Basic elements of metrology and introduction to the various techniques

André Chrysochoos, Yves Surrel

Chapter 1

Basics of Metrology and Introduction to Techniques

Introduction

Full-field optical methods for kinematic field measurement have developed tremendously in the last two decades, due to the evolution of image acquisition and processing. Infrared (IR) thermography has also dramatically improved due to the extraordinary development of IR cameras. Because of their contactless nature, the amount of information they provide, their speed and resolution, these methods have enormous potential both for the research lab in the mechanics of materials and structures and for real applications in industry.

As for any measurement, it is essential to assess the obtained result. This is the area of metrology. The ultimate goal is to provide the user with as much information as possible about the measurement quality. We deal with a specific difficulty for the quality assessment of the optical methods that arises precisely from their full-field nature. The metrology community is far more familiar with point-wise or average scalar measurements (length, temperature, voltage, etc.). As of today, the metrology of full-field optical methods is not yet fully settled. However, the wide dissemination of these techniques will only efficiently occur when users have a clear understanding of how they can characterize the measurement performances of the equipment that vendors put on the market.

First, the goal of this chapter is to present some basic elements and concepts of metrology. It is by no means exhaustive, and only aims at presenting the basics of the Chapter written by Andrž CHRYSOCHOOS and Yves SURREL.

domain in a simple way, so that the researchers, users, developers and vendors can exchange information based on well-established concepts. Second, we will rapidly present the different optical techniques based on their main characteristics (how information is encoded, interferential or not, etc.).

It should be noted that optical measurement techniques exhibit a non-negligible amount of complexity. Figure 1.1 outlines the typical structure of a measurement chain that leads from a physical field to a numerical measurement field using a camera. It can be seen that there are many steps required to obtain the final result which the user is interested in, and numerous parameters that may impair the result and effects are involved at each step. Most importantly, there are usually numerical postprocessing stages that are often "black boxes" whose metrological characteristics or impact may be difficult or even impossible to obtain from the supplier of the equipment in the case of commercial systems.

Software

Absolute or differential measurement

In any scientific domain, terminology is essential. Rather than enumerating the main terms to use (precision, sensitivity, resolution, etc.), let us try to adopt the final user point of view. What are the questions he generally asks, and in which context? There are, in fact, not so many questions, and each of them leads naturally to the relevant metrological term(s):

1) Is the obtained result "true", "exact" and "close to reality"? How to be confident in the result?

2) Is the equipment "sensitive"? Does it see small things?

These two questions lie behind the separation of metrology into two distinct domains, within which the metrological approach will be different: absolute measurement and differential measurement.

Absolute measurement

Here, we seek the "true" value of the measurand (the physical quantity to measure), e.g. to assess that the functional specifications of a product or system are met. Dimensional metrology is an obvious example. The functional quality of a mechanical part will most often depend on the strict respect of dimensional specifications (e.g. diameters in a cylinder/piston system). The user is interested in the deviation between the obtained measurement result and the true value (the first of the two questions above). This deviation is called the measurement error. This error is impossible to know, and here is where metrology comes in. The approach used by metrologists is a statistical one. It will consist of evaluating the statistical distribution of the possible errors, and characterizing this distribution by its width, which will represent the average (typical) deviation between the measurement and the true value. We generally arrive here at the concept of measurement uncertainty, which gives the user information about the amount of error that is likely to occur.

It is worth mentioning that some decades ago, the approach was to evaluate a maximum possible deviation between the measurement and the real value. The obtained uncertainty values were irrelevantly overestimated because the uncertainty was obtained by considering that all possible errors were synergetically additive in an unfavorable way. Today, we take into account that statistically independent errors tend to average each other out to a certain extent. In other words, it is unlikely (and this is numerically evaluated) that they act coherently together to impair the result in the same direction. This explains the discrepancy between the uncertainty evaluation formulas that can be found in older treatises and those used today. As an example, if c = a + b, where a and b are independent measurements having uncertainties Δa and Δb, the older approach (maximum upper bound) would yield Δc = Δa + Δb, but the more recent approach gives Δc = √ Δa 2 + Δb 2 , these two values being in a non-negligible ratio of √ 2 = 1.414 in the case Δa = Δb.

Differential measurement

Now, let us consider that the user is more interested in the deviation from a "reference" measurement. In the mechanics of materials field, the reference measurement will most likely be the measurement in some initial state, typically before loading. It is basically interesting to perform measurements in a differential way, and this is done for two reasons:

-As the measurement conditions are often very similar, most systematic errors will compensate each other when subtracting measurement results to obtain the deviation; typically, optical distortion (image deformation) caused by geometrical aberrations of the camera lens will be eliminated in a differential measurement.

-Measurement uncertainty is only about the difference, which implies that interesting results can be obtained even with a system of poor quality; let us take an example of a displacement measurement system exhibiting a systematic 10% error. Absolute measurements obtained with this system would probably be considered unacceptable. However, when performing differential measurements, this 10% error only affects the difference between the reference and actual measurements. Consider the following numerical illustration: with a first displacement of 100 μm and a second displacement of 110 μm; this hypothetical system would provide measured values of 90 and 99 μm, roughly 10 μm error each time, probably not acceptable in an absolute positioning application, for example. But the measurement differential displacement is 9 μm, which is only a 1 μm error.

Regarding this second example, we should emphasize the fact that it is not possible to use relative uncertainty (percentage of error) with differential measurements because this relative uncertainty, ratio between the uncertainty and the measurand, is related to a very small value, the difference of measurements, that is nominally zero. Hence, "percentage of error" is strictly meaningless in the case of differential measurements. Only absolute uncertainty is meaningful in this case.

Main concepts

We will consider in this section the main concepts of metrology. The corresponding terms are standardized in a document (international vocabulary of metrology, abbreviated as "VIM", [VIM 12]) which can be downloaded freely from the BIPM website.

Measurement uncertainty

The VIM definition is as follows: non-negative parameter characterizing the dispersion of the quantity values being attributed to a measurand, based on the information used.

The underlying idea is that the measurement result is a random variable, which is characterized by a probability density function centered at a certain statistical average value. This probability density function is typically bell-shaped. Note # 2 in the VIM states:

The parameter may be, for example, a standard deviation called standard measurement uncertainty (or a specified multiple of it), or the half-width of an interval, having a stated coverage probability.

So the idea is really to characterize the width of a statistical distribution. There is obviously a conventional feature to perform this characterization. We may choose the width at half the maximum, the width at 1/e, the usual standard deviation, etc.

In industry, the need to assess the quality of a measurement instrument can be slightly different: it is most often necessary to be "sure" that the measurement deviation will not exceed some prescribed value. So, the chosen width will include as much as possible the total spreading width of the function. Of course, no real 100% certainty can be obtained, but we can obtain confidence intervals at x%, which are intervals having a probability of x% to include the real measurand value. For example, for a Gaussian distribution of the measurement result probability, an interval of ±3σ has a probability of 99.5% to englobe the true value. Hence, the concept of expanded measurement uncertainty, whose VIM definition is: product of a combined standard measurement uncertainty and a factor larger than the number one.

The "combined standard measurement uncertainty" is the final uncertainty obtained when all sources of uncertainty have been taken into account and merged. In general, this is what is referred to when we speak of "uncertainty" in short.

Measurement uncertainty is the key notion to use when dealing with absolute measurement.

It should be noted that the two major uncertainty sources are those related to noise, introducing random fluctuations of null average value, and those related to systematic errors (calibration errors, poor or insufficient modeling, external permanent biasing influences, etc.). With full-field optical methods, noise can easily be characterized (see section 1.2.2.2).

Resolution

The VIM definition is as follows: smallest change in a quantity being measured that causes a perceptible change in the corresponding indication. This is the key notion to use when performing a differential measurement. In practice, with full-field optical methods, noise (optical, electronic, etc.) will be the factor limiting the resolution. A practical definition of resolution that we can propose is (non-VIM): change in the quantity being measured that causes a change in the corresponding indication greater than one standard deviation of the measurement noise.

As it happens, with techniques that use cameras, it is easy to measure the measurement noise because a large number of pixels are available to obtain significant statistics. To evaluate the measurement noise, it suffices to make two consecutive measurements of the same field, provided, of course, that it does not vary significantly in the meantime. Let us denote by m 1 (x, y) and m 2 (x, y) two successive measurements at point (x, y). These values are the sum of the "signal" s (the measurand value) and the noise b, as:

m 1 (x, y) = s(x, y) + b 1 (x, y) m 2 (x, y) = s(x, y) + b 2 (x, y) [1.1]
where the signal s is unchanged, but the noise has two different values. The subtraction of the two results yields:

Δm(x, y) = m 2 (x, y) -m 1 (x, y) = b 2 (x, y) -b 1 (x, y) [1.2]
Assuming statistical independence of the noise between the two measurements, which is often the case1 , we can evaluate the standard deviation of the noise b (we always assume that the noise is stationary, i.e. its statistical properties do not change in time) by using the theorem which states that the variance (square of the standard deviation) of the sum of two statistically independent random variables is equal to the sum of their variances, which gives:

σ 2 (Δm) = σ 2 (b 2 -b 1 ) = σ 2 (b 2 ) + σ 2 (-b 1 ) = 2σ 2 (b) [1.3]
An estimator of the statistical variance of the noise difference b 2b 1 is obtained by calculating, for all the pixels of the field, the arithmetic variance:

σ2 (Δm) = 1 N pixels pixels [Δm(x, y) -Δm] 2 [1.4]
where Δm is the arithmetic average of Δm within the field:

Δm = 1 N pixels pixels Δm(x, y) [1.5]
We thus obtain for the resolution r:

r = σ b ≈ 1 √ 2 σ(Δm) [1.6]
For the sake of mathematical rigor, we have chosen to denote by an ~sign the real statistical values, and not their estimators obtained from arithmetic averages over a large number of pixels. This number being typically much larger than 10,000 (which corresponds to a sensor definition of 100 × 100 pixels, a very low definition), we can ignore the difference and consider the estimators to be faithful.

Let us insist on the fact that this estimate of the noise level is very easy to perform, and should be systematically performed during full-field measurements.

Characterizing resolution using the noise level is common in IR thermography. An IR camera is characterized with noise equivalent temperature difference (NETD), which is nothing other than the output noise level converted into the input, i.e. converted into the temperature difference that would cause a reading equal to one standard deviation of the noise. Temperature variations will begin to "come out of the noise" when they reach the order of magnitude of the NETD. To change an output noise level into an input level, we use sensitivity.

Sensitivity

The VIM definition is as follows: quotient of the change in an indication of a measuring system and the corresponding change in a value of a quantity being measured. This corresponds to the coefficient s that maps a small variation of the measurand onto the corresponding variation of the measurement reading (the output m)

s = ∂m ∂e [1.7]
Sensitivity is not always relevant for optical field measurements. As an example, correlation algorithms directly provide their results as displacement values; their sensitivity is equal to one. On the contrary, the grid method presented later in this AQ1 book provides a phase after the detection step. The relationship between the phase Φ and the displacement u is:

Φ = 2π u p [1.8]
where p is the grid pitch because the phase varies by 2π when the displacement is equal to one grid period. Thus, the sensitivity according to the VIM is:

s = 2π p [1.9]
This notion is rarely used in optical field methods. However, in IR thermography, it remains fully meaningful and represents the voltage or current variation at the sensor level relative to the received irradiation.

Repeatability

The VIM definition is as follows: measurement precision under a set of repeatability conditions of measurement to which we add the definition of measurement precision closeness of agreement between indications or measured quantity values obtained by replicate measurements on the same or similar objects under specified conditions and the definition of repeatability conditions: condition of measurement, out of a set of conditions that includes the same measurement procedure, same operators, same measuring system, same operating conditions and same location, and replicate measurements on the same or similar objects over a short period of time.

Actually, the underlying idea is fairly simple: repeatability is supposed to characterize the measurement instrument alone, having excluded all external influences: same operator, same object under measurement, short delay between successive measurements, etc. In short, repeatability tests will characterize the noise level of the measurement instrument.

When using IR thermography, it is essential to evaluate repeatability only after the radiometric system has reached its thermal equilibrium. The non-stationary feature of the parasitic radiations coming from the optical elements and from the rest of the camera may significantly bias the results. It is noteworthy that the time to thermal equilibrium can be some hours, even in a stabilized environment. This is a noticeable constraint [BIS 03].

The "dual" notion, which supposes, on the contrary, different operators, times, locations and even measurement systems, is reproducibility.

Reproductibility

The VIM definition is as follows: measurement precision under reproducibility conditions of measurement to which we add the definition of the reproducibility conditions: condition of measurement, out of a set of conditions that includes different locations, operators, measuring systems, and replicate measurements on the same or similar objects.

To emphasize the fact that very much can be changed in this case, Note 1 in the VIM states:

The different measuring systems may use different measurement procedures.

As can be seen, as little as possible should change when performing repeatability tests (in short, noise evaluation), and as much as possible may change when doing reproductibility tests (in short, all possible error sources can be involved).

Calibration

The VIM definition is as follows: operation that, under specified conditions, in a first step, establishes a relation between the quantity values with measurement uncertainties provided by measurement standards and corresponding indications with associated measurement uncertainties and, in a second step, uses this information to establish a relation for obtaining a measurement result from an indication. Thus, calibration enables, from artifacts producing known values of the measurand, the identification of the transfer function of the measurement system. As an example, for an instrument having a linear response, measuring a single standard allows us to identify the slope of the straight line that maps the measurand to the output indication. Note in passing that this slope is nothing other than the sensitivity of the instrument according to the VIM definition presented in section 1.2.2.3.

A measurement standard is a realization of the definition of a given quantity, with stated quantity value and associated measurement uncertainty, used as a reference.

In IR thermography, the ideal measurement standard is the black body, a radiating object with unity emissivity. For cameras, it is practical to use plane black bodies that present isothermal surfaces (e.g. within ±0.02 K). In this case, temperatures and radiated energies unequivocally correspond. Classic calibration procedures use two black body temperatures that include the temperature range of the scene that is to be measured. The procedure involves a non-uniformity correction (NUC), which sets the offsets of all matrix elements such that the represented thermal scene appears uniform and detects and replaces the bad pixels (bad pixel replacement (BPR)); bad pixels are those which, according to a user-prescribed criterion, provide an output signal that deviates too far from the average. Recently, this calibration step, which is convenient and fast, has tended to be replaced by a pixel-wise calibration, which is longer and more costly but offers improved precision over a wider measurement range [HON 05]. The interested reader will find in Chapter 16 more information on this subject.

Illustration

Let us recall here an elementary result. If we average the results of N nominally identical measurements (in other words, measurement performed in repeatability conditions, section 1.2.2.4), we obtain something that can also be considered a random variable, because another set of N measurements would provide a different value for the average. The classic result is that the standard deviation of the fluctuations of the average of N measurements is equal to the standard deviation of the fluctuations of a single measurement divided by √ N . -The true value of the measurand (it is permissible to speak of the "true value", explicitly referred to in the VIM in section 2.11).

-The true value biased by the systematic errors; measurement values will fluctuate around this value.

-The result of a single measurement; many measurements will provide values that will fluctuate according to some probability density function of standard deviation σ n , where n stands for noise.

-A value resulting from the averaging of N measurement results; many such averages will fluctuate with a standard deviation that is √ N smaller than for a single measurement.

-The standard deviation σ m , where m stands for "model", which corresponds to the probability density function of systematic errors that could be determined by a proper modeling and investigation of the physics of the instrument.

-The combined uncertainty σ 2 m + σ 2 b , which takes into account the uncertainty related to systematic errors, as well as the noise.

-The expanded uncertainty that can be used as a confidence interval.

In practice, it is often the uncertainty component not related to noise (the systematic errors) that is the most difficult to evaluate.

Spatial aspect

Full-field optical measurement methods have a special aspect for metrology: the fact that they provide a spatial field instead of a single scalar. Concepts adapted to this spatial nature are lacking in the VIM. The most important is spatial resolution, which depends on numerous factors, especially all the digital postprocessing that can take place after the raw measurements are obtained, for example, to decrease the amount of noise. Before presenting the possible definitions, let us recall some basic results concerning spatial frequency analysis.

Spatial frequency

The relevant concepts here are commonly used by optical engineers when dealing with image forming. Indeed, the process of forming an image from an object using an imaging system can be seen as the transfer of a signal from an input (object irradiance) to an output (image intensity). This transfer will change some features of the signal, according to some transfer function. In a way similar to an electronic filtering circuit, which is characterized by a gain curve as a function of (temporal) frequency, an imageforming system can be characterized by the way it will decrease (there is never any amplification) the spatial frequencies. In lens specifications found in catalogs, we can sometimes find "gain curves" (called optical transfer function) that correspond exactly to gain curves characterizing electronic amplifiers or filters.

The difficulty of spatial frequency is related to its vectorial aspect because we have to deal with functions defined on a two-dimensional (2D) domain, e.g. the irradiance L(x, y) of the object to be imaged. When dealing with a time function f (t), the variable t is defined over a unidimensional space, and the Fourier conjugated variable, the frequency, is a scalar variable. With a function defined on a plane, f (x, y) or f ( r) with vector notation, the Fourier variable is of dimension 2: (f x , f y ) or f .

To understand the notion of spatial frequency, the simplest way is to consider an elementary spatial periodic function, for example z(x, y) = cos[2π(f x x + f y y)], where f x and f y are constants. This "corrugated iron sheet" function is illustrated in Figure 1.3. We can rewrite its definitive equation as z(x, y) = cos(2π f . r), where r is the AQ2 vector of components (x, y) and f is the spatial frequency vector of components (f x , f y ). It is easy to convince ourselves that:

-The direction of vector f is perpendicular to the function z(x, y) isovalue lines.

-The norm (length) of f is equal to the reciprocal of the function period p:

|| f || = 1/p.
The history of instrumental optics has been a race to obtain instruments that transmit as much as possible all the spatial frequencies present in an object, in the same way as audio electronics developed to transmit with high fidelity all the acoustic frequencies present in voice or music signals. In the optical domain, test objects are often targets made up of equidistant straight lines that implement "single frequency" objects2 (Figure 1.4). The investigation of these target images, describing whether the image-forming system has correctly transmitted ("resolved") the lines, allows us to determine the instrument cutoff frequency beyond which the lines will not be distinguished one from the other. We can also see in Figure 1.4 trumpetshaped patterns that correspond to increasing spatial frequencies, which is the spatial implementation of what is known as "chirps" in signal processing. We can suppose that Fourier analysis is perfectly well adapted to deal with all these notions, and that the optical transfer function is nothing else than the filtering function in the Fourier plane (the spatial frequency plane) where the spatial frequencies present in the object are represented. Light intensity is always non-negative, so a constant average value has to be superimposed onto the sinusoidal variation, yielding the irradiance:

I(x) = A 1 + γ cos 2πx p [1.10]
Visibility (or contrast) is the dimensionless ratio of the modulation and the average. Visibility is unity when "blacks are perfectly black", i.e. when the irradiance minimum reaches zero. The change in the irradiance signal by a system having the transfer function G(f ) that attenuates nonzero frequencies causes a loss of visibility. For a spatial frequency f 0 , as represented in Figure 1.5, visibility loss is For certain spatial frequencies, visibility can even vanish completely. Also, if the transfer function G(f ) oscillates around zero, visibility will change its sign, causing a phase lag of π of the output signal: minima and maxima will exchange their places; this is called visibility inversion. This effect is shown in Figure 1.6, where the visibility changes its sign when crossing the zones where it vanishes. Historically, of course, this mathematical background was not available. The spatial resolution of an image-forming system was defined from the minimum distance between the images of two neighboring points that allowed the points to be distinguished ("resolved"). We recognize the spatial equivalent of the resolution of a measuring instrument as the "smallest distance between two points whose images can be separated". We can state this in other words: "the smallest change in position that causes a perceptible change in the corresponding image", which is the copy mutatis mutandis of the VIM definition. This concept relates to what is known in optical engineering as the Rayleigh criterion.

γ γ = G(f 0 ) G(0) [1.11]
Considering the images of grids having various frequencies instead of considering neighboring points is the dual approach (in the Fourier sense). In this case, we seek the highest frequency that is transmitted by the instrument without perceptible degradation (e.g. without loss greater than 50%). The reciprocal of this spatial frequency is a geometrical wavelength that can be considered as the spatial resolution. This explains why the following definition can be found in [AST 08]:

-"Optical data bandwidth: Spatial frequency range of the optical pattern (e.g. fringes, speckle pattern, etc.) that can be recorded in the images without aliasing or loss of information". We can recognize the notion of performance of an image-forming system, characterized by a cutoff frequency f c . The bandwidth is the interval [0, f c ].

-"Spatial resolution for optical data: One-half of the period of the highest frequency component contained in the frequency band of the encoded data". This is the quantity 1/2f c . The factor 2 is something of a convention and has no precise justification. However, there is always a conventional aspect in these definitions as the considered quantities vary in a continuous way. The above-mentioned Rayleigh criterion also has a conventional aspect. A factor of 2.5 or 1.5, for example, might have been used without the possibility of justifying that choice any more clearly.

For image correlation techniques, the minimum spatial resolution is the size of the subimages used to calculate the correlation, because we obtain only one measurement per subimage position, for the whole subimage area. Of course, the subimage can be (and is, in general) moved pixel by pixel to obtain a displacement field populated with as many pixels as the original image, but this does not change the spatial resolution, as all measurements corresponding to a distance smaller than the subimage size will be correlated and not independent.

To end this section, let us emphasize that we should not use the term "resolution" to designate the number of pixels of the camera sensor, but definition. Remember that we speak of high-definition TV (HDTV) to evoke a very large number of pixels in the image. High resolution is obtained with a high magnification of the imaging system. Thus, we can have a very good resolution with a low definition, with a sensor that does not have a very high number of pixels but covers a very small field of view3 .

Spatial filtering

A very common operation for reducing the spatial noise that is present in the image is spatial filtering, which consists of replacing every pixel in the image by an average, weighted or not, performed with respect to its neighbors. This operation is very well described using the Fourier transform, and it is easy to calculate the consequences on spatial resolution. This kind of filtering is basically a convolution operation. For the sake of simplicity, let us use a one-dimensional description with continuous variables, as sampling introduces some complexity without changing the basic concepts. The simplest filtering is the moving average, where each point of a signal g(x) is replaced by the signal average over a distance L around this point:

g(x) = x+ L 2 x-L 2 g(u)du [1.12]
This expression can be described as a convolution product with a rectangle function Π(x) defined as:

Π(x) = 0 if x < -1/2 or x > 1/2 1 else [1.13]
Equation [1.12] can, indeed, be rewritten as:

g(x) = +∞ -∞ g(u)Π x -u L du = (g * Π L )(x) [1.14]
where * denotes a convolution product and Π L (x) = Π(x/L). The effect of such a filtering can be seen in the Fourier space (or frequency space), by taking the Fourier transform of the previous equation:

ĝ(f x ) = ĝ(f x ) × ΠL (f x ) [1.15]
which gives:

ĝ(f x ) = ĝ(f x ) × L sinc(Lf x ) [1.16]
where sinc is the "cardinal sine" function: sinc(u) = sin(πu)/πu. The initial frequency spectrum (the Fourier transform of signal g) is attenuated by the transfer function, in this case sinc(Lf x ) which reaches its first zero for Lf x = 1, or

f x = 1/L (Figure 1.7).
Gaussian filtering is also used very frequently:

g(x) = +∞ -∞ g(u)G σ (x -u)du [1.17]
where

G σ (x) = 1 σ √ 2π exp - x 2 2σ 2 [1.18]
is a normalized Gaussian function having a standard deviation σ. Its Fourier transform is:

Ĝσ (f x ) = exp(-2π 2 σ 2 f 2 x ) = σ √ 2πG σ (f x ) [1.19]
where σ =1/2πσ. It is also a Gaussian function, which has the property of decreasing very rapidly when its variable increases. This provides interesting properties for noise filtering because spatial noise is mostly present at high frequencies (typically, noise changes from one pixel to another, which corresponds to the highest frequency in a sampled image). More generally, any (linear) filtering can be described as a convolution with a certain function that is usually called the filtering kernel.

Numerically, linear filtering is efficiently implemented in the Fourier plane because efficient discrete Fourier transform algorithms (the so-called fast fourier transform -FFT) are available. In the Fourier plane, the convolution is replaced by a simple multiplication with the transfer function, the Fourier transform of the filtering kernel. However, these FFT algorithms can only be used if the image topology is rectangular, in other words when no invalid pixels or holes exist in the image. Holes are zones with no measurements and cannot be simply replaced by zero. If holes are present, some kind of interpolation has to be used to fill them so that no discontinuity arises along their edges, because these possible discontinuities will introduce adverse effects in the signal spectrum. This is not a trivial operation, and it may finally be simpler to implement the convolution.

Successive filterings correspond to successive convolution products. As the convolution product is associative, this can be considered as a single filtering using a kernel that is the convolution product of all the different kernels used. As an example, if three filterings having kernels K 1 (x), K 2 (x) and K 3 (x) are used:

g(x) = {[(g * K 1 ) * K 2 ] * K 3 }(x) = [g * (K 1 * K 2 * K 3 )](x) [1.20]
we obtain something equivalent to a single filtering with kernel

(K 1 * K 2 * K 3 )(x).
It can be shown [ROD 78] that with a high number of successive filterings with the same filter, we tend toward Gaussian filtering; this is a consequence of what is known as the central-limit theorem.

As for spatial resolution, each filtering widens an object point, since the result of the filtering of a point located at x 0 and described by a Dirac function δ(xx 0 ) is simply the filtering kernel translated at the same point, because:

δ(x -x 0 ) * K(x) = K(x -x 0 ) [1.21]
It can also be shown [ROD 78] that the "width" Δ f * g of the convolution product of two functions f and g is the quadratic sum of the widths of each function:

Δ f * g = Δ 2 f + Δ 2 g [1.22]
This equation allows us to calculate how the spatial resolution evolves as a function of successive spatial filterings.

To end this section, let us mention that this approach for the study of spatial resolution by the frequency transfer function was the basis of the work performed by the GDR 2519 research group, reported in [BOR 09], with respect to image correlation.

Classification of optical measurement techniques

In this section, we propose a systematic classification of different optical techniques for the measurement of kinematic fields. This classification is based on a limited number of basic key concepts.

In this context, infrared thermography has a slightly special position. It enables the measurement of a surface temperature, and not a kinematic value such as displacement, strain, slope and curvature.

In fact, the signal output by infrared sensors depends on the irradiance received from emitting bodies, and its transformation into a temperature is not a trivial task. The signal-to-energy relationship first involves Stefan-Boltzmann's and Planck's laws. Then, ignoring any parasitic radiation, translating received energies into the temperature of the target is only possible if the target has a known emissivity, which is a necessary condition. Other aspects of course need to be taken into account to ensure the accuracy of the temperature measurement. They are presented in Chapter 16 of this book.

White light measurement methods

In this family, the measurand is encoded in the spatial variation of light intensity, this variation being obtained in a non-interferometric way; in other words, we are excluding everything related to interferometric fringes. Purely optical aspects may be restricted to the image-forming process: measuring displacements by using image correlation has nothing really "optical" in nature, but is only based on a geometrical phenomenon that is present in images.

Encoding techniques

The measurand encoding, shown in Figure 1.1, is mainly of two kinds:

Encoding through a random signal: the signal is characterized by its local random variation, acting as a signature; the receiving system will have to identify this signature to complete the measurement; in this category lie all the methods using image correlation, including the so-called (laser) speckle correlation; these methods are presented in Chapter 6.

Encoding through a periodic signal, more precisely through the modulation of the phase (or, equivalently, of the frequency) of a spatial sinusoidal signal, called a "carrier"; as an example, we can cite the displacements of the lines of a grid deposited on a substrate, or the displacements of the lines of a grid reflected by a mirrorlike surface where the local slopes are not uniform; these methods are presented in Chapter 3.

It should be noted that each technique exists under both forms (random encoding or phase encoding), even if the terminology does not always help to recognize this fact. There are of course major differences in performance resulting from these different encoding approaches:

-The practical realization of random encoding, which is essentially noise, is difficult to fully characterize, using complex notions such as statistical moments (there are plenty of such "moments") or average power spectral density (PSD); the correlation method for in-plane displacement measurements often requires paint to be sprayed on the body under examination to produce a "speckle", a random contrasted pattern; it is obvious that this manual process cannot easily be made repeatable, and the "quality" of the obtained pattern is difficult to characterize.

-On the other hand, encoding through the modulation of a spatial periodic carrier can be fully characterized by its frequency, its local phase, its local average level, its local contrast and its harmonic content.

-Random encoding is not quantitative by itself ; the information lies within a local contrast morphology or signature that the detection system has to identify.

-On the contrary, encoding by the phase modulation of a carrier is quantitative because the signal (e.g. the displacement of a grid line) corresponds to a number which is the amount of phase modulation. Phase detection techniques are very well established and efficient (they mostly rely on Fourier analysis) and allow easy characterization.

-A drawback of phase encoding is its periodicity: the same code value periodically repeats as the signal increases, which leads to ambiguities. Removing these ambiguities corresponds to what is called phase unwrapping that suppresses the 2π jumps appearing in the detection process that only outputs the phase modulo 2π. Phase unwrapping is, in fact, simply numbering the fringes (or lines, depending on the method).

-In general, correlation methods are much easier and cheaper to implement; either the part under test is sufficiently textured to allow the use of digital image correlation, or it suffices to spray paint on it. This is much simpler than gluing or engraving or in some way depositing a grid onto the surface, not to mention the fact that grids can only be placed on flat or cylindrical surfaces.

Examples

Almost all white light techniques consist of measuring a position or a displacement in an image. A simple geometrical analysis of the measurement system allows us to understand the measurement principle.

1) Measurement of in-plane displacements: here, the object undergoing displacements is simply observed using a camera. The displacements of marked points of the object correspond to displacements of image points. The primary output of the technique is the displacement field of the image points. The available techniques are the following. i) Grid technique: a grid has to be deposited on the surface; the local displacements will modulate the phase of the grid acting as a periodic carrier. Its main drawback is the required surface preparation.

ii) Moiré4 is only an additional layer on the grid technique, since the nature of the encoding is the same. It consists of decreasing the spatial frequency of the carrier using a beat phenomenon, exactly as stroboscopy decreases the temporal frequency of a vibration.

iii) Deflectometry: in this technique, derived from the previous one, the object reflects a fixed regular grid pattern. Distortion of the grid image is caused by nonuniformity of the surface slopes. Thus, this technique enables slope fields to be measured. It is necessary that the surface be at least partially reflective, in which case the technique is quite easy to implement since no surface preparation is required. If not, a revealing fluid can be wiped onto the surface to make it reflective. iv) Digital image correlation: this is the speckle implementation of the same concept, and the surface points are marked using the surrounding local random contrast pattern.

2) Shape measurement: Shape measurement techniques derive from displacement measurement techniques. The fundamental geometrical arrangement (Figure 1.8) is the same for stereocorrelation, where two cameras observe the object from two different points of view, and for fringe projection (or structured light projection). If the position in space of the optical centers C 1 and C 2 are known, knowing the position of points M 1 and M 2 allows the position of point M to be determined. The difference between the two techniques lies in the trajectory and nature of the information: i) With stereocorrelation, the information starts from point M and propagates toward points M 1 and M 2 , located on two camera sensors; the analysis software has to recognize the local signature around M in the images to pair M 1 and M 2 .

ii) With fringe projection, the information (which is quantitative as it is a fringe phase, proportional to the abscissa or ordinate of M 1 ) starts from M 1 , which is most often a video projector pixel, and propagates toward M and afterward M 2 . The analysis software has only to detect the phase and unwrap it5 to know exactly the emitting point because its coordinates are known from the phase.

Interference methods

The temporal phase ψ(t) = ωt + φ of an electromagnetic wave in the visible domain, such as the one emitted by an helium-neon (λ = 633 nm) or YAG (λ = 532 nm) laser, vibrates at a frequency around one hundred terahertz (10 14 Hz).

There does not exist any sensor capable of recording temporal variations at such high frequencies, and they are only sensitive to the average light power value. This is why the interference phenomenon is useful to obtain phase information. The nature of interference is a beat phenomenon between two periodic signals of same frequency, as in stroboscopy or moiré, that will remove the term ωt present in ψ. The formula that gives the light intensity in two-wave interferences is:

I = I 0 (1 + γ cos Φ) [1.23]
where γ is the visibility (or contrast) and the phase Φ of the interference fringes is:

Φ = ψ 2 -ψ 1 = φ 2 -φ 1 = 2π δ λ [1.24]
where δ is the optical path difference between the two interfering beams and λ is the wavelength in the propagation medium, most often air. In fact, an interferometric measurement is always performed between an initial state that acts as the reference (due to imperfections, we never have an initial state without any interference fringes) and a final state. It is therefore always an interference fringe phase variation

ΔΦ = (φ 2,final -φ 1,final ) -(φ 2,initial -φ 1,initial ) [1.25]
which is used (double difference). -In the first case, the surface is a mirror. All the energy is reflected in a single direction, following Snell's law, and the wave front remains smooth.

-In the second case, the surface is rough (diffusive) and the energy spreads in all directions. The wave front shape becomes very complicated, which is the reason why they are referred to as 'random'; this will create spatial noise in an image obtained by an imaging system placed downstream. This spatial noise is called speckle.

-In the last case, a diffraction grating 6 is deposited (in general, molded) onto the surface so that the first diffracted order is normal to the surface. In this case, a noticeable amount of energy is re-emitted along the normal direction, and the wave front remains smooth.

Sensitivity vector

When a surface point that is illuminated by a monochromatic wave undergoes a small displacement characterized by the vector u, the phase variation of the beam coming from the light source and re-emitted toward the observer T is calculated from the variation in the optical path. It is easily shown that this phase variation Δφ is

Δφ = g. u [1.26]
where the difference between the illumination and observation wave vectors g = k ik o is called the sensitivity vector. Its direction indicates the displacement component the measurement will be sensitive to. In the case of a mirror-like reflection, the sensitivity vector is normal to the surface; thus only out-of-plane displacements can be measured (Michelson interferometry).

Synthetic sensitivity vectors

After a measurement, an interference fringe phase variation field is obtained, which is locally proportional to the sensitivity vector g. If different mesurements of the same kinematic field can be made with different illumination conditions, different phase variations for the same displacement are obtained: With a simple linear combination of these equations, that is of the obtained phase images, the displacement vector appears factorized with the corresponding linear combination of sensitivity vectors, which is called a synthetic sensitivity vector:

⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ Δφ 0 = g 0 . u Δφ 1 = g 1 . u . . . Δφ N -1 = g N -1 . u [1.27]
N -1 i = 0 α i Δφ i = N -1 i = 0 α i g i . u = G. u [1.28]
Such a linear combination may also appear in an analog way with a setup that uses simultaneously different illumination directions, as in interferometric moiré (see section 1.4.5.2).

The different types of interferometric measurements

These simply correspond to the various possible interactions of the incident beam with the surface presented in Figure 1.9 and to the different ways of choosing the interfering beams. In the following, we will use the term "object beam" to designate the incident beam; it is the beam that illuminates the object.

Interference between the object beam and a fixed reference beam

In this case, we have for the double difference formula [1.25]:

ΔΦ = Δφ obj -Δφ ref = Δφ obj = g. u [1.29]
so it can be seen that the measured quantity is the displacement component along the sensitivity vector g. For example, the measurement of the approximate out-of-plane displacement using interferometry in diffuse light (speckle interferometry) is shown in Figure 1.11, where the measured displacement component u g is aligned along the bissector of the illumination and observation directions. It can be seen that there is AQ3 some degree of approximation, as this bissector is not exactly normal to the surface. Existing commercial systems may or may not take this effect into account. The two beams come from the same object point, but with different incident illumination directions, so the sensitivity vectors are different. Then the double difference formula [1.25] is written:

ΔΦ = Δφ 2 -Δφ 1 = ( g 2 -g 1 ). u = G. u [1.30]
Thus, we obtain, in an "analog" way, a synthetic sensitivity vector. As a typical example, we have what is often referred to as interferometric moiré, but is more relevantly called grating interferometry, outlined in Figure 1.12. Regarding grating interferometry, the main drawback is the difficulty in depositing the grating on the surface. A typical maximum value of the grating size that can be placed is 40-50 mm. The main advantage is the absence of speckle noise in the image, leading to excellent spatial resolution for the measurements.

The same approach can be used with diffuse light, as indicated in Figure 1.13. The major difference (not speaking of the absence of the complicated process of depositing a grating onto the surface) is that the incident beams are not collimated in general, in order to investigate large surfaces.

Interference between object beams coming from two contiguous points (differential interferometry, shearography)

A splitting system placed in the imaging arm of the setup enables us to obtain on the sensor two images of the object, laterally shifted by a small quantity δ l (Figure 1.14). The double difference formula [1.25] becomes in this case: What is measured is then a differential displacement, which is very interesting for mechanical engineering, since the differential displacement basically relates to strain. With different illumination directions, we can acquire different phase fields that can be combined in order to obtain synthetic sensitivity vectors enabling the measurement of in-plane and out-of-plane displacements. Once again, grating interferometry or interferometry in diffuse light can be used (in other words, differential interferometry can be used with or without a grating), with the already mentioned drawbacks and advantages. The term "shearography" [HUN 07] is in general reserved for realizations in diffuse light.

ΔΦ = Δφ 2 -Δφ 1 = g.( u + δ u) -g. u = g.δ u [1.31]
Regarding terminology, it should be noted that the term "shear" which appears in many papers dealing with differential interferometry (and from which "shearography" derives) designates the lateral displacement introduced by the splitting component in the imaging system. It has nothing to do with "shear" as the non-diagonal strain component as understood by mechanical engineers. When aligning the lateral shift direction with the x and y axes, and using different illumination directions, all the derivatives of all component displacements can be obtained. Thus, we can obtain all the in-plane strain components and all the slope7 (out-of-plane displacement gradient) components.

To conclude, let us emphasize a very interesting feature of differential interferometry: it is basically insensitive to vibrations, as vibrations introduce rigid body displacements but not displacement gradients, making the technique very usable in industrial environments. This is why shearography is now becoming accepted as a non-destructive technique in the aeronautical industry.

Holography, digital holography

Holography is not, strictly speaking, a measurement technique; it is a recording technique for an electromagnetic field, both in amplitude and in phase, so that it can be reconstructed afterward. The principle is to make the field interfere with a so-called "reference" beam, and to record the resulting interference fringes. The recording used to be photographic, with special high-resolution photographic plates, but is now mostly digital.

Holography offers the possibility to create interferences between waves that do not exist simultaneously, for example waves diffused by an object before and after deformation. Thus, holography can be seen as a complement to all the interferometric techniques presented before.

It should be noted that there is no real difference between digital holography and the interferometric setup using a smooth reference beam like the one presented in Figure 1.11, as it is in both cases the recording of interferences between an object and a reference beam.

The only difference is that in cases called "speckle interferometry", the recording takes place in a location where the object has already been imaged, so the object reconstruction required in digital holography is not necessary. When we remove the camera lens shown in Figure 1.11 and reconstruct the object from the recorded interference fringes, we perform digital holography.

Conclusion

We have presented in this section an approach to classify a large number of optical techniques in terms of their fundamental features (white light or interferometric techniques, random encoding or phase modulation, nature of the measurand). Table 1.1 proposes a very short synthesis, briefly indicating their performances. Of course, such a table is only a very coarse presentation of reality. However, it is hoped that it may be useful for a first approach to the choice of a full-field optical measurement technique.

Figure 1 . 1 .

 11 Figure 1.1. Outline of the many steps involved in a measurement chain using a camera

Figure 1 . 2 .

 12 Figure 1.2. Measurement, error and uncertainty

Figure 1 . 3 .

 13 Figure 1.3. Function cos[2π(fxx + fyy)]

Figure 1 . 4 .

 14 Figure 1.4. Mire ISO 12233

Figure 1 .

 1 Figure 1.5 illustrates the process of image forming, starting from a sinusoidal grid object. The instrument gain (or optical transfer function) is represented in the central box, at the top.

Figure 1 . 5 .

 15 Figure 1.5. Transmission of sinusoidal grid irradiance through an image-forming system

  Figure 1.6. Contrast inversions

Figure 1 . 7 .

 17 Figure 1.7. Cardinal sine function sinc(Lfx), which is the transfer function of a moving average over a length L

Figure 1 . 8 .

 18 Figure 1.8. Shape measurement using stereocorrelation or fringe projection

Figure 1 . 9 .

 19 Figure 1.9. Different interaction modes between incident light and a surface: specular (mirror-like) reflection, diffusion, diffraction

Figure 1 .

 1 Figure 1.10. Sensitivity vector

6

  A grating is a very dense pattern of straight parallel lines. A grating has the property of splitting an incident ray into many different rays (called diffraction orders) having different directions.

Figure 1 . 11 .

 111 Figure 1.11. Interferometry in diffuse light for the measurement of out-of-plane displacements ("out-of-plane speckle" setup)

Figure 1 . 12 .

 112 Figure 1.12. Measurement of in-plane displacements: grating interferometry (also called interferometric moiré); corresponding sensitivity vector

Figure 1 . 13 .Figure 1 . 14 .

 113114 Figure 1.13. Measurement of in-plane displacements ("in-plane speckle setup")

Table 1 .1. Synthesis

 1

		White light
	Measurand	Random encoding Phase modulation Remarks
	In-plane disp.	Image correlation	Grid (with or without moiré)	Coupling with out-of-plane disp.
	Shape	Stereocorrelation	Fringe projection (structured light)	Transverse calibration of camera required
		Stereocorrelation
	3D disp.	with deposited	Impossible	id.
		speckle
	Slopes	Not used	Deflectometry	Coupling with shape
		Interferometry
	Measurand	Reflected light	Diffuse light	Diffracted light
	In-plane disp.	Impossible	In-plane speckle	Interferometric moiré
	Out-of-plane disp.	Michelson interferometry	Out-of-plane speckle	Not used, but a setup is conceivable
	Differential setup (slopes, strain)	e.g. Nomarski microscopy	Shearography	Grating differential interferometry
		Performances
		White light, random	White light, phase mod.	Interferometry
	Simplicity	++	+	-
	Cost	-	-	+
	Performances	-	-+	++

Counter example: atmospheric turbulence has typical correlation times of the order of one or many seconds, possibly larger than the interval between successive measurements if we do not take great care.

We ignore here the fact that sharp-edged lines have in their frequency spectrum many harmonics with frequencies that are integer multiples of the basic frequency.

This is a little theoretical; in practice, of course, a high definition is usually chosen when a high resolution is available.

The first letter should not be capitalized within a sentence, as it is a common noun and not the name of an inventor.

In this technique, unwrapping should also preserve an absolute phase origin.

We are speaking here of slopes introduced by mechanical loading.

Author Queries

[AQ1] The term [unity]


Marta Severo

Tommaso Venturini

Intangible Cultural Heritage Webs Comparing national networks with digital methods

Keywords: intangible cultural heritage, Internet, digital methods, social networks, UNESCO, States, cultural policy, cartography, Web

The 2003 Unesco Convention for the safeguarding of the intangible cultural heritage (ICH) is addressed to States and assigns them several tasks. No State, however, can accomplish all these tasks without mobilizing a wide network of institutions, associations and individuals. The national ICH policies intersect, overlap and often transform the existing relationships among these actors. This paper aims at comparing several national networks (France, Italy, Switzerland) involved in the implementation of the 2003 Unesco Convention in order to highlight national trends and specificities. The analysis will employ an innovative methodology based on digital methods and aimed at exploring the landscapes of websites dedicated to the intangible heritage. Analyzing the hyperlinking strategies of ICH actors, we will identify the specific web topology of each nation, showing which actors are central and peripheral, whether clusters or cliques are formed and who plays the roles of authority and hub.

Introduction

In recent years, globalization and social transformation started to pose dangerous threats to the preservation of the cultural heritage based on oral transmission and traditional culture. If, after the Second World War, governments felt the need to preserve important parts of their culture represented by built heritage such as the pyramids at Giza or the Great Wall of China, today societies (especially in non-western countries) are afraid to loose portions of their cultural identity related to orality and tradition. In countries such as Korea and Japan, industrialization, urbanisation, and westernisation are clearly threats for cultural items (music, drama, martial arts, skills, crafts…) completely based on oral expression, that can be exemplified with the case of the Living National Treasures, people identified as keepers of important intangible cultural properties.

In 2003, recognizing these risks, the Unesco decided to endorse the label intangible cultural heritage (from now on ICH) 1 to protect 'the practices, representations, expressions, knowledge, skills -as well as the instruments, objects, artifacts and cultural spaces associated therewith -that communities, groups and, in some cases, individuals recognize as part of their cultural heritage. ' (art. 2, Convention). By issuing the 2003 Convention for the safeguarding of the intangible cultural heritage, the Unesco acknowledged the importance of oral expressions and traditional practices and the urgency of their preservation.

To assure such preservation, the Convention established the need for an international system of safeguard analogous to the one that, since 1972, protects the tangible heritage (such monuments, cities, landscapes..) through the Convention concerning the Protection of the World Cultural and Natural Heritage. As the previous 'World Heritage Convention' for tangible properties, the 2003 ICH Convention is explicitly addressed to States and assigns them several tasks, such as: ensure the safeguarding (art.11) ; draw up inventories of intangible properties (art.12) ; designate or establish one or more competent bodies for protecting them ; foster scientific, technical and artistic studies and adopt appropriate legal, technical, administrative and financial measures (art.14) for assuring their safeguard ; support education, awareness-raising and capacity-building concerning this heritage (art.15) ; and foremost ensure the participation of communities (art.16) in all actions of preservation.

While granting intangible practices and expressions the same consideration accorded to material legacies, UNESCO experts recognized that the two types of heritage require radically different preservation systems. 2 For one thing, intangible practices are impossible to preserve simply through the State-centred approach that Unesco adopted for cultural properties, such as monuments and sites. Intangible heritage is by definition a living heritage, a heritage that is nurtured by the communities that initiated it and continue recreating it. Preserving the intangible heritage means first of all assuring the life and persistence of such communities of practice, a goal that calls for bottom-up and decentralized approaches (Blake, 2008).

As a consequence, although national States remain the first addresses of the Unesco, the 2003 Convention recognizes that numerous other actors play an irreplaceable role in the preservation of oral traditions and cultural practices (Kurin, 2004). Intangible cultural heritage is created and sustained by vast and complex networks of institutions, associations, NGOs, groups and even single individuals. To be sure, no State can accomplish all the tasks imposed in the Convention without involving a wide network of actors.

In the last years, the States that ratified the Convention have coped with the urgency of building a preservation system capable of involving all the actors that contribute to safeguard the intangible heritage. The emergence of a new governance to manage ICH has intersected, overlapped and often transformed the existing routines affecting the relationships among the different actors in charge of cultural heritage, with specific dynamics in each country. As we will see, in each State, the structure of the ICH network tends to mirror the national approach to ICH and its management. In this paper, we will explore a few national ICH networks, trying to understand who are the main actors and how they interact to create a (more or less) integrated system of preservation.

Such type of investigation is difficult for at least four reasons:

1.

ICH networks are wide and widespread. They count dozens, sometimes hundreds, of actors spread across several regions and sometime across several countries.

2.

ICH networks are heterogeneous. They gather actors coming from different universes, from amateurs associations to international institutions, from cultural establishments to economic enterprises, from traditional experts to academic scholars. The connections that bound these actors are not less varied, spanning from counseling to funding, from collaboration to competition, from scientific to market interests.

3.

ICH networks often embrace different languages. Not only different national languages, but also different dialects and technical jargons.

4.

The construction of a national ICH preservation system is a relatively new phenomenon and one that has not yet been thoroughly studied.

These four obstacles make it difficult to reconstruct even the smallest ICH networks, let alone comparing different networks. How to identify the myriad of actors engaged in the preservation of oral expressions and cultural practices? How to follow their multiple relations across national and linguistic borders? How to reconstruct a web of formal and information interactions in constant transformation? Since answering to these questions with traditional research methods is difficult for the reasons explained above, we decided to turn to digital methods.

Methodology: the digital methods

By 'digital methods' we refer to a series of techniques designed to explore the traces of online interactions as source of information on social phenomena. 3 The first evidence of the potential of such methods has been provided by the famous Google study on flu epidemics in United States. 4 By screening the queries addressed to their search engines between 2003 and 2008, Google's engineers devised an indicator that not only obtained an amazing 0.97 correlation with the data of the Centre for Disease Control data, but did it with a couple of weeks of advance. Published by Nature, the Google flu study convincingly demonstrated that online traces can be used to investigate offline phenomena (Ginsberg et al, 2009).

Besides the analysis of search engine data, many other digital methods entered the toolkit of social sciences in the last few years (Lazer et al, 2009) 5 . In this research, we will draw on 'web mapping' a method that proved particularly helpful in tracing complex social networks. The idea behind such method is that hyperlinks can be used as proxy of social connections. Despite the marginal cost required to create a hyperlink, it has been repeatedly observed that Web authors tend to be extremely careful in establishing connections and in particular:

1. they cite preferentially websites that share their thematic or social focus; 2. they do not cite websites that, though socially or thematically close, have opposite viewpoints.

If the first behaviour is not surprising, the second is more intriguing. People and groups having opposite position tend to ignore each other on the Web: they do not cite negatively, they do not cite at all. 6 The result is that the Web is not randomly organized. Linking their discourse to other online discourses, users establish hierarchies and clusters (Gibson, Kleinberg and Raghavan, 1998). Like the Internet, the Web is not a single network, but a network of networks, a graph where densely connected zones are separated by relatively empty spaces. Most of the time, these territories correspond to thematic communities: clusters of people gathering around interests and viewpoints. The hyperlinks connecting the websites dedicated to ICH can therefore reveal much about the networks of actors concerned ICH preservation. To say in other words, knowing which sites are hyperlinked online, we can infer which actors are connected offline.

Our analysis went through four successive steps. 1) As a first step we identified, in each country, the main actors related to intangible heritage. Generally, we started from websites of national agencies in charge of intangible heritage (such as Ministry of culture and the Unesco national commission) and from the websites dedicated to the items inscribed on the Unesco lists. Then, using several automatic and manual crawlers (especially the Issuecrawler 7 and the Navicrawler 8 ) we explored their websites keeping track of all the links that they contain, to discover other interesting websites and build the networks of connections among them.

2) As a second step, we categorized each website according to the type of actor it represents and to the dimension at which the actor operates.

-As for the type of actor, drawing on the information available on the websites we distinguished among institutions (governing bodies at international, national or local level), associations (profit or non-profit organizations) and individual (single individual or group of individuals with no formal organisation).

-As for the dimension of actors, drawing on the information available on the website we tried to define the focus of the activities of the actor: international (if the activities exceeds the boundaries of the country); national (if the activities concern the whole country or several areas of it); and local (if the activities concern a specific region or city). 9

3) As a third step, we analyzed and visualized the resulting networks through a graphs manipulation tool (Gephi 10 ). Analyzing the linking strategies of actors, we tried to identify the specific topology of each national preservation network, showing which actors are central and peripheral, if and how websites are gathered into separated clusters and who plays the role of authority in the networks.

1) As a fourth step, in order to enhance the readability of our networks, we used a script developed at Sciences Po médialab to turn our graphs into heatmaps (more below).

In the next few pages, we will discuss several graphs and heatmaps representing the network of ICH actors in three different countries: Italy, France and Switzerland. In order to interpret the following images, it is important to keep in mind that these visualisations are not geographical maps. The websites are not positioned in the image according to their geographical coordinates, but to their connectivity: nodes (the white dots in the image) are closer if there are directly or indirectly connected by hyperlinks. The coloured areas in the images represent the concentration of websites of the same type in the same region of the network (for example a very green area indicates an high density of red nodes). To be more precise, these are the design rules that have been followed in drawing them:

• The position of the nodes is significant and depends on their connections. Unlike, geographical maps, scatter plots and other Cartesian representations, the space of graphs do not pre-exist to the data that it contains and the position of each point does not, in itself, provide any useful information. In our images, there is no background map that would give sense to the absolute position of the nodes. Still the relative disposition of the nodes is not meaningless. All the networks that we will show are spatialized according to a force-vector algorithm called Force Atlas 2 (Jacomy et al, 2011). Such algorithm work by attributing a repulsive force to nodes and an attractive force to links. Once the algorithm is launched it changes the disposition of nodes until reaching the equilibrium that guarantees the best balance of forces. Such equilibrium guarantees that if two nodes are close in the specialized the graph, they are connected directly or indirectly (connected to the same set of nodes). In other words, the fact that a nodes is positioned at the top, bottom, right or left margin of the images is fortuitous, but the fact that it is positioned toward the margin (and not toward the centre) and the fact that it is positioned close to some nodes (and not others) is meaningful. Running the same spatialization algorithm several times, the images could be rotated or flipped, but the relative position of the nodes would not change (close nodes will always be close, far nodes will always be far).

• The size of the nodes is used to rank them. In particular, we chose to rank node by their 'visibility' in the network, computed as the number of links that they receive from other nodes (their 'in-degree'). In the following graphs, the size of each node is therefore proportional to the number of websites that cite it.

• The colour of the nodes is used to represent their category. As we said, websites have been categorized according to their type (blue points represent institutions, green points represent associations and red points represent individuals and groups) and to their dimension (red points represent international actors, blue points represent national actors, green points represent local actors). The two colour codes are consistent throughout all the graphs.

• Since in our graphs the positions and colours of nodes express respectively the connectivity and the categorization, the presence of many nodes of the same colour in the same region of the graph is meaningful. It allows to know if nodes cluster by category (that is to say, if nodes of the same colour are more connected among themselves than with nodes with a different colour) and to infer the relative position of different categories (i.e. which categories are central and which are marginal). To make this type of information more readable we employed a heatmap visualization. To obtain such visualization each node is represented as a source of light. A coloured light emanates from the centre of each node with a colour that depends on the node colour and an intensity and irradiation that are proportional to the node size. The result is an image where different areas are coloured according to the predominant type of nodes and lighter areas correspond to regions of the graph with a higher density of nodes 11 .

Before moving to the analysis, as a disclaimer for the rest of this article, let us underline that hyperlink networks do not always match the state of offline relationships. For one thing, websites are not always up to date. For another, hyperlinks in different sections of a website may have different meanings that our method is incapable to distinguish (for example we do no differentiate between links in the news, links in the partners page and links in banners). Still, although web mapping cannot provide an exhaustive description of ICH networks, it may suggest interesting research directions and provide discussion ideas.

Italian ICH Web

Starting from the websites of the Ministry of Culture (www.beniculturali.it), the National Commission for UNESCO (www.unesco.it) and several websites related to Italian items inscribed on the Unesco list, [START_REF]The Canto a tenore, Sardinian Pastoral Songs; the Opera dei Pupi, Sicilian Puppet Theatre and the Mediterranean Diet[END_REF] the analysis identified a network of 218 nodes and 802 connections. Such network has a relatively centralized structure and the centre is occupied by national (24,5% of the nodes) and international (9%) websites. The majority of the actors, however, operate on a local dimension: regional bodies, urban organizations and even actors based in little villages (66,5%).

Figure 1. Heatmap of the Italian network of ICH websites (coloured by dimension)

The network shows a relatively low density: around the central core (composed by the most visible nodes) the other actors organize independently occupying the margins of the network (see Figure 1). The central group, manly composed by institutional actors, is surrounded by more or less interconnected groups of local actors. We can identify, for example, some geographic clusters such as Sardinia's websites (mostly related to The Canto a tenore and occupying the top of the graph), Sicilia's websites (mostly related to Opera dei Pupi at the right of the image) and Lombardy' websites (not related to a specific item, at the bottom right of the image). It is important to remind the reader that our images are not based on a geographical projection, if the Sardinian websites are close in the network it is not because they concern the same Italian region, but because there are many hyperlinks connecting them.

It is also possible to notice several thematic clusters: websites related to lace (a dense and separated cluster in the top right corner of the image) or to traditional dances (pizzica and tarantella at the left of the image) or to the preparation of a candidature (such as seven-year ritual of penance in honour of the Assumption, a small cluster at the middle right of the image).

As regards the type of actor (see Figure 2), institutional actors (38% of the nodes) clearly dominate the network for their position and visibility. However several clusters of associative actors (43%) can be identified: i.e. the cluster at the top left that includes associations focusing on folk music and, at the right, the cluster of the Opera dei Pupi associations. Clusters of individual actors (19%) are also visible at the margins of the image: i.e. the actors related to lace (merletto), taranta or pizzica. Looking closer, two main groups may be identified. In the centre, we find governing bodies that are promoting the ICH Convention at international, national and local level. On the margins and particularly on the left, we can recognize an equally noteworthy group of associations and individuals that strongly invested in ICH preservation by starting new projects or using the label ICH to give legitimacy to existing preservation initiatives. Since 2003, several initiatives (emanating from private and public actors, amateur and professionals, associations and institutions, individuals and groups) started to talk about ICH.

Beside the rare official declarations on institutional websites, 15 the label ICH appeared on numerous websites: from folk manifestations to ethnographic research, from craft production to oral cultures. As a consequence, web mapping allows representing effectively the unstable and fragmented scenario of the Italian ICH safeguard system, where the initial latency of national bodies favoured the emergence of various peripheral projects.

French ICH Web

The analysis of ICH in France started from the website of the National Commission for Unesco (www.unesco.fr), the website of the ethnology mission of the heritage direction (http://www.culture.gouv.fr/mpe/) 16 , the institution in charge of the "Inventory of inventories of intangible cultural heritage" in France and the very recent portal Patrimoine vivant de la France (http://www.patrimoinevivantdelafrance.fr/) created by the Ministry of Culture to promote ICH at national dimension. Websites related to the ten French items 17 already inscribed in the Unesco lists have been also taken into account. The network consists of 264 nodes and 885 edges.

As regards the dimension of activity (see Figure 3), what emerges at a first glance is the gap between the quantity of local nodes (the green shapes on the heatmap) and the weight (measured as the number of incoming and outgoing links) of national actors. Although national nodes are only 30% (against 65% of local and 5% of international), they are clearly the most connected, not only as authorities (target of most incomings links) but also as hub (origin of most outgoing links -see for example www.patrimoinevivantdelafrance.fr).

Figure 3. Heatmap of the French network of ICH websites (coloured by dimension)

In particular, the Ministry of Culture, with its institutional website (www.culture.gouv.fr) and its informational portal (www.culture.fr), is the undisputed centre of the network and is surrounded by several national branches with different territorial or thematic competency extending the Ministry action to the whole graph. The international website of Unesco (www.unesco.org), while remaining one of the authorities of the graph, does not seem to play a key role as in the Italian case: the relation between local and international actors is generally mediated by national institutions. Indeed, once ratified the Convention in 2006, the French Ministry of Culture was very active in the implementation through two types of initiatives: the construction of national inventories (and the identification of the existing inventories); and the preparation of nomination files to be submitted to Unesco. This means that numerous new projects (with new websites) started under the aegis of the Ministry and several existent projects lead by local institutions and associations were enclosed.

This centralized structure, typical of the French cultural system, has many effects on the French world of intangible heritage. First, there is a similarity between the arrangement of groups per dimension of actor (with the central group of national actors) and per type of actor (with the central group of institutions see Figure 4). Conversely, it is also important to notice that the identification of the groups on the margins of the network is quite difficult (except for the network generated by the portal Patrimoine Vivant, which cannot be considered a real cluster of actors, but simply a technological artefact 18 ). Both in the graph per dimension and per type, actors are positioned in relation with the centre rather than in relation to each other. The result is a structure where local associations and institutions are mainly related to the national level and individuals are dispersed all around.

Figure 4. Heatmap of the French network of ICH websites (coloured by type)

Another interesting peculiarity of France is the importance assumed by the institutions more directly related to the Ministry, such as museums, libraries and archives (i.e. bnf.fr, archivesnationales.culture.gouv.fr, archivesdefrance.culture.gouv.fr, quaibranly.fr etc.). The presence and strength of this type of actor may reveal an approach to intangible heritage, more oriented to conservation, inventorying and communication than to "capacity-building" in the communities, as recommended by Unesco. Also the research and education institutions seem to be fairly influential in the French map (especially CRNS). Not only several research laboratories are involved in the safeguard and inventory activities, but also training schools (especially related handcraft) and education institutes (especially related to traditional music) are involved in the enhancement of the practices of heritage transmission.

Interesting insights can emerge also from the observation of groups by type of actor. As seen, institutions (45%) play the role of both authorities and hubs by guaranteeing the connection of the network and, on the other hand, associations (35%) and individuals (20%) are interconnected among each other with weak peripheral relations et constitute few thematic and geographic groups in graph. Among them, the few that show a densely connected texture are defined by the overlapping of two types of grouping, thematic and geographic. Possibly, groups such as the Occitan community (the green group on the top of the map per type), which do not only share a geographical location, but also an independent culture and language, may find in their cultural diversity the force to emancipate from the centre in the graph.

As a conclusion, what these maps make clear is that the label ICH has spread in the French web in an organized and controlled way, manly through the action of national institutions. If in the Italian network we recognized several kinds of group organizing themselves (not always coherently with the Unesco's rules and definitions), the French network appears more homogeneous. Although new websites related to ICH have appeared and the category of ICH has absorbed several existing websites thanks to the new inscriptions on the Unesco list (see the cluster of websites related to Compagnonnage [START_REF]The Compagnonnage, network for on-the-job transmission of knowledge and identities has been inscribed on the Unesco representative list in[END_REF] at the bottom of the graph), the network has grown around a unique nucleus, leaving little space for clusters and groups autonomous from the centre.

Swiss ICH Web

The analysis of ICH network in Switzerland started from the website of the National Commission for UNESCO (ww.unesco.ch), the website of the official national inventory (traditionvivantes.ch see below) and the website of CIOFF Switzerland (International Council of Organizations of Folklore Festivals and Folk Arts traditional), which created a directory of intangible heritage in Switzerland some years ago (www.cioff.ch). 20 The analysis of this network has been particularly complex because of the multilingual nature of the country. Different domain names proposing different linguistic versions of the same website have been aggregated in a unique node (see for example traditions-vivantes.fr, diversiteculturelle.fr etc.).

Figure 5. Heatmap of the Swiss network of ICH websites (coloured by dimension)

The network consists of 215 nodes and 1159 connections. The high density of connection in the graph makes it difficult to identify separated clusters, yet some interesting insights may be pointed out. As regards the dimension of actor (see Figure 5), what emerges very clearly is the marginal role of international actors (6%). Not only the international nodes are dispersed in the graph, but even the international website of Unesco is marginal compared to national and local nodes (at the bottom right of the graph). Conversely, the distribution of local nodes (62%) and national nodes (32%) is more balanced than in other countries. While it is possible to identify a core group of national institutions (around www.bak.admin.ch and www.admin.ch, the official sites of the Swiss Confederation), several national actors are also included in local groups and vice versa, generating a decentralized structure. As a result, in the dimension heatmap the blue area (national) and the green area (local) show several overlapping areas. This phenomenon may derive from the cantons organization of Switzerland (see the overlapping area around the points be.ch of the canton of Bern, ar.ch of Appenzell Outer Rhodes ai.ch of Appenzell Inner Rhodes), but it is also evidence of a democratic network open to local actors (see the overlapping area of nodes related to folk music).

This openness is also confirmed by the distribution of nodes per type (see Figure 6) that is remarkably different from the other countries. First of all, even if, similarly to other countries, the Swiss network presents a central group of institutions (32%), associations (37,5%) and notably of individuals (30,5%, against the 19% in the Italian network and the 20% of the French network) are also very active.

Figure 6. Heatmap of the Swiss network of ICH websites (coloured by type)

As revealed by the heatmap representation, the network shows a more balanced presence of various types (the three colours cover areas with similar size). Second, if nodes belonging to the same category tend to link each other, they also are connected with nodes of other categories. As a result, the coloured areas are clearly overlapping in the heatmap. Third, authorities are not only institutions (www.admin.ch, www.unesco.ch), but also associations (www.vsvonline.ch the Swiss association of folk music, www.hausdesvolksmusik.ch the House of Folk Music) and individuals (the blog folkmusic.ch). In particular, we can notice the weight of the website SUISA, the Cooperative Society of Music Authors and Publishers (www.suisa.ch). It is not only one of the most influential and central nodes of the network, but it is also one of the crossing points between local and national groups and between institutions and associations.

The distinctive overlapping of national and local actors is a key feature of the Swiss ICH system. Let's consider for example the case of the portal www.traditions-vivantes.fr (lebendigetraditionen.ch in German, tradizioni-viventi.it in Italian), the initiative of Swiss inventory recently launched (September 2010) by the Swiss Federal cultural office in collaboration with the National commission for Unesco. After the ratification of the Convention in 2008, the Swiss government decided to organize the preparation of national inventories and nomination files with a strictly democratic and decentralized procedure. Each canton has been charged of preparing its own list of items. Each regional government tried to involve the local communities by inviting the population to signal items they consider ICH. As a result, 389 propositions have been collected (and published on the website www.bak.admin.ch/traditionsvivantes). A national Committee will evaluate these proposals and draw the official inventory that will be used to select items to submit to Unesco lists (spring 2012). 21 As a consequence of such procedure, the website www.traditions-vivantes.fr, which may have centralized all the regional inventories, is quite peripheral on the graph (at the bottom right). Its creation mirrored the existing scenario of oral cultures and traditional practices preservation rather than affecting it. Even more important, this inventorying approach sheds light on the distinctive structure of the Swiss network. On the one hand, as regards the distribution per dimension, the involvement of cantons in the inventory building favours the inclusion of national nodes in local networks and makes the distinction between groups less clear-cut. On the other hand, as regards the distribution per type, the inventory process explains the increasing importance of institutions in a preservation system until recently dominated by associations and individuals. 22 Indeed, locally, the web mapping shows deeply interconnected groups representing vital communities active in preserving their heritage, including music (see the group of individuals around the blog folkmusik.ch at the left, the group of associations around the Swiss association of folk music at the top centre), traditional customs (see the cluster at the top) and handcraft (the cluster related to cutting around scherenschnitt.ch at the bottom). Sometimes, inside these groups, it is also possible to identify smaller clusters for specific type of musical tradition or of instrument (see for example the small cluster of nodes related to accordion at the top right or the cluster of nodes related to the jodler at the top left). This structure, however, does not cause dispersion of the network (as in the Italian case). This structure remains very clustered but also very dense thanks to the presence of national associations playing a key networking role both at national and local level.

Final remarks

In this paper we proposed a new methodology (web mapping) and new form of representation (heatmaps) to describe the networks of intangible cultural heritage in three different countries. We chose this approach because it seemed particularly suitable for comparative and multilingual analysis and we have not been disappointed by its results. Not only the analysis has provided empirical evidence of some well-known features of the analyzed preservation systems, but it also offered some interesting and unexpected observations.

As for the first type of observations, the analysis confirmed that national nodes and institutional nodes (particularly the overlapping of the two categories, that is to say national institutions) play the role of authorities of the networks, receiving most of the links and consequently being highly visible websites in the corpus. The Unesco Convention clearly entrust its implementation to States. It is not surprising, therefore, that the agencies to which States delegate this task (the Ministry of Culture in all three cases) end up being the central nodes guaranteeing the interconnection of the network. If national institutions occupy the centre of the networks, local and individual nodes tend to be at the margins of the graphs and local websites are often densely clusterized around specific cultural practices. Moreover, as it could be expected, the network structure of each country mirrors the main characteristics of its cultural system. For example, we can easily oppose the centralised system of France and the decentralised system of Switzerland.

Besides these predictable observations, our method also provides several original cues both on the specific national networks and on ICH global preservation system. First, web mapping helped us to investigate in depth the hyperlinking strategy of each country. While heatmaps helped us distinguishing zones with unequal density of connections, zooming in the web maps helped us to understand why connections are established. Thanks to the colour thresholds based on the density of connections, heatmaps allowed us to identify clusters and groups. Comparing the images, we could observe that the Italian network has several local groups autonomous from the centre, while France shows very few peripheral groups and Switzerland has a very clustered and dense structure that privileges big agglomerates where national and local nodes on the one hand and institutions, associations and individuals on the other hand, coexist and interact in the same cluster. As regards the reasons for establishing connections, the navigation of web maps allowed us to distinguish two main types of rationale that explain why nodes belong to specific groups. Some groups coalesce around a common thematic interest; others share the same geographic location. The analysis also allowed us to reveal some interesting cases, as the Occitan cluster in the French map, where both reason coexist. Moreover, throughout web maps, we could identify some exceptions such as the very dense area around patrimoinevivantdelapfrance.fr (Figure 7). In the case, this area doesn't correspond to an actual group or a cluster, but it is simply the effect of a hub-website with links toward several thematic related websites not interlinked among each other. Second, web mapping helped us to compare the weight of international bodies, especially UNESCO, in the different national systems. Graphs per dimension emphasize the different importance and role of the Unesco website (www.unesco.org). While in Italy there are two major international clusters and the node unesco.org is central and higly connected, in France and Swiss international nodes, and notably unesco.org, are less important than we expected. In the French graph, unesco.org is a visible node but it doesn't play a key role in the global texture. In Switzerland it is not even particularly visible.

Third, web mapping helped us to investigate the involvement of local communities: an issue that is attracting more and more attention of both policy-makers and scholars. Indeed, the graphs allow observing the participation of individuals, foremost heritage bearers, in the safeguard of ICH.

Although websites of individuals and groups are a minority in all graph, all images highlighted some common trends. Individual nodes are generally not directly related to the authorities of the graph, they are related to local associations or to other individuals. Groups constituted by individuals are usually dense and share a thematic focus: often they represent non-professional and non-institutional safeguard initiatives supported by amateur blogs or web portals managed by informal groups of people. Despite their informal organisation, these groups represent dense and active web communities (in particular, see the Italian groups gathered around pizzica.it, totarella.it et merlettoitaliano.it and the Swiss groups gathered around the blog folkmusik.net and scherenschinnt.ch). Conversely, we have the case of institutional portals (such as the already mentioned French patrimoinevivant.fr) that assemble individuals who don't recognize themselves as groups (as shown by the lack of direct hyperlink connections). This disconnection between the clusters of local bearers and the national institutions may derive from a bias of our methodology (the relations may just not be visible on the Web). Yet, the lack of connections may be explained also by a different interpretation of the ICH label. People that recognize themselves as bearers may not correspond to the interpretation of the State of the Convention or to the institutional priorities of preservation. If this is the case, our results would confirm the observation of several scholars that national institutions still find it difficult to involve communities in the implementation of the Convention.

Finally, the comparative analysis of ICH networks allowed us to highlight the importance of different actors in different countries. If in France the actors of the education sector are numerous and important, less so in Italy and Switzerland. Conversely, in Switzerland we noticed the importance of copyright institutions and associations, almost absent in the other countries.

To be sure, all these insights need to be confirmed by a more traditional ethnographic approach, but we believe that web maps have proven their amazing value as exploratory tools. To encourage readers to explore even further, interactive versions of the web maps discussed in the article are available on the website www.patrimoineimmateriel.net.

Figure 2 .

 2 Figure 2. Heatmap of the Italian network of ICH websites (coloured by type) The websites of the Ministry of Culture and of the UNESCO are by far the most visible nodes in the graph (the ones receiving the most of hyperlinks). The very central position of www.unesco.org (linked by national agencies, local governments, but also by independent projects of safeguard 13 ) is particularly significant. Even if the ICH Convention was approved in 2003 and entered into force on 20 April 2006, Italy ratified it only in 2007 and the Italian government started very recently to organize ICH safeguard actions at national dimension. At the two first nominations rounds (2009 and 2010), Italy didn't submit any proposal 14 and, until now, there is no Italian item inscribed on the Unesco lists (except the items formerly proclaimed Masterpieces and incorporated to the ICH list in 2008). Nevertheless, the multitude of connections between Unesco.org and several Italian websites show the generalized interest toward the Convention.

Figure 7 .

 7 Figure 7. Zoom on the patrimoinevivantdelafrance.fr sub-network

On the relation between the two Conventions see D.[START_REF] Munjeri | Tangible and Intangible Heritage: from Difference to Convergence[END_REF][START_REF] Kirshenblatt-Gimblett | Intangible Heritage and the Metacultural Production of Heritage[END_REF].

The development of digital methods is relatively recent and followed the diffusion of digital media. Three main phases can be distinguished in this development.1. During the years of the advent of Internet, social scientists conceived electronic media as nothing more than new terrains for old methods. Notions such as "cyber-culture"[START_REF] Negroponte | Being Digital[END_REF], "virtual communities"[START_REF] Rheingold | The Virtual Community: Homesteading on the Electronic Frontier[END_REF], "online identities'"(Turkle, 1995) were therefore introduced to channel the novelty of new media within the tradition of social sciences.2. Such enterprise, however, has soon been defeated by the speed at which digital technologies have infiltrated modernity. Electronic interactions have become so pervasive that they can no longer be conceived as a separate social

This list was created before the official ratification of the State to the 2003 Convention. This list, that is meant to collect the ICH bearers rather than the items, was built through a very participatory method: everyone can add his name on the list. Outgoing links from this website have been drawn only partially because of technical issues (the list is organized as a pdf file so it couldn't be scanned by the crawler).

Indeed, Switzerland has no item inscribed on the Unesco lists yet.

We carried out a previous web mapping study in July 2010 that revealed a quite different structure(Severo, 2010).

1 Initiated in 1973, when for the first time Bolivia asked for a protocol to protect folklore, the UNESCO reflection on intangible heritage was developed through numerous international meetings and not without lively controversies (for a summary of principal meetings see UNESCO website http://www.unesco.org/culture/ich/). The discrepancy between the English "intangible cultural heritage" and the French "patrimoine culturel immateriel" (both in the official Glossary) exemplifies the difficulty of reconciling opposing conceptions. The coexistence of the two terms is the result of a delicate compromise (Van Zanten, 2004).