# Spectrophotometers

## Holographic Sensors

Izabela Naydenova PhD, MSc, in Optical Holography, 2020

### Spectrophotometers

Spectrophotometers are often used as detection systems in holographic sensors because they can provide information about both the spectral characteristics and the intensity of the zero order and/or of the diffracted beam. The measurement of the characteristics of the diffracted beam provides better signal to noise ratio. Fiber-based spectrophotometers are particularly suitable for this task. The signal is collected by a collimating lens from a predetermined direction and then coupled to an optical fiber and sent to the spectrophotometer. When a double channel spectrophotometer is used, both the zero- and first-order diffracted beams can be measured.

URL: https://www.sciencedirect.com/science/article/pii/B9780128154670000074

## Color for Science, Art and Technology

Robert T. Marcus, in AZimuth, 1998

### 2.5.4Tristimulus colorimeters and specirocolorimeters

Early spectrophotometers were expensive and required skilled technicians to run and maintain them. Colorimetric calculations had to be done by hand and with mechanical calculating machines. Industrial color measurement became a common practice with the development of the colorimeter. Colorimeters were developed in the 1940s and, because of their lower cost and simplicity of operation, were in common use by the 1950s. Colorimeters have been made in all four of the CIE recommended geometries. They use three or four broad response filters to modify their light source in an attempt to duplicate a CIE illuminant and standard observer combination. Sample measurements do not result in spectral reflectance readings but give a direct conversion to either CIE tristimulus values or the coordinates of a uniform color space, such as L*a*b*.

The main problem with colorimeters is their inability to measure metamerism. Colorimeters generally allow for only one illuminant/observer combination and the determination of metamerism requires a minimum of two such combinations. Colorimeters using polychromatic illumination have been modified by filtering their light sources to have two illuminant/observer combinations. Another problem with colorimeters is their lack of accuracy caused by the difficulty of finding filters to accurately duplicate the CIE illuminant and observer functions. Colorimeters Can determine the color difference between two materials more accurately and are often referred to as color difference meters. Measurements with filter colorimeters should be made in accordance with standardized practices (AATCC 0002; American National Standard 1899; ASTM 0023).

As optics and computer technology progressed, spectrophotometers became much less expensive, faster and easier to operate. When the difference in cost between a spectrophotometer and a colorimeter narrowed, it appeared that spectrophotometers would entirely replace colorimeters. About that time, portable colorimeters were developed. Portability allowed color measurement to be taken directly to the shop floor or even to a remote location. The recent development of relatively inexpensive portable spectrophotometers make them likely candidates to replace the portable colorimeters. This is especially true for spectrocolorimeters – a spectrophotometer that only outputs tristimulus values and/or uniform color space coordinates. Spectrocolorimeters are less expensive than full function spectrophotometers, but can be used to determine of metamerism.

Colorimeters have been developed using video camera technology. These instruments are coupled with advanced image technology to make color measurements on small areas in a complex scene. This technology is particularly useful for materials whose appearance is naturally or intentionally non-uniform. Woven fabrics, patterned fabrics and marbled materials are examples of materials where conventional color measurement technology has not been particularly successful. Video based instruments may also be used for on-line applications, such as controlling the production of colored paper made as a continuous sheet.

URL: https://www.sciencedirect.com/science/article/pii/S1387678398800056

## Spectrophotometry

Peter A. van Nijnatten, in Experimental Methods in the Physical Sciences, 2014

### 5.2.5.1Changeover Points

In dispersive spectrophotometers, a scan over a wide wavelength range typically contains several wavelength points at which the instrument exchanges one or more components, such as filters, gratings, or detectors. If a step or jump occurs in a measured spectrum that cannot be contributed to the properties of the sample, the first thing, we have to check is whether the wavelength at which this step or jump occurs coincides with a changeover point.

A well-known changeover point in an ultraviolet/visible/near-infrared (UV/Vis/NIR) spectrophotometer is the wavelength at which the instrument switches from a NIR detector, typically a PbS or InGaAs photodetector, to a UV/Vis detector, typically a Si photodetector or photomultiplier tube (PMT). The detector changeover point is often at a wavelength for which both detectors are at the end of their usable wavelength range and have low sensitivity. For a PbS/PMT combination, the changeover point is typically set around 860 nm. For an InGaAs/PMT combination, it can be set to shorter wavelengths.

A typical problem is a jump at the detector changeover point due to the poor sensitivity of the PMT for longer wavelengths. This can be caused by a high gain setting of the detector electronics needed to cope with the lower signal but also amplifies stray-light. The same amount of stray-light should be measured when the beam is blocked (0% transmittance). Therefore, a proper baseline correction should include the 0% transmittance or reflectance measurement to avoid this jump.

Another important changeover point is the grating changeover wavelength, which for a UV/Vis/NIR spectrophotometer is usually chosen to coincide with the detector change. A grating change can lead to a large change in the beam polarization, as well as wavelength resolution. Both can have an impact on the response of the sample to the beam and lead to spectral artifacts. This effect we discuss in more detail in Sections 5.2.5.2 and 5.2.5.3.

URL: https://www.sciencedirect.com/science/article/pii/B9780123860224000054

## Sun Protection in Man

Colin M.H. Driscoll, in Comprehensive Series in Photosciences, 2001

### 24.4.1.3The scanning spectrophotometer

The scanning spectrophotometer differs from the previous two methods in that the fabric is illuminated using monochromatic rather than polychromatic radiation. A scanning monochromator is used to illuminate the sample with each wavelength of radiation. Transmitted radiation is collected using an integrating sphere and detected using a PM tube. When a sample is illuminated with monochromatic radiation any fluorescence from the sample must be taken into account. Fluorescence is the absorption of radiation of a given wavelength followed by emission at a longer wavelength and occurs in many fabrics. A common example of fluorescence occurs in white fabrics which are usually treated with optical brightening agents (OBAs) to improve their whiteness. OBAs are fluorescent materials, absorbing over the wavelength range 340–400 nm. A wide range of OBAs is available commercially. Many OBAs are stilbene derivatives, while benzoxazole and styryl derivatives are used also for polyester. They emit at blue wavelengths, typically 435–440 nm. In this measurement method, there is no further selection of wavelengths after the sample, so that if fluorescence occurs, the longer-wavelength emitted radiation will be attributed to the incident wavelength, resulting in an erroneous value for the fabric transmittance at that incident wavelength. Fluorescent radiation is accounted for by the use of UVR filters, such as Schott UG11, after the sample.

URL: https://www.sciencedirect.com/science/article/pii/S1568461X01800594

## Spectrophotometry

Joanne C. Zwinkels, ... James E. Leland, in Experimental Methods in the Physical Sciences, 2014

### 7.4.2Spectral Measurement Methods

The fluorescence spectrophotometer, also known as a fluorescence spectrometer or spectrofluorimeter, has been commercially available for more than 50 years. Conventional fluorescence spectrometers have typically used a broadband light source, such as a xenon (Xe) lamp, radiating over a wavelength range from the UV to the NIR, monochromators for wavelength selection of both excitation and emission light, and a photomultiplier tube (PMT) for the detection of emission. This arrangement allows for the collection of a single photocurrent at any given pair of excitation and emission wavelength values, Φijj, λi). This value is expressed here as a radiant power, Φ, since the measured photocurrent should be directly proportional to the radiant power entering the detection system in Watts, assuming that the detector response is linear with Φ and the dark current is zero. An excitation spectrum is measured at a fixed λ, while μj is scanned from j = 1, …, m. Similarly, an emission spectrum is measured at a fixed μ, while λi is scanned from i = 1, … , n.

The fluorescence spectrometer most commonly used for the collection of spectra is a steady-state instrument, meaning that the excitation beam is continuous, not pulsed, and the integration time of the detector is on the order of seconds, resulting in a signal that is time averaged. This “steady-state” signal does not give fluorescence lifetimes or other time-resolved information related to the excited-state kinetics of the fluorophore. The use of the steady-state fluorescence spectrometer is the main focus of this chapter. The power of the excitation beam may change during the collection of a spectrum, either due to time-dependent fluctuations at a fixed wavelength or due to wavelength-dependent differences due to the spectral shape of the lamp radiation. A compensated fluorescence spectrometer uses a reference detector to monitor these power changes and to compensate for them. Since the sample's measured fluorescence signal (S) is directly proportional to the excitation reference signal (R), changes in the sample signal due to power changes in the excitation beam can easily be corrected by taking the ratio S/R to give a corrected signal SC.

In the past 10 years, multichannel detectors have replaced PMTs, and polychromators or spectrographs have replaced monochromators in some instruments, enabling the collection time of spectra to be shortened by collecting intensity values at multiple wavelengths, simultaneously. It should be recalled that the actual radiometric quantity being measured can be a radiant flux, spectral irradiance, or spectral radiance, depending upon the geometric configuration, although it is common practice to simply use the term “intensity” (see Section 7.2.2).

The use of these multichannel detectors has opened up new fluorescence applications in the areas of in situ monitoring, chemical fingerprinting, and spectral imaging. The use of EEMs has also increased significantly due to the improved speed of collection that these components make possible, a factor of 10 faster being common. The ability to collect an entire spectrum at once has also made multichannel detectors desirable in portable instruments, where a fixed grating makes the instrument more rugged in the field and much cheaper to produce. Photodiode arrays (PDAs) and charge-coupled devices (CCDs) are the multichannel detectors most commonly used. Each photodiode or pixel in these detectors gives an independent signal, measuring the amount of light incident on it for a given sampling geometry. The polychromator is used to image the fluorescence spectrum onto the multichannel detector, such that each diode or pixel is measuring the intensity of light at a different wavelength.

Each of these fluorescence detection systems has its advantages and disadvantages. Multichannel detectors, in addition to having faster collect times for spectra, are less likely to be damaged by bright light, such as room light and sunlight, than PMTs. Si photodiodes and CCDs typically used for visible light detection are also more sensitive in the NIR out to 1100 nm, whereas corresponding PMTs are only sensitive out to about 800 nm.

The main advantage of a PMT is a larger dynamic range, as much as six orders of magnitude without the use of attenuators, which is one to two orders of magnitude greater than that of silicon-based multichannel detectors. A PMT also has a larger active area per channel, making it more sensitive under typical light-collection conditions. In addition, the most commonly used PMTs for visible light detection are more sensitive in the UV down to about 250 nm, whereas the corresponding Si-based multichannel detectors are only effective down to about 400 nm. PDA and CCD detectors have similar performance in most areas, but the CCD is typically more sensitive than the PDA, making the CCD more effective for low-light intensity applications.

URL: https://www.sciencedirect.com/science/article/pii/B9780123860224000078

## On-line Measurement

R.A. Potyrailo, in Encyclopedia of Materials: Science and Technology, 2001

### 3.1Process UV/Visible Spectroscopy

Two types of spectrophotometers commonly used for UV/visible process applications include scanning and photodiode array (PDA) analyzers. The relatively delicate scanning instruments are typically located in a safe area such as a control room and are used with a fiber-optic link to couple the analyzer to the sample. PDA analyzers usually are rugged enough to be located directly in the process area. They can be also used with fiber-optic links multiplexing several probes with a single instrument. In the absence of special considerations, fiber-optic instruments are generally slightly less accurate and stable compared to instruments without fiber-optic links because of the smaller amount of light transmitted through the fibers and fiber-induced instabilities in the measurement system. Other types of process UV/visible analyzers are single-and multichannel filter-based photometers. They are generally robust enough for in-line operation (Sherman 1996).

Advances in optoelectronic components have significantly improved the performance of process UV/visible analyzers. These advances include discharge lamps with lifetimes of thousands of hours, heat-resistant interference filters with high optical transmission, and silicon UV photodiodes with high signal-to-noise ratio and temperature resistance. In addition, probe construction and materials have been considerably improved, which have made possible in-line applications of probes in high-temperature chemical processes. Figure 3 shows the performance of a fiber-optic UV probe for monitoring a high-temperature industrial chemical process.

Characterization of analytes with excessively high or limited absorbance requires special designs of process probes or flow cells. For example, opaque liquids are measured using single- or multiple-bounce attenuated total reflectance (ATR) elements (Danielsson and Sheng 1994) or multimode evanescent-wave optical fiber sensors (Potyrailo et al. 1999). Long-path, small-volume capillary cells (hollow waveguides) are used for analysis of weakly absorbing analytes. Use of 1–4 m long hollow waveguides for spectroscopic analysis of liquids can provide up to a 1000-fold enhancement in sensitivity over a conventional 1 cm long transmission cell (Wang et al. 1995) if the analyte solution has a higher refractive index than that of the hollow-fiber material. In this case, the light is guided in the liquid that serves as the fiber core. Also, materials for hollow fibers are now available that have a refractive index less than of that of water, permitting analysis of aqueous solutions (Dreb and Franke 1996).

One of the possible limitations of UV monitoring is the potential for an activation of photochemical reactions in process samples. Another limitation is the solarization of conventional quartz optical components exposed to wavelengths below 230 nm for extended periods of time. This effect is manifested as a decrease in UV transmission at short wavelengths and is induced by the formation of impurity-based color centers with an absorption band at 214 nm. For deep UV applications, special optical fibers are available with hydrogen infused into the silica core of the fiber.

URL: https://www.sciencedirect.com/science/article/pii/B0080431526011335

NIKOLAI V. TKACHENKO, in Optical Spectroscopy, 2006

### 6.2.1Optical Scheme

A general purpose fluorimeter should provide the widest possible range of the excitation wavelengths and should be capable of measuring the emission spectrum in the broadest wavelength range. Combination of a lamp and monochromator can be used as the excitation source, as shown in Fig. 6.2. This is a typical solution to cover a wide spectrum range of excitation. The excitation part of fluorimeters is schematically similar to spectrophotometers (Figs. 5.3 or 5.4), although different types of lamps are usually used in these two types of devices.

When there are no demands for wide excitation spectrum range, fluorimeters can be built up using excitation sources with a fixed wavelength or relatively narrow wavelength range. Then the monochromator can be replaced by a set of color or interference band pass filters. Also an emitting diode or a laser can be used in place of the lamp and monochromator. This usually makes the system cheaper, compact and more reliable.

The excited sample emits photons in all possible directions and a carefully designed instrument should collect as much as possible of the emission. Therefore, the detection part of the instrument starts from the light collecting mirror M3 in Fig. 6.2. The purpose of the instrument is to measure the spectrum of the collected light. This can be done by a photomultiplier tube coupled with a monochromator. The photomultipliers are the most sensitive photo-detectors in UV and visible parts of the spectrum and are a natural choice if the emission efficiency of the samples is expected to be low.

One can notice that in spectrophotometer the monitoring light was modulated to increase the accuracy of the light intensity measurements, whereas in case of the fluorimeter modulation and synchronous detection was not used in the scheme presented in Fig. 6.2. From the standpoint of the light intensity measurements the difference between these two types of instruments is in the value of the intensity to be measured. The spectrophotometers are working with relatively high light intensities and must provide a high relative accuracy of the intensity measurements, whereas the fluorimeters are designed to detect as low as possible intensities. For detection of a very weak photon flux the photon counting is the best approach.3 The difference in application of the photon counting to measure absorption and emission spectra is illustrated in the following example.

#### Example 6.1Comparison of the photon counting method for applications in emission and absorption spectra measurements

A typical maximum counting rate of a photon counting module is 20 MHz, e. g. 2 × 107 counts per second. At this rate the probability to count two incoming photons as one is relatively high and to keep response of the module in a linear regime the acceptable counting rate is ≲ 106 s−1. At 106 s−1 rate during 1 second the signal, i. e. the average number of counts, is N = 106 counts, and its standard deviation is $\Delta N=\sqrt{N}={10}^{3}$ counts (see square root law, eq. (4.23)). Thus, the intensity is measured with relative accuracy δ = 0.001, or 0.1%, which is very good accuracy for the emission spectrum measurement, but being used in absorption spectra measurements provides the absorbance resolution of 0.005 (see Section 5.3.3),4 which is rather poor result in comparison to spectrophotometer specifications listed in Section 5.4.1. In the same conditions, if the collection time at single wavelength is reduced to 0.01 s, the emission spectrum is still measured with acceptable accuracy of 1%, while the absorbance resolution is dropped down to 0.05 value, which is unacceptable in most cases.

URL: https://www.sciencedirect.com/science/article/pii/B9780444521262500307

NIKOLAI V. TKACHENKO, in Optical Spectroscopy, 2006

### 5.3.1Spectrum range

The spectrum range of the considered spectrophotometers is determined by a number of factors. The most essential are:

the spectrum of the source of monitoring light,

the sensitivity spectrum of the photo-detector used, e. g. photomultiplier tube,

the spectrum range of the wavelength selecting device, e. g. monochromator.

In the visible and near infrared spectrum the tungsten halogen lamps are usual sources of the light for general purpose spectrophotometers. In the ultra-violet (UV) part of the spectrum the thermal sources of the light are inefficient (see the black body emission discussion in Section 1.2.1). Specially designed deuterium lamps are used as the sources of the monitoring light in the UV range. They can be used in far UV range, but at shorter wavelengths another problem arises – the transparency of the output window of the lamp bulb. The high quality quartz absorbs the light at wavelengths shorter than 200 nm. Synthetic silica, sapphire and magnesium fluoride are materials which allow to expand the range to 180, 170 and 120 nm respectively.

The photo-detectors were discussed in Section 4.2 on 72. The principal UV limit for the photomultiplier tubes (PMT) is also determined by the material of the entrance window.6 Therefore, 190 nm seems to be also a reasonable limit from the viewpoint of the PMT availability, also there are PMTs which can work up to 160 nm (Cs-Te photo-cathode and synthetic silica window), or even up to 115 nm (Ce-I photo-cathode and magnesium fluoride window). The red limit is determined by the material of the photo-cathode and for a popular S-20 photo-cathode it is roughly 840 nm. There are only few photo-cathode which can work up to 1000 nm, and if longer wavelengths are needed another photo-detector have to be used. For example, with a Ge photodiode the red limit can be shifted to 1.7 μ in expense of sensitivity (as compared to the photomultiplier).

Monochromators (diffraction gratings) can be designed to operate in any optical range, see Section 2.3 for more information on gratings and monochromators. There are, however, a few things to keep in mind while selecting a grating for a spectrophotometer. The gratings are designed to have the highest diffraction efficiency at a certain wavelength which is usually specified as blazed wavelength. The grating can be optimized for diffraction order other than the first. In other words, the grooves number is important characteristic of the grating but not the only one to be considered in design of an optical instrument. Another important property of the gratings is that the diffraction takes place in all possible diffraction orders. For example, if one wants to obtain the monitoring light at 300 nm and has found a suitable grating providing 300 nm light in the first diffraction order, then, unavoidably, there will the second order diffraction at 600 nm, the third order at 900 nm and so far, propagating in the same direction as the first order diffraction. The efficiency of the second and higher diffraction orders is much lower than that of the first order, but the higher order diffraction cannot be eliminated completely. Therefore, for devices working in a wide spectrum range the wavelength selecting monochromators are usually combined with a set of color filters which are used to cut off the light diffracted at higher orders and which are changed during the wavelength scan.

In conclussion, typical wavelength range of a simple spectrophotometer is 300–900 nm, which can be provided by a single ligth source (tungsten halogen lamp) and a general purpose photomultiplier tube. To extend the range further to the ultraviolet part an editional light source have to be used. To cover the infrared part of the spectrum a combination of detectors must be used.

URL: https://www.sciencedirect.com/science/article/pii/B9780444521262500290

## Spectrophotometry

Arnold A. Gaertner, ... Thomas A. Germer, in Experimental Methods in the Physical Sciences, 2014

The types of detectors used in spectrophotometers can range from PMTs to various semiconductor photovoltaic or photoconductive devices. PMTs have very high sensitivity and rely upon the photoelectric effect, followed by cascaded secondary electron amplification by a dynode structure. The spectral range of PMTs is dependent upon the photocathode material, and extends from the deep ultraviolet to the near infrared. Their responsivity depends upon the details of their construction (size and shape) and operating parameters (e.g., temperature and voltages applied to the photocathode and dynode elements). They can be operated in a single photon counting mode or as a conventional continuous detector. Of the photovoltaic or photoconductive detectors, silicon is the most popular, since it has high sensitivity, large area, and uniformity, and for some types can have very high linearity, but it is limited in its spectral response to wavelengths less than 1100 nm. For longer wavelengths, it is common to use InGaAs detectors, which operate between 800 and 1700 nm, and extended InGaAs detectors, which operate between 800 and 2500 nm. PbS detectors, which are photoconductive devices and used from 900 to 3000 nm, and germanium detectors, which operate from 800 to 1800 nm, are still used in commercial spectrophotometers but are falling out of favor, since their performance is generally superseded by regular and extended InGaAs detectors. Beyond this spectral region, thermal detectors such as pyroelectric and thermopile detectors are used. The infrared sensors generally need to be cooled or temperature stabilized, either thermoelectrically or with a cryogen. The infrared sensors are usually used with chopped radiation sources, due to their sensitivity to background radiation, and because many are inherently ac devices.

One- and two-dimensional array detectors are commonly constructed from the semiconductor materials. CCDs, PDAs, and complementary metal oxide semiconductor (CMOS) arrays fabricated from silicon find themselves used in a wide variety of consumer applications, including digital cameras and flat-bed scanners. As a result, they are relatively inexpensive. All of these detectors share the fundamental absorption properties of silicon, but differ in how they are addressed and read out. CCDs and CMOS sensors integrate charge that has accumulated at a junction, while PDAs are addressable photodiodes and measure photocurrent. For this reason, CCDs and CMOS sensors can have an extremely wide dynamic range, since the integration time can be varied accurately from milliseconds to many minutes. Array detectors using the other semiconducting materials are usually in the form of PDAs.

Detectors are often classified according to their noise equivalent power (NEP), with units of W Hz 1/2. When multiplied by the measurement bandwidth, the NEP indicates the radiant power level at which the signal-to-noise ratio would be unity. Because a detector has a responsivity that is wavelength dependent, the NEP also depends upon wavelength, but is usually quoted at a single wavelength. There are two dominant noise sources in solid-state detectors: Johnson noise and shot noise. Johnson noise results from the thermal motion of electrons in a resistor and is proportional to the square root of the device's resistance. Shot noise is due to the Poisson statistics associated with the random arrival time of the discrete electrons in the detector. For most solid-state detectors, the NEP is dominated by Johnson noise and thus is proportional to the square root of the area A of the detector. Thus, it is common to characterize detectors by a specific detectivity, given by

(3.44)${\mathit{D}}^{\ast }=\frac{\sqrt{\mathit{A}}}{\mathrm{NEP}}.$

The higher a detector's D∗, generally, the more sensitive it is. For further information, the reader should consult with the technical literature from specific manufacturers.

There are a few important considerations for detectors used in spectrophotometry. Spatial and angle of illumination uniformity is important if the detector is used directly behind or at the image of the exit slit of a monochromator. PMTs usually have a wire grid in front of the photocathode, which imparts strong spatial variations across its sensitive area. The use of a diffuser in front of the detector can improve the effects of nonuniformity. Even better, but usually at the loss of some signal, an integrating sphere can be used with a detector to give very good uniformity.

A very important consideration in all detector applications is linearity. That is, the signal recorded should be proportional to the radiant quantity incident upon the detector. It is important to verify the linearity of the detectors being used in spectrophotometry. Linearity should be considered with the detector and its associated electronics taken together as a package or detection system. The radiant quantity is radiant power if the beam underfills the detector aperture and is irradiance if the beam overfills this aperture. Usually, with modern electronics design, the low power end of detector responsivity can be extremely linear. However, all detectors have a level at which they saturate, usually due to the space charge that accumulates in its active region. As a result, detectors often exhibit nonlinearity that can either be a function of local irradiance (power density) rather than total radiant power. In cases where it is shown that the detection system nonlinearity is reproducible, the effects of this nonlinearity can be corrected [24].

There are a number of ways of checking for linearity. These methods can be divided into dependent methods and independent methods. The dependent methods are based upon performing spectrophotometric measurements on a set of known samples, such as a solution of different concentrations of an absorbing compound in a solvent or a set of independently calibrated optical filters, and testing for linearity in the measured result. For the method that uses absorbance measurements on different solutions, which is based on the Beer–Lambert law discussed in Chapter 2, it does not detect nonlinearity due to absorbance readings being off by a common factor; thus, it needs to be used in combination with a separate check for linearity [25].

The independent methods assess the linearity of the system, without the use of a standard. These can be broadly classified into three different methods: superposition, attenuation, and differential, which are described below.

The superposition method relies on exposing the detector to two independent sources of radiation [26–29]. One measures each of the two signals, S1 and S2, and then both at the same time S1 + 2. If the detector is linear, then S1 + S2 = S1 + 2. This test is performed over a range of S1 + 2 to assess the range over which this condition holds true. The measurements from the superposition method that sums light over two paths can be combined with a technique where each path has more than one attenuation setting. Such a device can be used to determine the nonlinearity function using a least-squares fit to a model nonlinearity [26,28,29].

A variant of this method, the flux doubling method, uses two apertures in the beam, opening and closing one or both of them to read the three signal levels. Figure 3.15 shows a schematic of a device that can be placed in the sample position of a spectrophotometer. Although the flux doubling method produces sparse, exponentially spaced data with cumulating uncertainties, it is a recommended method for checking the linearity of a spectrophotometer.

The attenuation method uses a set of unknown absorbing filters [29]. If the transmittances are τ1, τ2, …, τN, then combinations of filters, say τ1 and τ2, should yield the product τ1τ2. By performing a sufficient number of these measurements, using not just two, but every combination of the filters, one can determine the values of each of the transmittances and the linearity in the system over a wide signal range. This method is fairly easy to perform in a spectrophotometer, since it uses the established setup for which it is designed. However, one should be careful to avoid interreflections between the filters, which can cause the total transmittance to not follow the simple product rule. One way to minimize interreflections is to slightly tilt these filters in opposite directions.

The differential method applies a small, constant ac fluctuation to the lamp power and measures the ac fluctuation of the detected signal [30]. If the detector is linear, the ratio of the ac fluctuation to the dc value will remain constant. Different filters can be placed in the beam to change the overall power level. It may seem logical to perform this with a single sample having spectral features covering a wide range of transmittances (see, e.g., Fig. 3.13). However, the ac modulation of the lamp radiance will depend upon wavelength. This method is more difficult to perform in a standard spectrophotometer, because one does not necessarily have direct access to the lamp power.

URL: https://www.sciencedirect.com/science/article/pii/B9780123860224000030

## THE QUANTUM EFFICIENCY OF BENZENE AS A FUNCTION OF TEMPERATURE AND EXCITATION WAVELENGTH

Michael D. Lumb, L.C. Pereira, in Organic Scintillators and Scintillation Counting, 1971

### Experimental

The sample was contained in a cylindrical spectrophotometer cell of 12 mm. diam. and 15 mm. depth which(12) formed an integral part of a specially designed Dewar. Fig. 1 shows the observation conditions in the spectrofluorophosphorimeter.(19) Using this arrangement, the fluorescence and phosphorescence emission was observed from the same face of the sample on which the excitation radiation was incident and thus reduced considerably any self-absorption effects. Excitation was provided at 240 ± 2 mµ by a 150-watt water-cooled deuterium lamp and monochromator with D3P filter.(20) This incident radiation was prevented from interfering with the emission spectrum by placing at the entrance slit of the second monochromator, a 1 cm. thick filter which consisted of a 0.1 M solution of benzene in cyclohexane to which a few drops of carbon tetrachloride had been added.

The pure benzene (Matheson, Coleman and Bell, spectroscopic grade) was diluted with either EOA, a mixture of ether, iso-octane, and ethanol in the proportion by volume of 3: 3: 1 respectively or with EPA.(21)

For measurements on neat benzene, a single crystal was formed inside the spectrophotometer cell. The crystal was grown at 4°C from a benzene seed crystal produced previously by rapid freezing. This growing procedure took several hours but a clear benzene crystal which filled the spectrophotometer cell was eventually obtained.