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Multispectral imaging of ore minerals in optical microscopy

Université de Liège, GeomaC–MICA, Sart Tilman B52/3, 4000 Liege, Belgium

^* E-mail: eric.pirard{at}ulg.ac.be

	ABSTRACT

TOP ABSTRACT Introduction Principles of conventional video... From CCD imaging to... Multispectral image acquisition... Benefits of multispectral... Phase segmentation in... Discussion and perspectives Acknowledgements References

 
Multispectral imaging of ore minerals under the microscope is a logical extension of quantitative colour analysis and microspectrophotometric analysis of minerals. This paper describes, step by step, how the proper calibration of a scientific video camera can be performed in order to obtain precise reflectance measurements at each pixel within the field of view. After having reviewed the different sources of noise and aberration, practical formulae are presented that allow for the acquisition of a set of images at different wavelengths in the visible spectrum.

The advantage of using a multispectral image acquisition system based on narrow bandwidth (10 nm) interference filters is discussed and quantitatively compared to colour imaging using tri-stimulus (red, green, blue) filters.

Finally, the potential for automatic identification of ore minerals is discussed with reference to supervised multivariate image classification algorithms similar to those used in remote sensing. Additional comments on extending the principles for handling optical anisotropy and developing a multiradial imaging system are made.

KEYWORDS: multispectral imaging, ore minerals, optical microscopy, reflectance measurements, sulphide parageneses

	Introduction

TOP ABSTRACT Introduction Principles of conventional video... From CCD imaging to... Multispectral image acquisition... Benefits of multispectral... Phase segmentation in... Discussion and perspectives Acknowledgements References

 
SINCE the first studies of opaque minerals using reflected light microscopy, mineralogists have attempted to take advantage of physical characteristics of minerals under the microscope to ascertain their identity. Vickers microhardness indentation tests, selective etching of minerals with reagents and spectrophotometric measurements are among the techniques that have attracted major attention (Ramdohr, 1980). Microspectrophotometry (MSP) is among the most flexible and most reproducible methods because of its non-destructive character and well established theoretical basis, and given the availability of electronic sensors.

Since the 1970s, the Commission on New Minerals and Mineral Names has required the measurement of reflectance data between 400 nm and 700 nm at steps of 20 nm for each new mineral species submitted. This recommendation takes advantage of previous work including the development of reflectance standards and the measurement of reflectance properties of all known ore minerals. A first compilation was published by Henry (1977) and this work was later extended by Criddle and Stanley (1993) in order to include micro-chemical and structural data.

Microspectrophotometry and the related quantitative colour measurements received major interest in the 1960s and 1970s (Cervelle et al., 1971; Piller, 1966) when the development of apparatus suggested that automatic identification of minerals using their reflectance spectra could very soon become a routine technology. The development of electron microscopy coupled with faster Energy Dispersive X-ray Analysis (Sutherland and Gottlieb, 1991) systems has detracted from the development of optical sensing technologies in ore microscopy. Apart from a few theoretical papers pointing out the additional diagnostic potential of anisotropic rotation tints (Peckett, 1989), no real advances have been made. This is very surprising given the exceptional progress achieved in visible light sensing technologies over the last decade. In particular, the latest silicon-charged coupled devices (Si CCD) used in video cameras largely supersede in sensitivity and signal-to-noise ratios the photomultiplier tubes previously available.

It is timely to consider combining digital video imaging with the MSP database as concluded by Criddle (1998) in his introductory chapter in a recent textbook on ore mineralogy "... it is at last becoming feasible to consider image (areal) analysis based on optical properties. This field has great potential and is wide open now that reliable reflectance databases exist."

	Principles of conventional video imaging

TOP ABSTRACT Introduction Principles of conventional video... From CCD imaging to... Multispectral image acquisition... Benefits of multispectral... Phase segmentation in... Discussion and perspectives Acknowledgements References

 
Until recently, video cameras were exclusively designed for non-scientific purposes. As a consequence, digital imaging technology is affordable for most microscopists. On the other hand, such cameras have not been regarded as scientific instruments and have been used with a lack of knowledge of the image-formation principles. Practical suggestions for the optimal use of a triple-CCD video camera in reflected light microscopy were given by Pirard et al. (1999). Since then, digital still video cameras have appeared on the market, but this does not mean that significant improvements have been made in terms of reliability of optical measurements in video images. Two major technical demands are driving the development of video cameras for broadcasting purposes: a perception of colours as close as possible to human vision and the ability to picture moving objects. Such constraints do not apply in most microscopic imaging applications.

Human vision is usually modelled by a tri-stimulus theory of colour perception. This is why video cameras are fitted with red, green and blue (RGB) filters capable of rendering, at least approximately, our colour world. As can be seen from Fig. 1, such RGB filters are usually centred around wavelengths of 450 nm, 550 nm and 650 nm, respectively, and are ~100 nm in bandwidth. In a triple-CCD camera, the individual filters are fitted onto the facets of a prism in order to obtain full spatial resolution for each colour channel (Fig. 2). In a mono-CCD camera, which is the most popular technology for low-cost video or digital still video imaging, colour is obtained at the expense of spatial resolution by utilizing a Bayer filter wherein 50% of the pixels are covered with a green filter, 25% with a red filter and the remaining 25% with a blue filter (Fig. 3).

View larger version (21K): [in this window] [in a new window]   FIG. 1. Typical normalized transmittance curves for RGB colour filters fitted on a triple CCD video camera.

View larger version (21K): [in this window] [in a new window]   FIG. 2. Optical design of a prism for synchronous imaging of the red, green and blue channels with three individual CCD detectors.

View larger version (35K): [in this window] [in a new window]   FIG. 3. Bayer filter designed for colour imaging with a single CCD array. One pixel out of two is fitted with a green filter (G) and one out of four with a blue (B) or a red filter (R).

View larger version (14K): [in this window] [in a new window]   FIG. 4. Typical spectral sensitivity curve of a silicon CCD detector.

	From CCD imaging to spectrometry.

TOP ABSTRACT Introduction Principles of conventional video... From CCD imaging to... Multispectral image acquisition... Benefits of multispectral... Phase segmentation in... Discussion and perspectives Acknowledgements References

 
Each individual cell within a CCD sensor acts as a photometer and needs to be properly calibrated using the principles given by Galopin and Henry (1972). This involves calibration of a CCD sensor with respect to known reflectance standards as well as a series of corrections that can be grouped under the following terms: ‘short term’ and ‘long term’ electronic noises, ‘dark current’ and ‘spatial drift’. Interested readers will find more detailed information in Holst (1998).

Short-term electronic noise
Charge-coupled devices are affected by read-out noise such that individual pixel values randomly oscillate around their mean intensity. This punctual noise is best eliminated by averaging a sequence of images instead of taking a single image. The number of images to be taken into account depends on the camera model and should be checked by measuring the stabilization of the variance of individual pixels when imaging under strictly invariant conditions. Cameras equipped with a Peltier cooling stage are less prone to short term noise. This advantage is utilized in practice to digitize the signal into a larger number of grey level values (typically 10 to 12 bits which is equivalent to 1024 to 4096 grey-levels). Hence, it is not acceptable with such cameras to ignore time averaging. For more details about time averaging of signals, the reader is referred to the literature on Kalman filtering (Brown and Hwang, 1992).

Additive dark current
Any CCD device is sensitive to heat. As a consequence, the output voltage of a photocell is always incremented by a quantity known as ‘dark current’, independent of the amount of light hitting the photocell. The simplest way to correct for this and similar noise is to take a ‘black reference image’ i.e. to grab an image from the camera while preventing any light hitting the sensor. This black reference image must be kept in the memory as it will serve to correct any further pictures taken with the same camera (see equation 1 below). Dark current values are typically of the order of a few percent (2–5%) of the maximum intensity.

Long-term electronic noise
Additionally, since any device warms up with time, it is unavoidable that a CCD sensor displays a progressive drift of its output voltage with time. Experience with both Peltier cooled and uncooled CCD cameras shows that output currents are stabilized after sufficient warm-up time. A reasonable delay when operating with uncooled cameras is ~90 min (Pirard et al., 1999).

Spatial drift correction
Even the best optical microscope will never achieve perfectly homogeneous illumination conditions throughout the field of view. Typically, light intensities will always be stronger at the centre of the field and suffer from a progressive concentric decrease towards the outer limits (vignetting). Moreover, individual cells on a 1 Mpixels CCD array may have differential responses and sometimes no response at all (scientific grade CCDs are categorized with respect to the number of defective pixels). Finally, many intermediate lenses and filters within the optical pathway, as well as dust particles, also contribute to an uneven response when imaging a perfectly homogeneous surface. The only practical way to compensate for all possible defects along the optical pathway is to grab a ‘white reference image’ i.e. the image of a uniformly reflecting surface (Fig. 5). Such a white reference image will be kept in the memory so that it can be retrieved anytime imaging is performed using the same objective, the same camera and strictly the same settings of the microscope (light bulb centering, optical axis centering, diaphragm apertures, filters, etc.). Although uneven illumination is barely perceptible to the human eye and is therefore often neglected, it is very important to account for it when trying to develop automated mineral identification from intensity values in digital images.

View larger version (90K): [in this window] [in a new window]   FIG. 5. White reference image obtained with a 10x MS-PLAN objective lens at 438±10 m. The original image appears homogeneous to the human eye as it displays grey-level values between 180 and 206 (left). After stretching of the histogram (right), attenuations due to dust, interference patterns and optical aberrations are clearly perceptible which demonstrates the importance of a background correction for proper imaging of mineral spectra.

View larger version (9K): [in this window] [in a new window]   FIG. 6. Plot of reflectance standards of 4.3%; 14.7%; 25.1% and 87.3%, respectively, at 550 nm against grey levels measured with a CCD sensor fitted with a 550±10 nm interference filter. The grey levels are average intensities from a 20x20 pixels region taken in the centre of the field of view. The quality of the regression demonstrates the perfect linearity of the CCD response under the chosen imaging conditions.

Calibrated imaging
By taking into account the above-mentioned operational protocols, it is possible to obtain a properly calibrated grey-level image under strictly controlled optical conditions. The whole procedure can be summarized as follows: (1) Select the optics and filters to be used throughout the study.

(2) Fix the desired illumination voltage, making sure that no mineral will saturate the sensor at any wavelength, and that the power unit is properly stabilized.

(3) Allow the CCD sensor to warm up and stabilize (up to 90 min).

(4) Make sure that all images are taken using the same image acquisition and digitization protocols. In particular, the time averaging filter must be applied to all images and image file formats should not include a compression option.

(5) Store a black reference image (Bl) by preventing any light from hitting the sensor.

(6) Select a standard reflectance surface such that the CCD will be properly exposed under the fixed illuminations conditions. Grab and store a white reflectance image (Wh).

(7) Start acquiring the series of images without modifying any operational conditions and by systematically applying the following correction:

(1)

where I_x,y designates the pixel at coordinates (x,y) of the input image; Bl_x,y is the intensity of the dark current at the same (x,y) coordinates; Wh_x,y is the intensity of the standard reflecting surface at the same (x,y) coordinates; and O_x,y designates the corrected output pixel at coordinates (x,y).

A visual illustration of this correction is given in Fig. 7 by plotting grey-level values along a horizontal profile within the original, time-filtered and corrected images.

View larger version (18K): [in this window] [in a new window]   FIG. 7. The calibration procedure for digital imaging aims to equalize the grey-level values of pixels corresponding to the same mineral species wherever they are located in the field of view. A line drawn through the image of a single crystal illustrates how the original values are distributed (a). The use of a time averaging of successive frames drastically reduces the punctual noise (b). The additional correction for uneven illumination and uneven pixel response leads to an almost constant rendering of the uniform mineral surface (c).

(2)

	Multispectral image acquisition principles

TOP ABSTRACT Introduction Principles of conventional video... From CCD imaging to... Multispectral image acquisition... Benefits of multispectral... Phase segmentation in... Discussion and perspectives Acknowledgements References

 
Up to this point, we have been dealing with the acquisition of a single image per field of view. Relying on the same principles and performing sequential acquisition at different wavelengths, it is now possible to envisage multispectral imaging under the optical microscope.

A filter wheel equipped with a selection of narrow bandwidth (10 nm) interference filters is an ideal solution if one wants the results to be close enough to the spectral resolution of the Quantitative Data File (Criddle and Stanley, 1993). Because the transmittance of such filters is limited, it is advisable to select a Peltier cooled CCD sensor with a tuneable integration time ranging between a few milliseconds and several tens of seconds. Given that the sensitivity curve of a silicon CCD extends from ~350 nm up to 1100 nm (Fig. 4), it is, in practice, possible to take pictures outside the visible light range. However, most optical microscopes are not designed for working in the very near infrared as they are commonly fitted with heat blocking filters that limit emission from the light sources above 700 nm. Table 1 suggests some possible choices for interference filters with 10 nm bandwidth and lists indicative exposure times.

(3)

where refers to the specific wavelength used for imaging.

Clearly, optimal exposure of the CCD at any wavelength cannot be achieved without varying the integration time and thus altering the grey level to reflectance correspondence scale. But, taking advantage of the linearity of response of the CCD it is easy to predict, through simple multiplication, the grey-level output of a standard reflector at any integration time without having to grab a new white reference image. Thanks to this elegant property, the straightforward relationship between G and R will not be lost. This is no longer the case if one alters the input voltage of the light source. Typically, by increasing the voltage of a halogen-tungsten bulb, the relative intensities of shorter wavelengths (red) tend to increase with respect to the longer ones (blue).

By following the spectral calibration rules for each successive wavelength, one ends up with a stack of images. But, in order to take advantage of truly spectral information at each individual pixel location, the perfect geometrical co-registration of images must be checked.

Misalignment of the optical axis, as well as chromatic aberration, cannot be completely eliminated and often accounts for a shift of the order of several pixels between the shorter and longer wavelengths (Fig. 8). Hopefully, unless there is a strong geometrical aberration, the perfect co-registration of images only implies a first-order image translation but no polynomial warping. This can be achieved automatically through the computation of co-occurrence matrices between images or, more simply, through the practical estimation of a systematic shift from one wavelength to the next.

View larger version (135K): [in this window] [in a new window]   FIG. 8. The superposition of pictures from the same scene but taken at a 200 nm interval in wavelength show a distinct geometrical shift of the order of a few pixels. This chromatic aberration can be reduced by means of an image-translation operation.

	Benefits of multispectral imaging over colour imaging

TOP ABSTRACT Introduction Principles of conventional video... From CCD imaging to... Multispectral image acquisition... Benefits of multispectral... Phase segmentation in... Discussion and perspectives Acknowledgements References

View larger version (1045K): [in this window] [in a new window]   FIG. 9. Calibrated digital video images taken with interference filters at wavelengths of 438 nm, 591 nm and 692 nm (from left to right). The upper sequence pictures a copper sulphide paragenesis in Kipushi, the central sequence is taken on a stannite-bearing ore from Vernerov and the lower sequence is from the sulphide paragenesis of the Panasqueira tin-tungsten deposit. Variable reflectance intensities are clearly noticeable for minerals such as bornite (Bo), pyrite (Py), arsenopyrite (Apy), chalcopyrite (Cp) and stannite (Sta).

Relying on the reasonable assumption that reflectance data from a given mineral surface do obey a multigaussian distribution (Fig. 10), spectral information for each set of 400 pixels per mineral was summarized into a mean vector:

View larger version (12K): [in this window] [in a new window]   FIG. 10. Reflectance values from a given mineral surface obey a reasonably multigaussian distribution as shown here for true colour intensities from a 20x20 pixels region in bornite from Kipushi.

(4)

and a correlation matrix:

with

where N is the number of pixels within the selected region (typically 400); µ designate different wavelengths (I)_i designates the intensity of the i^th pixel at selected wavelength ; Ī is the mean of intensities of N pixels at wavelength ; designates the covariance between intensities at wavelength and ; and designates the variance of the intensities at wavelength .

From the above statistical parameters the discrimination potential for both the 438 nm, 489 nm, 692 nm and the RGB spectral spaces can be compared using a measure of the Mahalanobis distance as developed in basic multivariate statistical analysis (Swan and Sandilands, 1995). Such a measurement expresses the distance in the spectral space between the clouds of pixels corresponding to any pair of minerals. This is not strictly a measure of the distance between centres of gravity (mean vectors), but it accounts for the dispersion of the pixel clouds (covariance matrix).

As shown in Table 2, pairs of minerals taken from an image of the Sudbury ore give systematically larger Mahalanobis distances when using the narrow bandwidth imaging technique instead of the RGB colour filters. Taking into account that a complete set of filters extends out of the visible region it is obvious that multispectral imaging will bring additional information and always supersede the conventional colour imaging mode.

	Phase segmentation in multispectral images

TOP ABSTRACT Introduction Principles of conventional video... From CCD imaging to... Multispectral image acquisition... Benefits of multispectral... Phase segmentation in... Discussion and perspectives Acknowledgements References

In practice, the use of a simple Fisher Linear Likelihood discriminant analysis has proved to be very efficient (Pirard and Bertholet, 2000). The result is a mapping wherein each pixel is attributed to the highest probable mineral class. It is left to the user to consider whether pixels that appear to be too far away, in Malahanobis terms, from a given mineral species should be classified or not. Leaving unclassified regions is often good practice in order to allow for detection of unexpected mineral species or for correct assignment of pores and fractures.

As for MSP, multispectral imaging performs best with minerals having average reflectances above 5%; this is particularly true if they are to be imaged together with strongly reflecting minerals such as sulphides. In the latter case, the supervised training phase must consider grouping all transparent gangue minerals into a single class.

The raw classification, even in optimal conditions, will always display assignment errors due to polishing artefacts or to optical aberration. Hence, at the interface between a strongly reflecting mineral and a more weakly reflecting mineral, pixels of intermediate brightness will appear and be mistaken for those belonging to a mineral of intermediate reflectance. Figure 11 clearly shows that pixels at the interface between pyrite and sphalerite might appear as a virtual chalcopyrite.

View larger version (199K): [in this window] [in a new window]   FIG. 11. Optical smearing at the interface between pyrite and sphalerite (cf. zoomed circle) is responsible for the appearance of virtual ‘chalcopyrite’ (‘Cp’) and ‘pyrrhotite’ (‘Po’) rims after image classification. This effect due to mixed pixels spectra (mixels) can be removed in practice through posterior filtering.

	Discussion and perspectives

TOP ABSTRACT Introduction Principles of conventional video... From CCD imaging to... Multispectral image acquisition... Benefits of multispectral... Phase segmentation in... Discussion and perspectives Acknowledgements References

 
Studies by MSP have always emphasized the importance of the correct selection of sensing areas. In particular, avoiding any artefact affecting the reflectance properties of a mineral, such as scratches, pits, grain boundaries, and that the polishing has not affected the mineral surface composition or that no tarnishing has taken place. Using optimal conditions it has been shown that reflectance analysis is able to identify limited compositional changes (Cervelle et al., 1971) without needing recourse to microprobe analysis, but the drawback of this is that reference reflectance curves must be accompanied by microchemical data, as is the case for most major minerals of the Quantitative Data File (Criddle and Stanley, 1993). Although, image processing, as compared to conventional MSP, is capable of overcoming the problems of a certain number of artefacts, such as pits or scratches, it is essential that sample preparation be carried out with utmost care.

The biggest problem with optical image analysis, compared with SEM-based imaging techniques, is probably the spatial resolution. Indeed, if standard magnifications do allow for a typical 0.5 µm per pixel resolution, it should be clear that the degradation of reflectance properties for minute inclusions as well as the necessary post-processing of classified images very often limits the practical resolution of optical image analysis to the quantification of minerals with a minimum size of 10–50 µm.

As for any analytical technology, optical imaging is constrained by detection limits. As stated above, it is reasonable that very weakly reflecting minerals (<5%) are pooled together when in the presence of reflecting phases such as oxides or sulphides. Although reflected light image analysis might sometimes appear a credible alternative to the analysis of transmitted light information, it seems clear that with few exceptions, optical image analysis is not the first-choice technique for identification of gangue minerals. In addition to low light levels, the ubiquitous presence of internal reflections will often hinder the correct measurement of reflectance values.

Multispectral imaging must be considered as a logical extension of all previous efforts made to quantify reflectance data and to understand the relationship between optical properties and mineralogical compositions. Further experimental work is still needed in order to make routine use of the Quantitative Data File (Criddle and Stanley, 1993) as a basis for automatic recognition of mineral species in reflected light, but the technology is now mature. Optical imaging will obviously not replace all alternative imaging approaches, but it does offer much flexibility and it relies on widely available and cost-effective sensors. From this point of view, it is obvious that optical sensors deserve more attention in the move towards automated quantitative mineralogical analysis systems.

Among the potential applications that are worth consideration are the fast discrimination of some pairs of minerals that remain problematic with backscattered electron imaging (chalcopyrite/pentlandite; hematite/pyrite) or with EDX mapping (hematite/magnetite/goethite; marcasite/pyrite).

In this paper, anisotropy has been disregarded, and only simply polarized light images have been processed. In order to take full advantage of the optical information it would seem logical to add multiradial imaging capabilities, in other words to stack images obtained from different angular positions of the polarizer or polarizer/analyser filters. Preliminary work (Pirard and de Colnet, 2001) combining reflectance, bireflectance and optical anisotropy information has shown promise in improving phase segmentation in a magmatic ilmenite-magnetite-hematite paragenesis. However, when considering the quantitative analysis of polarized-light images it appears that the classical design of the reflected light microscope should be re-examined to fit the needs of scientific imaging through a video camera, rather than those of a human observer.

	Acknowledgements

TOP ABSTRACT Introduction Principles of conventional video... From CCD imaging to... Multispectral image acquisition... Benefits of multispectral... Phase segmentation in... Discussion and perspectives Acknowledgements References

 
The author would like to acknowledge the help of the late Alan Criddle in measuring the reflectance spectra of specimens used as standard reflectors, and is indebted to him for encouragement to pursue investigations in optical image analysis.

TOP ABSTRACT Introduction Principles of conventional video... From CCD imaging to... Multispectral image acquisition... Benefits of multispectral... Phase segmentation in... Discussion and perspectives Acknowledgements References

 
Dedicated to the memory of Dr A. J. Criddle, Natural History Museum, London, who died in May 2002

[Manuscript received 24 January 2003: revised 4 June 2003]

	References

TOP ABSTRACT Introduction Principles of conventional video... From CCD imaging to... Multispectral image acquisition... Benefits of multispectral... Phase segmentation in... Discussion and perspectives Acknowledgements References

 

Brown, R.G. and Hwang, P.Y.C. (1992) Introduction to Random Signals and Applied Kalman Filtering, 2^nd edition. John Wiley & Sons, Inc., New York.

Cervelle, B., Levy, C. and Caye, R. (1971) Dosage rapide du magnesium dans les ilménites. Mineralium Deposita, 6, 34–40.[GeoRef]

Criddle, A.J. (1998) Ore microscopy and photometry (1890–1998). In Modern Approaches to Ore and Environmental Mineralogy (L.J. Cabri and D.J. Vaughan, editors). Short Course Series, 27. Mineralogical Association of Canada, Ottawa.

Criddle, A.J. and Stanley, C.J. (editors) (1993) Quantitative Data File for Ore Minerals, 3^rd edition. Chapman & Hall, London, UK, 635 pp.

Galopin, R. and Henry, N.F.M. (1972) Microscopic Study of Opaque Ore Minerals. Heffers, Cambridge, UK, 322 pp.

Henry, N.F.M. (1977) IMA/COM Quantitative Data File, 1^st Issue. McCrone Research Associates Ltd, London, UK.

Holst, G.C. (1998) CCD Arrays, Cameras and Displays. SPIE Optical Engineering Press Washington, USA.

Peckett, A. (1989) The colours of opaque minerals. Mineralogical Magazine, 53, 71–78.

Piller, H. (1966) Colour measurements in ore microscopy. Mineralium Deposita, 1, 175–192.[GeoRef]

Pirard, E. and Bertholet, V. (2000) Segmentation of multispectral images in optical metallography. Revue de Métallurgie – Sciences et Génie des Matériaux, 219–227.

Pirard, E. and de Colnet, L. (2001) Multiradial Imaging in Optical Ore Microscopy. Proceedings of the Annual meeting Belgian Society for Microscopy.

Pirard, E., Lebrun, V. and Nivart, J.-F. (1999) Optimal acquisition of video images in reflected light microscopy. European Microscopy and Analysis, 60, 9–11.

Ramdohr, P. (1980) The Ore Minerals and their Intergrowths, 2^nd English edition. Pergamon, Oxford, UK, 2 vol., 1205 pp.

Sutherland, D. and Gottlieb, P. (1991) Application of automated quantitative mineralogy in mineral processing. Minerals Engineering, 4, 735–762.

Swan, A.R.H. and Sandilands, M. (1995) Introduction to Geological Data Analysis. Blackwell Scientific, 446 pp.

Van der Meer, F. (2002) Imaging spectrometry for geological applications. In Encyclopedia of Analytical Chemistry: Applications, Theory, and Instrumentation. (R. Meyers, editor). Wiley, 14,344 pp.

This Article Abstract Figures Only Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Similar articles in ISI Web of Science Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via ISI Web of Science (4) Citing Articles via Google Scholar Google Scholar Articles by Pirard, E. Search for Related Content GeoRef GeoRef Citation