Prior art Interferometric measurements are commonly used for determining physical properties of specimens of transparent materials and, in particular, of the refractive index of a material, or else, where this parameter is known, of geometrical properties of the specimen, such as, for example, the thickness.

The measurement of the refractive index of a material and, more in particular, of the properties of dispersion of the refractive index, is of considerable importance in different technological fields, such as, for example, microelectronics and opto- electronics and laser technologies, such as ultrashort-pulse laser technologies.

White-light interferometry is one of the preferred means for carrying out measurements of this type with high precision. In particular, with thick specimens or highly dispersive materials, the time method is preferably applied. In this case, an interferometer (for example, a Michelson interferometer or Mach-Zehnder interferometer) is commonly used and, by means of the Fourier transform, the spectral analysis of the interferogram (of cross-correlation) obtained by placing the specimen in one of the two branches of the interferometer is carried out; by comparing said interferogram with the interferogram (of self-correlation) obtained in the absence of the specimen, the delay that the specimen produces on the light beam that traverses it is obtained for the various wavelengths that compose the radiation used. Where the geometrical characteristics of the specimen are known, it is possible to calculate the refractive index as a function of the wavelength.

The above method hence comprises a comparison procedure for identifying a point (the maximum of intensity of the spectrum of self-correlation) to be used as the zero value to which the delay time introduced by the specimen is referred.

This procedure is often complicated and constitutes a possible source of error.

Furthermore, the spectral phase difference introduced by the specimen and determined by means of Fourier-transform analysis is determined but for multiples of 2. A direct measurement of the refractive index n (X) is thus not possible, but it is necessary to know a priori the refractive index at least for a specific wavelength.

It is consequently desirable to be able to carry out measurements of the refractive index of a material with a limited number of operations over a wide spectrum of wavelengths. It is moreover necessary to be able to determine in a way simple the absolute refractive index of the material for at least one wavelength.

Summary of the invention The aforementioned problems have now found a solution thanks to a method for the measurement of physical properties of transparent materials, comprising one or more steps which include the following operations: a) generation of a primary beam of polychromatic light ; b) splitting of said beam into at least one reference beam and one analysis beam, which traverses a specimen of material to be analysed in at least one of said steps; c) re-superposition in a single secondary beam of said at least two beams, namely, the reference beam and the analysis beam, after they have followed different paths; and d) analysis of said secondary beam in a spectrophotometer comprising an interferometer, said analysis comprising the decomposition of said secondary beam into at least two tertiary beams and their re-superposition.

According to a preferred aspect, the purpose of the method is to determine the refractive index of a material, more preferably of the refractive index at different wavelengths. Preferably, the polychromatic light is white light, the spectrum of which covers at least the range of wavelengths from 0. 5 um to 5 lim.

Preferably, the spectrophotometer comprises an interferometer (for example, a Michelson interferometer), comprising means for carrying out the analysis of spectral phase of the secondary beam. According to an aspect of the invention, said spectrophotometer is a frequency-transform spectrophotometer, preferably a Fourier-transform spectrophotometer, in which the path of one of the two tertiary beams can be varied in order to perform a scan over range of appropriate

differences of times of travel between the two tertiary beams.

The method comprises at least one step in which said analysis beam traverses a specimen of the material to be analysed, whilst said reference beam does not.

Preferably, the method also comprises a comparison step, in which neither the reference beam nor the analysis beam traverses a specimen.

Preferably, the operations b) and c) of the method are performed in an interferometer provided with means for varying the length of the path of one between the reference beam and the analysis beam, preferably the reference beam. The method can thus comprise the adjustment of said path.

Furthermore, the method preferably comprises the analysis of spectral phase for at least two different angles of incidence of the analysis beam on the specimen; for example, it is possible to envisage rotation of the specimen with respect to said analysis beam with appropriate means. Preferably, the difference between the said two angles is such as to introduce an optical-path difference such that the variation of phase is certainly less than 2s at least for a wavelength on which the variation of phase is measured.

The angle of incidence on the specimen is the angle of incidence on one face of the specimen, which preferably has two plane parallel faces.

The invention also comprises an apparatus designed to implement the method indicated above.

List of figures The present invention will now be illustrated via a detailed description of preferred, but non-exclusive, embodiments, provided purely by way of example, with the aid of the attached figures, in which: - Figure 1 is a schematic illustration of an apparatus for carrying out a method according to the present invention; - Figure 2 represents an interferogram obtained in a step of the method according to the present invention; - Figure 3 represents the phase difference introduced by a rotation through 1 ° of the specimen in the analysis beam as a function of the wavelength, at different starting angles; - Figure 4 represents the variation of phase at different angles of incidence of the

analysis beam on the specimen with respect to the phase corresponding to a zero angle of incidence, for two different wavelengths; and - Figure 5 represents the values of n ( ?,) on a plate of fused silica obtained with the method according to the present invention, compared with the theoretical and experimental values which can be found in the literature.

Detailed description of an embodiment Figure 1 shows a possible scheme of embodiment of the present invention. The apparatus used comprises a first interferometer 1 (delimited in the figure by a box with a dashed outline), which may be an appropriately modified Mach-Zehnder interferometer, and a spectrophotometer 2 (delimited in the figure by another box with a dashed outline), preferably a Fourier-transform spectrophotometer. The light source 3 (comprising, for example, a halogen lamp) generates the primary beam 4, which is split, by appropriate means 5 (for example, a half-transparent mirror), into the analysis beam 6 and the reference beam 7. The apparatus preferably comprises means 8, which are designed to position a specimen 9 in such a way that the analysis beam 6 will traverse it in an appropriate way and are preferably designed to rotate the specimen about an appropriate axis, for example, one perpendicular to the incident analysis beam. Preferably, said means consist of a rotatable specimen-holder 8 with a high angular resolution, for example 0. 001°.

Appropriate means 9, for example, another half-transparent mirror, are provided for re-superposing accurately the analysis beam and the reference beam, after they have followed two different paths, so generating a secondary beam 11.

Further means, such as, for example, a series of mirrors 10, are provided for appropriately guiding the light beams, as occurs in a normal interferometer.

Preferably, the interferometer 1 is provided with means 12 for modifying arbitrarily the path of one of the beams generated by splitting of the primary one, preferably the reference beam 7. Said means may comprise mirrors 13, preferably at least two, which can move fixedly with respect to one another in the direction indicated by the arrows A. Preferably, there is provided a system of adjustment that enables adjustment of the position of the mirrors with nanometric precision.

The spectrophotometer 2 can comprise, as has been said, an interferometer, for

example, a Michelson interferometer, as represented in the figure and can carry out the analysis of spectral phase, for example, via Fourier transform. Said instrument is positioned so as to analyse the secondary beam produced by the first interferometer and may be of a known type, so that it does not call for any further description herein.

The method according to the present invention may comprise a step in which a primary light beam 4, preferably white light, is generated by the source 3, and is split by the means 5 into the analysis beam 6 and the reference beam 7. These two beams follow different paths, and the analysis beam traverses the specimen 14. The two beams are re-composed by the means 9 into the secondary beam 11, which undergoes analysis in the spectrophotometer 2. According to a possible mode of operation, the secondary beam is decomposed by the interferometer into two tertiary beams 15 and 16, which are then re-superposed, by varying appropriately the difference of the optical paths with appropriate means 17 (for example, a mobile mirror). The spectrophotometer hence detects one self- correlation peak (of light intensity), which is used as zero in the time scale, and two cross-correlation peaks (symmetrical with respect to the self-correlation peak), out of phase in a time scale with respect to the former by a time interval depending upon the difference between the optical paths followed by the analysis beam 6 and the reference beam 7. For more clarity, the self-correlation peak is due to the re-superposition in the two tertiary beams of the component deriving from the analysis beam 6 with itself and to re-superposition of the component deriving from the reference beam 7 with itself. Since the radiation is a polychromatic one, there will exist just one self-correlation peak, corresponding to a zero difference in optical paths between the two tertiary beams. The cross- correlation peak derives from the superposition in the tertiary beams of the component deriving from the analysis beam with the one deriving from the reference beam. Figure 2 provides an example of interferogram (the ordinate represents light intensity, the abscissa represents time), in which there is visible the self-correlation peak 20 (used as the origin for the time scale) and the cross- correlation peaks 21, separated from the former by a time interval proportional to the optical-path difference OPD between the analysis beam and the reference

beam. Via Fourier analysis of a cross-correlation peak, it is possible to obtain, for the different wavelengths, the phase difference between the analysis beam and the reference beam, introduced by the optical-path difference (which is also a function of k).

Said phase difference will be linked to the thickness d of the specimen and to the refractive index n (X) for that given wavelength by the following relation: where L is the difference between the optical paths in the absence of the specimen, which, as has been seen, is preferably adjustable, and d is the thickness of the specimen.

The method according to the present invention preferably also comprises a step in which the operations listed (with determination of the phase difference between the reference beam and the analysis beam) are carried out in the absence of the specimen, maintaining the configuration of the first interferometer (and hence L) unvaried. In this way, it is possible to determine (by subtraction) the phase difference 8) introduced by the specimen, from which n (.) can be obtained according to the equation: It may be seen how, with the methodology followed, it is possible to determine in a single step the distance between the self-correlation peak and the cross- correlation peaks, which appear on a single interferogram. By proceeding according to the known art, with just one interferometer, it is possible to measure in a single step only the self-correlation peak or the cross-correlation peak, with a laborious a posteriori calibration to establish the actual delay times, said calibration possibly giving rise to errors. The spectral phases measured with the method according to the present invention, both in the absence and in the presence of the specimen are, instead, obtained in a simple and precise way, eliminating spurious contributions due to possible alterations in the configuration of the spectrophotometer between the various steps of the operations.

As has been said, the length L can be preferably adjusted and is chosen so as to

obtain a good separation between the peaks in order to prevent any possible superposition.

The phase difference is determined, according to what has been seen above, but for an addendum equal to or a multiple of 27c. Hence, for determining n (.), it is necessary to know the refractive index for at least one wavelength.

For the absolute determination of the refractive index, the method according to the present invention preferably comprises also the measurement at different angles of incidence of the analysis beam impinging upon the specimen.

If a specimen of material to be analysed is positioned in the first interferometer at an initial angle f0 with respect to the incident analysis beam and is rotated through an angle, the variation of phase for a given wavelength will be: Also in this case, the phase difference A) will be determined but for 2x or multiples thereof. However, there can conveniently be chosen a rotation Ai30 sufficiently small as to have a variation of phase comprised between 0 and 2jet, which enables, by application of Equation (3), the value of refractive index to be obtained for at least one wavelength. For example, assuming n < 5, which is the case for the majority of the materials in the spectral region of transparency, if d = 1 mm and o= 0, we obtain: 15 < 2. 86° for X > 1 pm.

It is evident that, if the refractive index of a material is known to start with, the method according to the present invention can also be used for carrying out measurements of other characteristics of a specimen, in particular the thickness.

The method according to the present invention is suited, with certain minor adjustments, also to measurements of refractive index on anisotropic materials.

For this purpose, it is possible to operate on an apparatus according to the present invention comprising means for obtaining an appropriate polarization of at least the analysis beam (for example, the source can be a polarized-light source, or else appropriate means of polarization can be provided along the path of the primary beam or of the analysis beam).

In this case, the method according to the present invention envisages proceeding with at least the analysis beam appropriately polarized, for example, with a

rectilinear polarization, at least in the steps in which the beam traverses the specimen. The latter can be preferably set and made to rotate in an appropriate way, taking into account its properties of anisotropy (for example, a uniaxial crystalline material can be set with the optical axis coinciding with the axis of rotation, which, as has been said, is preferably perpendicular to the direction of the incident analysis beam), according to the expertise of the person skilled in the sector and to the analysis requirements. There may also be provided means for varying the plane of polarization of the analysis beam for carrying out different tests.

EXAMPLE In order to test the method according to the present invention, experiments were conducted in an apparatus like the one represented schematically in Figure 1, provided with a rotatable specimen-holder with an angular precision of 0. 001 °, on a plate of fused silica having a thickness of 1238 1 m, with accurately controlled parallelism between the faces and homogeneity of the refractive index.

Cross-correlation interferograms were obtained by varying the angle of incidence of the analysis beam on the plate at intervals of 1 ° from 0° to 10°.

Figure 3 provides the phase differences produced by the rotation through 1° of the specimen at different angles, increasing in the direction indicated by the arrow C, and as a function of the wave number. In Figure 4, the difference between the phases measured at an angle 15 and at 0° for two different wavelengths X m (white squares) and 2 = 2 Rm, (black squares), where the squares represent the experimental points and the lines are the curves according to Equation (3) which yield the best interpolation. From the values of said curve, n (X1) = 1.4053 0.0005 and n (x2) = 1.4381 0.0008 is obtained. The errors are imposed by the uncertainty in the evaluation of the thickness of the specimen, which lead to An/n A 10.

The quantity n (X) can be obtained for each wavelength with Equation (2). Figure 5 provides the results n (<\.) obtained (solid line), as compared to the theoretical data (Sellmeier) (white circles) and to the data provided by the literature (Palik) (black squares). By extending the range of angles investigated, higher levels of

precision can be obtained (thanks to better interpolations with Equation (3) ) or else it is possible to introduce the thickness of the specimen as variable in the interpolation. It is to be noted how large angles. 0 will cause a lateral displacement of the analysis beam that can be the source of error in the subsequent measurements; it is therefore necessary to take this into account in the construction of the apparatus and in its configuration, if it is desired to proceed in this way.