quantitative analysis using suitable calibration standards, the technique is able to analyze various types of materials in which no matching standards are available, or where the calibration procedures are time-consuming and expensive. This feature has become possible thanks to the development of powerful "standard-less" analysis software programs using stored calibration graphs. It is generally accepted that the higher performance and better capabilities of WDXRF are helping to push the analytical boundaries traditionally associated with the XRF technique. 

On the other hand, X-ray diffraction (XRD) is an analytical technique that looks at the X-ray scattering from crystalline or polymorphic materials. Each material produces a unique X-ray "fingerprint" of X-ray intensity versus scattering angle that is characteristic of its crystalline atomic structure. Qualitative analysis is possible by comparing the XRD pattern of an unknown material with a library of known patterns. Although its principles are different, XRD can be considered complementary to XRF. For example, XRF can tell you that a material is composed of iron and sulfur, but XRD can tell you that both iron sulfide (FeS) and elemental iron (Fe) are present. Furthermore, because XRD works with any crystalline solid, there is almost no limit to the types of materials that can be studied (6). Some of the materials that are typically characterized by XRD include chemicals, environmental dusts, rocks, minerals, metals, cements, pigments, and forensic samples.  

One of the major applications of XRD is to identify and quantify specific compounds or phases in materials that are organic in nature, such as foodstuffs or pharmaceutical compounds. These kinds of applications have evolved over the last few years mainly because of a new generation of solid-state detectors, higher quality optics, and the availability of sampling attachments. These technological improvements have led to both higher sensitivity, which is needed for the detection of minor and trace levels of crystalline compounds in pharmaceutical compounds, and higher resolution for improved spectral specificity in the presence of interfering species. 

To demonstrate the benefits of both the WDXRF and XRD techniques, let us take a closer look at some of the more challenging applications that are being carried out today in the pharmaceutical and food industries.  

Application of WDXRF to the Analysis of Foodstuffs

WDXRF has been widely used for the chemical analysis of foodstuffs, pharmaceutical raw materials, and agricultural crops (7,8). Standard element coverage is from sodium (Na) to uranium (U), with typical concentration levels from sub-part-per-million levels up to 100%. However, lighter elements (Be to O) can be determined in certain matrices with the use of synthetic multilayer crystals. Sample preparation is very simple. Sometimes, the sample can be analyzed as it is received, or the more common procedure is to dry the sample, grind it into a powder, and then press it into a pellet or tablet. The XRF data shown in this study were generated either on the low-powered (50-W) ARL OPTIM'X or the medium-powered (1.2-kW and 2.5-kW) ADVANT'X, (Thermo Electron SA, Ecublens, Switzerland) WD-XRF spectrometers. They both have been described in the open literature (9). A schematic of the ADVANT'X showing the principles of sequential operation is shown in Figure 2.  

Figure 2: Schematic of the WDXRF instrument used in this study.			

The analysis of infant cereals and milk powders is becoming an increasingly important application for XRF (7). However, one of its greatest challenges has been to determine the low-level nutrients like Se, Mn, Fe, and Zn with good precision and accuracy. For that reason, a comparison of the limits of detection (LOD) in ppm was made on a series of pelletized milk powders using three different excitation sources. This comparison is shown in Table I. The quantitative detection limits are similar for all three approaches, but there is a definite trend toward lower detection limits as the power is increased. Typical measurement precision values (ppm) for six separate analyses of the same pellet (using low power) are shown in the last two columns of the table. However, it is important to emphasize that even though this kind of precision is considered typical for low-level XRF work, the accuracy of the measurements depends on many other factors, including operator experience, sample preparation, calibration standards, and whether appropriate background correction is used.  

Table I:  Comparison of limits of detection (LODs) of a high (up to 4.2 kW), medium (1.2 kW), and low (50 W) power WDXRF system for the analysis of pelletized milk powders (t = measurement/integration time; NM = not measured) (Note: All precision and LOD date are ppm)			

Another example of the progress made in the capability of XRF to detect very low atomic numbers is shown in Figure 3, which shows a spectral scan of nitrogen in plant material. Ten years ago, nitrogen belonged to the list of the elements that could not be determined by WDXRF. Advances in multilayer crystal technology, the thickness and material of detector windows, and instrument sensitivity now allow nitrogen to be included in the list of elements that can be determined by XRF.  

Figure 3: A spectral scan of nitrogen in plant material obtained using a high-power WDXRF system.			

This is exemplified in Figure 4, which shows the nitrogen calibration curve obtained for various plant materials (tomato, hay, cabbage, lettuce, wheat, grass, leaves) using the same instrument.  

Figure 4: Calibration of nitrogen using various plant materials.			

Application of X-Ray Diffraction to the Analysis of Pharmaceutical Materials

Let us now turn our attention to X-ray diffraction. The new generation of X-ray diffractometers has stimulated the growth of the technique in the pharmaceutical and food industries both for research and development purposes and for routine quality control testing (10). For example, crystallographic, structural, and phase analysis can give pharmaceutical companies more complete characterization of new materials. However, in such applications, it is absolutely critical that the instrument offers high sensitivity combined with extremely good resolution down to low angles.  

Stability of pharmaceutical formulations as a function of relative humidity also can be tested using specially designed environmental chambers. To ensure that formulations will be stable under all possible storage conditions, it is important to know how the material reacts to changes in temperature. In particular, it is possible to know whether thermal expansion is isotropic (identical in all directions) or not (anisotropic). If a given formulation has preferred orientation and anisotropic thermal expansion, changes in storage temperature can result in tablet breakage or other formulation problems. For these kinds of manufacturing quality control applications, it is therefore important that in addition to high performance, the instrument also is fitted with suitable sampling accessories. 

With that in mind, let us look at some typical XRD applications that are being carried out in the pharmaceutical industry. The XRD data shown in this study were generated using an ARL X'TRA powder X-ray diffractometer (Thermo Electron SA) (11). A schematic of the instrument's geometry is shown in Figure 5.  

Figure 5: Schematic of the X-ray diffractometers used in this study showing the Î¸-Î¸ geometry.			

The design of this instrument makes it very suitable for the identification of polymorphic (crystalline) and pseudo-polymorphic compounds generally encountered in pharmaceutical and food compounds (12). Thanks to its high sensitivity, low concentration levels of polymorphic phases can be detected more easily. This can be seen in Figure 6, which shows a 1-h diffraction scan of X-ray intensity against scattering angle of a drug compound. The boxed area in green has been expanded to show the detection of trace levels of a secondary phase of the polymorph. This phase of the compound (ranitidine hydrochloride) was then quantified by standard calibration methods based on peak area measurements shown in Figure 7.  

Figure 6: Detection of a polymorphic compound present at trace levels (

September 2006. The authors discuss the benefits of X-ray fluorescence (XRF) for the determination of elemental nutrients in foodstuffs and X-ray diffraction (XRD) for the measurement and characterization of different compounds used in the pharmaceuticals industry.

Spectroscopy-09-01-2006

Limitations in Analytical Accuracy, Part I: Horwitz's Trumpet

Photoacoustic Spectroscopy

33rd Annual FACSS Meeting

Market Profile: Double-Beam UV-Vis Spectrophotometers

Chemically Selective Imaging with Broadband CARS Microscopy

New Developments in Wavelength-Dispersive XRF and XRD for the Analysis of Foodstuffs and Pharmaceutical Materials