TECHNICAL FIELD OF THE INVENTION

The invention relates to a system and method for analyzing the wavefront of an electromagnetic radiation in the terahertz (THz) range.

More precisely the invention relates to a device and a method for measuring the wavefront spatial distribution of a THz beam.

Within the present disclosure, the THz frequency range extends from about 0.1 to 10 THz, or, equivalently, the THz spectral range extends in wavelength between 3 mm and 30 μιη.

BACKGROUND INFORMATION AND PRIOR ART

Numerous documents describe devices and methods for measuring the wavefront of an electromagnetic radiation in the visible spectral range. The Hartmann sensor was invented more than a century ago for optical beam analysis. A Hartmann sensor generally comprises a mask consisting of an absorbing plate with an array of holes placed just in front of a 2D sensor. The Hartmann sensor enables to locally measure the wavefront slopes of an incoming optical radiation. In 1970, Shack improved the Hartmann sensor by replacing the mask by an array of micro-lenses, thus forming a Shack-Hartmann sensor. The Hartmann and Shack-Hartmann wavefront sensors are widely used in the visible spectral region to reveal optical aberrations such as astigmatism, coma and spherical aberration.

In the THz spectral domain, it remains challenging to fully measure the spatial profile and wavefront of a THz beam due to the effective lack of cameras sensitive to THz radiation, especially in pulsed mode. Moreover, contrary to optical beams, the wavelengths associated to the THz beams are not negligible compared to the size of the optical elements used in the experimental setup. For example a 3 THz radiation corresponds to a wavelength of 100 microns. Thus, a THz radiation generates diffraction and a possible deviation from standard Gaussian beam propagation.

M. Cui, J. N. Hovenier, Y. Ren, A. Polo, and J. R. Gao, "Terahertz wavefronts measured using the Hartmann sensor principle", Opt. Express 20, 14380 (2012) disclosed a system comprising a Hartmann mask with an array of apertures combined to a single point pyroelectric detector which is scanned in two dimensions. This system enables reconstructing the wavefront of a continuous THz laser beam at a selected frequency. However, two-dimension scanning is time-consuming. This method is incompatible with measurement of pulsed THz beam. Moreover, the low sensitivity of this system is not suitable for spectral analysis.

H. Richter, M. Greiner-Bar, N. Dessmann, J. Pfund, M. Wienold, L.

Schrottke, R. Hey, H. T. Grahn, and H. -W. Hubers, Appl. Phys. Lett. 101 , 2012, disclosed a Terahertz wavefront measurement system based on a Hartmann sensor. This THz Hartmann sensor comprises a metal plate with an array of holes, acting as a Hartmann mask, and mounted directly on a microbolometer array camera, which is sensitive in the THz frequency range. Conventional calculation based on Zernike polynoms is used for reconstructing spatial distribution of the wavefront. This sensor enables measuring the wavefront of a continuous THz beam emitted by a quantum cascade laser at a selected frequency of 3.1 THz. However, this method and system cannot be applied to the measurement of short THz pulses due to the low sensitivity of the microbolometer array camera. Moreover, the spatial resolution of this system is low, which results in low signal- to-noise ratio.

THz spectral measurements are commonly performed using commercially available THz time-domain spectrometers (THz TDS), which are flexible, compact and affordable systems. However, existing THz TDS systems do not provide spatial imaging of THz beams.

F. Molloy, M. Naftaly, and R. A. Dudley, "Characterization of Terahertz beam profile and propagation," IEEE JSTQE 19, 8401508, 2013, described two techniques for analyzing THz beam profiles based on a THz time-domain spectrometer. This THz TDS comprises a pulsed laser generating infrared pulses at a wavelength of 800 nm. This infrared laser is divided in a pump beam used for generating a THz beam and in a probe beam used for detecting the THz beam. The ultrashort (20 fs) pump beam is incident on a GaAs emitter which generates THz radiation in the frequency range from about 0.1 THz to 3 THz. The THz beam is focused on an electro-optic ZnTe crystal in front of a photodiode detector for single point detection. Fourier transform of the detected signal as a function of time delay between pump beam and probe beam enables time-domain spectroscopy analysis of the THz signal. For spatial wavefront analysis, Molloy et al. disclose placing a Hartmann mask in the THz beam path for generating multiple THz beams, and scanning in two dimensions an aperture at two locations behind the mask in the THz beam path, so as to create an image of the THz beam. However, the spatial extent of the aperture scanned image is rather low (30x30 pixels).

SUMMARY OF THE INVENTION

Therefore one object of the invention is to provide a system and method for analyzing the wavefront of a pulsed electromagnetic radiation in the THz frequency range, providing higher spatial resolution, higher sensitivity and shorter acquisition time than previous systems and methods.

A further object of the invention is to provide a Terahertz wavefront measurement system and method enabling both spatial and spectral analysis.

The above objects are achieved according to the invention by providing a Terahertz wavefront measurement system comprising a spatial mask selected among a Terahertz lens array or an array of apertures, the spatial mask being configured and placed for receiving an incident beam in a Terahertz frequency range and for generating an array of multispots in the Terahertz frequency range.

According to the invention, the Terahertz wavefront measurement system further comprises an infrared camera having an array of pixels, a nonlinear electro-optical crystal placed between the spatial mask and the infrared camera, the nonlinear electro-optical Terahertz detection crystal having a first face and a second face, the first face being placed adjacent to the spatial mask for receiving the array of multispots in the Terahertz frequency range and the second face being placed for receiving an ultrashort pulsed infrared probe beam, the nonlinear electro-optical crystal being configured for providing nonlinear electro-optical interaction through the Pockels effect between the array of multispots in the Terahertz frequency range and the ultrashort pulsed infrared probe beam and for generating a reflected beam in the infrared frequency range having a wavefront spatial distribution depending on the array of multispots in the Terahertz frequency range, the infrared camera being configured for detecting an image of the reflected beam in the infrared frequency range and a processing system for analyzing the image of reflected beam in the infrared frequency range and for reconstructing a wavefront spatial distribution of the incident beam in the Terahertz frequency range for a determined frequency range.

Thus, the Terahertz beam profile is detected in two dimensions without aperture scanning. As a result, acquisition time is much faster.

Moreover, the Terahertz beam profile properties are transferred electro- optically to an infrared reflected beam through the Pockels effect, enabling image detection in the infrared frequency range. In contrast to single point low sensitivity detectors in the Terahertz range, the availability of high sensitivity cameras in the near IR frequency range enables two-dimension image acquisition with high sensitivity and high spatial resolution. Signal-to-noise ratio of the detected images is thus considerably improved. As a result, wavefront analysis of Terahertz beam is considerably improved both spatially and temporally.

The Terahertz wavefront measurement system of the present disclosure enables measuring the wavefront of an electromagnetic radiation in the Terahertz range, at a selected frequency or frequency range, preferably in the frequency range between 0.1 and 10 THz.

The Terahertz wavefront measurement system of the present disclosure also enables measuring deformations of the wavefront and thus quantitative evaluation of aberrations, such as coma or spherical aberration, induced by optical systems or materials in the Terahertz frequency range.

According to particular aspects of the invention:

- the nonlinear electro-optical Terahertz detection crystal comprises a thin plate of zinc telluride, gallium phosphide, LiNbO ₃ or DAST for example;

- the distance between the spatial mask and the nonlinear electro-optical crystal is generally comprised between 1 mm and about 10 mm, and preferably between 5 and 10 mm;

- the spatial mask comprises a plate with a two-dimension periodic array of apertures or, respectively, of lenses, the period(s) of the two-dimension periodic array being comprised between 1 and 5 mm, and the dimensions of the apertures, respectively of the lenses, being comprised between 0.5 and 2.5 mm.

According to other particular aspects, the Terahertz wavefront measurement system further comprises:

- a polarizer placed on a beam path of the ultrashort pulsed infrared probe beam, an analyzer placed between the Terahertz detection nonlinear electro-optic crystal and the infrared camera and a beam splitter for separating the ultrashort pulsed infrared probe beam from the reflected beam in the infrared frequency range; - an optical delay line placed on a beam path of the ultrashort pulsed infrared probe beam, the infrared camera being configured for detecting a plurality of images as a function of a time delay of the delay line and the processing system being configured for analyzing the plurality of images as a function of a time delay;

- a modulator for modulating the incident beam in the Terahertz frequency range, and a synchronization line for synchronizing the infrared camera with the modulator;

- optional: a Terahertz beam expander placed on a beam path of the incident beam in the Terahertz frequency range, and/or an infrared beam expander placed on a beam path of the ultrashort pulsed infrared probe beam;

- a Terahertz source comprising an air plasma, or an interdigited photoconductive antenna or another nonlinear optical crystal configured for receiving an ultrashort laser pulsed beam and for generating by optical rectification the incident beam in the Terahertz frequency range.

The invention also concerns a Terahertz wavefront measurement method comprising the steps of:

- directing an incident beam in a Terahertz frequency range on a spatial mask selected among a Terahertz lens array or an array of apertures, the spatial mask being configured so as to generate an array of multispots in the Terahertz frequency range;

- directing the array of multispots in the Terahertz frequency range on a first face of a nonlinear electro-optical crystal adjacent to the spatial mask and directing an ultrashort pulsed infrared probe beam on a second face of the nonlinear electro-optical crystal, the nonlinear electro-optical crystal being configured for providing nonlinear electro-optical interaction between the array of multispots in the Terahertz frequency range and the ultrashort pulsed infrared probe beam and for generating a reflected beam in the infrared frequency range having a wavefront spatial distribution depending on the array of multispots in the Terahertz frequency range;

- detecting an image of the reflected beam in the infrared frequency range on an array of pixels of an infrared camera; - analyzing the image of reflected beam in the infrared frequency range and reconstructing a wavefront spatial distribution of the incident beam in the Terahertz frequency range for a determined frequency range.

The invention applies in particular to THz time-domain spectrometers and imaging apparatus for the measurement of THz wavefront.

BRIEF DESCRIPTION OF THE DRAWINGS

This description is given for non limiting illustrative purposes only and will be better understood when referring to the annexed drawings wherein:

- Figure 1 represents schematically a THz wavefront measurement system according to an embodiment of the invention;

- Figure 2 illustrates schematically a front view of an exemplary Hartmann mask applied to a THz beam;

- Figure 3 represents schematically a detailed view of an electro-optic THz detection system according to an embodiment of the invention using a Hartmann mask;

- Figure 4 represents schematically a detailed view of an electro-optic THz detection system according to a variant of the invention using an array of lenses;

- Figure 5 represents schematically a THz wavefront measurement system according to an embodiment of the invention, applied for example to measuring THz wavefront perturbations induced by an object;

- Figure 6 represents schematically a side view of an electro-optic THz detection system in collimated THz beam for measuring a plane wavefront;

- Figure 7 represents schematically a side view of the electro-optic THz detection system in focused THz beam for measuring a spherical converging wavefront;

- Figure 8 illustrates exemplary infrared images obtained by a system of the invention, respectively, on Fig. 8(a): a Hartmann mask as seen by the probe beam without THz incident beam; Fig. 8(b): the Hartmann mask at 1 .2 THz when illuminated by a collimated incident THz beam with planar wavefront; and Fig. 8(c) the Hartmann mask at 1 .2 THz when illuminated by a converging THz beam with spherical wavefront;

- Figure 9(a) represents the reconstructed THz wavefront of a planar THz beam and Fig. 9(b) represents the corresponding amplitudes of the Zernike coefficients; Figure 9(c) represents the reconstructed THz wavefront of a converging spherical THz beam and Fig. 9(d) represents the corresponding amplitudes of the Zernike coefficients.

DETAILED DESCRIPTION OF EXAMPLE(S)

Device

The wavefront measurement system of the present disclosure relies on a two-dimension (2D) electro-optic detection system, illustrated schematically on Figure 1 .

The 2D electro-optic detection system mainly comprises a Hartmann mask 4, a nonlinear electro-optic crystal 5 placed at a distance D from the Hartmann mask 4 and an infrared camera 9. Alternatively, the Hartmann mask may be replaced by an array of THz lenses. Optionally, the detection system comprises furthermore a modulator, such as a mechanical chopper 3, an imaging lens 8 placed in front of the camera 9 and/or an infrared polarization analyzer 17 placed between the camera 9 and the nonlinear electro-optic crystal 5.

In an example illustrated on Figure 2, the Hartmann mask 4 consists of a 1 mm-thick metallic plate with an array of circular holes of 1 mm diameter with 2 mm periodicity in the horizontal and vertical directions.

The Hartmann mask 4, represented in dashed line on Fig. 1 , is combined with a large aperture nonlinear electro-optic crystal 5. As an example, the nonlinear electro-optic crystal 5 is a ZnTe crystal having a diameter of 25 mm and a thickness of 1 mm. A thicker electro-optic crystal 5 provides a stronger electro- optic effect, but reduces the spectral bandwidth. A thickness of about 1 mm results from a compromise between signal intensity and bandwidth. The nonlinear electro- optic crystal 5 has a first face 51 and a second face 52. The faces 51 , 52 of the electro-optic crystal 5 may or may not be parallel.

For example, the Hartmann mask 4 is placed at a distance D of 10 mm of the first face 51 of the nonlinear electro-optic crystal 5. This distance D is selected as a compromise between THz beam diffraction and wavefront slope measurement. This distance can be slightly reduced to a few millimeters in order to limit the diffraction of the THz beam. However, the displacements of the hole spots will be also reduced.

The physical phenomena taking place in the electro-optic detection system will be better understood in reference to figure 3. Let's consider first a THz pulse 1 forming a THz beam 10 with a planar wavefront 100. We will detail later the propagation of a spherical wavefront. The THz beam 10 of planar wavefront 100 is incident on the Hartmann mask 4. The Hartmann mask 4 generates an array of THz multispots 60. This array of THz multispots 60 is projected on the first face 51 of the electro-optic crystal 5. The distribution of the array of THz multispots 60 modifies locally, by electro-optic effect without applying any external voltage, the optical properties of the electro- optic crystal 5 over a broad spectral range. More precisely, the electro-optic crystal 5 becomes spatially birefringent through the Pockels effect induced by the incoming THz electric field which depends on the local intensity distribution of the THz multispots 60.

As illustrated on figure 1 , a probe pulse 2, for example a femtosecond pulse at a wavelength of 800 nm forms a probe beam 20 in the infrared frequency range. The probe beam 20 in the infrared frequency range is directed on the second face 52 of the electro-optic crystal 5. The polarization of the infrared probe beam 20 is modified through the Pockels effect induced by the spatially dependent THz electric field and forms an infrared reflected beam 30, by reflection of the probe beam 20 on the first face 51 of the electro-optic crystal 5. Due to the electro- optic effect, the distribution of the THz multispots 60 modifies the spatial distribution of intensity of the infrared reflected beam 30.

The camera 9 is for example a CMOS camera having 232x232 pixels. An imaging lens 8, made for example of glass or bk7, is placed between the nonlinear electro-optic crystal 5 and the camera 9 so as to form an image of the electro-optic crystal 5 on the camera 9. It should be outlined that the camera 9 is sensitive in the near infrared frequency range, generally up to 1 μιη, but is not directly sensitive to THz radiation. Another infrared camera can be used depending on the IR probe laser output wavelength.

A polarizing analyzer 17 enables to analyze the infrared reflected beam 30 as a function of polarization.

The camera 9 combined with the imaging lens 8 forms an image of the infrared reflected beam 30. The reflected beam 30 has a spatial distribution which is modified by interaction with the THz multispots in the electro-optic crystal 5. Thus, the detected image represents an image of electric field distribution of the incident THz beam in time-domain. Fourier transform is applied to the detected image and selected at certain frequencies to derive the amplitude of the electric field distribution at a selected THz frequency.

Figure 3 also shows the effect of a modification of the THz wavefront. Let's now consider a THz incident beam 10 having a supposed spherical wavefront 101 . The spherical wavefront 101 incident THz beam 10 is projected through the Hartmann mask and forms an array of THz multispots 61 . The positions of the multispots 61 corresponding to a spherical wavefront 101 are displaced relatively to the reference positions of the array of THz multispots 60 formed by a planar THz wavefront 100. Thus, the spatial distribution of electro- optic effect in the nonlinear electro-optic crystal 5 is modified accordingly. The spatial distribution of the THz electric field through the Hartmann mask modifies locally the optical properties (refractive index and/or absorption) of the nonlinear electro-optic crystal 5 in the infrared spectral range. In turn, the intensity distribution of the infrared reflected beam 30 that is finally imaged by the camera 9 is modified as a function of the local optical properties of the nonlinear crystal 5. As a result, the detected infrared image of the reflected infrared beam 30 also presents a modified spatial distribution depending on the THz electric field distribution, and thus depending on the spherical wavefront 101 .

Combining the Hartmann mask 4 with a nonlinear electro-optic crystal 5 thus enables to transfer THz wavefront information to the infrared reflected probe beam through the Pockels effect in the crystal 5.

Alternatively, as illustrated on Figure 4, the Hartmann mask 4 may be replaced by a THz matrix lens 24 comprising an array of lenses 34 operating in the THz frequency range. For example, the lenses 34 can be made of high density polyethylene or Teflon, have a plane-convex shape, with a radius of about 1 mm, and are placed on a two-dimension periodic array having a period of about 2 mm in both directions. In the example illustrated, the first face 51 of the nonlinear electro-optic crystal 5 is placed in the focal plane of the array of lenses. In other words, the distance D is equal to the focal length of the array of lenses. The THz matrix lens receives a THz incident beam 10 with a planar wavefront 100 and forms an array of multispots 70 focused on the first face 51 of the nonlinear electro-optic crystal 5. When the THz incident beam 10 has a for example a spherical wavefront 101 , the spatial positions of the array of multispots 71 focused on the first face 51 are modified. The displacement of the positions of the focused multispots enables to detect wavefront deformations. Similarly, as on figure 3, the infrared probe beam 20 is reflected on the first face 51 of the nonlinear electro- optic crystal 5 and forms a reflected infrared beam 30. The reflected infrared beam 30, which is imaged by the infrared camera 9, has a spatial intensity distribution which depends on the electric field distribution of the THz wavefront focused on the nonlinear electro-optic crystal 5 by the THz matrix lens 24. Since the THz microspots 70, 71 are focused on the electro-optic crystal, they present higher intensity than multispots generated by a Hartmann mask. The Shack-Hartmann mask thus enables to obtain a THz measurement system with higher sensitivity.

We will now describe in relation with Figure 5 an example of a THz time- domain imaging spectrometer according to an embodiment of the invention. We use amplified femtosecond laser pulses for generating both the THz beam and the infrared probe beam. An amplified femtosecond infrared pulsed laser beam 50 is separated by a beam splitter 16 in a first and a second femtosecond infrared pulsed laser beam 40, respectively 20. The first femtosecond infrared pulsed laser beam 40 is modulated using for example a mechanical chopper 3. For example, the femtosecond infrared pulsed laser beam 40 has a wavelength of 800 nm, a power of 1 mJ and pulse duration of 150 fs. The modulated infrared beam 40 is directed, using a mirror 23, on a nonlinear electro-optic crystal 15 for generating a THz pulsed beam 10 by optical rectification. For example, the nonlinear optical crystal 15 is a 1 mm-thick ZnTe crystal. A spectral filter 13, made for example of Teflon, stops any remaining infrared radiation and passes selectively THz radiation. The THz beam 10 generated by optical rectification has a broadband spectral distribution in the frequency range from 0.1 to 4 THz and a pulse duration of about 0.5 ps. An optical system comprising for example a beam expander 1 1 forms a collimated THz incident pulsed beam 10. As described above, the collimated THz incident pulsed beam 10 is directed on a Hartmann electro-optic sensor comprising a Hartmann mask 4 and another nonlinear electro-optic ZnTe crystal 5.

On the other side, the second femtosecond infrared pulsed laser beam

20 (150 fs pulse duration) is directed on an adjustable delay line 22 comprising a mirror system 25, 26. The mirror system 26 is movable so as to adjust a variable delay At (typically from -5 ps to 30 ps) between the probe pulse 20 and the THz pulse 10. An infrared beam expander 12 forms an infrared collimated probe beam having approximately the same diameter as the THz beam 10 on the nonlinear electro-optic crystal 5 so that these two beams 10, 40 overlap spatially in the nonlinear electro-optic crystal 5. A polarizer 7 is placed on the beam path of the infrared probe beam 20, so as to polarize, for example linearly, the infrared probe beam 20. The time-delayed infrared pulsed probe beam 20 is directed on the second surface 52 of the crystal 5 and forms a reflected infrared beam 30 by reflection on the first surface 51 of the nonlinear electro-optic crystal 5. A beam splitter 6 enables separating the reflected infrared beam 30 from the incident infrared beam 20. The reflected infrared pulsed beam 30 is finally captured by a 232x232 pixels CMOS camera 9 after passing through the analyzer 17 and the imaging lens 8. The polarizer 7 and analyzer 17 enable measurement of the Pockels effect in dark field imaging mode.

In the ZnTe crystal 5, the spatial distribution of the broadband (0.1 ^1 THz) THz electric field modifies, by Pockels effect, the intensity distribution of infrared beam reflected by the first surface 51 of the crystal 5.

The system of figure 5 may be used to analyze wavefront perturbations induced by a device or material 80 placed on the collimated THz beam path.

Using a well-known dynamic subtraction technique, high signal-to-noise ratio and video rate imaging can be achieved by adopting phase sensitive detection for image acquisition and processing. For a given time delay between the THz beam 10 and the probe pulse 20, the system is able to provide a 2D (X- horizontal and Y-vertical directions) image corresponding to the distribution of the THz electric field at the position of the electro-optic crystal 5. This image can be obtained at a 500 Hz acquisition rate using dynamic subtraction. Signal-to-noise ratio higher than 100 usually requires an averaging time of 0.5 to 1 s. By changing the time delay At between the THz beam 10 and the probe pulse 20, it is possible to record the temporal evolution of this THz electric field.

For example, the images are recorded as a function of the time delay At between the probe beam 20 and the THz beam 10. A Fourier transform enables to obtain spectra for each point in the detected image. Moreover, a spectral image scan may be derived at a selected THz frequency.

For effective two-dimension electro-optic sampling in the electro-optic crystal 5, THz pulses with electric field strengths larger roughly than 1 kV/cm are required. Therefore, it requires THz pulses generated by optical rectification optical rectification in a nonlinear crystal, for example a crystal of ZnTe, as disclosed in Figure 5, or in a crystal of LiNbO ₃ , or DAST. Alternatively, the THz beam may be generated by ambient air plasma or by a large interdigitized photoconductive antenna.

For evaluating the performances of the system illustrated on Figure 5, measurements are performed in two configurations illustrated respectively on figures 6 and 7. On figure 6, the THz electro-optic detection system analyzes a collimated THz beam having a substantially planar wavefront. In contrast, on figure 7, a converging THz lens 18 is inserted on the beam path of the incident THz beam 10 so as to form a substantially spherical wavefront converging on the electro-optic crystal 5. As an example, the lens 18 is made of Teflon and has a focal length of 100 mm.

The performances of the system and method are tested by a complete and quantitative evaluation of the planar and respectively converging THz wavefronts.

First, we record a reference image for indicating the locations of the mask holes at the CMOS camera pixel positions. This is achieved by recording the image of the mask illuminated by the laser probe beam 20, without incident THz beam 10. For this reference image acquisition, the strong direct reflection from the ZnTe crystal surface is removed by tilting the ZnTe crystal 5 without inducing any noticeable deviation of the holes positions in the detected image. This reference image is represented on Fig. 8(a) and can be used for any further THz wavefront measurement.

Then, Fig. 8(b), respectively Fig. 8(c), show the image of the mask in the presence of a planar, respectively converging, THz beam 10 combined with the probe pulse. Both images have been calculated at 1 .2 THz after Fast Fourier Transformation of the temporal data acquired as a function of the time delay. However, the method can be extended to the complete spectral bandwidth of the THz source.

The calculation of the reconstructed wavefront is performed as follows.

For each image presented in Figures 8(a), 8(b) and 8(c), we determine the coordinates of the centroid of each spot that are directly related to the local slopes of the THz wavefront. The final calculation of the reconstructed wavefront is performed by using a least-squares method wherein the wavefront is represented by a linear combination of Zernike polynomials. The calculated waveform of the planar, respectively converging, THz beam is presented on Fig. 9(a), resp. respectively Fig. 9(c). The vertical scale represents the deformation U of the wavefront with respect to the reference image (vertical scale is different for figures 9(a) and 9(c)). Fig. 9(b), respectively 9(d), represents the amplitudes of the 14 first Zernike polynomials for the calculated wavefront of Fig. 9(a), respectively Fig. 9(c). The reconstructed planar wavefront presents a small tilt in the X-direction corresponding to amplitude of 18 microns (λ/14 at 1 .2 THz) for the second order polynomial. Similarly, a small negative astigmatism can be noticed (12 microns or λ/21 at 1 .2 THz). For the converging spherical wavefront, it is worth noting first that the same X-tilt is present, which means that the lens 18 is properly adjusted since it does not produce any additional wavefront tilt. A large defocus of 272 microns (0.9λ at 1 .2 THz) is measured together with the presence of negative spherical aberration (25 microns or λ/10 at 1 .2 THz). Assuming a perfect spherical wavefront, this defocus amplitude a ₄ can be used to evaluate the radius of curvature of the THz beam at the mask position, where the THz wavefront slopes are measured. In that case, the wavefront can be expressed by the expression:

W(r) = = 2V3a ₄ r ²

ZK

where a=r/p is a normalization factor since the Zernike polynomials are defined for a maximum circular aperture with p=1 . In our measurement, a=8.48 corresponding to the analysis of the 5 by 5 central spots in Fig. 8, and gives R=38 mm, which is close to the theoretical value of 45 mm.

Finally, the performances of the system and method of the present disclosure have been evaluated taking into account the accuracy of the centroid coordinates, the distance D between the mask 4 and the crystal 5 and the distance between two adjacent holes 14. The main features of the wavefront sensor are as follows: aperture dimension: 20x20 mm, Hartmann mask composed of 9x9 holes of 1 mm diameter and 2mm period in X and Y directions; tilt dynamic range ±1 1 .3 degrees (or 6,7χλ at 1 THz); minimum radius of curvature 40 mm; wavefront measurement accuracy λ/3.5 at 1 THz; tilt measurement sensitivity 8.7 mrad; operating frequency range 0.1 - 4 THz.

The system disclosed herein enables 2D electro-optic imaging for the quantitative wavefront determination of THz pulses, by combining a Hartmann mask and a ZnTe crystal for the EO conversion of multispots from an incoming THz pulse using infrared probe pulsed beam which is reflected for forming an image on an infrared camera. The measurement requires an infrared laser reflected beam and an infrared camera.

Alternatively, the Hartmann mask may be replaced by a Shack-Hartmann mask consisting of a THz matrix lens. This alternative enables to improve the wavefront measurement accuracy, due to a better focusing of the THz multispots in the electro-optic crystal, which provides an efficient method to limit optical aberrations in THz time-domain spectrometers and imaging apparatus.

The system and method provide easy, fast and accurate analysis of THz wavefront, enabling for example correction of aberrations in the THz frequency range.

The method and system are easily implemented physically. It requires basically a THz Hartmann mask or matrix lens combined to a nonlinear electro- optic crystal for converting the THz wavefront information into the infrared spectral range using an infrared probe beam. The reflected infrared beam is detected using an infrared imaging camera. The numerical data treatment must however be adapted to obtain quantitative reconstruction of the THz wavefront.

The THz wavefront measurement system provides 2D measurements frequency-resolved wavefront analysis of THz pulses, without requiring aperture scan across the THz beam section. This system enables quantitative determination of the frequency-resolved wavefront of THz pulses by using 2D electro-optic imaging and a Hartmann mask. For demonstration, a Zernike modal reconstruction method has been applied to measure wavefronts and optical aberrations of planar and convergent THz beams, with good agreement with theoretical predictions.

The wavefront measurement system and method as disclosed above find applications in the field of control and/or beam shaping of a THz beam in THz imaging or spectrometry. The THz beam may either be focused on a sample for spectrometry or point by point imaging or, in contrast, the THz beam may be collimated with a large aperture for a large area analysis.

The applications of THz imaging are in strong development and find numerous applications extending from security to non-destructive control.