Classifications

• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B21/00—Microscopes
  • G02B21/06—Means for illuminating specimens
  • G02B21/08—Condensers
  • G02B21/14—Condensers affording illumination for phase-contrast observation

Definitions

• the present invention relates to a quantitative phase imaging device, in particular for the characterization of nano-objects.
• Prior technique When a transparent or semi-transparent object is observed in conventional transmission microscopy, that is to say in a bright field, the contrast observed in the image is generally low. This complicates the study of the object, particularly when the size of the object is less than a micrometer.
• Phase contrast microscopy developed by Frederik Zernike is an imaging method consisting of exploiting the phase changes of a light wave passing through an object to be imaged.
• a disadvantage of the phase contrast microscope is the halo it introduces into the image around the objects observed.
• Phase contrast microscopy is based on measuring the intensity of the light wave, and on the hypothesis that part of the phase information is transmitted in the intensity by interference phenomena. Thus, it has the major disadvantage of not quantifying the phase of the wave, and does not make it possible to isolate the intensity contribution from the phase contribution. However, as described below, the precise measurement of the phase is particularly important in numerous applications, in particular for the study of microorganisms or the characterization of nanoparticles.
• Quantitative phase microscopy is another imaging method based on the analysis of the wavefront of light that illuminates and interacts with the object to be imaged. It measures the optical phase, or a proportional quantity of this wave. In most cases, it simultaneously measures light intensity.
• Quantitative phase microscopy generates contrasts superior to those obtained in conventional microscopy for transparent or semi-transparent objects, and thus makes it possible to study smaller objects in detail than with conventional microscopy.
• the quantitative measurement of the phase makes it possible in particular to access the measurement of density or mass of an observed object.
• phase microscopy techniques based on the measurement of interference between a reference wave and a wave having interacted with the object to be imaged, such as holography
• self-referenced techniques can be implemented using a wavefront analyzer imaging the object.
• the wavefront analyzer can be based on the use of an optical mask, for example a matrix of holes of the Hartmann type, a matrix of microlenses of the Shack-Hartmann type, a grating, a mask of Modified Hartmann, a diffuser, or meta-surface, upstream of a camera.
• Quantitative phase microscopy has many applications, particularly in biology to image weakly diffusing subcellular components while obtaining characteristic biophysical values. But observation at the molecular scale is complex, if not impossible, due to the weak light-matter interaction of semi-transparent nano-objects. Quantitative phase microscopy also makes it possible to detect and characterize nanoparticles or to monitor chemical reactions. The detection limit of objects or material flows depends directly on the phase sensitivity of the method used. Quantitative phase microscopy also makes it possible to map variations in the refractive index resulting from thermal disturbance. It thus makes it possible to map a temperature distribution with micrometric spatial precision.
• phase sensitivity would then make it possible to increase the temperature sensitivity. This would also make it possible to map with greater sensitivity changes in the refractive index resulting from electrical, acoustic or magnetic disturbance.
• quantitative phase microscopy makes it possible to measure the profile of a surface, with variations in thickness inducing a local variation in the measured phase shift. Good phase sensitivity is crucial for quantifying sub-nanometric thickness variations.
• a defect common to known quantitative phase microscopy techniques is the fact that the amplitude of the field scattered by the object(s) to be imaged is very low compared to the amplitude of the incident field.
• the invention proposes a quantitative phase imaging device comprising: - an optical imaging system for imaging an object in an image plane, - a light source for emitting light radiation on at least part of the plane of Fourier of the imaging optical system, - an optical spatial filter extending in the Fourier plane of the imaging optical system and comprising a zone of less attenuation of the light radiation and a zone of greater attenuation of the light radiation, - a front sensor wave for measuring, in the image plane, the intensity and phase of the electromagnetic field associated with the light radiation emitted by the light source and which has passed through the imaging optical system and the optical spatial filter, and of which at least part has interacted with the object, in order to quantify the phase induced by the object, the light source, the optical imaging system and the optical spatial filter being arranged so that in the absence of the object to be imaged, the light radiation is focused on the zone of greatest attenuation.
• the “Fourier plane” of the imaging optical system is the plane in which the Fraunhofer diffraction pattern, that is to say the Fourier transform of the object studied, can be observed.
• the user of the device can visualize, in the Fourier plane, the spatial frequencies of the object studied.
• the imaging optical system is telecentric, that is to say that its entrance pupil or its exit pupil is at infinity, and the Fourier plane is coincident with a pupil plane of the imaging optical system.
• a “pupillary plane” of the imaging optical system is a plane in which the pupil of the optical system, or an image of it by a part of the optical system, is observed.
• the incident light radiation coming from the light source and not diffracted and/or not scattered by the object is focused on the zone of greatest attenuation of the spatial filter, while the light radiation diffracted and/or scattered by the object is localized at least in part on the zone of least attenuation.
• the optical spatial filter specifically attenuates the intensity of the incident light radiation not diffracted and/or scattered by the object, while keeping the intensity of the radiation diffracted and/or scattered by the object virtually unchanged outside the zone. greater attenuation.
• the invention makes it possible to attenuate the contribution of the incident electromagnetic field associated with the incident light radiation emitted by the light source and not diffracted and/or scattered by the object to the electromagnetic field detected by the wavefront sensor, which amplifies the phase signal. From the measurement of the phase and the intensity, and taking into account the complex transmittance of the zones of greatest and least attenuation, an analytical model or numerical processing makes it possible to determine the quantified value of the phase which would be measured in the absence of the optical spatial filter, with an increased signal-to-noise ratio. It is thus possible to calculate relevant quantitative quantities, such as the dry mass of the object, the index value of the object, or the thickness of the object, from this quantified value of the phase.
• Wavefront sensor measures at least one variation, in particular a gradient, of the phase of the light radiation having passed through the object, the imaging optical system and the optical spatial filter, or a characteristic quantity of said phase such as the difference in optical path traveled by two light rays.
• the phase induced by the object can be determined from the characteristic quantity, by integration of the measured gradient.
• the wavefront sensor further measures the intensity of said radiation.
• the wavefront sensor preferably comprises a detector of light radiation, for example a camera, and in particular comprises a two-dimensional sensor making it possible to sample the intensity.
• the wavefront sensor comprises a wavefront analysis mask placed in front of the detector along the optical path of the light radiation, in order to determine the spatial distribution of the gradient of the phase of the light radiation or a signal proportional to said phase.
• the wavefront analysis mask can in particular simultaneously measure the phase and the intensity of the detected light radiation.
• the wavefront analysis mask preferably comprises a diffractive, periodic or aperiodic optical element, and/or a refractive optical element.
• the wavefront analysis mask can be placed close to the detector or close to a plane conjugate to the plane in which the detector extends.
• the wavefront analysis mask can be chosen in particular from a mask comprising an array of microlenses, for example a Shack-Hartmann mask, a modified Hartmann mask, for example as described by P. Bon et al. In “Quadriwave lateral shearing interferometry for quantitative phase microscopy of living cells”, Opt. Express, 17, 13080-13094 (2009), and a thin diffuser, for example as described by P. Berto, H. Rigneault and M. Guillon in “Wavefront sensing with a thin diffuser”, Opt. Lett. 42, 5117-5120 (2017).
• the light radiation detector preferably comprises a digital camera for acquiring the light radiation which, preferably, has interacted with the wavefront analysis mask.
• the digital camera may include a light sensor, for example CMOS or CCD, to acquire the light radiation and which measures the intensity of said light radiation.
• a light sensor for example CMOS or CCD
• Optical spatial filter The zone of greatest attenuation and, optionally, the zone of least attenuation, are adapted to attenuate the intensity of the light radiation. Preferably, the zone of least attenuation does not attenuate the intensity of the light radiation, in order to maintain maximum light intensity for the measurement.
• the zone of greatest attenuation induces a greater attenuation of the intensity of the light radiation than the zone of less attenuation.
• the zone of greater attenuation and/or the zone of less attenuation can induce a phase shift between the light radiation which is incident on said zones respectively and the light radiation attenuated by said zones so as to amplify the signal-to-noise ratio of the phase signals and intensity measured
• the optical spatial filter is adapted to reflect the light radiation, the zone of greatest attenuation being semi-reflective.
• the area of least attenuation may be semi-reflective or, preferably, reflective.
• the zones of less attenuation and greater attenuation can have different thicknesses, in order to induce different phase shifts in the light radiation that they attenuate.
• the spatial filter is adapted to transmit the light radiation, the zone of greatest attenuation being semi-transparent.
• the area of least attenuation may be semi-transparent or, preferably, transparent.
• the optical spatial filter may comprise a transparent support and a semi-opaque coating partially covering the support, the area of greatest attenuation being defined by the superposition of the support and the semi-opaque coating.
• the transparent support may be made of glass.
• the semi-opaque coating may have the shape of at least one disk of radius r fs , preferably less than 0.1*r p , r p being the maximum radius of the disk within which the collected spatial frequencies are distributed in the Fourier plane. For example, rfs ⁇ 100 ⁇ m.
• the Fourier plane is confused with a pupil plane.
• r p then represents the radius of the image of the aperture pupil of the imaging optical system in the Fourier plane.
• the semi-opaque coating is shaped like a ring. It can present any shape corresponding to the angular spectrum of illumination.
• the semi-opaque coating may be centered on the optical axis of the optical spatial filter.
• the semi-opaque coating may have a thickness of less than 100 nm.
• the semi-opaque coating may comprise a semi-opaque layer of a metal chosen from gold, silver, aluminum, chrome, titanium, and their alloys, for example gold.
• the semi-opaque coating may include an adhesion layer sandwiched between and in contact with the support and the semi-opaque layer, for example made of chrome and/or titanium.
• the zone of greatest attenuation may present a variable complex transmittance, in particular as a function of the polarization of the light radiation and/or the temperature of said zone, and/or modifiable by the user.
• the zone of greatest attenuation may include a thermochromic material, the transmission of which may vary as a function of the temperature, and/or a polarizing material, the transmission of which may vary as a function of the polarization of the light radiation.
• the thermochromic material can be chosen from thermochromic liquid crystals, thermochromic leuco-dyes, thermochromic oxides, optionally doped, and their mixtures, for example being chosen from the group formed by VO 2 , BiVO 4 , NbO 2 and their mixtures.
• the zone of greatest attenuation and/or the zone of least attenuation may comprise at least one layer of a material capable of inducing a phase shift between the radiation incident on said zones respectively, and the radiation attenuated by said zones.
• they include a layer comprising a polymer, a glass, or titanium dioxide. They may include a stack of layers made of at least two different materials, for example a stack of a layer of titanium dioxide, a layer of silicon dioxide and another layer of titanium dioxide, or a layer of titanium dioxide. metasurface.
• the zone of greatest attenuation and/or the zone of least attenuation may comprise a layer of a birefringent material which induces a phase shift between the radiation incident on said zones respectively and the radiation attenuated by said zones, adjustable by rotation of the direction of polarization of the light source.
• the zone of greatest attenuation and/or the zone of least attenuation may comprise a layer of a material having a non-zero thermo-optical coefficient, which induces a phase shift varying as a function of the temperature, in particular a liquid, for example glycerol , or a polymer, for example polydimethylsiloxane.
• the device may include a thermal regulation module to modify the temperature of the zone of greatest attenuation and/or of the zone of least attenuation in order to modify the transmission of said zones and/or the phase shift induced by said zones.
• the thermal regulation module may include an optical, electric or magnetic heating member, for example by the Joule effect.
• the optical heating of said layer modifies the refractive index of the layer, which results in a variation in the optical phase shift induced by the zone of greater attenuation between the radiation incident on said zone and the radiation attenuated by said zone.
• the heating can be induced electrically by a resistive wire, in particular an indium tin oxide (ITO) wire.
• ITO indium tin oxide
• the optical spatial filter may include a spatial light modulator, known by the abbreviation SLM (Space Light Modulator), or a phased optical network, in particular in order to modulate the complex transmittance.
• the spatial light modulator may optionally be coupled to an opaque mask in order to attenuate some of the radiation diffracted and/scattered by the object.
• the spatial filter may include several zones of greater attenuation of light radiation which are separated from each other.
• the device may include several optical spatial filters.
• the optical spatial filters can be arranged one after the other along the propagation path of the light radiation.
• the optical spatial filters may be removable, the addition or removal of at least one of the optical spatial filters modifying the equivalent complex transmittance of all of said spatial filters.
• the optical imaging system can combine an object plane with the image plane, the object being for example located outside the object plane but close to it.
• the device makes it possible to digitally refocus an object located outside the object plane.
• the optical system may include a lens.
• the optical system preferably comprises one or even several additional lenses, in particular converging lenses, and/or one or even several mirrors.
• the optical system is preferably stigmatic or substantially stigmatic.
• the optical system is preferably aplanatic.
• the object NAobject numerical aperture of the optical system is preferably between 0.12 and 1.7 to maximize the light radiation diffracted and/or scattered by the object which will be detected by the wavefront sensor.
• Light source preferably comprises a light generator for generating the light radiation, for example chosen from a lamp, in particular a halogen lamp, and an intense laser, in particular a super-continuum laser.
• the light radiation emitted by the light source has an angular spectrum which can be shaped by an additional optical system upstream of the object to be imaged in order to distribute the energy of the incident light radiation over the area of greatest attenuation.
• the zone of greatest attenuation has the shape of a disk centered on the optical axis and the light source may include an additional optical system to generate Köhler illumination.
• the additional optical system can be arranged between the light generator and the object, in the direction of propagation of the light radiation, in particular in order to collimate the light radiation incident on the object.
• the light source can be configured to emit monochromatic or polychromatic radiation.
• ⁇ nominal HW ⁇ correspond to the phase shift and the phase shift variation induced by the optical spatial filter for ⁇ ⁇ and on the spectral range ⁇ respectively.
• the spectral extent of the light radiation is preferably fixed by the way of generating the phase shift induced by the optical spatial filter. For a phase shift induced by the optical spatial filter generated by refractive effect, 1 ⁇ ⁇ 50%.
• the radiation can be visible, X-ray or infrared radiation.
• the light radiation emitted by the light source can be polarized.
• the light source may include a filter for selecting at least one wavelength of the light radiation emitted by the light generator and/or a filter for polarizing said light radiation.
• the selection filter and/or the polarization filter can be arranged, along the path of the light radiation, between the light generator and the object to be imaged.
• the device may include an additional digital camera, in particular for measuring the intensity of the light radiation in the Fourier plane of the optical imaging system.
• the additional digital camera makes it possible in particular to image the Fourier plane in order to precisely position the optical spatial filter in this plane.
• the device may include a microscope having an objective, the optical spatial filter being distant or not from the microscope.
• the microscope may include the light source, in particular the microscope may itself emit Köhler illumination.
• the microscope may include a sample holder.
• the microscope may include other elements of the optical system, including one or more lenses and/or one or more mirrors.
• the device may comprise one or more additional optical elements, for example chosen from a lens, in particular a converging lens, a reflecting mirror, a semi-reflecting mirror, a dichroic mirror, and wavelength filters.
• a lens in particular a converging lens, a reflecting mirror, a semi-reflecting mirror, a dichroic mirror, and wavelength filters.
• the invention also relates to a method of acquiring at least one digital image of a sample comprising an object by means of the device according to the invention, the method comprising: a) the emission with the light source of incident light radiation directed onto the object, b) detection by the wavefront sensor of the total light radiation having interacted with the object, transmitted by the imaging optical system and the optical spatial filter, and c) processing the signal detected in step b) to quantify a quantity chosen from the phase of the radiation and/or a variation of the phase of the radiation, and optionally to generate a digital image of said quantity.
• the processing in step c) further comprises the quantification of the intensity of the light radiation and preferably the generation of a digital image of the intensity of the light radiation.
• the processing in step c) is quantitative, ie it includes the correction of the signal detected in step b) by taking into account the effect of the phase shift and attenuation induced by the optical filter on the value of the quantity .
• the sample may include one or even several objects whose size is less than the resolution of the optical imaging system.
• the resolution of the imaging optical system is defined by R, where ⁇ is the wavelength of the radiation luminous and ⁇ ⁇ is the object numerical aperture of the imaging optical system.
• the object can be transparent or semi-transparent to light radiation. Alternatively, the object may be opaque to said radiation.
• the sample can be chosen from a biological material comprising a microorganism, a powder, a biological culture solution, a group of cells or micro-tissues, an inert material comprising a nanoparticle or a solution of mixture of particles.
• the microorganism can be a bacteria, a vesicle or a virus.
• the light radiation may have a wavelength spectrum as described above.
• the invention finally relates to the use of the device for the study of one or more nanoparticles, or for the analysis of a chemical reaction or an electrochemical reaction, or of a photografting or photopolymerization reaction, or for the mapping of a temperature distribution or the specific detection of molecules via their absorption in a pump-probe regime.
• Figure 1A represents, schematically and partially, an example of a device according to the invention
• Figure 1B represents, schematically and partially, an example of a wavefront sensor
• Figures 2A and 2B illustrate in a schematic manner schematically the spatial distributions of the incident and diffused fields in the Fourier plane, for the device according to the invention, respectively without and with the presence of the spatial filter
• the figures 2C, 2D and 2E show the complex representations of the incident, diffused and total fields, in the case of Figure 2A for Figure 2C and in the case of Figure 2B for Figures 2D and 2E
• - Figures 3A, 3B and 3C represent results of digital simulations of phase images
• Figures 3D, 3E and 3F represent digital simulations of intensity images of a spherical object, respectively without filtering (3A and 3D), with filtering
• FIG. 1A illustrates an example of a quantitative phase imaging device 1 according to the invention.
• the device comprises a light source 2, a telecentric imaging optical system 3, an optical spatial filter 4 and a wavefront sensor 5.
• Part of the optical system 3 is housed in a microscope 9.
• This part of the optical system 3 comprises an objective 31, a mirror 32 and a tube lens 33.
• the microscope 9 also includes a sample holder 10 arranged in the object focal plane A of the optical system 3.
• the user of the device 1 places a sample 14 comprising the object on the sample holder 10.
• the light source 2 comprises a light generator 21 and can include, between the light generator 21 and the object focal plane A, an optical system 22 making it possible to create illumination of the type Köhler at the level of the object focal plane A, and therefore at the level of sample 14 if necessary.
• the incident radiation I, coming from the source 2 is thus collimated and at normal incidence in the object focal plane A, on the sample holder 10. A part D of this radiation is then scattered by the sample 14.
• the image focal plane B of the objective 31, corresponding to the Fourier plane of the optical system is inaccessible because located inside the microscope 9.
• the spatial filter 4 can be arranged in a plane conjugated C to the plane of Fourier B, transferred after the tube lens 33 by a converging lens 34 of the imaging optical system 3.
• the conjugate plane C thus corresponds to the Fourier plane of the optical system 3.
• the front sensor of wave 5 may include a digital camera 51 and a wavefront analysis mask 53, for example of the Shack-Hartman type, arranged upstream of the camera 51. Radiation R characterized by its front wave F arrives on the wavefront analysis mask 53 before being detected by the camera 51.
• the wavefront analysis mask 53 can modify the path of the light radiation and the variation of The complex amplitude generated makes it possible to simultaneously measure the phase and intensity of the light radiation.
• the wavefront sensor illustrated in Figure 1B measures the intensity and phase of the total light radiation that it receives.
• the wavefront sensor 5 is preceded, in the example illustrated in Figure 1A, in the direction of propagation of the light radiation, by a converging lens 35 forming part of the optical imaging system 3 and making it possible to image the sample 14 on the digital camera 51.
• the device 1 also includes an additional camera 15 for imaging the Fourier plane C using a pivoting or semi-transparent mirror 16 and an optical system 17 with two lenses.
• the spatial filter 4 can thus be positioned precisely in the Fourier plane C, centered on the optical axis, for example using a translation stage, not shown.
• the optical spatial filter 4 has a zone of greater attenuation 41 and a zone of lower attenuation 42.
• the spatial filter comprises a support 43 having the shape of a transparent plate, for example made of glass, and square shape, covered with a metallic coating 44 having the shape of a disk of radius r fs placed in the center of the plate.
• the zone of least attenuation 42 can be delimited by the portion of the support 43 not covered by the coating 44 and the zone of greatest attenuation is delimited by the superposition of the support 43 and the coating 44.
• Figure 2A schematically illustrates the spatial distributions in the Fourier plane of the incident and scattered electromagnetic fields obtained by the device 1 according to the invention, without the presence of the spatial filter 4.
• the incident electromagnetic field corresponding to the incident radiation I not impacted by the sample is denoted ⁇ ⁇ and the scattered electromagnetic field corresponding to the scattered radiation D is denoted ⁇ ⁇ .
• ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ represent the spatial Fourier transforms of the scattered fields ⁇ ⁇ and ⁇ ⁇ respectively.
• the incident radiation I being collimated at the level of the sample 14, it presents a point distribution at the center of the Fourier plane C, corresponding to the image of the pupil of the optical system 3.
• the sample 14 is smaller than the or the wavelengths of the incident radiation, for example of dimension less than 100 nm, the radiation D is diffused in an almost isotropic manner. It thus presents a homogeneous distribution on the image of the pupil of the optical system 3 in the Fourier plane C.
• the fields ⁇ ⁇ and ⁇ ⁇ can be observed in the Fourier plane C as illustrated schematically in Figure 2A, thanks to the additional camera 15 which images the Fourier plane C.
• the field ⁇ ⁇ fills the Fourier plane C while the field ⁇ ⁇ is here concentrated at a point in the center of the Fourier plane C. More generally, the field ⁇ ⁇ is distributed according to the angular distribution of the light radiation I emitted by the light source 2.
• of the scattered field is small compared to the module of the incident field
• the phase shift ⁇ is low, notably less than 0.05 rad, so that we can use the Taylor expansion in ⁇ , hence the relation (4 ): ⁇ ⁇ ⁇ ⁇ (1 ⁇ ⁇ ) (4)
• the diffused field ⁇ ⁇ can be written, according to relation (5), as the incident field ⁇ ⁇ ⁇ attenuated by ⁇ , and out of phase by approximately ⁇ :
• Figure 2C shows the complex representation of the incident ⁇ , scattered ⁇ and total ⁇ fields obtained with device 1 without spatial filter.
• the radius ⁇ ⁇ of the zone of lower transmittance is preferably at least 5 times lower than the radius ⁇ ⁇ of the image of the pupil of the optical system 3 in the Fourier plane.
• the amplitude t0 of the transmittance is chosen such that
• the total transmitted field ⁇ ⁇ ⁇ carries a new phase shift ⁇ ⁇ > ⁇ with respect to the field ⁇ .
• the phase shift ⁇ induced by the sample 14 can be quantified from the measurement of the intensity and phase of the field ⁇ ⁇ ⁇ .
• relation (10) ⁇ ⁇ and ⁇ are the relative intensities respectively of the total fields ⁇ in the case of a device 1 without spatial filter 4 and after filtering ⁇ ⁇ ⁇ in the case of a device 1 with spatial filter 4.
• the relationships ( 11) and (12) can be formulated: as well as relation (13) from relation (10):
• the wavefront sensor 5 measures a relative intensity, that is to say the ratio between a reference image without sample and an image in the presence of the sample 14.
• Relation (16) can then be formulated from relation (13):
• the sample 14 studied is a polystyrene ball with an optical index equal to 1.62, immersed in water with an optical index equal to 1.33.
• Sample 14 was illuminated by monochromatic light radiation of ORQJXHXU ⁇ G ⁇ RQGH ⁇ ⁇ QP ⁇ / ⁇ REMHFWLI ⁇ 31 used had a numerical aperture 1.4.
• Spatial filtering was simulated on the field ⁇ ⁇ , spatial Fourier transform of the total field ⁇ ⁇ .
• the simulated electromagnetic field included in a disk of radius ⁇ ⁇ , radius of the zone of greatest attenuation 41 of the spatial filter 4 was then multiplied by the complex transmittance ⁇ ⁇ ⁇ ⁇ of the spatial filter 4 to simulate the interaction with said spatial filter 4.
• the field ⁇ ⁇ ⁇ ⁇ was thus simulated, according to the relation (17): with k the image vectors in the pupil, and ⁇ being the numerical aperture of the optical system 3 and ⁇ the wavelength of the light radiation.
• Figure 3B the obtaining of an amplification of the measured phase ⁇ ⁇ , the value of which is up to more than ten times higher than the value of the phase shift ⁇ calculated in the absence of the spatial filter and represented on Figure 3A.
• Figure 3E As for the intensity map in Figure 3E, it corresponds to a partially dark field image, where the light scattered by the object, in the center of the figure, is preponderant compared to the incident light.
• Figure 4A represents the phase amplifications
• the amplification of the phase is all the stronger as the transmission T is weak. This reflects that device 1 operates optimally when the ratio ⁇ ⁇ ⁇ is balanced.
• FIG. 5 modifying the complex transmission of spatial filter 4 leads to relative errors less than 10 ⁇ for phase ( Figure 5A) and 10 ⁇ for intensity (Figure 5B).
• Figure 6 illustrates the effect of the ratio ⁇ ⁇ ⁇ ⁇ of the radius of the spatial filter 4 on the radius of the image of the pupil of the optical system 3 in the Fourier plane C, on the relative phase and intensity errors.
• ⁇ ⁇ 10%
• the errors in phase are less than 1% (figure 6A) and those in intensity less than 10 % (figure 6B).
• this value of the ratio as a limit below which we consider reasonable the hypothesis according to which the presence of the spatial filter 4 does not modify the scattered field ⁇ ⁇ .
• Example 1 The microscope 9 used was a commercial Olympus IX71 microscope, equipped with a microscope objective of x60 magnification and 0.9 numerical aperture (Olympus UPlanFLN). The illumination of sample 14 was ensured using the native Köhler illumination of the microscope 9 (halogen lamp), filtered in wavelength.
• Wavefront sensor 5 was an ID4L analyzer (Quadrilateral Shift Interferometer) composed of an Andor Zyla 5.5 camera and a 2D diffraction grating with a periodicity of 10 ⁇ m, optimized for the wavelength 650 nm . This network was re-imaged on the camera via a x2 magnification telescope, composed of 2 achromatic lenses.
• the phase shift ⁇ 0.5 ⁇ was measured by interferometry.
• FIG 7A an image of the Fourier plane of the experimental device acquired by the additional camera 15.
• the white disk corresponds to the radiation scattered D by a sample formed from a superposition of sheets of paper, over the entire image of the pupil of the optical system 3 in the Fourier plane C, and the black disk in the middle corresponds to the spatial filter 4.
• the comparison of Figures 7B and 7C highlights the effect of the spatial filter 4 on the intensity of the incident radiation I .
• the results obtained in the case without spatial filter 4 and with spatial filter 4, as well as with the quantitative reconstruction, using equation 16 from the filtered images, are presented in Figure 8.
• Figure 8A shows the results obtained without spatial filter 4
• Figure 8B shows the results obtained with spatial filter 4
• Figure 8 C shows the results obtained with spatial filter 4 and following quantitative processing from the measurements.
• the angular spectrum of the incident light radiation I is a disk centered in the Fourier plane C, as can be observed in Figure 10A, the white zone corresponding to the incident light radiation I.
• the zone of greatest attenuation 41 is a disk at the center of the optical spatial filter 4, as shown in Figure 10D, the gray zone corresponding to the zone of greatest attenuation 41.
• the angular spectrum of the incident light radiation I is represented in the plane of Fourier C by several spaced disks, as observable in Figure 10B, the white zones corresponding to the incident light radiation I.
• the zone of greatest attenuation 41 is composed of several disks distributed over the optical spatial filter 4 in the same way as the radiation incident light I in the Fourier plane C, as shown in Figure 10E, the gray zones corresponding to the zone of greatest attenuation 41.
• the angular spectrum of the incident light radiation I is a ring in the plane of Fourier C, as can be observed in Figure 10A, the white zone corresponding to the incident light radiation I.
• the zone of greatest attenuation 41 is a corresponding ring on the optical spatial filter 4, as shown in Figure 10D, the gray zone corresponding to the zone of greatest attenuation 41.
• Example 2 The same sample 14 and the same device as for example 1 have been used, with the exception of the optical spatial filter 4.
• Chamber 48 made it possible, thanks to a focused laser heating system 47, to vary the phase shift induced by the optical spatial filter 4 on the incident field Ei.
• the total phase shift ⁇ total induced by the optical spatial filter 4 on the incident field E i was then the sum of a variable component ⁇ variable and a fixed component ⁇ fixed , as can be observed in Figure 11B, where ⁇ ⁇ , ⁇ ⁇ and ⁇ ⁇ ⁇ are respectively the complex representations of the incident after filtering, diffuse after filtering and total after filtering fields.
• the variable phase shift made it possible to optimize the values of the phase shift ⁇ ⁇ and the intensity

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