A method and system for the measurement of wavefronts

Abstract

In one embodiment, a method of measurement of wavefronts according to the invention, wherein a beam emitted by coherent light source 1 passes through a system that forms it into a widened light beam, which system comprises first microscopic lens 2 and first lens 3, wherein the beam then illuminates analysed object 4 that modifies the wavefront of the light beam, the beam subsequently passes through an array of vortex lenses 5, which divides the beam into smaller fragments and introduces optical vortex beams with topological charges m into each fragment, simultaneously focusing them on detector 6 that analyses the image by recording the distribution of intensity and visualises the focused optical vortex beams with a characteristic point of discontinuity with a zero level of intensity in its centre.

Description

[0001] A method and system for the measurement of wavefronts

[0002] BACKGROUND OF THE INVENTION

[0003] The invention relates to a method and system for the measurement of wavefronts applied in the measurement of optical elements and in the measurement of the coherent quality of light beams in optical systems.

[0004] A wavefront is a surface with a constant phase in a propagating light field. It is also one of the main parameters that define a light wave. Its shape directly defines the characteristics of the beam and the way it propagates. Therefore, when we relate to a wavefront, we define plane waves, spherical waves, or waves that have a more complex shape. Having sufficient information on the wavefront enables one to provide a quantified description of the aberrations that are present in the optical system and are relevant to the calibration of optical systems due to the direct possibility of their optimisation. A wavefront that is shaped by optical elements also carries information about their quality, the precision of their production, and the optimum methodology of forming beams in optical systems. An effective wavefront measurement represents a key metrological aspect.

[0005] Wavefronts are usually measured with very different methods, most frequently using interferometric methods that require a reference beam to create an interference pattern and to recover the wavefront shape by analysing this pattern. These methods, although highly sensitive, generate additional calibration problems and involve the need to work under strictly controlled conditions in order to reduce the systems’ mechanical vibrations, among other things. For this reason, the assessment of the quality of optical elements and the calibration of optical systems in laboratories is performed using systems based on the Shack-Hartmann architecture described in the paper by Platt, B. C., & Shack, R. (2001). History and Principles of Shack-Hartmann Wavefront Sensing. Journal of Refractive Surgery, 17(5), 127-192. The main feature of such systems is their easy implementation and that they can be integrated into most of the commonly used optical systems as detectors that measure the wavefront of the beam at the end of the optical system. The wavefront measurement system used in the Shack-Hartmann architecture is based on a lens array that consists of a number of identical lenses situated at regular intervals, which enable the projection of the analysed wavefront on a detector, usually a camera. The image recorded by the detector contains a network of focused light spots, with each of these spots being focused by an individual lens that is part of the array. The measurement process involves the determination of the distance of movement of each focused beam in the detector plane under the influence of the distorted wavefront, relative to the position of that beam without distortion. This allows the determination of the local radius of the wavefront curvature for each focused beam and subsequently the global shape of the wavefront.

[0006] The Shack Hartmann system and its measurement capabilities directly depend on its effectiveness in identifying a single focused spot. The position of the focused spot is typically established by determining the centre of gravity, with the consideration of the value of intensity in the distribution of intensity of this spot. One of the main challenges for Shack-Hartmann-type systems is the elimination of the scintillation effect which, due to the effect of air fluctuation and the refractive index, leads to disproportions in the intensity of the individual focused spots. This fact significantly affects the ability to locate individual spots, leading in extreme cases to their erroneous location, which translates into poor wavefront reconstruction. Additionally, the role of a detector in a typical Shack-Hartman system is performed by a CCD matrix device, which converts the intensity of incident light into an electrical current. These devices are susceptible to shot noise that can be described by Poisson’s distribution and which occurs in devices with a small number of energycarrying particles. In the case of measuring significant wavefront curvatures, the change of location of a focused spot may be so significant that it prevents its identification, as in extreme cases it may be interpreted as a spot assigned to another lens. It will be therefore impossible to assign a spot to a particular element of the lens array and hence to a particular part of the wavefront. As a result, it will be impossible to correctly reproduce the analysed wavefront.

[0007] The development of devices based on this architecture has led to a number of modifications aimed at increasing the usability of the classic Shack-Hartmann system, or adapting it to specific applications.

[0008] Application WO / 2003 / 051189 discloses a method for the selective control of the transmittance of individual apertures. An additional element - an LCD array - has been added to the system to darken some of the light so that it cannot be detected by the detector. The application presents use of this technology for eye examinations. The selective control of transmittance allows the device user to control the accuracy of measurement by limiting the number of sub-apertures. The authors of the application have indicated that when only the spherical component of the measured wavefront is required, the user can reduce the number of sub-apertures to nine and still get the correct result, at the expense of Zernike polynomials of higher orders. Although the proposed solution can effectively reduce errors associated with the migration of focused spots to neighbouring areas by selectively dimming them out, it needs to be informed on which area is responsible for a given migration. Additionally, this does not reduce the impact of scintillation on the target measurement. According to the presented solution, the user can only reduce the transmittance of light, but cannot enhance it. Therefore poorly lit areas cannot be compensated. Additionally, the problem of existence of shot noise still exists, as the proposed solution uses the same methods of location as typical solutions with the Shack-Hartmann architecture.

[0009] Application US 8705024 discloses a method and device for the positioning of a Shack-Hartmann sensor in a way that minimizes errors generated during the evaluation of a highly curved wavefront. The aim of this arrangement is to place the sensor in a location where the rays focused by the sensor array are as parallel as possible, i.e. so that the lens array is perpendicular to the local wavefront. The above system also divides the wavefront into segments, wherein each segment is evaluated separately. This minimizes the effect of the migration of adjacent focused spots that is typical of highly-curved wavefronts. The proposed solution can be implemented for the alignment of optical systems used for the inspection of semiconductors on a production line. Although this solution effectively eliminates the effects of migration, it nevertheless requires a sophisticated positioning system. Such a system divides the projected wavefront into sections, which requires the performance of several separate measurements and generates the risk of changing measurement conditions between the individual measurements, which can affect the final result. Especially if the system is applied in an industrial setting.

[0010] The authors of paper R. W. Bowman, A. J. Wright, and M. J. Padgett, "An SLM-based Shack- Hartmann wavefront sensor for aberration correction in optical tweezers," J. Opt. 12, (2010) demonstrated the applications of a Shack-Hartmann type system with the use of a spatial light modulator (SLM) in an optical tweezer system. The distribution of intensity that is typical of the Shack-Hartmann architecture is generated numerically and displayed as a hologram on a spatial light modulator, which uses a liquid crystal array to modulate the phase and amplitude of the incident light. The hologram itself contains an array of sub-apertures that all contain dedicated diffraction gratings. The role of the gratings is to control the separation of spots in the plane of the detector, which they are focused on by a single focusing element. The use of a single focusing element in the system further differentiates this solution from other proposed solutions based on the Shack-Hartmann architecture. The use of dynamic digital holography provides a number of advantages such as low chromatic aberration and operation in a wide spectral range that is restricted only by the spectral range of the spatial light modulator. Additionally, this solution allows the user to dynamically change the parameters of the Shack-Hartmann architecture without any system modification. These parameters may include the number and diameter of sub-apertures, which allows the control of sensor accuracy, as well as the separation of focused spots in the detector area, which limits their migration to adjacent areas. The solution also enables the selective control of each sub-aperture, similarly to the previously mentioned solution disclosed in application WO / 2003 / 051189. The solution proposed in paper by (Bowman et al., 2010) has a lower resolution capability than a classic Shack-Hartmann sensor based on refractive elements. It is limited by the effects of diffraction, which restrict the minimum diameter of sub-apertures in the projected hologram. On the other hand, this type of solution is ideal for systems that utilize spatial modulators such as optical tweezers or advanced light field shaping systems. In such systems, the wavefront can be evaluated directly and no external measuring equipment is necessary. It is therefore possible to quickly evaluate the quality of the system and then to correct it based on the obtained results, all without any additional external devices. The methodology of wavefront recovery in a holographic Shack-Hartmann sensor is similar as in analogous refractive sensors and involves the determination of the displacement of the focused spot (in the case of an aberration-affected optical system) relative to its axial position (without aberration), which can be simulated numerically. However, this solution does not solve the problems associated with the occurrence of shot noise, as the process of locating a single spot is similar to the one in the previous solutions. The scintillation effect can also distort the measurement and the proposed solution does not eliminate the occurrence of this effect.

[0011] A paper by M. Szatkowski, E. Burnecka, H. Dyla, J. Masajada titled "Optical vortex tracking algorithm based on the Laguerre-Gaussian transform," Opt. Express 30, 17451-17464 (2022) discloses a method of identifying the location of discontinuities without the use of an interferometric system.

[0012] None of the above-mentioned measurement methods are successful in the effective and comprehensive elimination of problems related to the effects of scintillation, spot migration or shot noise.

[0013] The aim of the invention is to provide a practical method and system for the measurement of wavefronts that are used to measure optical components and to measure the quality of coherent light beams in optical systems, that ensures better replicability of measurements by significantly reducing the effects of scintillation and shot noise.

[0014] The invention relates to a method of wavefront measurement, wherein a wavefront of a beam that is emitted by a coherent light source 1 is shaped into a widened light beam using a system comprising of a first microscopic lens 2 and a first lens 3, wherein the said beam subsequently illuminates the analysed object 4 and then, after passing through the analysed object 4, the wavefront is distorted and, using a lens array 5, divided into a number of smaller fragments that are focused on detector 6 which is used to analyse the intensity image and then to reproduce the shape of the tested wavefront, characterised in that optical vortex beams are introduced via a lens array that constitutes the vortex lens array 5 into the distorted wavefront that has passed through object 4, wherein the said optical vortex beams are characterised by stable phase discontinuity with topological charge integer values m in the range of -20 to 20, wherein the displacement of the individual discontinuities is determined by way of tracking based on the determination of the location of a discontinuity represented by the point of zero intensity in the focused beam, and the measurement of the displacement of the dark point in relation to the location of the dark point with the original settings and without the analysed object.

[0015] The topological charges of the introduced optical vortex beams preferably have the integer value of m=l.

[0016] The optical vortex beams are preferably introduced by means of a vortex lens array 5, which is comprised of a single refractive element 5.1.

[0017] The optical vortex type beams are preferably introduced using a vortex lens array 5 that comprises a set of spiral phase plate arrays 5.2 and lens arrays 5.3 that are arranged coaxially with respect to each other.

[0018] The optical vortex beams are preferably introduced using a vortex lens array 5 that comprises a liquid crystal reflective-type spatial light modulator 5.4 and a single focusing lens 5.5.

[0019] The optical vortex beams are preferably introduced using a vortex lens array 5 that comprises a liquid crystal transmissive-type spatial light modulator 5.4 and a single focusing lens 5.5.

[0020] The optical vortex beams are preferably introduced using a vortex lens array 5 that comprises a liquid crystal spatial light modulator 5.4 that uses a micromirror array for modulation and a single focusing lens 5.5.

[0021] The optical vortex beams are preferably introduced by means of a vortex lens array 5, which is comprised of a single refractive element 5.1 and is made of polymers.

[0022] The optical vortex beams are preferably introduced by means of a vortex lens array 5, which is comprised of a single refractive element 5.1 and is made of liquid crystals.

[0023] The optical vortex beams are preferably introduced by means of a vortex lens array 5, which is comprised of a single refractive element 5.1 and is made of quartz glass.

[0024] The optical vortex beams are preferably introduced by means of a vortex lens array 5, which is comprised of a single refractive element 5.1 and is made of metamaterials.

[0025] The optical vortex type beams are preferably introduced using a vortex lens array (5) that comprises a set of spiral phase plate arrays (5.2) and lens arrays (5.3) that are made of polymers.

[0026] The optical vortex type beams are preferably introduced using a vortex lens array (5) that comprises a set of spiral phase plate arrays (5.2) and lens arrays (5.3) that are made of liquid crystals.

[0027] The optical vortex type beams are preferably introduced using a vortex lens array (5) that comprises a set of spiral phase plate arrays (5.2) and lens arrays (5.3) that are made of quartz glass.

[0028] The optical vortex type beams are preferably introduced using a vortex lens array (5) that comprises a set of spiral phase plate arrays (5.2) and lens arrays (5.3) that are made of metamaterials.

[0029] The analysis of the image and the reproduction of the shape of the analysed object are preferably carried out using detector 6 that constitutes a CCD (Charged Couple Device) camera. The analysis of the image and the reproduction of the shape of the analysed object are preferably carried out using detector 6 that constitutes a CMOS (Complimentary Metal Oxide Semiconductor) camera.

[0030] Light is preferably emitted by light source 1 that constitutes a continuous -wave laser.

[0031] Light is preferably emitted by light source 1 that constitutes a pulsed laser.

[0032] Light is preferably emitted by light source 1 that constitutes a VCSEL (Vertical Cavity Surface Emitting Laser) diode.

[0033] Light is preferably emitted by a light source 1 that constitutes a laser diode.

[0034] The invention relates to a system for the measurement of wavefronts that consists of microscopic lens 2 that is used to focus a beam of light emitted from coherent light source 1 and first lens 3 that widens the beam of light to the size of the analysed object, wherein the beam is directed at analysed object 4 and after passing through it is distorted and illuminates the lens array, whereupon the individual beam fragments are focused on detector 6, characterised in that the lens array comprises vortex lens array 5 that introduces into the system optical vortex beams characterised by stable phase discontinuity with topological charge integer values m in the range of -20 to 20, which focus the individual beam fragments on detector 6 that is used to analyse the intensity image and to reproduce the shape of the tested wavefront.

[0035] The topological charges of the optical vortex beams preferably have the integer value of m=l.

[0036] Vortex lens array 5 preferably comprises a single refractive element 5.1.

[0037] Vortex lens array (5) preferably consists of a set of spiral phase plate arrays (5.2) and lens arrays (5.3) installed on a bracket, in order to ensure the axial linearity of the array.

[0038] Vortex lens array (5) preferably consists of a set of liquid crystals, a reflective-type spatial light modulator (5.4) and a single focusing lens (5.5).

[0039] Vortex lens array (5) preferably consists of a set of liquid crystals, a transmissive-type spatial light modulator (5.4) and a single focusing lens (5.5).

[0040] Vortex lens array (5) preferably consists of a set of liquid crystals, a spatial light modulator (5.4) that uses a micromirror array for modulation and a single focusing lens (5.5). Vortex lens array (5) preferably comprises a single refractive element (5.1) made of polymers.

[0041] Vortex lens array (5) preferably comprises a single refractive element (5.1) made of liquid crystals.

[0042] Vortex lens array (5) preferably comprises a single refractive element (5.1) made of quartz glass.

[0043] Vortex lens array (5) preferably comprises a single refractive element (5.1) made of metamaterials.

[0044] Vortex lens array (5) preferably consists of a set of spiral phase plate arrays (5.2) and lens arrays

[0045] (5.3) made of polymers.

[0046] Vortex lens array (5) preferably consists of a set of spiral phase plate arrays (5.2) and lens arrays

[0047] (5.3) made of liquid crystals.

[0048] Vortex lens array (5) preferably consists of a set of spiral phase plate arrays (5.2) and lens arrays

[0049] (5.3) made of quartz glass.

[0050] Vortex lens array (5) preferably consists of a set of spiral phase plate arrays (5.2) and lens arrays

[0051] (5.3) made of metamaterials.

[0052] Detector 6 preferably comprises a CCD (Charged Couple Device) camera.

[0053] Detector 6 preferably comprises a CMOS (Complimentary Metal Oxide Semiconductor) camera.

[0054] Light is preferably emitted by light source 1 that constitutes a continuous -wave laser.

[0055] Light is preferably emitted by light source 1 that constitutes a pulsed laser.

[0056] Light is preferably emitted by light source 1 that constitutes a VCSEL (Vertical Cavity Surface Emitting Laser) diode.

[0057] Light is preferably emitted by light source 1 that constitutes a laser diode.

[0058] The method and system for the measurement of wavefronts applied in the measurement of optical elements and in the measurement of the coherent quality of light beams in optical systems according to the invention ensures an 80% wider dynamic range of the illuminating beam intensity in comparison to the Shack-Hartmann system, without the need of reducing filters or modifying detector parameters, better replicability of measurements through the reduction of the effects of scintillation as a result of the possibility of locating the position of focused beam fragments at a contrast greater than 0.3, and the reduction of the effects of shot noise and precise location at a noise level that corresponds to Poisson noise of the variance of up to 0.2 of normalised intensity.

[0059] The method and system according to the invention facilitates the determination of the origin of focused spots in an image and introduces localisation methods that are immune to the presence of shot noise.

[0060] The use of a vortex lens array that introduces optical vortex beams in the method and system for the measurement of wavefronts used for the measurement of optical elements and for the measurement of the coherent quality of light beams in optical systems, changes the internal geometry of each fragment of the wavefront. Optical vortex geometry increases the dynamic range of the detector by reducing the intensity of the beam in comparison to the typically used Gaussian beam. The method of locating the focused beam has also changed, as according to the invention it comprises in the tracking the point of discontinuity that appears in the form of a dark area in the distribution of intensity registered by the detector. Tracking is carried out using an algorithm that enables the highly precise location of the point of discontinuity, in low-intensity conditions and without the use of interferometric systems. The reduction in intensity and the need to locate the dark spot reduces the effect of shot noise on the precision of location, which increases the metrological capabilities of the system in difficult conditions. Similarly, the effect of scintillation is significantly reduced, as the process of location is not based on the bright points of intensity, which are significantly affected by scintillation, but only on the dark area. Neither is it based on the determination of the centre of gravity of the dark area, but on the determination of the position of the point of discontinuity on the basis of a pseudo-complex amplitude, which is not affected by the increase in intensity value as a result of the scintillation effect.

[0061] BRIEF DESCRIPTION OF THE DRAWINGS

[0062] The subject of the invention has been explained in more detail using embodiments shown in the Figures, where:

[0063] Figure 1 shows a diagram of a system in which the vortex lens array comprises a single refractive element. Figure 2 shows the structure of a vortex lens array together with the phase-type distribution of a single vortex lens.

[0064] Figure 3 shows the distribution of intensity with the analysed object in place.

[0065] Figure 4 shows the distribution of intensity without the analysed object.

[0066] Figure 5 shows the phase-type distribution of the measured wavefront.

[0067] Figure 6 shows a diagram of a system in which the vortex lens array consists of two independent elements, a spiral phase plate array and a lens array.

[0068] Figure 7 shows the structure of a spiral phase plate array together with the phase-type distribution of a single spiral phase plate.

[0069] Figure 8 shows the structure of a lens array together with the phase-type distribution of a single lens.

[0070] Figure 9 shows a system in which the vortex lens array is provided by means of a hologram projected onto a liquid crystal spatial light modulator and a single focusing lens located behind this modulator.

[0071] Figure 10 shows an example of a hologram that is projected onto a liquid crystal spatial light modulator.

[0072] DETAILED DESCRIPTION AND BEST MODE OF IMPLEMENTATION

[0073] EMBODIMENT 1

[0074] A method of measurement of wavefronts according to the invention, wherein a beam emitted by coherent light source 1 passes through a system that forms it into a widened light beam, which system comprises first microscopic lens 2 and first lens 3, wherein the beam then illuminates analysed object 4 that modifies the wavefront of the light beam, the beam subsequently passes through an array of vortex lenses 5, which divides the beam into smaller fragments and introduces optical vortex beams with topological charges m into each fragment, simultaneously focusing them on detector 6 that analyses the image by recording the distribution of intensity and visualises the focused optical vortex beams with a characteristic point of discontinuity with a zero level of intensity in its centre. The reproduction of the analysed wavefront that carries information on analysed object 4 involves the tracking of the location of individual focused optical vortices by determining the centre of their point of discontinuity, represented by the dark area in the centre of the focused optical vortex, wherein this location is registered with test object 4 installed in position, as shown in Figure 3. The above tracking procedure is performed with reference to analogous locations registered by a system without test object 4 in place, as shown in Figure 4. The displacement of positions of the focused optical vortices is proportional to the local curvature of the wavefronts, wherein the analysed wavefront is reproduced on the basis of the registered displacements. Fig. 5 shows a reproduced wavefront.

[0075] The method according to Embodiment 1 involves the emission of a light beam from coherent light source 1 that constitutes a continuous-wave laser and the application of vortex lens array 5 in the form of a single refractive element 5.1, made of quartz glass, which introduces optical vortex beams of the topological charge of m=1, as well as a CCD camera as detector 6.

[0076] EMBODIMENT 2

[0077] The method of measurement of wavefronts according to Embodiment 1 , wherein optical vortices of the topological charge of m=l are introduced using a vortex lens array 5 that comprises a set of spiral phase plate arrays 5.2 and lens arrays 5.3, made of quartz glass, installed on a bracket that facilitates a sliding movement in the x, y and z directions, which allows the positioning of lens array 5.3 in relation to spiral phase plate arrays 5.2 so as to ensure the axial alignment of these elements. The structure of the spiral phase plate array together with the phase-type distribution of a single spiral phase plate 5.2 is shown in Fig. 7, while the structure of lens array 5.3 together with the phase-type distribution of a single lens is shown in Fig. 8. The diagram is shown in Fig. 6.

[0078] EMBODIMENT 3

[0079] The method of measurement of wavefronts according to Embodiment 1, wherein optical vortices of the topological charge of m=l are introduced using a vortex lens array 5 that comprises a liquid crystal reflective-type spatial light modulator 5.4 and a single focusing lens 5.5. Liquid crystal spatial light modulator 5.4 displays a hologram that includes phase-type distribution, shown as a greyscale image, the values of which correspond to the phase shift introduced by the modulator in each point. This hologram operates similarly to a phase diffraction grating, while the resulting structure generated in the focal plane of lens 5.5 represents the Fourier transform of the phase-type distribution displayed on liquid crystal spatial light modulator 5.4. The Fourier plane image is projected through the second microscopic lens 7 onto detector 6. Atypical hologram displayed on liquid crystal spatial light modulator 5.4 includes a matrix of circular apertures arranged in the form of a hexagon, as shown in Fig. 9. Each aperture includes a combination of two phase-type distributions: a spiral phase-type distribution that generates an optical vortex beam similarly to the spiral phase plate array 5.2, and a phase-type distribution, which generates a blazed diffraction grating that controls the separation of the beams in the Fourier plane once they are focused by the lens 5.3. The spatial frequency of the diffraction grating is variable and is different for each aperture. It is calculated in relation to the frequency of the SB base grid and takes into account the vector that connects the centres of a given aperture and the base aperture located on the perimeter of the hologram. Phase Φkfor the individual apertures is calculated using the following formula:

[0080] Where factor imφ generates an optical vortex of the charge of m=1, while φ defines the angle in polar coordinates. X, Y represent coordinate system matrices expressed in Cartesian coordinates, nxand nydefine the number of diffraction grating grooves per resolution pxand pyof the implemented spatial light modulator, s represents the scale factor, which is equal to 1 by default, but can be used to control the separation of spots in the detector plane, vxand vyare the coordinates of vector that connects the aperture that contains base grating SB with the aperture that the phase-type distribution is calculated for. In the case of the aperture that contains base grating SB, the values of these coordinates are . The diagram is shown in Fig. 9. Fig. 10 shows a typical example of a hologram.

[0081] EMBODIMENT 4

[0082] The method of measurement of wavefronts according to Embodiment 3, wherein the light beam is emitted by a coherent light source 1 comprising a Vertical Cavity Surface Emitting Laser (VCSEL) diode and optical vortices of the topological charge of 20 are introduced using a vortex lens array 5 that comprises a liquid crystal transmissive-type spatial light modulator 5.4 and a single focusing lens 5.5.

[0083] EMBODIMENT 5

[0084] The method of measurement of wavefronts according to Embodiment 3, wherein optical vortices are introduced using a vortex lens array 5 that comprises a liquid crystal spatial light modulator 5.4 that uses a micromirror array for modulation and a single focusing lens 5.5.

[0085] EMBODIMENT 6

[0086] The method of measurement of wavefronts according to Embodiment 1, wherein optical vortex beams are introduced using a vortex lens array 5 that comprises a single refractive element 5.1 made of liquid crystals.

[0087] EMBODIMENT 7

[0088] The method of measurement of wavefronts according to Embodiment 1, wherein optical vortex beams are introduced using a vortex lens array 5 that comprises a single refractive element 5.1 made of metamaterials.

[0089] EMBODIMENT 8

[0090] The method of measurement of wavefronts according to Embodiment 1, wherein the light beam is emitted by a coherent light source 1 that comprises a pulsed laser, optical vortex beams are introduced using a vortex lens array 5 that comprises a single refractive element 5.1 made of polymers, which introduces optical vortex beams of the topological charge of m = -20, and the image is analysed using detector 6 that comprises a CMOS camera.

[0091] EMBODIMENT 9

[0092] The method of measurement of wavefronts according to Embodiment 2, wherein optical vortex beams are introduced using a vortex lens array 5 that comprises a set of spiral phase plate arrays (5.2) and a lens array (5.3) made of polymers.

[0093] EMBODIMENT 10 The method of measurement of wavefronts according to Embodiment 2, wherein optical vortex beams are introduced using a vortex lens array 5 that comprises a set of spiral phase plate arrays (5.2) and a lens array (5.3) made of liquid crystals.

[0094] EMBODIMENT 11

[0095] The method of measurement of wavefronts according to Embodiment 2, wherein optical vortex beams are introduced using a vortex lens array 5 that comprises a set of spiral phase plate arrays (5.2) and a lens array (5.3) made of metamaterials.

[0096] EMBODIMENT 12

[0097] A system for the measurement of wavefronts according to the invention constitutes a coherent light source 1 that emits a light beam. This beam passes through a beam widening system that comprises of a first microscopic lens 2, which focuses the light beam on the primary focus of a first lens 3, which broadens the beam to the size of analysed object 4. Analysed object 4 is located behind the first microscopic lens 2, at a distance of no more than 20 cm. After passing through analysed object 4, the wavefront of the light beam is distorted by this object and therefore provides information about its shape. The light beam then illuminates the vortex lens array 5. Vortex lens array 5 is located behind the analysed object 4, no further than 10 cm away. Vortex lens array 5 divides the analysed wavefront into fragments and introduces an optical vortex geometry of the topological charge of one into each fragment, simultaneously focusing all fragments within a distance of 5 mm on detector 6, which registers the intensity image.

[0098] System parameters:

[0099] - coherent light source 1, which constitutes a continuous- wave laser of the wavelength of 632.8 nm,

[0100] - microscopic lens 2 with a magnifying ratio of 5x and a numerical aperture of 0.10,

[0101] - focal lens 3 f=200mm,

[0102] - vortex lens array 5 with the aperture resolution of 70 x 45 and the single aperture diameter of 150 pm, which constitutes a single refractive element 5.1, made of quartz glass, - detector 6, which constitutes a CCD camera with the pixel size of 4.8x4.8 pm and the resolution of 1920x1200 px.

[0103] EMBODIMENT 13

[0104] The system for the measurement of wavefronts according to Example 12, wherein optical vortex beams are introduced using a vortex lens array 5 that constitutes a set of spiral phase plate arrays 5.2 and lens arrays 5.3 made of quartz glass and installed on a bracket that facilitates a sliding movement in the x, y and z directions, which allows the positioning of the lens array 5.3 in relation to spiral phase plate arrays 7 so as to ensure the axial alignment of these elements. The structure of the spiral phase plate array together with the phase distribution of a single spiral phase plate is shown in Fig. 7, while the structure of lens array together with the phase distribution of a single lens is shown in Fig. 8. A diagram of the system is shown in Fig. 6.

[0105] EMBODIMENT 14

[0106] The system for the measurement of wavefronts according to Example 12, wherein optical vortex beams are introduced using a vortex lens array 5 comprising of a liquid crystal reflective-type spatial light modulator 5.4 and a single focusing lens 5.5. Liquid crystal spatial light modulator 5.4 displays a hologram that includes phase-type distribution, shown as a greyscale image, the values of which correspond to the phase shift introduced by the modulator in each point. This hologram operates similarly to a phase diffraction grating, while the resulting structure generated in the focal plane of second lens 5.5 represents the Fourier transform of the phase-type distribution displayed on liquid crystal spatial light modulator 5.4. The Fourier plane image is projected through the second microscopic lens 7 onto detector 6. A typical hologram displayed on liquid crystal spatial light modulator 5.4 includes a matrix of circular apertures arranged in the form of a hexagon, as shown in Fig. 9. Each aperture includes a combination of two phase-type distributions: a spiral phase-type distribution that generates an optical vortex beam similarly to the spiral phase plate array 5.2, and a phase-type distribution, which generates a blazed diffraction grating that controls the separation of the beams in the Fourier plane once they are focused by the lens array 5.3. The spatial frequency of the diffraction grating is variable and is different for each aperture. It is calculated in relation to the frequency of the SB base grid and takes into account the vector that connects the centres of a given aperture and the base aperture located on the perimeter of the hologram. Phase Φkfor the individual apertures is calculated using the following formula:

[0107] Where factor inup generates an optical vortex of the charge of m=1, while φ defines the angle in polar coordinates. X, Y represent coordinate system matrices expressed in Cartesian coordinates, nxand nydefine the number of diffraction grating grooves per resolution pxand pyof the implemented spatial light modulator, s represents the scale factor, which is equal to 1 by default, but can be used to control the separation of spots in the detector plane, vxand vyare the coordinates of vector that connects the aperture that contains base grating SB with the aperture that the phase-type distribution is calculated for. In the case of the aperture that contains base grating SB, the values of these coordinates are . A diagram of the system is shown in Fig. 9. Fig. 10 shows a typical example of a hologram.

[0108] EMBODIMENT 15

[0109] The system for the measurement of wavefronts according to Embodiment 14, wherein the light beam is emitted by a coherent light source 1 comprising a Vertical Cavity Surface Emitting Laser (VCSEL) diode and optical vortex beams of the topological charge of m = 20 are introduced using a vortex lens array 5 that comprises a liquid crystal transmissive-type spatial light modulator 5.4 and a single focusing lens 5.5.

[0110] EMBODIMENT 16

[0111] The system for the measurement of wavefronts according to Embodiment 14, wherein optical vortex beams are introduced using a vortex lens array 5 that comprises a liquid crystal spatial light modulator 5.4 that uses a micromirror array for modulation and a single focusing lens 5.5.

[0112] EMBODIMENT 17

[0113] The system for the measurement of wavefronts according to Embodiment 12, wherein the coherent light source 1 is a laser diode, while optical vortex beams are introduced using a vortex lens array 5 that constitutes a single refractive element 5.1 made of liquid crystals.

[0114] EMBODIMENT 18 The system for the measurement of wavefronts according to Embodiment 12, wherein optical vortex beams are introduced using a vortex lens array 5 that constitutes a single refractive element 5.1 made of metamaterials.

[0115] EMBODIMENT 19

[0116] The system for the measurement of wavefronts according to Embodiment 10, wherein the light beam is emitted by a coherent light source 1 that constitutes a pulsed laser, while vortex beams of the topological charge of m = -20 are introduced using a vortex lens array 5 that comprises a single refractive element 5.1 made of polymers. Image analysis is performed by detector 6, which constitutes a CMOS camera.

[0117] EMBODIMENT 20

[0118] The system for the measurement of wavefronts according to Embodiment 13, wherein optical vortex beams are introduced using a vortex lens array 5 that comprises a set of spiral phase plate arrays (5.2) and a lens array (5.3) made of polymers.

[0119] EMBODIMENT 21

[0120] The system for the measurement of wavefronts according to Embodiment 2, wherein optical vortex beams are introduced using a vortex lens array 5 that comprises a set of spiral phase plate arrays (5.2) and a lens array (5.3) made of liquid crystals.

[0121] EMBODIMENT 22

[0122] The system for the measurement of wavefronts according to Embodiment 2, wherein optical vortex beams are introduced using a vortex lens array 5 that comprises a set of spiral phase plate arrays (5.2) and a lens array (5.3) made of metamaterials.

Claims

ClaimsWe claim:

1. A method of measurement of wavefronts, wherein a wavefront of a beam that is emitted by a coherent light source (1) is shaped into a widened light beam using a system comprising of a first microscopic lens (2) and a first lens (3), wherein the said beam subsequently illuminates the analysed object (4) and then, after passing through the analysed object (4), the wavefront is distorted and, using a lens array, divided into a number of smaller fragments that are focused on detector (6) which is used to analyse the intensity image and then to reproduce the shape of the analysed wavefront, characterised in that optical vortex beams are introduced via a lens array that constitutes the vortex lens array (5) into the distorted wavefront that has passed through the analysed object (4), wherein the said optical vortex beams are characterised by stable phase discontinuity with topological charge integer values m in the range of -20 to 20, wherein the displacement of the individual discontinuities is determined by way of tracking based on the determination of the location of a discontinuity represented by the point of zero intensity in the focused beam, and the measurement of the displacement of the dark point in relation to the location of the dark point with the original settings and without the analysed object.

2. The method of measurement of wavefronts according to claim 1 , characterised in that the topological charges of the introduced optical vortex beams have the integer value of m=l.

3. The method of measurement of wavefronts according to claim 1, characterised in that the optical vortex beams are introduced using a vortex lens array (5) that constitutes a single refractive element (5.1).

4. The method of measurement of wavefronts according to claim 1 , characterised in that the optical vortex type beams are introduced using a vortex lens array (5) that comprises a set of spiral phase plate arrays (5.2) and lens arrays (5.3) that are arranged coaxially with respect to each other.

5. The method of measurement of wavefronts according to claim 1, characterised in that the optical vortex type beams are introduced using a vortex lens array (5) that comprises a liquid crystal reflective-type spatial light modulator (5.4) and a single focusing lens (5.5).

6. The method of measurement of wavefronts according to claim 1 , characterised in that theoptical vortex type beams are introduced using a vortex lens array (5) that comprises a liquid crystal transmissive-type spatial light modulator (5.4) and a single focusing lens (5-5).

7. The method of measurement of wavefronts according to claim 1, characterised in that the optical vortex type beams are introduced using a vortex lens array (5) that comprises a liquid crystal spatial light modulator (5.4) that uses a micromirror array for modulation and a single focusing lens (5.5).

8. The method of measurement of wavefronts according to claim 1, characterised in that the optical vortex beams are introduced using a vortex lens array (5) that constitutes a single refractive element (5.1) made of polymers.

9. The method of measurement of wavefronts according to claim 1, characterised in that the optical vortex beams are introduced using a vortex lens array (5) that constitutes a single refractive element (5.1) made of liquid crystals.

10. The method of measurement of wavefronts according to claim 1, characterised in that the optical vortex beams are introduced using a vortex lens array (5) that constitutes a single refractive element (5.1) made of quartz glass.

11. The method of measurement of wavefronts according to claim 1, characterised in that the optical vortex beams are introduced using a vortex lens array (5) that constitutes a single refractive element (5.1) made of metamaterials.

12. The method of measurement of wavefronts according to claim 1, characterised in that the optical vortex type beams are introduced using a vortex lens array (5) that comprises a set of spiral phase plate arrays (5.2) and lens arrays (5.3) made of polymers.

13. The method of measurement of wavefronts according to claim 1, characterised in that the optical vortex type beams are introduced using a vortex lens array (5) that comprises a set of spiral phase plate arrays (5.2) and lens arrays (5.3) made of liquid crystals.

14. The method of measurement of wavefronts according to claim 1, characterised in that the optical vortex type beams are introduced using a vortex lens array (5) that comprises a set of spiral phase plate arrays (5.2) and lens arrays (5.3) made of quartz glass.

15. The method of measurement of wavefronts according to claim 1, characterised in that the optical vortex type beams are introduced using a vortex lens array (5) that comprises a set of spiral phase plate arrays (5.2) and lens arrays (5.3) made of metamaterials.

16. The method of measurement of wavefronts according to claim 1, characterised in that adetector (6) that constitutes a Charged Couple Device (CCD) camera is used to analyse the image and to reproduce the shape of the analysed object.

17. The method of measurement of wavefronts according to claim 1, characterised in that a detector (6) that constitutes a CMOS (Complimentary Metal Oxide Semiconductor) camera is used to analyse the image and to reproduce the shape of the analysed object.

18. The method of measurement of wavefronts according to claim 1 characterised in that the wavefront of the beam is emitted by a coherent light source (1) that constitutes a continuous- wave laser.

19. The method of measurement of wavefronts according to claim 1 characterised in that the wavefront of the beam is emitted by a coherent light source (1) that constitutes a pulsed laser.

20. The method of measurement of wavefronts according to claim 1 characterised in that the wavefront of the beam is emitted by a coherent light source (1) that constitutes a VCSEL (Vertical Cavity Surface Emitting Laser) diode.

21. The method of measurement of wavefronts according to claim 1 characterised in that the wavefront of the beam is emitted by a coherent light source (1) that constitutes a laser diode.

22. A system for the measurement of wavefronts that consists of microscopic lens (2) that is used to focus a beam of light emitted from coherent light source (1) and first lens (3) that widens the beam of light to the size of the analysed object, wherein the beam is directed at analysed object (4) and after passing through it is distorted and illuminates the lens array, whereupon the individual beam fragments are focused on detector (6), characterised in that the lens array comprises vortex lens array (5) that introduces into the system optical vortex beams characterised by stable phase discontinuity with topological charge integer values m in the range of -20 to 20, which focus the individual beam fragments on detector (6) that is used to analyse the intensity image and to reproduce the shape of the tested wavefront.

23. The system for the measurement of wavefronts according to claim 22, characterised in that the topological charges of optical vortex beams introduced using a vortex lens array (5) have the integer value of m=l.

24. The system for the measurement of wavefronts according to claim 22, characterised in that the vortex lens array (5) constitutes a single refractive element (5.1).

25. The system for the measurement of wavefronts according to claim 22, characterised in that the vortex lens array (5) consists of a set of spiral phase plate arrays (5.2) and lens arrays (5.3) installed on a bracket, in order to ensure the axial linearity of the array.

26. The system for the measurement of wavefronts according to claim 22, characterised in that the vortex lens array (5) consists of a set of liquid crystals, a reflective-type spatial light modulator (5.4) and a single focusing lens (5.5).

27. The system for the measurement of wavefronts according to claim 22, characterised in that the vortex lens array (5) consists of a set of liquid crystals, a transmissive-type spatial light modulator (5.4) and a single focusing lens (5.5).

28. The system for the measurement of wavefronts according to claim 22, characterised in that the vortex lens array (5) consists of a set of liquid crystals, a spatial light modulator (5.4) that uses a micromirror array for modulation and a single focusing lens (5.5).

29. The system for the measurement of wavefronts according to claim 22, characterised in that the vortex lens array (5) constitutes a single refractive element (5.1) made of polymers.

30. The system for the measurement of wavefronts according to claim 22, characterised in that the vortex lens array (5) constitutes a single refractive element (5.1) made of liquid crystals.

31. The system for the measurement of wavefronts according to claim 22, characterised in that the vortex lens array (5) constitutes a single refractive element (5.1) made of quartz glass.

32. The system for the measurement of wavefronts according to claim 22, characterised in that the vortex lens array (5) constitutes a single refractive element (5.1) made of metamaterials.

33. The system for the measurement of wavefronts according to claim 22, characterised in that the vortex lens array (5) consists of a set of spiral phase plate arrays (5.2) and lens arrays (5.3) made of polymers.

34. The system for the measurement of wavefronts according to claim 22, characterised in that the vortex lens array (5) consists of a set of spiral phase plate arrays (5.2) and lens arrays (5.3) made of liquid crystals.

35. The system for the measurement of wavefronts according to claim 22, characterised in that the vortex lens array (5) consists of a set of spiral phase plate arrays (5.2) and lensarrays (5.3) made of quartz glass.

36. The system for the measurement of wavefronts according to claim 22, characterised in that the vortex lens array (5) consists of a set of spiral phase plate arrays (5.2) and lens arrays (5.3) made of metamaterials.

37. The system for the measurement of wavefronts according to claim 18, characterised in that detector (6) constitutes a CCD (Charged Couple Device) camera.

38. The system for the measurement of wavefronts according to claim 18, characterised in that detector (6) constitutes a CMOS (Complimentary Metal Oxide Semiconductor) camera.

39. The system for the measurement of wavefronts according to claim 18, characterised in that the coherent light source (1) constitutes a continuous-wave laser.

40. The system for the measurement of wavefronts according to claim 18, characterised in that the coherent light source (1) constitutes a pulsed laser.

41. The system for the measurement of wavefronts according to claim 18, characterised in that the coherent light source (1) constitutes a VCSEL (Vertical Cavity Surface Emitting Laser) diode.

42. The system for the measurement of wavefronts according to claim 18, characterised in that the coherent light source (1) constitutes a laser diode.

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