How is the reflectance spectrum of solids measured?

I was reading this question about autumn leaf colors. One of the answers refers to an article by Archetti et al. In the article, box 4 (page 5) shows the reflectance spectra of leaves of different color. How is the reflectance spectrum of such solid materials measured? There was a recent question about spectrophotometers but it appears to assume the sample is in a liquid form.

As the name implies, reflectance spectra are measured from light reflected off an object. Any object with reflects light, such as any opaque object) will work for this technique; to me this seems like solids are ideally suited for reflectance spectrphotometry. You might be used to transmission or absorbance spectrophotometry, which measures the amount of light transmitted or lost after passing through a sample. These methods are typically used for liquids which allow passage of light to some extent.

The paper (1) cited by the review you mention says that they used a "RAMSES-ARC hyperspectral radiance sensor," which is probably just as awesome as it sounds. In principle reflection spectrophotometry works very similarly to transmission-based spectrophotometry: generate monochromatic light, shine it at the sample, and measure the intensity of light that comes back at that wavelength (or over a range of wavelengths)$^†$. If you do this for many different wavelengths of light, you have a reflectance spectrum. This link might have some useful information.

$^†$ Edit: Modern-day spectrophotometers use a more efficient method in which broad-band light is passed onto the sample and the response at a single wavelength can later be mathematically reconstructed. If you're interested in these types of details, refer to Fourier Transform spectroscopy.

(1): Doring TF, Anchetti M, Hardie J. (2009). Autumn leaves seen through herbivore eyes. Proc. R. Soc. B 282(1801): 121-127.

Diffuse reflectance spectroscopy of fibrous proteins

UV–visible diffuse reflectance (DR) spectra of the fibrous proteins wool and feather keratin, silk fibroin and bovine skin collagen are presented. Natural wool contains much higher levels of visible chromophores across the whole visible range (700–400 nm) than the other proteins and only those above 450 nm are effectively removed by bleaching. Both oxidative and reductive bleaching are inefficient for removing yellow chromophores (450–400 nm absorbers) from wool. The DR spectra of the four UV-absorbing amino acids tryptophan, tyrosine, cystine and phenylalanine were recorded as finely ground powders. In contrast to their UV–visible spectra in aqueous solution where tryptophan and tyrosine are the major UV absorbing species, surprisingly the disulphide chromophore of solid cystine has the strongest UV absorbance measured using the DR remission function F(R). The DR spectra of unpigmented feather and wool keratin appear to be dominated by cystine absorption near 290 nm, whereas silk fibroin appears similar to tyrosine. Because cystine has a flat reflectance spectrum in the visible region from 700 to 400 nm and the powder therefore appears white, cystine absorption does not contribute to the cream colour of wool despite the high concentration of cystine residues near the cuticle surface. The disulphide absorption of solid l -cystine in the DR spectrum at 290 nm is significantly red shifted by

40 nm relative to its wavelength in solution, whereas homocystine and lipoic acid showed smaller red shifts of 20 nm. The large red shift observed for cystine and the large difference in intensity of absorption in its UV–visible and DR spectra may be due to differences in the dihedral angle between the crystalline solid and the solvated molecules in solution.

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Visible and Near-Infrared Reflectance Spectroscopy for Investigating Soil Mineralogy: A Review

Clay minerals are the most reactive and important inorganic components in soils, but soil mineralogy classifies as a minor topic in soil sciences. Revisiting soil mineralogy has been gradually required. Clay minerals in soils are more complex and less well crystallized than those in sedimentary rocks, and thus, they display more complicated X-ray diffraction (XRD) patterns. Traditional characterization methods such as XRD are usually expensive and time-consuming, and they are therefore inappropriate for large datasets, whereas visible and near-infrared reflectance spectroscopy (VNIR) is a quick, cost-efficient, and nondestructive technique for analyzing soil mineralogic properties of large datasets. The main objectives of this review are to bring readers up to date with information and understanding of VNIR as it relates to soil mineralogy and attracts more attention from a wide variety of readers to revisit soil mineralogy. We begin our review with a description of fundamentals of VNIR. We then review common methods to process soil VNIR spectra and summary spectral features of soil minerals with particular attention to those <2 μm fractions. We further critically review applications of chemometric methods and related model building in spectroscopic soil mineral studies. We then compare spectral measurement with multivariate calibration methods, and we suggest that they both produce excellent results depending on the situation. Finally, we suggest a few avenues of future research, including the development of theoretical calibrations of VNIR more suitable for various soil samples worldwide, better elucidation of clay mineral-soil organic carbon (SOC) interactions, and building the concept of integrated soil mapping through combined information (e.g., mineral composition, soil organic matter-SOM, SOC, pH, and moisture).

1. Introduction

Soils are open, complex, and dynamic systems as well as fundamental natural environments for animals, plants, microorganisms, and human interaction [1]. Mineral composition is the most fundamental property of a soil, and soil minerals account generally for half the soil volume [2]. According to Churchman [3], clay minerals in the soil context are “secondary inorganic compounds of <2 μm size” including Fe, Al, and Mn oxides (hydroxides and oxyhydroxides), as well as noncrystalline phases. Importantly, they are the most reactive and important inorganic components in soils, and they occur commonly in close association with the most reactive organic matter [4, 5]. Clays influence soil function through both their bulk properties and their associations with their huge outer/inner surfaces (e.g., cation exchange capacity [6]). The effort involved in comprehensive understanding of the nature of soil minerals is of particular importance as they may help us explain and predict how different soil types function [7].

However, soil mineralogy (mainly clay mineralogy) is still a minor topic in soil sciences. This may be due partly to the unjustified assumption that a given soil mineral will have the same properties as those of its better-crystallized counterpart that formed in a more “geologic” context (e.g., sedimentary kaolinite will have the same properties as pedogenic kaolinite) [4]. Revisiting soil mineralogy has been gradually important, for instance, in terms of the manner by which soil minerals are defined and investigated [8].

The most commonly used method to characterize soil minerals is XRD, which is fundamentally qualitative. Since soil clay minerals are generally more complex and less well crystallized than those of geological environments [9–11], they display more complicated XRD patterns [12, 13]. Despite quantitative improvements of XRD [14], mineral characterization is usually expensive and time-consuming [2]. Some chemical extraction procedures can be useful in the analysis of Fe oxides. However, this is expensive, time-consuming, and can complicate our scientific interpretation of the soil by changing the chemical equilibrium between soil solution and solid phases in soil specimens [15, 16]. Thus, these conventional analyses are not appropriate for larger scale soil studies, and we must use an alternative method to target and characterize soil minerals.

Visible and near-infrared reflectance spectroscopy (VNIR, 350–2500 nm), that is, the study of light of the visible and near-infrared reflected from material surfaces, is a quick, cost-efficient, and nondestructive technique in soil sciences [17, 18]. This technique has been greatly developed in soil sciences in the past several decades and has seen apparent exponential growth over the past 20 years [19]. VNIR has been of increasing interest for the analyses of soil parameters including soil organic carbon, pH, bulk texture, elemental concentration, and cation exchange capacity [20, 21]. In soil mineralogy, VNIR can be used to characterize various soil mineralogic properties such as clay mineral composition, clay content, and mineral weathering/alteration degree, although quartz and feldspar have weak/nonexistent absorption in the VNIR range [22–24]. In this paper, we aim to bring readers up to date with VNIR as it relates to soil mineralogy and we seek to attract more attention from readers to revisit soil mineralogy.

2. Fundamentals of VNIR

The VNIR part of the electromagnetic spectrum includes both the visible (350–780 nm) and near-infrared (780–2500 nm) ranges, which overlaps with the optical radiation range (100–1000 nm Figure 1). Sometimes, the 350–1000 wavelength range is referred as VNIR (visible-near-infrared), and the 1000–2500 range is referred as the SWIR (short-wave infrared) in remote sensing literature [25]. The human eyes and brain can process spectral information from the visible region and see color, while modern spectroscopy can observe precise details over a much broader wavelength range.

2.1. Absorption, Scattering, and Emission

When photons enter a solid, liquid, or gaseous material, they will either be absorbed, reflected from its surface, or pass through it [26]. The reflective process is defined as scattering, and the scattered photons can be detected and measured. Photons can also be detected when they are emitted from a surface with a temperature above absolute zero [25]. Three general physical processes (i.e., electronic transitions, vibrational transitions, and rotational transitions) result in the absorption bands in the spectra of materials. The absorption bands in the VNIR range are derived from both the electronic and vibrational transitions [27, 28].

2.2. Causes of Absorptions in the VNIR Region
2.2.1. Electronic Transitions

Discrete ions and atoms have independent energy states. A photon is emitted from an atom when one of its electrons moves to a lower energy state. When an atom absorbs a photon of a given wavelength, its electrons move from a relatively low electron state to a higher one [25]. These electron processes occur because of their high energy and mobility. The electronic processes are mainly caused by (1) crystal-field effects. Since iron is a very common transition element in minerals, a common electronic process revealed in the visible region is due to unfilled d-orbitals of Fe-oxide minerals [24, 29]. Electron energy levels are influenced by many factors, including the valence state of the atom (e.g., Fe 2+ and Fe 3+ ), the type of ligands, the asymmetry of the location it occupies, the distance between the metal ion and the ligand, and the deformation degree of the site [28]. (2) Charge transfer: it is dominated by mineralogy, and it is hundred times more powerful than the crystal-field effects. It is the main reason of the red color of hydroxides and Fe oxides. Moreover, the conduction bands and color centers can also be causes of the electronic transitions in some minerals [25].

2.2.2. Vibrational Transitions

The bonds in a crystal lattice or molecule vibrate like springs. The molecule’s mass and the strength of each molecular bond dominate their vibration frequency [25]. The absorption bands in the VNIR range are observed as a consequence of molecular vibrations [30]. Soil minerals (e.g., phyllosilicate and carbonate minerals), in particular, have unique absorption features in the VNIR region due to overtones and vibrational combinations related to the stretching and bending of the molecular bonds such as O-H, C-H, C-C, and N-H [31].

3. Spectroscopic Measurements

3.1. Spectral Preprocessing

The raw spectra are usually preprocessed through various approaches to accentuate features and remove signal noise [32]. The processed soil spectra facilitate mineral identification, and the accuracy of soil mineral prediction is greatly improved through the use of various preprocessing methods [33]. The following preprocessing methods for spectra have been used in previous soil mineralogic studies.

3.1.1. Continuum Removal Approaches

The continuum removal approach aims to remove background noise and isolate particular absorption features for identification and analysis [34]. The continuum is usually determined using local maxima to generate a hull of boundary points (Figure 2(a)) [22]. All the boundary points are fitted by straight-line segments, and then, the continuum removal is calculated by removing the original reflectance intensities from corresponding intensities of the continuum (Figure 2(b)) [23]. Continuum removal analysis is a particularly robust tool for detecting and predicting iron oxides and phyllosilicate minerals. Thus, it is feasible to substitute a statistical method to apply to soil mineralogy studies [10, 20, 22, 24].

Absorption bands in the VNIR region can be described by geometrical parameters derived from the continuum removal curve (Figure 2(b)). Four parameters are directly displayed in Figure 2(b), which include position (P), width (W), depth (D), and full width at half maximum (FWHM, abbreviated to “F”). The parameter asymmetry (AS) is calculated as follows:

where represents the left width at half maximum, and represents the right width at half maximum [20].

3.1.2. Smoothing Techniques

Smoothing techniques are used to extract the maximum amount of information from each spectrum possibly by minimizing the influence of background noise [32]. Commonly used smoothing techniques include the Savitzky–Golay transform (SG [35]), Norris smoothing filter (NG [36]), and averaging spectra [37]. SG smoothing eliminates the influences of ground interference noise and baseline float, thus enhancing the signal-to-noise ratio. NG smoothing removes the effects of particle-size variation when the soil samples vary in texture, moisture, and grain size [32].

3.1.3. Derivative Algorithms

Derivative algorithms can rapidly identify characteristic positions of spectral minimum, maximum, and inflection point values [32]. Additionally, the effect of variation in optical setup and sample grinding is eliminated after derivative transformation [38]. Because the spectral noise tends to amplify with derivative transform, a smoothing technique is often used before the derivative algorithm [37]. The spectral curve after the first derivative, for example, is better at discriminating goethite and hematite and estimating their abundance, with two peaks at 435 and 535 nm for goethite and a single absorption at ∼570 nm for hematite (Figure 3) [39].

3.2. Spectral Features of Soil Minerals
3.2.1. Fe-Oxide Minerals

Fe-oxide minerals are known to be pedogenic indicators for investigating soil temperature and moisture regimes, which are directly related to pedogenic climate evolution [24, 40]. Fe-oxide minerals are the main active components in the VNIR region (350–1000 nm) since most electron transitions are caused by various kinds of iron oxides [41, 42]. The most common Fe-oxide minerals in soils are goethite (α-FeOOH) and hematite (α-Fe2O3), which can track climate change [43, 44]. Goethite and hematite exhibit diagnostic spectral features in the VNIR region, and the absorption bands are generally broad and smooth (Figure 3). A strong absorption band near 920 nm indicates the presence of goethite (Figure 3(a)), and four absorption bands at 420, 480, 600, and 1700 nm can be used to map its distribution [39]. Hematite is dominated by three absorption bands at 520, 650, and 880 nm [45]. Both goethite and hematite have an absorption band at around 500 nm (480 for goethite and 520 for hematite, resp.) the band for goethite (at 480 nm) is narrow with intense reflectance, while the band for hematite (at 520 nm) is wide with low reflectance (Figure 3(a)). The absorptions in the VNIR region cause the vivid colors of Fe oxides, for example, yellow goethite and red hematite [37]. For a spectral curve representing a sample soil mixture, the width of the absorption band at ∼870 nm (W870) is higher when the soil sample contains more Fe oxides [46]. The concave shape of the 800–1000 nm range indicates the crystallinity of the Fe-oxide minerals. When a soil sample is composed of well-crystallized minerals, the corresponding spectrum reveals a symmetric and deeper feature in this range [47].

3.2.2. Clay Minerals

Clay minerals are frequently used as climatic indicators since their nature is directly influenced by the temperature and amount of precipitation at the site during pedogenesis [9, 48]. As climate conditions shift from cool/dry to warm/moist, the dominant clay minerals go from chlorite/illite → vermiculite → montmorillonite → kaolinite [24, 49]. The dominant clays in soils show diagnostic absorptions in the SWIR domain [39]. These absorption bands are caused by vibrational transitions and commonly display sharp and narrow features (Figure 4). The diagnostic bands are mainly focused on ∼1400 nm (overtones caused by OH), ∼1900 nm (overtones caused by molecular water), and ∼2200 nm (combination tones caused by Al-OH [50, 51]). Additionally, some weak absorption bands in the 2300–2500 nm region are related to the presence of Fe-OH and/or Mg-OH in the clay minerals [24].

The spectral characteristics of some clay minerals are showed in Figure 4 and Table 1. Chlorites are a group of clay minerals containing specific octahedral cations such as Fe, Mg, and Al [52]. Their reflectance spectra exhibit a weak absorption band at approximately 1400 nm and triple absorption features near 2300 nm. The bands at 2250 and 2350 nm are related to Fe-OH and Mg-OH, respectively [53]. Illite is characterized by three prominent absorptions at ∼1400, ∼1900, and ∼2200 nm. Two secondary diagnostic Al-OH absorption peaks close to 2344 and 2445 nm are modified by Fe and Mg tschermak cation exchange [24, 31]. Vermiculite has two broad absorptions at 1400 and 1900 nm and two weak absorptions near 2200 and 2300 nm [39]. Montmorillonite has three strong and sharp absorption bands at ∼1400, ∼1900, and ∼2200 nm, which are similar to but generally stronger than illite.

Additionally, the combination bands produced by the vibrations of absorbed water cause weak shoulders near 1468 nm and 1970 nm for montmorillonite spectra [37]. Kaolinite is featured by two spectral doublets: one is near 1400 nm (1390 and 1410 nm), and the other is near 2200 nm (2160 and 2210 nm).

3.2.3. Carbonates

In soils, carbonates are leached from the surface with time and accumulate in the subsoil at a certain depth [54]. The presence of carbonate is widely used as a basic soil characteristic to describe soil types and quantify soil erosion [22]. Carbonates are characterized by several absorptions in the VNIR domain, caused by overtones and combinations of fundamental vibrations of the CO3 2− ion (Figure 5) [31, 37]. A strong absorption band at ∼2350 nm and three weak absorption bands at ∼1900, ∼2000, and ∼2160 nm were reported by Hunt and Salisbury [55] for carbonates in the NIR region, with the ∼2350 nm absorption showing obvious double-band structures (Figure 5).

3.3. Prediction from the Continuum Removal Spectra

As discussed in Section 3.1.1, several geometrical features of the absorption bands can be extracted through the continuum removal method. Those parameters (e.g., P, D, and AS) from the continuum removal spectra are key to characterizing and predicting mineral compositions in soils. Viscarra Rossel et al. [23] quantitatively estimated the mineral composition by using the continuum removal method. Compositions of soil minerals such as kaolinite, illite, Al-smectite, goethite, and hematite are considered in this study, and the parameter D is selected for prediction. The spectroscopic predictions are generally in consistence with those interpreted by XRD analysis. According to Dufrechou et al. [20], the parameter D at ∼1400, ∼1900, and ∼2200 nm was strongly affected by the amounts of kaolinite, illite, and montmorillonite in soil mixtures. Additionally, the estimation of montmorillonite abundance shows reliability when compared with XRD results. Five parameters (P, D, W, F, and AS) were used in the work by Zhao et al. [24] for assessing the utility of the continuum removal method. We compared these parameters with the results from both XRD and DRS analyses and found that some of the parameters are good at mineral content prediction. Furthermore, some parameters (e.g., AS at ∼2200 nm) are confirmed as reliable proxies for soil weathering and paleoclimate reconstruction.

4. Chemometric Methods

VNIR spectra of soil mixtures are commonly weak and nonspecific due to (1) low concentration of particular soil minerals, (2) scatter effects caused by soil structure, (3) overlapping absorptions of soil attributes, and (4) influences of specific constituents such as quartz [37]. All of these factors pose a challenge for VNIR analyses. Therefore, useful information needs to be mathematically extracted from the spectra and correlated with soil attributes [45]. The development of VNIR in soil studies would have been impossible without the parallel application of chemometric methods [56].

Building a predictive soil mineral abundance model (i.e., multivariate calibration) is an important first step in chemometric analysis. Overall, we should understand the data and the objective of the modeling prior to building a model. Then, the spectral dataset is preprocessed and subdivided. Finally, we can proceed to build, evaluate, and select models [57].

4.1. Prior to Model Building

The first step in any model building process for the study of spectral pedology is to understand the characteristics of the dataset. We need to consider three main concepts in understanding the dataset process [57]: (1) understanding the distribution of the responses (i.e., outcomes): the responses are either numerical or categorical. In the model building process for soil mineral analysis, the outcomes (e.g., contents of clay/Fe-oxide minerals) are described numerically. Understanding the characteristics of responses provides better ways for partitioning the data into calibration and validation sets (2) understanding the nature of the predictors: the predictors in the spectral dataset are numerical, since they are usually the spectral signals between 350 and 2500 nm. In fact, these predictors are highly related, leading to numerically redundant information. Different predictors are suitable for different kinds of models. For example, partial least squares can be used for correlated predictors, while recursive partitioning can manage missing predictor information [58] (3) the relationship between the amount of the predictor set (

): when building a model for a soil mineral study, the dataset commonly has far fewer samples (

). Therefore, a model that can handle dataset where is preferred.

After understanding the dataset, a preprocessing procedure is often used for improving the performance of the model [47, 59]. For a model used in a soil mineral study, the data transformations for multiple predictors contain the following methods: (1) data reduction: principal component analysis (PCA [60]) is a commonly used data reduction technique. In this technique, the number of datasets is largely reduced by seeking principle components (PC)—linear combinations of the predictors that capture the greatest possible variance (2) removing predictors: in some cases, removing predictors prior to modeling has potential advantages. For example, Adeline et al. [59] showed that performances of the predictive models were globally stable and accurate when the spectral resolution decreased from 3 nm to 60 nm. Additionally, for a model based on a spectral signal dataset, the spectra were transformed to apparent absorbance:

prior to developing a regression model, and the spectral preprocessing methods discussed in Section 3 also have potential for model performance improvement [18, 23].

4.2. Candidate Models

Once we fully understand the dataset, the next step is to setup several candidate models. The most commonly used type of model in soil mineral analysis is a regression model, which is defined as a model that predicts numerical outcomes [57]. Establishing a regression model related to the soil VNIR spectral data is the basic role of chemometric analysis [61]. The regression models are subdivided into linear and nonlinear regressions. Linear regressions are the dominant calibration methods for spectral pedology and include partial least squares regression (PLSR [62]) and principal component regression (PCR [63]). The nonlinear data are managed by data mining techniques, namely, multivariate adaptive regression splines (MARS [38]), neural networks (NN [64]), and regression tree analysis (RTA [65]).

4.2.1. Linear Regression Models

Both PLSR and PCR can deal with predictors that are highly collinear and are effective in situations where the number of predictors is far beyond the number of available samples [37]. Furthermore, PLSR and PCR are closely related and share similar prediction errors in most situations [61]. Regardless, the PLSR algorithm is usually preferred in spectral pedology analysis because (1) it maximizes covariance between response variables and predictors so that the model is more interpretable, and (2) it is a faster algorithm [45].

PLSR has been widely and successfully used in predicting the mineralogic compositions of weathering levels of soils. Viscarra Rossel et al. [2] accurately predicted the concentrations of kaolinite, illite, and smectite (

) in mineral mixtures, although the prediction for Fe oxides was biased against measurement. Summers et al. [66] and Ostovari et al. [67] showed that the PLSR method is good at predicting CaCO3 content with values of 0.69 and 0.71 for soil samples from Australia and Iran, respectively. The total clay content and free iron in soils were also proven to be predictable attributes by the PLSR model [68, 69].

4.2.2. Nonlinear Regression Models

The use of models that are inherently nonlinear in nature (i.e., data mining techniques) has gained increasing attention in recent years [37, 61]. A more detailed description of the nonlinear models is available in Kuhn and Johnson [57]. Previous studies have suggested that nonlinear regression models or the combination of nonlinear and linear models may provide better predictions for soil properties. Mouazen et al. [70] showed that a combined PLSR-NN model was better at predicting soil properties than a PLSR model. Viscarra Rossel and Behrens [45] proposed that the combined FSVIP-ANN and FSMARS-ANN models were the best models for predicting clay content, pH, and soil organic carbon (SOC) when both the parsimony and accuracy of the model were taken into consideration. Mulder et al. [71] determined the mineral composition of a soil by coupling an RTA model with exponential Gaussian optimization results. The abundances of kaolinite and calcite were predicted with acceptable RMSE values (<0.1) in both laboratory and field samples.

4.3. Model Evaluation

Two techniques are commonly used to test the prediction performance of the model [33, 56]. In the first, the soil spectral configuration database is randomly divided into a calibration dataset and a validation dataset [72]. The calibration dataset (usually ∼2/3 of the complete database) is used to derive the model, while the validation dataset (commonly contains 1/3 of the complete database) is set aside to exclusively validate the derived model. This process is used to obtain realistic estimates of prediction accuracy. The second is a procedure called cross validation. It uses the “leave-group-out” method (namely, repeated random subsampling validation method [73]) and was adopted to verify the predictive capability for the calibration dataset. A calibration dataset containing

samples is built from the total database (

). The soil property value of the other − samples for validation is predicted. The prediction of relative soil mineral abundance is obtained by repeating the cross-validation process [74].

ParLeS version 3.0 is usually used for multivariate calibration performance [75]. The bias and accuracy of the prediction models are assessed by adjusting the coefficient of determination ( ) between observed and predicted values, the mean error (ME)

and the root mean-square error (RMSE)

where is the number of the dataset, is the observed value, and represents the predicted value [18, 23].

We compromise between model parsimony and model accuracy to find the most satisfactory model [76]. The Akaike information criterion (AIC) is suggested for best-performing algorithm selection [45]:

where is the number of factors, and n is the number of samples used in the prediction. The best model will have the minimum AIC value.

4.4. Feature Selection

Feature selection is mainly applied to remove redundant and/or noninformative predictors from the model [57] and may improve model accuracy. Some models such as PLSR, MARS, and RT will provide a feature selection procedure by default.

The variable importance of the projection (VIP) and b-coefficient scores obtained by the PLSR model help us measure the statistical significance of predictors and select the most important ones [77]. The VIP score of the

predictor is calculated as follows:

where represents the total number of the predictor variables,

is an optimal number of latent variables selected by the PLSR model, is the loading weight for the latent variable, and represents the adjust coefficient of determination of the latent variable in the PLSR model [78]. A predictor (such as wavelength) is selected and considered to be very important if (1) the VIP exceeds the threshold value of one (Chong and Jun [77]) and (2) its b-coefficient is higher than the b-coefficient based on all spectral bands [23].

According to Gomez et al. [22], the important spectral bands selected by the PLSR model are related to the presence of clay minerals such as kaolinite and illite. Additionally, surrogate spectral features selected by VIP and b-coefficient approach contain enough information to satisfactorily estimate the studied soil attributes. According to Viscarra Rossel and Behrens [45], a combined NN and feature selection model (FSvip-ANN) is the best method to predict clay content and pH and produce smaller RSME and AIC values.

5. Comparison between Spectral Measurement and Multivariate Calibration

The relative abundance of minerals in a soil sample can be predicted either by spectral analyses (e.g., continuum removal) or chemometric methods (e.g., PLSR and NN) [20, 24, 45, 47]. Although both types of methods correlate the spectral signal with information about the soil minerals, they differ in many ways, including their focused spectral bands, complexity, and how they are applied.

5.1. Focused Spectral Bands

Spectral analyses focus on specific absorption bands representative of the corresponding soil minerals, while the multivariable regression algorithms commonly use the signals from the whole 350–2500 nm region. In some cases, the 350–400 nm and 2450–2500 nm ranges with low instrumental signal-to-noise ratios are removed [59, 79]. Therefore, a multivariable regression model deals with over 1000 spectral bands—many more than the number of focused bands in a continuum removal study. Moreover, several geometric parameters can be extracted from each band in a spectral measurement, including P, W, D, F, and AS, whereas only the information of depth for each band can be gleaned from a chemometric study. Note that some algorithms intrinsically provide a feature selection method (e.g., SMLR and PLSR), and it has been shown that the most important features selected by a regression model are the ones that we should pay the most attention to in a spectral measurement study [22].

5.2. Complexity

Theoretically, multivariate calibration is very complicated because it involves a larger number of algorithms and because different algorithms have the potential to be combined into better predictive models, depending on the situation [45, 70, 79]. However, in practice, multivariate modeling and prediction is not that complicated. Thanks to the development of executable and fast running software such as ParLeS and Unscrambler [75, 80], the difficult calculation process can be done much more easily. On the other hand, spectral measurement studies cost more time because we must (1) identify a soil mineral based on the spectral features, (2) extract parameters from the bands, and (3) relate those parameters with the information about the soil mineral.

5.3. Application Preference

The geometric features of the spectra are more suitable for monitoring the molecular structural changes of soil minerals, since the variations of the absorption bands are caused by electron transitions (e.g., Fe 2+ to Fe 3+ ) and molecular vibration (e.g., Al-OH versus H2O). Thus, spectral measurement is widely and successfully applied to (1) measure mineral physicochemistry that is sensitive to changes in metamorphic grade [53, 81], (2) map and monitor mineral erosion, deposition, and weathering of minerals [24, 51], and (3) explore water and potential life on extraterrestrial objects [10, 21]. Chemometric methods are more often used in monitoring overall soil properties, since almost all of the signals in the VNIR domain are involved in the modeling process. Several soil attributes are successfully determined by an appropriate multivariate calibration technique, including soil clay [23, 69], organic matter [32, 67], and nitrogen content [82, 83].

Table 2 is a review of some soil mineralogic attributes predicted by VNIR spectroscopy using either chemometric analysis or spectral-based measurement. In this summary, most of the studies used soil samples for analysis, and many of them are among diverse soil types (Table 2). The predictions of the soil properties are still good when there is great range of soil types (e.g., 22, 45, 84, and 85). A single mineral (e.g., kaolinite and goethite) is more precisely predicted when mineral mixtures are used in the measurements [2, 86]. The studies in Table 2 include both data collected in the laboratory and data based on field soil sensing. In the lab, the sample pretreatment and illumination conditions can be controlled to eliminate the influences of the moisture and the grain size of the soil sample [18]. While in the field, the VNIR spectroscopy may be affected by many potential problems such as variable distances between the sensor and the soil, the smearing of soil surfaces, the size of the soil aggregates, and the amount of moisture [87]. These potential problems may reduce the prediction accuracy of field-based analysis [22, 85]. However, the field-based VNIR spectroscopy is more attractive because it (1) enables the potential analysis of soil properties with promising results in previous studies [87] and (2) reduces the cost of the measurement by simplifying the sample preparation. Based on the results of the studies, PLSR is proved to be the most robust soil mineralogic analysis method amongst all of the multivariate calibrations (Table 2

). The CR-based model is good at predicting clay mineral concentration (e.g., 20, 47, and 88

). In some cases, the nonlinear models (NN and MARS) exhibit better estimation in predicting soil mineralogy than the PLSR model (e.g., 45 and 89). In general, when a soil mineral is investigated by spectroscopy, the PLSR and the CR-based models are the most promising methods to provide estimates of mineral abundance.

6. Conclusions and Future Research Directions

Clay minerals in soils are more complex and less well crystallized than those in sedimentary rocks. Traditional characterization methods such as XRD are usually expensive and time-consuming, whereas VNIR is a quick, cost-efficient, and nondestructive technique for analyzing the soil mineralogic properties of large datasets. The major strength of soil mineralogy studies is that there is a direct relationship between soil minerals and their spectra, since the diagnostic absorption bands of soil minerals lie within the VNIR region. Therefore, the nature of soil mineralogy can be approached through both spectral measurement and multivariate calibration. The spectral measurement is focused on geometric information extracted from several bands (e.g., 350–400, ∼1900, ∼2200, and 2450–2500 nm) that relate to soil minerals. The parameters derived from the continuum removal method are mainly used for mineral identification and prediction. In a multivariate calibration analysis, the dataset contains the entire VNIR domain. The most robust model for soil mineral estimation is selected after understanding the data, data preprocessing, candidate model building, and performance assessment.

Firstly, VNIR has been greatly developed in soil sciences over the past several decades. However, no definitive results on theoretical calculations have yet been found because most soil studies occur on a regional scale so their results are only regionally representative. Thus, it is essential to further develop the theoretical calibrations of VNIR that are more suitable for soil samples worldwide, despite difficulties due to high soil variability across the globe.

Secondly, more field analyses are required for obtaining full potential of VNIR. The in situ data collection in the field is one of the advantages compared with conventional techniques. The heterogeneity of the technical and environmental factors (e.g., soil moisture, soil surface condition, and biological residue) will directly influence the characteristics of the absorption bands, causing increased uncertainty of the spectral measurements. Nevertheless, multivariate calibration models for field data show good or even better mineral prediction than laboratory data. There has been a lack of more systematic studies on the various effects of field sample data and variations in mineralogy, moisture, organic matter, and their interactions. Therefore, future work should focus on these types of studies rather than laboratory spectra.

Thirdly, VNIR may have the potential to help us investigate interactions between soil clay minerals and SOC. Mechanisms of SOC stabilization have attracted increasing interest due to their potential to influence the global carbon cycle. It is widely suggested that soil clay minerals play a central role in capturing and permanently sequestering atmospheric CO2. Both clay content and clay mineral type exert important influences on the carbon sequestration. Because VNIR is capable of characterizing most of carbon- and hydroxyl-related properties, it should allow us to study clay-SOC interactions when combined with the other common or state-of-the-art techniques.

Finally, integrated soil mapping is needed in future large-scale soil analysis. The VNIR spectrum contains integrative information (e.g., mineral composition, SOM, SOC, pH, and moisture) of the soil attributes that reflect the nature of a soil system. Thus, we could use VNIR to map soils. More collaborative and strategic spectral studies are needed to better understand the complete nature of soil [101, 102]. Some global or national spectral libraries [103, 104] have been established to build collaborative networks for soil spectroscopy, but more spectral libraries will facilitate the wider use of VNIR and make global-scale soil monitoring possible.

Conflicts of Interest

The authors declare that they have no conflicts of interest.


This study was supported by the Special Funding for Soil Mineralogy (CUG170106), NSF of China (41772032 and 41472041), NSFC for Young Scholars (41402036 and 41602037), NSF of Hubei for Young Scholars (2016CFB183), and Postdoctoral Science Foundation of China (2015M582301). Thanks to Jiacheng Liu and Feng Cheng for their valuable suggestions and Yeqing Liu for his help with sample analysis. Qian Fang and Lulu Zhao acknowledge the China Scholarship Council (CSC) for financial support (201706410017 for Qian Fang and 201706410006 for Lulu Zhao).


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Copyright © 2018 Qian Fang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

How does a spectrophotometer work?

  • A sample of the subject being studies is placed in the spectrophotometer.
  • The light source shines the sample and the monochromator splits the light into each color/individual wavelength.
  • The light’s wavelength hits the subject that is held in cuvette – a tiny container. Careful handling should be observed as even the slightest fingerprint can alter the result
  • The light that passes through the sample is read and interpreted as seen on the output screen. (5, 6)

Image 4: These are the basic components of a spectrophotometer.
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What are the three main components of a spectrophotometer?

The main components of a spectrophotometer are the light source, a device that separates the light into component wavelengths, a sample holder and a detector.

Image 5: It is an example of a visible light spectrophotometer.
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Image 6: The image above is an example of a UV/visible spectrophotometer.
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Image 7: An example of a near infrared spectrophotometer.
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Image 8:A nuclear magnetic resonance spectroscopy.

Image 9:An atomic absorption spectrophotometer.
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Image 9: This is how a mercury analyzer in a laboratory setting looks like.
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Image 10:A fluorometer is a simple device that measures fluorescence release once the object is exposed to a single wavelength of light.
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Click Here for the Digital Spectral Library Data Table.

Clark, R.N., 1980. A Large Scale Interactive One Dimensional Array Processing System, Pub. Astron. Soc. Pac., 92, 221-224. (Software online at ).

Clark, R.N., 1981. The Spectral Reflectance of Water-Mineral Mixtures at Low Temperatures, J. Geophys. Res. , 86 , 3074-3086.

Clark, R.N., T.V.V. King, and N.S. Gorelick, 1987. Automatic Continuum Analysis of Reflectance Spectra: Proceedings of the Third Airborne Imaging Spectrometer Data Analysis Workshop, JPL Publication 87-30, 138-14.

Clark, R.N., A.J. Gallagher, and G.A. Swayze, 1990a. Material Absorption Band Depth Mapping of Imaging Spectrometer Data Using a Complete Band Shape Least-Squares Fit with Library Reference Spectra, Proceedings of the Second Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) Workshop . JPL Publication 90-54, 176-186.

Clark, R.N., T.V.V. King, M. Klejwa, G. Swayze, and N. Vergo, 1990b. High Spectral Resolution Reflectance Spectroscopy of Minerals: J. Geophys Res. 95, 12653-12680.

Clark, R.N., G.A. Swayze, A. Gallagher, T.V.V. King, and W.M. Calvin, 1993. The U. S. Geological Survey, Digital Spectral Library: Version 1: 0.2 to 3.0 microns, U.S. Geological Survey, Open File Report 93-592, , 1340 pages, 1993.

Clark, R.N., 1993. SPECtrum Processing Routines User's Manual Version 3 (program SPECPR), U.S. Geological Survey, Open File Report 93-595, 210 pages. (Software online at ).

Clark, R.N., G. A. Swayze, K. E.. Livo, R. F. Kokaly, T. V.V. King, J. B. Dalton, J. S. Vance, B. W. Rockwell, T. Hoefen, and R. R. McDougal, Surface Reflectance Calibration of Terrestrial Imaging Spectroscopy Data: a Tutorial Using AVIRIS, AVIRIS Workshop Proceedings, 2003a. Online at:

Clark, R.N., G. A. Swayze, K. E. Livo, R. F. Kokaly, S. J. Sutley, J. B. Dalton, R. R.McDougal, and C. A. Gent., 2003b. Imaging Spectroscopy: Earth and Planetary Remote Sensing with the USGS Tetracorder and Expert Systems, Journal of Geophysical Research , In Press.

Fleischer, M., 1980. Glossary of Mineral Species, Mineralogical Record, Tucson, 192pp.

Fleisher, M., and Mandarino, J.A., 1995, Glossary of Mineral Species 1995: The Mineralogical Record Inc., Tucson, 280 p.

Green, Robert O., James E. Conel, Veronique Carrere, Carol J. Bruegge, Jack S. Margolis, Michael Rast, and Gordon Hoover, 1990, Determination of the In-Flight Spectral and Radiometric Characteristics of the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS), in Proceedings of the Second Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) Workshop, JPL Publication 90-54, pp. 15-22.

Green, R. O., D. A. Roberts, J. A. Conel, 1996, Summaries of the Sixth Annual JPL Airborne Earth Science Workshop, JPL Publication 96-4, 135.

Hapke, B., 1981. Bidirectional reflectance spectroscopy 1. Theory, J. Geophys. Res. 86, 3039-3054.

Reflectance in Minerals

Reflected light microscopy is used to examine opaque minerals (and other materials, e.g.. ceramics) to determine the paragenetic relationships between different mineral phases and their identification. Often, the same specimen which is viewed using the light microscope can be analyzed using advanced x-ray and ion microprobe techniques.

The process to measure reflected light is very simple. The sample (polished thin section, epoxy grain mount, or polished section) is placed in the appropriate reflected light microscope. The reflectivity is measured by observing the incident and reflected light at different wavelengths. The reflective index is the percentage of light that bounces off the solid surface and is not absorbed. The apparatus is calibrated using reflective standards such as silicon carbide (SiC) or other materials with a known response.

Method to Display RGB Values

Reflectance measurements for opaque minerals consists of a table of wavelength values versus % reflectivity at that wavelength. The measurements are generally made in air but oil is sometimes used for high magnifications. In addition, reflectance values for pleochroic materials are listed as R1 and R2 values. These values are calibrated to known standards and represent the "standardized intensity" of that mineral.

To regenerate the original macroscopic color from reflectance measurements, the red, green and blue (RGB) values for each mineral are added from the spectral data, normalized, and recalculated as ∑ R (λ).

Wavelength vs RGB Values
Red Green Blue Color.BMP Wave
Red Green Blue Color.BMP
400 131 0 181 560 195 255 0
410 126 0 219 570 225 255 0
420 106 0 255 580 255 255 0
430 61 0 255 590 255 223 0
440 0 0 255 600 255 190 0
450 0 70 255 610 255 155 0
460 0 123 255 620 255 119 0
470 0 169 255 630 255 79 0
480 0 213 255 640 255 33 0
490 0 255 255 650 255 0 0
500 0 255 135 660 255 0 0
510 0 255 0 670 255 0 0
520 54 255 0 680 255 0 0
530 94 255 0 690 255 0 0
540 129 255 0 700 255 0 0
550 163 255 0

RGB measurements are based on the the component colors for pure red (255,0,0), green (0,255,0), and blue (0,0,255). In this system, black is (0,0,0) and white is (255,255,255). There are 16,581,375 colors based on the RGB nomenclature. Since RGB color is based on human perception, there is no "correct" value of RGB to wavelength.

Because the color response of computer monitors is also a variable, the colors represented from these examples is only approximate.

Calculated Relative Intensity Colors

The calculated relative intensity colors are approximated by taking the reflection measurements of the "standardized intensity" values and multiplying by a percentage from 0% to 1,000%. These values are then normalized, and recalculated as ∑ R (λ) as a function of relative intensities based on the 0 to 10 values (0 to 1 ,000%). The range of colors are selected to span all values of RGB from (0,0,0) to (255,255,255). The representative ranges for each species are selected by picking those ranges to display a reasonable color spectrum. The following examples represent a selection of colors calculated for common opaque minerals:

Calculated Relative Intensity Colors of Anatase in Air
0% 50% 100% 150% 200% 250% 300% 350% 400% 450% 470%

Calculated Relative Intensity Colors of Bornite in Air
0% 50% 100% 150% 200% 250% 300% 350% 400% 450% 490%

Calculated Relative Intensity Colors of Enargite in Air
0% 40% 80% 100% 120% 160% 200% 240% 280% 320% 350%

Notice the extreme pleochroism in graphite.

Calculated Relative Intensity Colors of Graphite in Air
0% 100% 200% 300% 400% 500% 600% 700% 800% 900% 1000%

Calculated Relative Intensity Colors of Millerite in Air
0% 30% 60% 90% 100% 120% 150% 180% 210% 230%

Calculated Relative Intensity Colors of Pyrite in Air
0% 30% 60% 90% 100% 120% 150% 180% 200%

Calculated Relative Intensity Colors of Silver in Air
0% 20% 40% 60% 80% 100% 120%

In all cases, the color represented in these tables approximates the pleochroic color (R1 & R2) or color (R) viewed in a polished section of that mineral under plane polarized light. The relative intensities in the tables show how much illumination is required to see the colors from each species.

Click here to view a table of all the opaque-mineral reflected-light calculated colors.

Other References to Reflectivity and "Color"

An Atlas of Opaque and Ore Minerals and their Associations from the SME

Data from the "Visible Light Spectrum" program from efg's Computer Lab was used to obtain the spectral colors used in the calculation of the macroscopic color based on reflectance measurments.

Search the Mineralogy Database

Example: "reflectivity" finds all minerals that have reflected light spectral data.
Example: "short uv-yellow*" finds all minerals that are fluorescent yellow in the short ultra violet.

Principles and Techniques of Diffuse-Reflectance Spectroscopy

The prerequisites for applicability of the Kubelka-Munk theory of diffuse reflectance for obtaining characteristic color curves of powders are discussed, and some experimental support for the theory is given. Methods are described for eliminating surface reflection, which is always superimposed upon the diffuse reflection and which therefore distorts the spectrum. The effect of interactions with the adsorbent on the reflection spectra of adsorbed molecules is demonstrated by means of examples, and the special suitability of the method for investigating chemisorption and for following reactions at phase boundaries is pointed out. By analogy to the Beer-Lambert law, the Kubelka-Munk function can be used for quantitative photometric analysis. The reflectance curves of white standards are presented, and measurements relating to the conditions for “infinitely thick layers” are reported. The scattering coefficient of the Kubelka-Munk functions has been estimated for several samples of color-filters as a functions of grain-size and wavelength. The effect of moisture on diffuse reflectance spectra is discussed, and details of the measuring techniques are presented.


Space-weathering as well as shock effects can darken meteorite and asteroid reflectance spectra. We present a detailed comparative study on shock-darkening and space-weathering using different lithologies of the Chelyabinsk LL5 chondrite. Compared to space-weathering, the shock processes do not cause significant spectral slope changes and are more efficient in attenuating the orthopyroxene 2 μm absorption band. This results in a distinct shock vector in the reflectance spectra principal component analysis, moving the shocked silicate-rich Chelyabinsk spectra from the S-complex space into the C/X complex. In contrast to this, the space-weathering vector stays within the S complex, moving from Q type to S type. Moreover, the 2 μm to 1 μm band depth ratio (BDR) as well as the 2 μm to 1 μm band area ratio (BAR) are not appreciably affected by shock-darkening or shock melting. Space-weathering, however, causes significant shifts in both BDR and BAR toward higher values. Application of the BDR method to the three distinct areas on the asteroid Itokawa reveals that Itokawa is rather uniformly space-weathered and not influenced by regolith roughness or relative albedo changes.

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How is the reflectance spectrum of solids measured? - Biology

Department of Biology
St. Mary's College of Maryland
St. Mary's City, MD 0268
[email protected]

The study of photobiology is interdisciplinary, with light being the unifying theme among such diverse fields as photosynthesis, vision, phototropism, sunburn, and low level light therapy (LLLT). Photobiologists studying different systems depend on similar photochemical and photobiological principles, and similar questions arise about vastly different light-controlled biological systems. For example, light is doing something, but what light? A central question is what wavelengths of light elicit a particular response, and the goal of action spectroscopy is to answer that question. An action spectrum is simply a plot of biological effectiveness as a function of the wavelength of incident light, and it can provide fundamental information about the system under study.

Why Measure Action Spectra?

Classically the goal of making an action spectrum was to help identify the process's photoreceptor pigment, which is often the first step in understanding the whole chain of events from absorption to signal transduction and amplification to one or more responses. The concept behind using action spectra to help identify photoreceptor pigments is simple. The First Law of Photochemistry (the Grotthus-Draper Law) states that light must be absorbed in order to have an effect, but not all light is absorbed equally. The absorption spectrum of the pigment describes how strongly different wavelengths of light are absorbed. Because more absorption leads to more action, peaks in an absorption spectrum will have corresponding peaks in an action spectrum. Thus, if a pigment can be found that has an absorption spectrum that matches a process's action spectrum, it is likely that pigment is the photoreceptor for that process. Although the concept is simple, obtaining action spectra that correspond to absorption spectra is a challenge.

Many reviews and book chapters detail the conditions that must be met to obtain a true action spectrum, i.e., one that matches the photoreceptor's absorption spectrum. Authors generally agree about these conditions they are the same no matter what experimental system is under investigation (Setlow, 1957 Jagger, 1967 Kleczkowski, 1972 Shropshire, 1972 French, 1977 Coohill, 1984 Schäfer & Fukshansky, 1984 Sliney, 2006 Björn, 2008). This module will describe the conditions for rigorous action spectroscopy, and will also discuss examples of action spectra obtained when the classical conditions are not all fulfilled. If action and absorbance spectra do not match, one can learn a great deal about the system by finding out why. In addition, we will discuss other uses for action spectroscopy besides identifying photoreceptor pigments, uses for which experimental requirements may be simpler.

Representative Action Spectra: Learning from the Classics

Characterizing the light that effects a biological change is an obvious thing to do, so it is not surprising that scientists have used some form of action spectroscopy since the early days of experimental science, but it has taken scientists a long time to appreciate the subtleties of the measurement. We will discuss the development of action spectroscopy through representative historical examples, which any student of photobiology should know. In each case, the goal of the experiment was to help identify photoreceptor pigments. Each of these examples will inform our analysis of how action spectra should best be performed.

When first considering the effectiveness of different wavelengths of light, one might be tempted simply to shine different colors of light on the subject, and evaluate the resulting response. That is a common strategy seen in middle-school science-fair projects, and it is what the earliest steps toward action spectroscopy involved. For example, in the early 1800s, Daubeny investigated what colors of light might influence a range of plant responses, including photosynthesis, diurnal leaf movements, greening of leaves, and transpiration (Daubeny, 1836). He used colored glass filters, as well as bottles of colored solutions such as copper sulfate or, more interestingly, port wine. His methods were rudimentary, but he did provide simple transmittance spectra of his filters, and he quantified how much light came through each by measuring how much each color treatment would raise the temperature of a thermometer with a blackened bulb. Although Daubeny tried to measure how much light he was giving, he did not control it in any way. Clearly, with Daubeny's approach, the amount of light given at each wavelength must be the same if the action spectrum is to be meaningful.

The earliest action spectrum that survives in today's biology textbooks is Engelmann's photosynthesis action spectrum (Engelmann, 1882 Drews, 2005). The work endures in today's texts largely because of Engelmann's exceptionally ingenious experimental design. He modified a microscope with a prism so that light from a gaslight source was projected as a microspectrum across the microscope slide, covering about three long cells of his subject, the filamentous green alga, Cladophora. Engelmann's goal was to determine which colors of light produced the most photosynthesis, but it's not easy to see that process under a microscope. Engelmann knew that photosynthesis produced oxygen, and his trick was to use motile bacteria that were attracted to oxygen in order to visualize where photosynthetic oxygen evolution was occurring in the Cladophora filaments. His visual assay consisted of observing what colors of light caused the greatest accumulation of the aerotactic bacteria around the periphery of the alga (Figure 1). He noted that the bacteria accumulated along regions of the algal filament that were illuminated by red or blue light, and he concluded that those spectral regions were the most effective in stimulating photosynthesis in Cladophora. Most importantly, he concluded that the green pigment chlorophyll, which absorbs red and blue light most strongly, was involved in the photosynthetic process. He extended his work with similarly obtained photosynthetic action spectra for brown, red, and blue-green algae, and his results gave evidence for participation of the different photosynthetic accessory pigments in these taxonomically distinct algal groups (Engelmann, 1884). We know these pigments today as fucoxanthin, phycoerythrin, and phycocyanin.

For an action spectrum like Engelmann's to make sense, one must assume that there were equal amounts of light in each part of the spectrum, but in Engelmann's case this assumption would have been incorrect. The gaslight he used would have emitted more red than blue photons, which may explain why he saw much more bacterial accumulation in the red region of the spectrum. Nonetheless, the broad pattern he observed for photosynthetic activity in the red and blue correctly led to the identification of chlorophyll as a major photosynthetic pigment. Engelmann's action spectra are crude by today's standards, but they were the first with good spectral resolution, and his conclusions remain valid.

Even if Daubeny and Engelmann were able to give equal amounts of light at all wavelengths, this method for measuring action spectra is problematic. In order to understand why this is so, consider how a photobiological response varies with the amount of light. In many, but certainly not all, photobiological systems, the magnitude of the response is proportional to the log of the amount of light. This concept, called the Weber-Fechner law, was articulated in the 19th century for human perception of various stimuli, including light. This relationship stems from signal transduction and amplification, which allow sensory systems in animals and plants to be sensitive over many orders of magnitude of light stimulus. Consider a hypothetical photoreceptor pigment with an absorption maximum at 550 nm. Figure 2 shows how a response mediated by this pigment varies logarithmically with fluence at each wavelength. Fluence is a measurement of light coming from all directions using a spherical detector. Typically it is calculated from the energy fluence rate (Wm -2 ) or photon fluence rate (mol m -2 s -1 ) by the duration of the irradiation, yielding energy fluence (Jm -2 ) or photon fluence (µmol m -2 ). For more information, see the PDF file on Radiometric Quantities and Units Used in Photobiology in the section on Photophysics.

The strategy of measuring the response to equal fluences of light at different wavelengths can give different results depending on the fluence chosen. Consider the fluence-response curves in Figure 2, and suppose that the investigator measured the response to 1 µmol m -2 at each wavelength. That fluence is above saturation for 550 and 575 nm, and close to saturation for 525 nm. Plotting the response to this fluence as a function of wavelength would lead to artificial flattening of the peaks of the action spectrum (Figure 3, red curve).

A better procedure is to plot the fluence necessary to generate a constant response wavelengths that are less strongly absorbed require more light to give the same response as wavelengths that are more strongly absorbed. Today it is common to plot action spectra as the reciprocal of the fluence required to give a particular level of response, generally 50% of the saturated response (Figure 3, blue curve). For each wavelength, the reciprocal of the fluence required to give a constant response should be proportional to the absorption coefficient of the pigment at that wavelength (Shropshire, 1972). In addition, plotting the reciprocal of the required fluence gives a curve that matches our intuitive expectation, with peaks for the most active wavelengths.

In the early 1900s, there was intense interest on the effects of UV irradiation on organisms, and by that time the benefits of using fluence-response curves to generate action spectra were understood. When Gates studied the bactericidal effect of UV radiation on Staphylococcus aureus, he generated fluence-response curves (Figure 4) to determine how much light was necessary to induce 50% killing at each wavelength, and plotted the reciprocal of those values as his action spectrum (Figure 5). Gates noted that his action spectrum followed the absorption spectrum of nucleic acid derivatives (Figure 5) (Gates, 1928 1930). His action spectra provided an early indication of the possibility that DNA was the genetic material.

By the 1940s the study of the relative efficacy of different wavelengths of visible and UV radiation was common, and it had become known as action spectroscopy (Kleczkowski, 1972). Plant biologists were working to understand the red/far red photoreversible control of a number of plant responses, including seed germination, photoperiodic flowering, and stem elongation. Action spectra for red-light induction and far-red light reversal of these and other light-mediated responses were similar, suggesting that they were all mediated by the same pigment system, one we know today as the phytochrome system. By the mid 1900s, techniques for obtaining reliable action spectra that reflect the absorption spectra of photoreceptor pigments were well developed, and there are many examples of action spectra for phytochrome-mediated responses. The action spectra for red-light induction and far-red-light reversal of stem straightening (hypocotyl hook opening) in bean (Phaseolus) seedlings are classic (Figure 6).

Note that Gates's UV fluence-response curves, and hence his action spectrum expressed fluence in energy units his focus was on how much UV energy was required to inactivate the bacteria. But recall that photochemistry occurs on a photon-by-photon basis. Thus, to aid in identifying a photoreceptor molecule, what is important is how many photons are necessary, not how much energy. The phytochrome action spectra developed by Withrow et al. (Figure 6) reflect this understanding. These sorts of spectra provided a tool with which to measure phytochrome, a prerequisite to isolation of the pigment. Today we know that the phytochrome responsible for stem straightening exists in two forms, which are interconvertible by light. Absorption of photons by the inactive, red-absorbing form of phytochrome, P r , converts it to the active far red absorbing form, P fr , which then triggers a physiological response. P fr absorbs far red light most strongly, and absorption converts it back to inactive P r . The phytochrome system is described in more detail in the module on Basic Photomorphogenesis.

Let us consider some other examples to demonstrate the importance of using photon units rather than energy units in action spectroscopy. We will use Gates's UV action spectrum again, and also a well-constructed photosynthetic action spectrum. Because the energy per photon is inversely proportional to wavelength, the amount of distortion in an action spectrum caused by using energy units depends on the wavelength range. For example, the Gates action spectrum for the bactericidal action of UV radiation covered only 225-302 nm, so the shape of the action spectrum is not changed dramatically whether it is calculated on a photon or energy basis (Figure 7a). In contrast, action spectra covering a broader wavelength range may be more distorted. For example, an action spectrum for photosynthesis in the green alga Ulva covered 410-718 nm, and has an artificially low peak in the blue when calculated on an energy basis (Figure 7b).

Most readers are familiar with absorbance spectra where:

Absorbance = -log 10 (Transmittance)
Absorbance is commonly used in biochemical work, because it is proportional to concentration (see the module on Basic Photochemistry, for more information). However, note that absorptance, not absorbance, spectra are plotted in Figure 7. Absorptance is simply the fraction of incident light that is absorbed:

Absorptance = 1 - Transmittance - Reflectance
Because the number of photons absorbed is important, absorptance rather than the log quantity absorbance is more appropriate for comparison with action spectra. Absorptance and absorbance spectra can have very different shapes. For example, compare Figure 5, showing Gates's UV action spectrum plotted with the absorbance spectrum of DNA, with Figure 7a, showing the same action spectrum (blue squares) plotted with the corresponding absorptance spectrum (Figure 7a). The action spectrum is a somewhat closer fit to the absorptance spectrum than to the absorbance spectrum. In another example, Haxo's action spectrum for photosynthesis in Ulva fits the absorptance spectrum of the thallus better than it fits the absorbance spectrum (Figure 8). At very low concentrations of absorbing substances (less than 5% absorptance), absorptance is proportional to absorbance, and the spectra have the same shape (French, 1977).

Obtaining Action Spectra: Additional Considerations.

We have seen the historical development of our current understanding of action spectra, including the accurate measurement of the light and the use of fluence-response curves, photon units and absorptance. There are a number of additional considerations relevant to the acquisition of an action spectrum that matches the absorptance spectrum of the photoreceptor pigment.

The sample should be practically transparent to all wavelengths tested (Kleczkowski, 1972). For an in vitro system, this means that the photoreceptor molecules must be diluted in a non-absorbing, stirred medium. If this condition is not met, then photoreceptor molecules might shade each other such that photons absorbed most strongly would be absorbed close to the surface while those absorbed less strongly would penetrate more deeply into the sample. Those less strongly absorbed wavelengths could still be absorbed, however, because they penetrate further, they have a longer pathlength, and the probability of absorption depends on pathlength. Thus, with increasing photoreceptor concentration, less-strongly-absorbed photons get absorbed anyway, and peaks of an action spectrum are artificially broadened. At the extreme, if the sample is so concentrated that it looks black, all photons are absorbed, and the action spectrum becomes flat over the entire wavelength range tested.

While one can manipulate pigment concentration in vitro, living systems present special challenges with respect to optical transparency. Often the photoreceptor is not close to the irradiated surface the investigator may not even know where it is, and is unlikely to be able to control its concentration. In addition, cells and tissues may be physically thick, and thick samples present the same problems as concentrated samples described above, changing absorptance and action. Compare the absorptance spectra of isolated photosynthetic pigments, disrupted chloroplasts, whole chloroplasts, and whole leaves (Figure 9a). Light scattering, and hence pathlength, increases with increasing level of organization, and the absorptance spectrum flattens. One can see the resultant effect of structural organization on action spectra by comparing an action spectrum for photosynthesis in a green alga with that for a leaf (Figure 9b). The algal specimen is thin green photons, which are not absorbed strongly by chlorophyll and carotenoids, pass through the thallus and out the other side without being absorbed. Absorptance, and hence action, is low for green light. In contrast, in the leaf, red and blue light are mostly absorbed in the first layer of photosynthetic cells, but green light can penetrate into the leaf interior, gaining chances to be absorbed as it travels a longer pathlength with multiple reflections at cell wall/air interfaces. Green light penetrates further into the leaf, but little escapes. The photosynthetic action spectrum for a leaf thus shows much more action in the green region of the spectrum than the corresponding action spectrum for an alga.

Consider Possible Screening Pigments. The consequences that occur when the photoreceptor pigment is at high concentration or in a thick sample have been discussed. In addition, other pigments that are inactive may distort action spectra by screening the active photoreceptor molecules. Screening can occur whenever there is another pigment that absorbs in the same spectral region as the photoreceptor of interest, a common situation. For example, the absorbance spectra of DNA and protein overlap, and absorbance spectra of phytochrome and chlorophyll overlap. These two examples will be discussed.

If one is looking at effects of UV radiation on nucleic acids, the nucleic acid is clearly the photoreceptor molecule it absorbs maximally at 260 nm, and the action maximum should be at 260 nm. However, proteins may also be present, and they have an overlapping absorbance spectrum with maximum absorbance at 280 nm (Figure 10a). This absorbance at is attributed to aromatic amino acids, especially tryptophan and tyrosine, and the absorbance peak can change in position and height depending on the amino acid composition of the protein. Protein absorbance at about 280 nm can screen nucleic acids, and shift the action spectrum for UV effects on nucleic acids to shorter wavelength (Figure 10b). The sharp increase in protein absorbance below 240 nm (Figure 10a) is attributable to absorbance by peptide bonds, and is a characteristic of all proteins. Thus screening proteins can also cause a decrease in action below 240 nm (Figure 10b). These screening effects may not be important for small cells like bacteria, but they may be important in larger cells, where absorption by cytoplasmic protein becomes more substantial.

Phytochrome, a blue/green pigment, is present in plant tissue in very low concentrations even dark-grown tissue that has maximal phytochrome levels and no chlorophyll does not look blue. In normal green plants, chlorophyll is present in much higher concentrations than phytochrome, and can distort phytochrome action spectra (Figure 11). The action spectrum for phytochrome-controlled inhibition of stem growth in chlorophyll-free plants peaks at 660 nm, the absorption peak of P r . However, in green seedlings, chlorophyll absorbs light in that region, phytochrome can only absorb light that is not strongly absorbed by chlorophyll, and the action peak is shifted to shorter wavelengths.

Constant Mechanism of Action and Quantum Yield. It only makes sense to relate an action spectrum to an absorptance spectrum if a single photoreceptor is involved, and the mechanism of action and the quantum yield are the same at each wavelength. If these requirements are met, then the slopes of all the fluence-response curves should be parallel. The fluence-response curves (Figure 4) that Gates used to build his classic action spectrum for the bactericidal action of UV radiation on S. aureus (Figure 5) were indeed parallel, or nearly so. However, the fluence response curves used to construct the phytochrome action spectrum (Figure 6) were not parallel (Figure 12). In this case, the slopes of the curves differ because the absorption spectra of the two forms of phytochrome overlap a given photon might be absorbed by P r , which would then convert to P fr and potentiate the response, but the photon might also be absorbed by P fr , which would convert to P r and reverse the response. The different slopes reflect the extent to which a given wavelength is absorbed by the two forms of phytochrome. Because the curves are not parallel, one could construct action spectra with different shapes depending on the level of response chosen. Withrow et al. (1957) constructed the action spectrum in Figure 6 by determining the energy fluence necessary to potentiate 8° of straightening, converting to photon fluence, and plotting the reciprocal of that photon fluence as a function of wavelength.

Reciprocity Should Hold. As we have seen, biological action is usually expressed in action spectra as the reciprocal of the fluence necessary to produce a given response. Thus, the extent of the response should depend on fluence (the total number of photons), rather than on fluence rate or duration of exposure. That is, reciprocity should hold over the range of irradiation conditions employed. Unfortunately, that condition is often not met (Shropshire, 1972). One factor determining whether reciprocity holds is the number of photoreceptor molecules present in the tissue relative to the number of incident photons (Jagger, 1967). If there are many photoreceptors (e.g., for bactericidal action, there are many DNA bases that can absorb UV radiation), then reciprocity may hold. However, if the number of photoreceptor molecules is limited, they may become saturated under intense irradiation, so that long, dim irradiations would be more effective than short, intense ones of equal fluence. On the other hand, if there is a reverse reaction occurring, short, intense irradiations might be more effective than long, dim ones. This is the case for UV radiation damage to DNA, when DNA repair is also occurring. With a long, dim irradiation, repair has a better chance of keeping up with damage. Reciprocity might also fail if a threshold concentration of photoproduct is required. For any biological system, reciprocity can only hold for a limited range of exposure times.

If reciprocity holds over the range of times and fluence rates desired, then one can obtain fluence-response curves by varying time, or by varying fluence rate, or a combination of the two. If reciprocity does not hold, it is important to keep irradiation time constant, and to control the fluence by varying fluence rate. Unfortunately, varying fluence rate without also varying spectral quality can be difficult. For example, varying voltage to a lamp may change color temperature, and neutral-density filters may not be perfectly spectrally flat. Changing slit width on a monochromator alters spectral bandwidth. One can control fluence rate without varying spectral quality by changing the distance between source and specimen, but the range of fluence rates obtainable in this way is usually only about two orders of magnitude, which might not be adequate.

The Extent of the Response as Well as the Wavelength and Amount of Light Must be Measured Accurately.

Consider the Light Source. When choosing a light source, consider the desired resolution of the action spectrum, the required irradiance, and the area that must be illuminated. It can be difficult to produce enough monochromatic light. For example, most monochromators produce light with nicely regulated bandwidth (typically 5-10 nm), but output and the area illuminated can be low. Broad-band filters may transmit enough light, but might not give adequate spectral resolution. One solution is to use a specialized facility such as the Okazaki Large Spectrograph, which projects a spectrum over a 10-m long focal curve, and allows simultaneous treatments with many wavelengths (Watanabe et al., 1982).

Note that bandwidth can affect the shape of the action spectrum, especially in spectral regions where the spectrum is changing rapidly (Chaney & Sliney, 2005). For example, many action spectra for UV damage show a dramatic decrease between 300 and 320 nm. The problem arises then because not all wavelengths in a spectral band are equally transmitted from the monochromator or equally absorbed, even for a relatively narrow (5-10 nm) band from a monochromator. One can, however, generate a true action spectrum mathematically, given knowledge of the monochromator slit width and transmitted energy distribution within each spectral band (Chaney & Sliney, 2005).

Convert to Photon Units. We have seen that it is appropriate to express the amount of light on a photon basis rather than on an energy basis (French, 1977 Coohill, 1984), but many light meters read in energy units. If this is the case, the readings should be converted to photon fluence rates. To do so, one needs to know the energy of a mole of photons. (A mole of photons is sometimes called an Einstein.)

where E mol is the energy of a mol of photons in Jmol -1 , h is Planck's constant (6.62 x 10 -34 Js), c is the speed of light (3.00 x 10 8 m/s), and is wavelength in meters, and N A is Avagadro's number. Photon fluence rate can then be calculated:

Consider Pigment Absorptance in vivo. Often investigators wish to match action spectra with absorptance spectra taken for isolated pigments in vitro. If the action spectrum and absorptance spectrum are to match, then the absorptance spectrum under consideration must be identical to the absorptance spectrum of the pigment in vivo. It is often difficult to determine the absorptance spectrum of a pigment in vivo, and in some cases it is not much changed upon extraction. However, absorbance of many pigments, for example chlorophyll, depends strongly on the solvent. Even in vivo, chlorophyll exists in different chemical microenvironments, and different pigment/protein complexes the absorbance maxima of chlorophyll a in these different complexes can easily vary by 30 nm (French, 1971).

SUMMARY: Criteria for Ideal Action Spectra.
* "Action" should be defined as the reciprocal of the fluence necessary
to produce some constant response
, generally 50% saturated.
* Use photon units to express fluence.
* Use absorptance rather than absorbance.
* Be aware of how the absorptance spectrum of the pigment might be
different in vivo vs in vitro.
* The system should be transparent or nearly so in the wavelength
range of interest.
* Mechanism of action and quantum yield should be constant over the
wavelength range of interest fluence-response curves should be
* Use a range of irradiation times over which reciprocity holds. If this is
not possible, hold time constant and vary fluence rate.
* Accurate measurement of response and light is important.

What if the System is Not Ideal?

Clearly, in many biological systems, one or more of these criteria simply cannot be met. The system might be thick it might have high concentrations of the photoreceptor molecule it might have screening pigments or light scattering that alter light penetration to the photoreceptor molecule. Such systems might not be the best choice to yield action spectra that match absorptance spectra and help identify photoreceptor molecules. However, that's not always the goal. Sometimes a match between action and absorptance spectra simply is not relevant. A photobiologist developing a clinical phototherapy treatment would be interested in knowing the identity of the photoreceptor, but also would want to know what wavelengths of light would penetrate the tissue to reach the photoreceptor. The absorption peaks of the photoreceptor molecule would only be part of the picture, and an action spectrum for phototherapy might bear little resemblance to the absorption spectrum of the photoreceptor.

Lack of agreement between absorptance spectra and action spectra is not always a bad thing. Sometimes, as for photosynthesis or nucleic acid damage, the photoreceptor molecules are known, and differences between the shape of action and absorptance spectra can provide information when scientists investigate the reasons behind the discrepancies. Such differences might provide information about tissue optics, the location of a photoreceptor molecule, the existence of a screening pigment, or differences in quantum yield with wavelength. For example, the action spectrum for photosynthesis in Ulva does not agree with the absorptance spectrum of the thallus (Figure 8). The dip in action relative to absorption around 500 nm occurs because of a slightly lower quantum yield for carotenoids, which function as photosynthetic accessory pigments. In addition, note that above 680 nm, the action spectrum drops off sharply, more so than the absorption spectrum. This phenomenon, known as red drop, indicates a reduced quantum yield for photosynthesis in this region, and it led to the understanding that optimal photosynthesis requires the coordinated action of two photosystems (see the module on Basic Photosynthesis). These two photosystems absorb at slightly different wavelengths photosystem II absorbs 680 nm light strongly, but it absorbs far red light above 680 nm only weakly. When chloroplasts are irradiated with far red light, excitation of the two photosystems becomes unbalanced, with photosystem I driven much more strongly, so the overall rate of electron transport declines.

Even if all of the conditions laid out above are met, and a system appears ideal, the resulting action spectrum might not help much to identify the photoreceptor. For example, many photomorphogenic responses in plants are mediated by blue light, and for decades the photoreceptor associated with them was unknown, and was called simply "cryptochrome." Controversy raged about whether action spectra were more similar to the absorption spectrum of carotenoids or flavins. There was simply no way to identify the blue-light photoreceptor based on action spectroscopy alone. It took molecular techniques to determine that there were three different classes of blue-light photoreceptors: cryptochromes and phototropins, which contain flavin/pterin chromophores, and carotenoids (see the modules on Basic Photomorphogenesis and Blue Light Sensing in Plants).

Action Spectroscopy Today

After more than one hundred years of action spectroscopy, is it still relevant? Photoreceptors have been identified for many photobiological processes: vision, photosynthesis, mutagenesis, phototropism, flowering, etc. What is left? One area where action spectroscopy has been especially valuable recently has been in identifying cytochrome c oxidase as a photoreceptor for Low Level Light Therapy (LLLT), an emerging phototherapy used in a variety of ways (see modules on LLLT by Smith, Hamblin, and Karu, in the Photomedicine section). A quick search finds many articles involving action spectra written in the last decade. In addition to LLLT, topics include melanopsin signaling, melanoma, photoinhibition of photosynthesis, circadian timekeeping, phototaxis, and many others. Some aim to identify new photoreceptors, some compare action of a known photoreceptor with its action in other systems, some discuss the role of screening pigments, some seek to understand the interaction of photoreceptors with other molecules, many deal with topics in photomedicine.

Investigators embarking on studies of action spectra have many resources. Many reviews have information relevant to all action spectroscopy, but in addition, contain more detailed information about circumstances unique to action spectroscopy in specialized areas: plant biology (Björn, 2008) phytochrome (Schäfer & Fukshansky, 1984), photosynthesis (French, 1977), mammalian cells (Coohill, 1984), UV photobiology (Setlow, 1957 Jagger, 1967 Kleczkowski, 1972 Sliney, 2006) These reviews will help investigators develop methodology appropriate to their systems, and also aid in the interpretation of the results.

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Chaney EK & Sliney DH (2005) Re-evaluation of the ultraviolet hazard action spectrum - The impact of spectral bandwidth. Health Physics: 89, 322-332.

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Band-gap energy estimation from diffuse reflectance measurements on sol–gel and commercial TiO2: a comparative study

A comparison of the band gap energy estimated from UV–vis reflectance spectra of TiO2 powders prepared by sol–gel route versus commercial TiO2 powders, nanopowder, bulkpowder and P25 is reported. The experimental results obtained from the optical absorption spectra were reported for all the TiO2 samples. Graphic representations were used to calculate Eg: absorbance versus λ F(R) versus E (F(R) ) n versus E, with n = ½ for an indirect allowed transition and n = 2 for a direct allowed transition. From the results, it could be seen that Eg strongly varied according to the equation used for the graphic representation. Differences in Eg up to 0.5 eV for the same semiconductor depending on the transition chosen were observed. Accurate Eg estimation in the four semiconductors studied was obtained by using the general equation α () ≈ B ( − Eg) n (where α

F(R)) and indirect allowed transition.

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