WO2007110395A1

WO2007110395A1 - Contactless method of measuring an optogeometrical characteristic of a material by interference spectroscopy

Info

Publication number: WO2007110395A1
Application number: PCT/EP2007/052833
Authority: WO
Inventors: Fabrice Gillot; Laurent Jeannot
Original assignee: Commissariat A L'energie Atomique
Priority date: 2006-03-27
Filing date: 2007-03-23
Publication date: 2007-10-04
Also published as: FR2898971A1

Abstract

Contactless method of measuring an optogeometrical characteristic of a material by interference spectroscopy. According to this method, to determine this characteristic, namely the thickness or the refractive index of the material (2), the latter is illuminated by means of a light source with a broadband (E<SUB>i</SUB>) in a transparency range of the material, light that is reflected and/or transmitted by material, has interference patterns and results from this illumination is collected, the collected light is analyzed by means of a high-resolution spectrometer, resulting in a channelled spectrum, and the thickness of the material is determined as a function of the refractive index of this material, or vice versa, based on this channelled spectrum. This method applies in particular to the measurement of the thickness of a non-planar object.

Description

METHOD FOR NON-CONTACT MEASUREMENT OF AN OPTO-GEOMETRIC CHARACTERISTIC OF A MATERIAL BY SPECTROMETRY

interferential

DESCRIPTION

TECHNICAL AREA

The present invention relates to a non-contact measurement method of an opto-geometric characteristic of a material.

In particular, the invention relates to a non-contact measuring method for the thickness of a transparent layer, in a thickness range from a few micrometers to several hundred micrometers.

It applies equally well to flat layers as to layers of spherical or cylindrical shape as well as to objects having only a transparent layer and to stacks of several transparent layers.

The measurement is done without contact, with a precision that can reach 10 nm.

It should be noted immediately that, according to one aspect of the invention, the acquisition of fluted spectra by white light interference spectrometry and a mathematical operator, namely the periodigram (or periodogram) of Lomb, is combined in an original manner. This combination makes it possible to accurately measure material thicknesses in a range from 5 μm to 500 μm; such The thicknesses are greater than those measured by conventional techniques and are often less than 1 μm.

STATE OF THE PRIOR ART

Interferential spectrometry in white light, or spectral interferometry in white light, has been the subject of numerous scientific publications and its principle is used in the industrial field, in particular in microelectronics, for the measurement of thicknesses and refractive indices. thin layers or stacks of thin layers.

However, current applications of this technique are restricted to the characterization of layers whose thickness is less than 1 micron. Moreover, until now, this technique has never been used to measure the thickness of an object that is not plane.

In fact, few techniques make it possible to measure the thicknesses of deposits or hollow objects in the interval [1 μm; 500 μm].

A known technique, making it possible to make measurements in this interval, uses probes that send ultrasonic pulses. With these probes, it is possible to characterize planar objects, comprising one or more layers, in the interval [10 μm; 500 μm]. However, the measure requires a contact with objects and the accuracy is at best 1 μm.

Optical tomography is another known technique that makes it possible to measure in the range [1 μm; 500 μm]. It is a non-contact measurement technique that applies to transparent or translucent objects. It can be implemented with non-planar objects and multilayer stacks. On the other hand, this technique does not make it possible to obtain resolutions better than 1 μm.

The method of measurement by interference spectrometry can be implemented at distances that vary from a few centimeters to several tens of centimeters if a suitable observation optics, such as a microscope-mirror telescope, is used. advantage of not being sensitive to the wavelength of the light source used. This remote measurement system can be useful for making measurements inside vacuum enclosures, through transparent portholes.

STATEMENT OF THE INVENTION

The present invention aims to solve the problem of measuring, without contact, the thickness of a material, in particular a non-planar object, and more particularly for thicknesses belonging to the interval [1 μm; 500 μm], if the refractive index of the material is known, or

- the refractive index of the material, if the thickness of the latter is known. To do this, the invention uses the technique of interferential spectrometry and preferably uses the Lomb periodigram to exploit the spectra obtained by this technique.

Precisely, the subject of the present invention is a measurement method, without contact, of an opto-geometric characteristic of a material, namely the thickness or the refractive index of this material, this method being characterized in that that: the material is illuminated by means of a broadband light source in a range of transparency of the material,

a light is collected which is reflected and / or transmitted by the material, exhibits interferences and results from this illumination, the collected light is analyzed by means of a high resolution spectrometer, which leads to a fluted spectrum, and

the thickness of the material is determined as a function of the refractive index of this material or the index of refraction as a function of the thickness, from this grooved spectrum.

The thickness or refractive index of the material can be determined from the Fourier transform of the fluted spectrum. In this case, the thickness or refractive index of the material can be determined from the peak or peaks of the Fourier transform.

But, preferably, the thickness or the refractive index of the material is determined from the Lomb periodigram of the fluted spectrum.

Preferably, the thickness or refractive index of the material is determined from the peak or peaks of the Lomb periodigram.

According to a first particular embodiment of the invention, the value of the refractive index of the material is known and the thickness of the material is determined from this value.

According to a second particular embodiment, the value of the thickness of the material is known and the index of refraction of the material is determined from this value.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will be better understood on reading the description of exemplary embodiments given below, purely by way of indication and in no way limiting, with reference to the appended drawings in which: FIG. 1 schematically represents reflected waves, created during the crossing of a plane blade by a light beam, FIG. 2 diagrammatically represents reflected waves, created during the crossing of a plane bilayer by a light beam,

FIG. 3 diagrammatically represents a fluted spectrum, simulated by computer and created by a glass slide BK7 80 μm thick,

FIG. 4 schematically represents a fluted spectrum, simulated by computer and created by an object consisting of a BK7 slab of 200 μm in thickness, superimposed on a high index glass slab, in LaSFN9, of 50 μm. thickness,

FIG. 5 shows the Lomb periodigram of the spectrum of FIG.

FIG. 6 shows the Lomb periodigram of the spectrum of FIG. 4, FIG. 7 represents a computer generated noisy spectrum created by a BK7 glass slide of 80 μm in thickness, FIG. 8 shows the periodigram of FIG. Lomb of the spectrum of Figure 7, Figure 9 represents a highly noisy spectrum, generated by computer and created by a glass slide BK7 80 microns thick,

FIG. 10 shows the Lomb periodigram of the spectrum of FIG. 9,

FIG. 11 schematically represents the illumination geometry of a plane object (on the left) and a spherical object (on the right) for the measurement. thicknesses or refractive indices by interferential spectroscopy,

FIG. 12 schematically represents transmitted waves created during the crossing of a bilayer structure by a light beam,

FIG. 13 is a schematic view of a device making it possible to acquire corrugated spectra; FIG. 14 shows the variations of the group index of the constituent material of a capsule, as a function of the wavelength, and Figure 15 shows the variations of the refractive index of this capsule as a function of the wavelength.

DETAILED PRESENTATION OF PARTICULAR EMBODIMENTS

Figures 1 and 2 schematically illustrate measurement methods according to the invention.

FIG. 1 shows reflected waves, created during the crossing of a plane plate by a light beam, and, in FIG. 2, reflected waves, created during the crossing of a plane bilayer by a beam luminous. The flat blade of Figure 1 has the reference 2 while the plane bilayer of Figure 2 has the reference 4 and has two flat blades 6 and 8, placed against each other.

In both cases, the object to be characterized 2 or 4 is placed in the air A and illuminated by an incident wave E ₁ , resulting from a broadband light source (not shown). The interfaces encountered by the light during the crossing of the object lead to the appearance of several reflected waves that will interfere with each other.

As can be seen, in the case of FIG. 1, there are two interfaces and therefore two reflected waves E _r i and E _{r 2} (it is assumed that higher order reflections are negligible) whereas, in the case of Figure 2, there are three interfaces and thus three reflected waves E _r i, E _r2 and E _r3 .

By collecting the reflected light and analyzing it by means of a spectrometer (not shown), particular spectra are obtained, which have wavelength-marked modulations and which constitute fluted spectra. The shape of each spectrum is characteristic of the structure of the corresponding sample (blade, or layer, 2 of FIG. 1 or bilayer 4 of FIG. 2) and its analysis makes it possible to go back to the thickness or the thicknesses of the object tested.

The analytical expression of the fluted spectra is considered below.

Consider first the case of a single-layer object.

For such an object (FIG. 1), the form of the fluted reflection spectrum is given by the expression: I _ψ {κ) = T ₁ ² + r ₁ (t _x i _x f +

cos (4πm (κ) e)

\ - nn - - 1 2 2n ^{with rχ =} Y ^ _n ^{r2 =} ^ and t _j - n - hl ^ ⁼ ^ \ + ^~ n ^and ^ = T + 1 - n ^(1: wherein Kκ- MMλλ = - kk / l22ππ eesstt the spectroscopic wave number (inverse of a wavelength), e is the thickness of the layer and n (κ) the refractive index of this layer in K; T ₁ and r ₂ are the Fresnel reflection coefficients for the input and output interfaces of the layer respectively, and ti and t'i are the Fresnel transmission coefficients relating to this layer.

In the example of FIG. 1, ri corresponds to E _r i and T ₂ to E _{r 2} .

By way of example, FIG. 3 represents the fluted spectrum (computer simulated) of a BK7 glass slide 80 μm thick.

In this figure 3, K is expressed in μm ^"1 and I _sp (K) in arbitrary unit.

For this blade, the refractive index of BK7 is given by a law of Briot:

n ¹ = 2.27189 - ° ^{Q 1 Q 1 Q81} ₊ 0.0105925κ- ² + 0.00020817Λ- ⁴

K

- 1.64125 x 1 (TV + 4,9241 x 1 (TV

Now consider the case of a two-layered object.

For such an object (FIG. 2), the equation of the fluted reflection spectrum is given by the expression: I _sp (κ) = T ₁ ² +

+ r ₃ ² (vi) ² (/ ₂ 4) ² + 2r _x r ₂ t _x i _x COs [AKm ₁ {κ) e _λ ] +

cos [4πκ (n _ι (κ:) e _ι + n ₂ (κ) e ₂ )] + 2r ₂ r ₃ (J ₁ J ₁ ) J ₂ J ₂ COS [4Λ ^" Î ₂ (κ) e ₂ ]

l - n, n, - ri _j H _J - 1 2, 2n, where ^ ₁ = - ^L , r ₂ = - -, r ₃ = - - -, ^ = -, ^ ₁ =

1 + ftj "j + n ₂ ^ ² _I ⁺ I 1 + W ₁ 1 + W ₁ t ₂ = ^! - and t ₂ = -.

U ₁ + n ₂ U ₁ + n ₂

where K - Mλ - kl2π is the spectroscopic wave number, e _± and θ2 are the respective thicknesses of the analyzed layers, and n _λ (κ) and n ₂ (κ) the respective refractive indices of these layers; ri, r ₂ and r3 are respectively the Fresnel reflection coefficients for the different interfaces of the object; and ti, t'i, t2 and t'2 are respectively the Fresnel transmission coefficients of the two layers. In the example of Figure 2, ri, r ₂ and r ₃ respectively correspond to i E _r, E and E _r2 _r3 and ti, t'i and t _2, t '2 correspond respectively to the transmissions to air interfaces / layer 6 and layer 6 / layer 8. By way of example, FIG. 4 (same units as for FIG. 3) represents the fluted spectrum (computer simulated) of a bilayer consisting of a 200 μm thick BK7 slide. thickness, superimposed on a glass slide, LaSFN9, 50 microns thick. The respective refractive indices of BK7 and LaSFN9 are given by a Briot law: - for BK7: n ¹ = 2.27189 - ° ^'Q1Q1Q81 0,0105925Λ- + ² + 0,00020817Λ- ^{4 to} 7.64725 x 10 ^{^"V" 6} + 4.9241 x 1 (TV

K

- and for the LaS FN 9:

n ² = 3,29943 - ^Q ' ^{Q 1 1} 6 ^8Q4 + 0,040133Λ- ² + 0,0013264Λ- ⁴ + 4,74388 x 10 ^"6 K ⁶ + 7,85072 x 10 ^{" 6} K " ⁸

K

The equations of the fluted spectra are easily generalized to multilayer structures (more than two layers).

Consider now the exploitation of fluted spectra.

This exploitation is carried out by passing through the Fourier space. The passage in the Fourier space is carried out either by calculating the Fourier transform of the spectrum, or by calculating the Lomb periodigram.

In what follows, we are interested in the use of the Lomb periodigram because this method is more general and provides better results than the Fourier transform.

In practice, an experimental fluted spectrum is composed of N points of measurement

U

¹ S _P (KN) - ^The Lomb periodigram of this fluted spectrum is defined by:

Now consider the Lomb periodigram of a single layer structure.

The Lomb periodigram of such a structure (for example of the kind shown in FIG. 1) has a single peak (FIG. 5). The position P ₁ of this peak is related to the thickness of the object tested by the following formula:

In equation (4), e is the thickness of the layer, [x:. |; X: _w ] is the measurement interval of the fluted spectrum, "(^ ₁ ) is the refractive index of the material composing the layer in Ar ₁ and n (κ _N ) the refractive index in κ _N.

FIG. 5 shows the Lomb periodigram of the fluted spectrum of FIG. 3. In this FIG. 5, the variable u represents the optical path difference (unit: μm); I _sp (u) is expressed in arbitrary units.

This figure 5 shows a single peak in P ₁ = 245.1. The spectrum of Figure 3 extends from Xr ₁ = 1.39 μrrf ¹ at "^ = 1.47 μm ^{" 1.} The refractive index of BK7 is 1.51257 to 1.39 μm ^-1 and 1.51361 to 1.47 μm ^-1 By using these data in equation (4), we obtain for e a value of 80.01 μm, thus the thickness of the BK7 plate, measured from the spectrum of FIG. This is compared to the nominal value of 80.00 μm used to generate the spectrum of Figure 3. The error committed is 10 nm.

Now consider the Lomb periodigram of a two-layer structure.

The Lomb periodigram of such a structure (for example of the kind shown in FIG. 2) has three peaks. The positions p _v p _{2 and} p ₃ of these peaks are related to the thicknesses e _± and θ2 of the layers composing the structure tested by the following formulas:

_ {N 2 ₂ κ ₂ _{N) κ _N - n ₂ _{κ λ) _κ λ) (5)

P ₂

K _N - K _λ

In Fig. 6 (same units as Fig. 5), the Lomb periodigram of the fluted spectrum of Fig. 4 is shown. The first peak at P ₁ = 189 is bound to the LaSFN9 slide. The position of this peak corresponds to a thickness measured for the LaSFN9 layer of 49.92 μm. The thickness of the LaSFN9 layer, defined to generate the spectrum of FIG. was equal to 50.00 μm. The error made on the determination of the thickness is therefore 80 nm.

The peak at p ₂ = 612.3 is bound to the BK7 glass layer. The position of this peak gives a measured thickness of 199.88 μm. The thickness of the BK7 layer, defined to generate the fluted spectrum, was 200.00 μm. The error made on the measurement is therefore 120 nm.

Now consider the case of multilayer structures.

One of the advantages of the Lomb periodigram analysis is that it is not necessary to calculate the equation of the fluted spectra to go back to the thicknesses of the analyzed object. Indeed, for a multilayer object, several peaks will appear on the periodigram, each peak corresponding to the interference created by a pair of reflected waves.

For example, for the two-layer structure (Figure 2), three peaks appear on the periodigram. The interference system created by E _r1 and E ^ _causes a first peak. This peak carries information on the index layer ni and allows to find the thickness ei of this layer.

Similarly, the interference system created by E _r2 and E _r3 causes the appearance of a second peak which carries information on the index layer / 12 and makes it possible to measure the thickness eΣ. Finally, the interferences created by E _r1 and E _r3 are at the origin a third peak that carries information on the total thickness e _λ + e ₂ of the two layers together.

It should be noted that in the present invention, the different peaks of the Lomb periodigram are connected to the different layers that make up the object to be tested.

For a two - layer material, the peak p ^ necessarily corresponds to the interference system created by E _ri and E _r3 . On the other hand, there is an ambiguity concerning the peaks p _± and P2: it is necessary to have an a priori knowledge of the tested object to know which peak is related to the system of interferences created by E _ri and E _r2 and which peak corresponds to the interference created by E _r2 and E _r3 . This knowledge is necessary because the refractive index of the layer to which each peak corresponds is involved in the calculation of the thicknesses.

However, the analysis of the spectra by the Lomb periodigram is very interesting because it filters very effectively the measurement noise.

By way of example, FIG. 7 represents the spectrum of a 80 μm thick BK7 plate with a low measurement noise and FIG. 8 represents the corresponding Lomb periodigram. The latter has a peak in P ₁ = 245.1. This peak corresponds to a measured thickness of 80.01 μm, ie 10 nm of error. FIG. 9 represents the spectrum of a 80 μm thick BK7 slide with a strong noise of measured. The corresponding Lomb periodigram is shown in Figure 10. This Lomb periodigram shows a peak in P ₁ = 245.4. This peak corresponds to a measured thickness of 80.11 μm, ie 110 nm of error.

Thus, even in the presence of a very important measurement noise, the method of the Lomb periodigram makes it possible to carry out a measurement of thickness with an excellent precision.

Now consider the geometry of the examined object.

For the measurement of a thickness by interferential spectrometry, the wavefront of the incident light beam must be adapted to the geometry of the object to be characterized. In particular,

a plane object must be illuminated by a collimated beam, a cylindrical object having a geometric axis Δ must be illuminated by a convergent cylindrical beam on Δ, and

a spherical object of center O must be illuminated by a spherical wave of center O. FIG. 11 shows the illumination geometry for a plane object 10 and a spherical object 12, for the purpose of a thickness measurement by interferential spectrometry .

From an optical point of view, the two geometries shown in FIG. 11 are equivalent. This equivalence comes from the fact that in both cases (incident beam formed by a plane light wave for the object 10 and a spherical light wave for the object 12), the wavefront of the incident beam is adapted to the studied geometry: the beams of the beam of illumination are perpendicular to the surface of the object.

Another way of perceiving the equivalence between the two geometries above is to consider the plane case as the limit of the spherical case when the radius of the sphere tends towards infinity.

In the foregoing, reference has been made to fluted reflection spectra. The measurement then rests on the analysis of the light reflected by the characterized object.

An equivalent measurement can be made by analyzing the light transmitted by this object. As for the measurement in reflection, the interfaces encountered by the light beam, during its propagation through the object, give rise to several transmitted waves.

By way of example, FIG. 12 shows the bilayer 4 illuminated by the incident beam E ₁ and the various transmitted waves E _t o, E _t i, E _{t 2} and E _t 3 which result therefrom are seen.

The transmitted waves interfere with each other and the analysis of the transmitted light, by means of a spectrometer, gives splined transmission spectra. As with the fluted reflection spectra, the transmission spectra carry information on the structure of the object and their Lomb's periodigram analysis makes it possible to measure thicknesses or refractive indices.

However, the measurement in transmission is less interesting than the measurement in reflection. Indeed, in the case of the measurement in transmission, the light transmitted directly by the object (order 0) dominates the signal and the contrast of the fringes on the fluted spectra is very weak.

It should be noted that it is even possible to perform a measurement according to the invention by analyzing both the reflected light and the light transmitted by the object.

Figure 13 is a schematic view of an exemplary device for implementing the method object of the invention. It is an interferential spectroscopy device for the measurement of contactless thicknesses.

This device comprises a white light source 14, a set of shaping lenses 16, a telescope 18, an optical fiber 20 of signal transmission, a spectrometer 22 and a computer 24.

The light source 14, which is used to illuminate the object to be characterized 26, is a white light source in the example under consideration. The illumination beam provided by this source is transmitted by an optical fiber 28 and shaped by the lens assembly 16, so as to adapt the profile of this beam to the geometry of the object to be studied. The telescope 18, for example of the kind that is marketed by Questar under the reference QM100, is used to illuminate the object to be analyzed and to collect the reflected light. The QM100 telescope allows a working distance D ranging from 15 cm to 38 cm.

At the output of the telescope, the reflected light signal is injected into the optical fiber 20 and conveyed to the spectrometer 22 to acquire the fluted spectrum. An injector 30 is provided for injecting light from the fiber 20 into the spectrometer.

The fluted spectrum is transmitted to computer 24 for analysis by the Lomb periodigram method. This computer is provided with means 32 for displaying the results obtained.

In the following, applications of the present invention are considered.

This invention can be used for non-contact and non-destructive measurement of the thickness of planar objects, for example polymer films such as those used in the packaging industry.

It can also be used to measure the thickness of coatings deposited on another material. It may for example be paints or deposits of polymer resins that are used to protect surfaces against abrasion. It can also be used to measure the thickness of hollow objects. For example, a reflection interferometric spectrometry technique according to the invention has been used to measure the thickness of hollow spheres of 2 mm in diameter. Measurements were made on spheres of 11 μm, 125 μm and 175 μm thickness. These results show the wide range of application of the invention in terms of thickness measurement. In addition, the measurement method, object of the invention, is particularly robust vis-à-vis the vibrations. This makes it particularly interesting compared to other interferometric methods which generally do not exhibit such robustness for industrial applications.

In the examples given above, it has been shown how to determine the thickness of a simple material, such as a single layer or a hollow object, or the thicknesses corresponding to a complex material such as a multiple layer, when the the refraction index or indices are known.

However, the invention also makes it possible to determine the refractive index or indices of a simple or complex material, which is very weakly dispersive, that is to say for which - is little different dλ from 0, when the thickness or thicknesses of this material are known.

In what follows, the measurement of the refractive index, between 500 nm and 900 nm, of a hollow polymer capsule 2 mm in diameter and

123.7 microns thick. To do this, spectra The fluted spectra were measured in steps of 10 nm over the range of wavelengths considered with the device that was described with reference to Figure 13. The fluted spectra were then exploited with the Lomb periodigram method. The periodigram of each spectrum has a single peak. According to equation (4), the position of this peak is given by:

_ 2e (n (κ _N ) κ _N -n (κ, K ₁ ) Pi - \ ^Ό I

^K N ^{~ K} l

where [K ₁ ; κ _N ] is the acquisition range of the fluted spectrum considered, e the thickness of the capsule and n {κ) its index. Since the acquisition range of the spectra is small (κ _N - K ₁ slightly different from 0.08 μm ^"1 ), it is possible to write:

or κ _m - (K ₁ + κ _N ) 1 2 and is the derivative

of n (κ) κ with respect to K and ≈ means "little different

of ". Size is known in optics as

being the group n _g index of the material. With the group index, equation (6) takes the form:

(TT _n ,) Thus, knowing p ₊ and e, it is possible to know the group index of the material. Figure 14 shows the group index values of the capsule, between 500 nm and 900 nm. The values measured experimentally are represented by the black squares. Each value corresponds to the acquisition of a fluted spectrum and its exploitation with the Lomb periodigram. In this figure,

is expressed in nm and the group index n _g is without unit.

Knowing the group index, it is possible to go back to the refractive index n (κ) of the material. Indeed, the dispersion of a material

(evolution of the refractive index as a function of the wavelength) can be represented by optical laws. By way of example and in a nonlimiting manner, mention may be made of the formulas of Sellmeier, Cauchy or Briot to represent the dispersion of a material. In the present case, the evolution of the index n of the polymer capsule is well represented by a Cauchy formula (presence of an absorption band in the blue):

\ _< BC

"-V ⁺ Y ⁺ Y ⁽⁹⁾

From equation (8) it is possible to calculate a theoretical expression for n _g (κ). This expression is used to perform a regression on the experimental points of Figure 14 and find the parameters A, B and C of equation (9). In FIG. 14, the continuous curve represents the result of the regression on the experimental points. For the polymer capsule, the regression gives A = 2.46191, B = 0.0164228 μm ² and C = 0.000620526 μm ⁴ . The index of the capsule is thus given by:

,,. - _Ar 0.0164 0.000621 "μ) = ₁ / 2.46 + - ^I - ₂ - + - ² - ^ (10)

A A

where λ is expressed in μm.

Figure 15 shows the refractive index of the polymer capsule. In this figure, λ is expressed in nm and n is without unit.

Claims

A non-contact measuring method of an opto-geometric characteristic of a material (2, 4, 10, 12, 26), namely the thickness or the refractive index of this material, this method being characterized in that

the material is illuminated by means of a broadband light source (E ₁ , E _p , E _s ) in a range of transparency of the material, light is collected which is reflected and / or transmitted by the material, interferes and results from this illumination,

the collected light is analyzed by means of a high-resolution spectrometer, which leads to a fluted spectrum, and

2. Method according to claim 1, wherein the thickness or refractive index of the material (2, 4, 10, 12, 26) is determined from the Fourier transform of the fluted spectrum.

The method of claim 2, wherein the Fourier transform has at least one peak and the thickness or refractive index of the material is determined from that peak.

The method of claim 1, wherein the thickness or refractive index of the material is determined from the Lomb periodigram of the fluted spectrum.

The method of claim 4, wherein the Lomb periodigram has at least one peak (p1, p2, P3) and the thickness or refractive index of the material is determined from this peak.

6. A method according to any one of claims 1 to 5, wherein the value of the refractive index of the material is known and the thickness of the material is determined from this value.

7. A method according to any one of claims 1 to 5, wherein the value of the thickness of the material is known and the refractive index of the material is determined from this value.