Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
  • G01J11/00—Measuring the characteristics of individual optical pulses or of optical pulse trains
• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B5/00—Optical elements other than lenses
  • G02B5/20—Filters
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
  • H04N23/00—Cameras or camera modules comprising electronic image sensors; Control thereof
  • H04N23/10—Cameras or camera modules comprising electronic image sensors; Control thereof for generating image signals from different wavelengths
  • H04N23/12—Cameras or camera modules comprising electronic image sensors; Control thereof for generating image signals from different wavelengths with one sensor only

Definitions

• This description relates to a system and a method for characterizing an electromagnetic radiation pulse by time-resolved optical windowing.
• an electromagnetic radiation pulse that is to say to know its complex electromagnetic field amplitude profile, when it is a pulse of very short duration. , called an ultrashort pulse.
• a pulse can last a few femtoseconds or a few tens of femtoseconds, or even a little more than a hundred femtoseconds, and have a nominal wavelength of about 1.5 ⁇ m (micrometer).
• nominal wavelength of ultrashort pulses to be characterized can be more generally between 1.2 ⁇ m and 2.4 ⁇ m, or between 1.7 ⁇ m and 3.4 ⁇ m, or even in other spectral ranges, including a nominal ultrashort pulse wavelength value that is close to 0.8 ⁇ m corresponding to emission from titanium:sapphire laser sources.
• Several methods have already been proposed to characterize the complex amplitude profile of such pulses. Some of these methods, known as multi-shot or “multiple shot” in English, cannot be implemented from a single pulse, because they require several pulse measurements to be carried out successively. Such is the case when an optical assembly is used which causes an electromagnetic radiation pulse to interfere with itself by introducing a delay which has a unique value for each measurement.
• the value of the delay is then varied between successive measurements.
• the number of measurements which is necessary in this case can be significant, depending on the precision desired for the characterization of the pulse, which imposes a total duration of characterization which can be long or very long. In practice, such a multi-hit method can even be unusable when the pulse repetition frequency is low.
• those which are called mono-shot, or “single shot” in English make it possible to characterize a pulse in a single measurement.
• FROG Frequency-Resolved Optical Gating
• Such FROG characterizations can be of the multi-shot type or of the single-shot type, as described in document US 8,068,230. They require the measurement of the spectrum and, because of this, their hardware implementation is complicated. All FROG methods implement a non-linear mechanism of radiation propagation, which is applied to pulse parts which are superimposed to form an interference, with a delay between these pulse parts which is denoted T. However, the non-linear mechanism that is used can vary between different FROG methods.
• Two-dimensional information is then collected, in the form of spectral detection signals S( ⁇ , T), where ⁇ is the optical pulsation which corresponds to the spectral intensity measurement carried out.
• ⁇ is the optical pulsation which corresponds to the spectral intensity measurement carried out.
• the complex amplitude of the pulse, denoted A(t), which characterizes its envelope shape, can then be deduced using iterative algorithms, from all the detection signals S( ⁇ , T) collected when the two parameters ⁇ and T have values that vary independently of each other.
• each detection signal S( ⁇ , T) corresponds to the following formula:
• document FR 3 034 577 describes yet another one-shot method for characterizing an electromagnetic radiation pulse.
• This alternative method uses a Fresnel biprism to form an interference pattern by superimposing two parts of the pulse in a portion of space, and the interference pattern is captured by an image sensor which is selected to n' be sensitive only to two-photon absorptions.
• the image sensor produces a current which is directly proportional to the probability of absorbing two photons at each location of the interference pattern. It is necessary to ensure that the image sensor does not detect photons by the usual linear absorption mechanism, by selecting it so that its spectral range of sensitivity does not contain the wavelength value(s) impulse.
• the detection signals which are delivered by the image sensor for an ultrashort pulse when the accumulation time of the image sensor is greater than that of the pulse, are proportional to the square of the module of the function of autocorrelation of the electric field, this electric field being again represented by a complex number.
• an object of the present invention is to propose a new method for characterizing an electromagnetic radiation pulse, which is of the single-shot type.
• An additional object of the invention is to provide a complete and exact characterization of the shape of a pulse, that is to say without an assumption on a type of parametric shape of pulse envelope be necessary.
• Yet another object of the invention is to use an optical assembly which is simple and inexpensive.
• Yet another object of the invention is to make it possible to characterize pulses whose nominal wavelength lies in the range between 1.2 ⁇ m and 2.4 ⁇ m, or between 1.7 ⁇ m and 3.4 ⁇ m, or is substantially equal to 0.8 ⁇ m.
• a first aspect of the invention proposes a new system for characterizing an electromagnetic radiation pulse by time-resolved optical windowing, which comprises:
• an interference formation device adapted to superimpose in an interference volume, several parts of an initial radiation which is incident on this device;
• an optical input path arranged to direct the pulse to be characterized on the interference formation device, so that the pulse constitutes the initial radiation which is incident on this device;
• a matrix image sensor which is arranged to selectively capture from two-photon absorptions, an interference figure formed by the pulse in the interference volume
• processing unit which is configured to deduce pulse shape characteristics from detection signals delivered by the matrix image sensor, and corresponding to the interference pattern formed by the pulse.
• the interference forming device is adapted to superimpose in the interference volume, four parts of the initial radiation, so as to form a four-wave interference and so that the detection signals delivered by the matrix image sensor vary according to two independent parameters associated with two different directions which are contained in the photosensitive surface of the matrix image sensor.
• two-photon absorption means photonic transformation mechanisms which consume two photons of the pulse. Such a mechanism can occur inside the matrix image sensor, in which case the energy of the two photons which are absorbed simultaneously is transformed into an electrical detection signal.
• the spectral range of sensitivity of the matrix image sensor which is defined in the usual way for the linear absorption mechanism, that is to say with a single photon, then corresponds to the total energy of the two photons absorbed .
• the spectral range of sensitivity of the array image sensor must contain a wavelength value which is equal to half that of each photon involved in the two-photon mechanism.
• the two photons can be absorbed simultaneously in an SHG crystal, this crystal then re-emitting a single photon which is detected by the matrix image sensor.
• the wavelength of the single photon which is re-emitted by the SHG crystal is equal to half that of each of the photons initially absorbed by this crystal.
• the characteristics of the pulse which are deduced by the processing unit from at least part of the detection signals delivered by the matrix image sensor comprise instantaneous values of the module and of the phase of the complex amplitude of the impulse field.
• the pulse characterization which is provided by the system of the invention is of the single-shot type, thanks to the sampling of the interference figure produced by the matrix image sensor.
• it is of the type with time-resolved optical windowing, since each location of the interference figure corresponds to values of two delays which are applied between several parts of the pulse by the device for forming the interference .
• the interference figure is two-dimensional, with intensity variations which are independent between the two directions of the matrix image sensor, much more complete information is collected on the pulse by the the invention. It is then possible to deduce therefrom a complete characterization of the shape of the pulse, by the instantaneous values of the modulus and of the phase of the complex amplitude of the field of the pulse, for example of its electric field. No assumptions about a type of pulse envelope parametric shape are necessary in this way, so the characterization of the shape of the pulse that is provided by the system of the invention is accurate.
• the four-wave interference forming device which is used in the system of the invention can be particularly simple. In particular, its implementation can be much simpler than that of a spectrometer.
• it may be a portion of a refractive material bounded by an optical input face which is flat and by four optical output faces which are also flat, the four output faces being images of each other by 90° rotations around an optical axis which is perpendicular to the entrance face.
• each output face forms a prism with the input face whose vertex angle is non-zero, and it is additionally oriented so that a part of the beam of the initial radiation which is incident on the entrance face parallel to the optical axis and which emerges through this exit face is deflected by the portion of refracting material in the direction of the optical axis downstream of the interference forming device .
• the interference forming device which is used in the system of the invention may comprise two biprisms each made of refractive material and which are arranged one after the other on a propagation path of the initial radiation, with respective edges of these two biprisms which have different orientations in projection on a plane perpendicular to the propagation path of the initial radiation.
• the edges of the two biprisms can be orthogonal in projection on the plane which is perpendicular to the propagation path of the initial radiation.
• the processing unit can be configured for:
• the processing unit can be configured so that the component which is selected in the decomposition by two-dimensional Fourier transformation of the interference figure has zero values outside the interference volume.
• the result of the pulse characterization which is provided by the system of the invention thus depends to a lesser extent, or does not depend, on the size of the spatial detection window constituted by the photosensitive surface of the matrix image sensor. .
• the component of the decomposition by two-dimensional Fourier transformation of the interference figure which is selected by the processing unit, can be associated with twice a nominal frequency of the pulse to be characterized according to one of the directions of the matrix image sensor, and associated with only once this nominal frequency of the pulse to be characterized according to the other direction of the matrix image sensor, when the detection signals delivered by the matrix image sensor are expressed as a function of delay contributions which are created by respective displacements in the two directions of the matrix image sensor.
• This component is called F2,I , and the instantaneous values of the modulus and of the phase of the complex amplitude of the pulse field are deduced from this component F2,I by the processing unit.
• the F2,I component has zero values outside the interference volume.
• the processing unit can be configured to select the component of the decomposition by two-dimensional Fourier transformation of the interference figure, called F2,o, which is associated with twice the nominal frequency of the pulse to be characterized according to a first of the directions of the matrix image sensor, but without being associated with any variation according to a second direction of the matrix image sensor, when the detection signals delivered by the matrix image sensor are expressed as a function of the delay contributions which are created by respective displacements in the two directions of the matrix image sensor.
• the instantaneous values of the modulus and of the phase of the complex amplitude of the field of the pulse are then deduced from this component F2,o by the processing unit.
• the values of the component F2,o are not zero outside the interference volume.
• the processing unit can be configured to select moreover the component of the decomposition by two-dimensional Fourier transformation of the interference figure, called F2.2, which is associated with twice the nominal frequency of the pulse to be characterized according to the first of the directions of the image sensor matrix, and which is also associated with twice the nominal frequency of the pulse to be characterized in the second direction of the matrix image sensor, again when the detection signals delivered by the matrix image sensor are expressed as a function of the contributions of delay which are created by respective displacements in the two directions of the matrix image sensor.
• F2.2 two-dimensional Fourier transformation of the interference figure
• the processing unit is also configured to calculate respective one-dimensional Fourier transforms of the components F2,o and F2,2 with respect to the delay contributions which are created by the displacements according to the first of the directions of the matrix image sensor , these one-dimensional Fourier transforms being denoted TFI(F2,O) for the component F2,o, and TFI(F2,2) for the component F2,2. It is then configured to deduce the instantaneous values of the modulus and of the phase of the complex amplitude of the field of the impulse, from a result of TFI(F2,O) - 2-Mod[TFi(F2.2 )], where Mod[.] denotes a complex number modulus.
• the electromagnetic pulse characterization system by time-resolved optical windowing may further comprise:
• a diaphragm which is arranged on an optical path between the SHG crystal plate and the matrix image sensor, for selectively transmitting in the direction of this matrix image sensor a beam of radiation which propagates parallel to a direction of propagation of the effective pulse upstream of the interference forming device, with respect to the direction of propagation of this pulse.
• the matrix image sensor is implemented or selected to detect only doubled optical frequency photons which are produced by the SHG crystal plate, to the exclusion of photons of the impulse that went through this SHG crystal blade.
• the spectral detection interval of the matrix image sensor which is used with such a plate of SHG crystal can be limited by a spectral filter which is located on the optical path between this plate and this sensor, so as to suppress a detection of the photons of the pulse which have passed through the SHG crystal plate.
• Such second embodiments are particularly suitable for characterizing pulses which have nominal wavelength values close to 0.8 ⁇ m. Indeed, for such nominal wavelength values, there is currently no matrix image sensor that is able to operate solely by the two-photon absorption mechanism.
• a second aspect of the invention provides a method for characterizing an electromagnetic radiation pulse by time-resolved optical windowing, which is performed using a system according to the first aspect above.
• the pulse to be characterized has a spectrum such that all the wavelength values which correspond to non-zero or substantially non-zero spectral amplitudes are outside a spectral detection interval of the sensor d 'matrix images, and such that results of divisions by two of these wavelength values of the spectrum of the pulse which correspond to non-zero or substantially non-zero spectral amplitudes, are inside the detection spectral interval of the matrix image sensor.
• the detection spectral range of the matrix image sensor can directly be its sensitivity spectral range.
• the spectral range of sensitivity of the matrix image sensor must exclude all the wavelength values of the spectrum of the pulse which correspond to non-zero or substantially non-zero spectral amplitudes, and contain the results of the divisions by two of these wavelength values of the spectrum of the pulse which correspond to non-zero or substantially non-zero spectral amplitudes.
• the matrix image sensor which is used in the system of the invention may be of a silicon-based type, in which case its spectral range of sensitivity extends from approximately 400 nm (nanometer) to 1200 nm, in wavelength values.
• the matrix image sensor may be of an indium-galium-arsenic (InGaAs) alloy-based type, and in this case all the wavelength values of the spectrum from the pulse to characterize which correspond to non-zero spectral amplitudes must be between 1700 nm and 3400 nm.
• InGaAs indium-galium-arsenic
• the spectral range of detection results from the combination of the spectral range of sensitivity of the image sensor matrix with a spectral transmission window of the filter.
• FIG. 1a is a perspective view of an interference forming device which can be used in a system according to the invention
• FIG. 1 b includes a plan view and sections of the interference formation device of [Fig. 1a];
• FIG. 1c corresponds to [Fig. 1a] for an alternative embodiment of the invention
• FIG. 2 is a block diagram of a first embodiment of a system according to the invention.
• FIG. 3 shows steps executed by a processing unit of a system conforming to [Fig. 2];
• FIG. 4 is a diagram that illustrates a characterization result of an electromagnetic radiation pulse, as provided by the system of [Fig. 2];
• FIG. 5 corresponds to [Fig. 2] for a second embodiment of a system according to the invention. Detailed description of the invention
• an interference forming device 1 comprises a portion of a homogeneous, transparent and refractive material for the nominal wavelength of an electromagnetic radiation pulse to be characterized. So designates an optical input face of this portion, which is flat, and Si, S2, S3 and S4 designate its four optical output faces which have identical shapes and are each also flat. The four exit faces S1-S4 are located on a side of the portion of refracting material which is opposite to that of the entrance face So.
• each exit face S1-S4 is inclined with respect to the entrance face So so that the device 1 divides the beam of the initial radiation Ro into four beam parts which emerge from the portion of refracting material a -to-one by each of the output faces S1-S4, with respective propagation directions which approach the optical axis AA.
• a lateral surface SL of the portion of refracting material which constitutes the interference forming device 1, between the input face So on the one hand and the output faces S1-S4 on the other hand, can have a selected shape to increase a cross-sectional area of the interference volume V.
• the angle between the respective bisectors originating from the vertex P of two of the exit faces S1-S4 which are opposite with respect to the optical axis AA is denoted a, and can be about 160° (degree).
• the reference 10 generally designates a system for characterizing pulses of electromagnetic radiation by time-resolved optical windowing which is in accordance with the invention.
• the system 10 comprises the interference forming device 1, an input optical path 2, a matrix image sensor 3 and a processing unit 4.
• the plan of [Fig. 2] contains the bisectors of two of the output faces of device 1 which are opposite with respect to the optical axis A-A, for example the respective bisectors of the output faces S2 and S4.
• the reference I designates the pulse to be characterized. It can be produced by a source 11 of ultrashort laser pulses, also called femtosecond laser and denoted FS-LASER, for example with a nominal wavelength ⁇ o which is close to the value 1550 nm.
• the input optical path 2 can be designed to adapt a beam section size of the pulse I in accordance with the size of the input face So of the interference forming device 1 . It may include input optics, for example based on a combination of several spherical mirrors and/or lenses.
• the input optical path 2 is preferably designed so that the pulse I is incident on the input face So parallel to the axis AA, and in a way that is centered on this axis. Thus, the pulse I constitutes the initial radiation Ro for the interference forming device 1 .
• the interference volume V begins at the common vertex P of the output faces S1-S4, is symmetrical with respect to the axis AA, and has a section perpendicular to the axis AA which is larger and larger until 'to a plane of maximum section, denoted SM.
• the matrix image sensor 3 has for example 600 ⁇ 600 photosensitive elements. It is arranged in the interference volume V, perpendicular to the axis AA, preferably close to the plane of maximum section SM. It is oriented so that its directions of rows and columns of photosensitive elements, denoted x and y respectively, are parallel one-to-one to the lateral sides of the interference volume V.
• the angle a of the forming device d interference 1 is salient, being sufficiently close to 180° for the interference fringes which are produced in the volume V to be resolved by the matrix image sensor 3.
• a pitch p of the photosensitive elements of this sensor d raster images determines a lower limit for the angle a.
• the angle 0 r introduced above must satisfy the inequality: where ⁇ o is again the nominal wavelength of the pulse I.
• the pitch p of the photosensitive elements can be equal to 1.6 ⁇ m when the nominal wavelength ⁇ o is equal to approximately 1550 nm.
• the matrix image sensor 3 is selected or implemented not to be sensitive to the nominal wavelength value ⁇ o of the pulse I, but sensitive in a spectral interval which contains the value half of this nominal wavelength value ⁇ o, that is to say ⁇ o/2, by extending sufficiently on either side of ⁇ o/2.
• the matrix image sensor 3 can be of the silicon-based type. Under these conditions, the matrix image sensor 3 is sensitive to two-photon absorptions which are generated by the pulse I and occur in its photosensitive elements, and the number of occurrences of which depends on the place where each element is located. photosensitive inside the interference volume V.
• the detection signal which is delivered by each element photosensitive matrix image sensor 3 is: where Etot is the electric field generated by pulse I at a point in the interference volume V and at time t.
• Etot is the electric field generated by pulse I at a point in the interference volume V and at time t.
• the electric field Etot is given by: + complex conjugate.
• T 1 and T 2 are the delays which result from displacements in the two directions x and y with respect to the wave taken as the phase shift reference
• ⁇ o is the nominal pulsation of the pulse I, equal to 2TT-C/ ⁇ 0 where C is the propagation speed of the radiation in the air.
• A(t) is the complex amplitude of the electric field of pulse I at time t, so that the instantaneous electric field of pulse I is:
• the delays ⁇ 1 and ⁇ 2 have the following expressions as a function of displacements in the two directions x and y:
• the detection signals S(T 1 ,T 2 ) which are then delivered by the photosensitive elements of the matrix image sensor 3 comprise twenty-five terms which can each be identified by two relative integer values n and m , where n is -2, -1, 0, +1 or +2 and m is independently also -2, -1, 0, +1 or +2.
• the term of the couple (n, m) is proportional to exp[-i(n-wo-T 1 + m.w0.T2)], where exp[.] denotes the exponential function.
• the processing unit 4 is denoted CPU in [Fig. 2], it is connected to receive as input the detection signals S(T 1 ,T 2 ) which are delivered by the photosensitive elements of the matrix image sensor 3, and to supply as output a characterization of the shape of the pulse I, as complex values of A(t).
• the steps which are executed by the processing unit 4 are now described with reference to [FIG. 3].
• the processing unit 4 digitizes the detection signals S( ⁇ 1 , ⁇ 2 ) at the step denoted NUM. It then calculates a two-dimensional Fourier transformation with respect to the two variables ⁇ 1 and ⁇ 2 , in the next step denoted FOURIER.
• a function with two variables TF(S)( ⁇ ) I , ⁇ 2 ) is thus obtained, where ⁇ 1 is the variable conjugate with ⁇ 1 , ⁇ 2 is the variable conjugate with ⁇ 2 , and TF(S) designates the transform two-dimensional Fourier structure of the signals S( ⁇ 1 , ⁇ 2 ).
• the function TF(S)( ⁇ ) I , ⁇ 2 ) consists of twenty-five peaks which correspond to the twenty-five terms indicated above for the function S( ⁇ 1 , ⁇ 2 ).
• An adaptive filtering is then applied to one of these peaks, in the step denoted FILT., to isolate at least one of the components, corresponding to a value of n and to a value of m.
• This filtering window width in the plane of the pulsation values ⁇ , ⁇ 2 is adapted to remain sufficiently far from the other peaks.
• a filtered function derived from TF(S)( ⁇ ) I , ⁇ 2 ) is then constructed, keeping in the filtering window the values of TF(S)( ⁇ ) I , ⁇ 2 ) without modifying them, and completing by null values outside the filter window.
• an inverse two-dimensional Fourier transform is applied to the filtered function TF(S)( ⁇ ) I , ⁇ 2 ).
• the filtering method which has just been described is commonly called adaptive filtering by those skilled in the art. It provides a sampling of the values of the function F2,1( ⁇ 1 , ⁇ 2)
• the inventors used an algorithm which is commonly called an evolution algorithm or a genetic algorithm.
• Such an evolution algorithm implements mechanisms which are inspired by natural selection to optimize a set of values, in order to reproduce a target.
• the purpose of the algorithm is to determine the instantaneous amplitude values A(t), in modulus denoted Mod[A(t)] and in phase denoted ⁇ (t), which make it possible to best reproduce the values of F 2.1 (T 1 ,T 2 ) supplied by step FILT., which constitute the target.
• the algorithm can determine the amplitude A( ⁇ ) of the spectral components of the function A(t), by their modulus Mod[A( ⁇ )] and their phase ⁇ ( ⁇ ).
• TF(S)( ⁇ 1 , ⁇ 2 ) which were obtained during the FILT step.
• Starting values are adopted for Mod[A( ⁇ )] and ⁇ ( ⁇ ), for a set of sample values of the pulse ⁇ . These starting values determine a starting shape for the I pulse, from which an estimate of TF(F2.I)( ⁇ 1 , ⁇ 2 ) is calculated, where TF(F2.I)( ⁇ 1 , ⁇ 2 ) is the two-dimensional Fourier transform of F2, 1(11, 12) deduced from the expression given above for the latter.
• the evolution algorithm starts with a set of individuals who are randomly selected, and who constitute an initial population.
• the function TF(F2,I)( ⁇ 1 , ⁇ 2 ) is calculated for each individual of the initial population, and the result obtained for each individual is compared to TF(S)( ⁇ 1 , ⁇ 2 ) filtered such that obtained at the end of the FILT step. from the detection signals S(T 1 ,T 2 ).
• a score is then assigned to each individual, which quantifies the level of coincidence between its evaluation for the function TF(F2,I)( ⁇ 1 , ⁇ 2 ) and the values of TF(S)( ⁇ 1 , ⁇ 2 ) filtered .
• This coincidence is sought between the two functions TF(F2,1) and TF(S) filtered when the two variables ⁇ i and ⁇ 2 vary independently of each other.
• Individuals with the lowest scores are eliminated, and those with the highest scores are selected to become parents of a new generation of individuals.
• the genes of each individual of the new generation are obtained by mixing those of two selected parents, and by introducing random mutations of one or more of the genes.
• the comparison of the individuals with the filtered values of TF(S)( ⁇ 1 , ⁇ 2 ) deduced from the detection signals is then repeated with the individuals of the new generation, and the whole process is repeated recurrently for each successive generation. . These repetitions are chained in this way until convergence is obtained, ie a situation is obtained where the individuals from one generation to the next no longer or almost no longer improve the coincidence scores.
• the individual with the best score constitutes the result for the form of the pulse I.
• the diagram of [Fig. 4] shows the result which was thus obtained from the component F2,I -
• the horizontal axis of the diagram identifies the time, denoted t and expressed in femtoseconds (fs).
• the vertical axis on the left of the diagram identifies the values of ⁇ (t), expressed in radians, and the vertical axis on the right of the diagram identifies the values of Mod 2 [A(t)] expressed in arbitrary units (au).
• the pulse I which has been characterized therefore has a duration of about 40 fs.
• This component F2,o is the following, according to the expressions of
• the component F2,o is not zero outside the interference volume V.
• Component F2.2 has the expression: so what :
• FIG. 5 illustrates another embodiment of the invention, for which the two-photon mechanism is produced independently of the matrix image sensor, that is to say produced outside of this sensor.
• the matrix image sensor is replaced inside the interference volume V by an SHG crystal plate which is designated by the reference 5.
• a relay optic 6 is used to image this SHG crystal plate 5 on the matrix image sensor 3. This can be a single convergent lens, but any other imaging optical device can also be used.
• the value of the magnification of the relay optics 6 is known, or it can be determined by a standard calibration procedure in the technical field of imaging.
• the interference forming device 1 divides the radiation of the pulse I into four oblique beams which converge towards the optical axis AA, with respective directions of propagation which are transformed between them by successive rotations of 90° (degree) around the optical axis AA.
• the SHG crystal plate 5 transforms these four beams which have as wavelength value that of the pulse I, into nine beams which have wavelength values substantially equal to half that of the pulse I.
• the other eight beams propagate obliquely to the optical axis AA having respective wave vectors that point to the vertices and midpoints of the sides of a square in reciprocal three-dimensional space, and being spatially distributed around the beam Fo.
• a diaphragm 7 is placed between the SHG crystal plate 5 and the matrix image sensor 3, for example just before the relay optics 6, to allow only the beam Fo to pass in the direction of the matrix image sensor 3, by blocking the oblique beams F 1-8 .
• the filter 8 can be placed between the relay optics 6 and the sensor 3.
• the filter 8 is selected to let through radiation whose length value wavelength is substantially equal to half of the nominal wavelength of pulse I, being opaque for this value of nominal wavelength of pulse I.
• the spectral range of sensitivity of the image sensor matrix 3 excludes the nominal wavelength value of pulse I by containing its half value, filter 8 is not necessary. Under these conditions, and using the notations already used, the detection signal which is delivered by each photosensitive element of the matrix image sensor 3 is:
• the function S(T 1 ,T 2 ) would have the same twenty-five terms as in the embodiment of the invention represented in [FIG. 2], and it is the optical filtering which is produced by the diaphragm 7, in the form of an adaptive spatial filtering, which reduces this function S(T 1 ,T 2 ) to the single term ⁇
• the interference forming device 1 may be different from that of [Fig. 1a] and [Fig. 1b].
• [Fig. 1c] shows another four-wave interference-forming device, which comprises two biprisms arranged one behind the other on the propagation path of the initial radiation Ro, intended to be constituted by the pulse I to be characterized.
• the references 1a and 1b which are indicated in [Fig. 1c] designate these two biprisms, respectively.
• the respective edges of the two biprisms 1a and 1b are preferably mutually perpendicular in projection in a plane which is perpendicular to the axis AA;
• a filtered component of the interference pattern other than F2,I and F2,o, or a combination of several filtered components of the interference pattern, other than TFI (F2,O) - 2-Mod[ TFi(F2.2)] can be used to deduce the shape of the pulse I to be characterized.
• components F1,2 and F0,2 can be used instead of F2,I and F2,O by permuting the roles of T 1 and T 2 in the equations and by calculating a one-dimensional Fourier transformation not on the first variable but on the second;

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