DE102015014387B3 - Apparatus and method for beam analysis with a variable optical element - Google Patents

Apparatus and method for beam analysis with a variable optical element Download PDF

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DE102015014387B3
DE102015014387B3 DE102015014387.5A DE102015014387A DE102015014387B3 DE 102015014387 B3 DE102015014387 B3 DE 102015014387B3 DE 102015014387 A DE102015014387 A DE 102015014387A DE 102015014387 B3 DE102015014387 B3 DE 102015014387B3
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lens
variable optical
focal length
light
objective
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Reinhard Kramer
Roman Niedrig
Otto Märten
Stefan Wolf
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Primes Messtechnik fur Die Produktion Mit Laserstrahlung GmbH
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Primes Messtechnik fur Die Produktion Mit Laserstrahlung GmbH
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01JMEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRA-RED, VISIBLE OR ULTRA-VIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
    • G01J1/00Photometry, e.g. photographic exposure meter
    • G01J1/42Photometry, e.g. photographic exposure meter using electric radiation detectors
    • G01J1/4257Photometry, e.g. photographic exposure meter using electric radiation detectors applied to monitoring the characteristics of a beam, e.g. laser beam, headlamp beam
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01JMEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRA-RED, VISIBLE OR ULTRA-VIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
    • G01J1/00Photometry, e.g. photographic exposure meter
    • G01J1/42Photometry, e.g. photographic exposure meter using electric radiation detectors
    • G01J1/4257Photometry, e.g. photographic exposure meter using electric radiation detectors applied to monitoring the characteristics of a beam, e.g. laser beam, headlamp beam
    • G01J2001/4261Scan through beam in order to obtain a cross-sectional profile of the beam

Abstract

The invention relates to a device for beam analysis of light rays, which allows a fast and accurate determination of geometric parameters of a light beam. For example, the beam parameter product or the beam propagation factor of a laser beam can be determined. The device comprises a variable optical element, an objective, and a spatially resolving detector. At this time, the variable optical element has an adjustable focal length and an image-side major surface, and the objective has a constant focal length and an object-side major surface. The distance between the image-side major surface of the variable optical element and the object-side main surface of the objective is equal to the constant focal length of the objective with a deviation of at most +/- 5%. The objective is connected downstream of the variable optical element in the beam direction. The spatially resolving detector is connected downstream of the objective in the beam direction. By changing the adjustable focal length of the variable optical element and by subsequently focusing the light beam through the objective, a focus position of the focused light beam relative to the spatially resolving detector is variably adjustable in the axial direction. The invention also relates to a method for the rapid and accurate determination of geometric parameters of a light beam.

Description

  • FIELD OF THE INVENTION
  • The invention relates to an apparatus and a method for beam analysis of light rays. The invention is suitable for the rapid and accurate determination of geometric parameters such as the beam diameter, the beam parameter product or the beam propagation factor. The apparatus and method can be used for beam analysis of laser beams.
  • BACKGROUND OF THE INVENTION
  • Geometric parameters of a light beam or a laser beam are important parameters for the characterization of the beam. Such parameters may be, for example, the beam diameter, the beam profile, or the beam parameter product. The beam parameter product describes the product of the radius of the beam waist and the aperture angle of the beam and is therefore an index for the focusability of a light beam or laser beam. Other measures or terms for the same thing are the beam quality, the beam quality index, the beam propagation factor, the mode factor, or the diffraction metric. Beam parameters must be measured at regular time intervals for quality control in many production processes using light beams. The definitions and mathematical relationships for the determination of geometric parameters of a light beam are described in ISO 11146. For a complete determination of a beam which also includes the propagation properties, scanning of the beam in multiple planes along the beam is required. The most accurate results are expected when the beam is scanned over a distance of several Rayleigh lengths in the region of its beam waist.
  • For scanning the intensity distribution in a cross-sectional plane of the light beam, various methods are known. A principal possibility for the measurement consists, for example, of directing the beam directly or indirectly onto a spatially resolving sensor or detector, for example onto a CCD camera, and in this way determining the intensity distribution in the cross section of the beam. From this data, further information such as the beam diameter, the beam profile or the position of the beam can be derived or calculated. Another possibility is the intensity distribution in a plane with an approximately point-shaped detector in a raster motion, z. B. scan line by line.
  • The use of a spatially resolving sensor has the advantage over the raster scanning in that the recording of the intensity distribution in a plane requires only a very short measuring time. A short measurement time is important if the intensity distribution in several different planes is to be scanned in order to determine the total beam parameter or the beam propagation factor.
  • For scanning in several levels, in turn, various methods and devices are known. For example, the spatially resolving sensor can be placed on a linear guide, so that the scanning unit can be moved in the axial direction along the beam.
  • In many cases, the beam waist of the light or laser beam is not directly accessible, or the beam is collimated, so that the Rayleigh length of the beam is very large and scanning across several Rayleigh lengths around the beam waist is impractical or impractical is. In these cases, it is customary first to focus the beam by means of a lens or by means of a lens and to position the linear guide with the sensor in the focus area behind the lens. Although the scanning of the beam and subsequent determination of the geometric parameters of the beam then delivers the image-side beam parameters, these can be converted into the object-side parameters via the imaging equations of the lens.
  • The conversion of the beam parameters can be simplified by not only placing the sensor on a linear guide, but also arranging the focusing lens together with the sensor on the same linear guide, so that the distance between the lens and the sensor is constant. and for scanning the beam, the lens and the sensor are displaced axially relative to the light beam. In this case, as it were, the object-side plane conjugate to the image-side sensor plane is virtually driven through the original beam.
  • A disadvantage of all the aforementioned systems and methods is that a precise and mechanically complex linear guide is required and relatively large masses must be moved. Thus, the positioning time for setting different measurement levels can not be arbitrarily reduced.
  • To solve the problem is in the WO 2011/127400 A2 proposed a device in which the light beam to be measured by means of partially transmissive mirror is divided into a plurality of parallel sub-beams, each with different path lengths laterally offset hit the same sensor, so that a simultaneous Recording multiple beam cross sections is possible. A disadvantage of this device is that the individual beam cross sections share the same sensor and therefore the area available for a single beam cross section and thus the pixel resolution is reduced by a considerable factor.
  • Another solution to the problem is in the US 8,736,827 B2 disclosed. The device shown there consists of a variable lens and a sensor. For the variable lens, for example, an electro-optical lens or a pressure-controllable fluid lens is proposed, whose focal length can be set variably. The moving mass when changing the focal length of the variable lens is very small. In this way, the image-side beam waist can be adjusted very quickly axially and beam cross sections in different planes can be quickly taken in a row. The disadvantage is that due to the variable focal length, the image-side parameters of the beam depend on the focal length and thus also be changed. An evaluation of the data according to the formulas defined in ISO 11146 is therefore not directly possible. Rather, a modified formula must be used for the evaluation (see the second formula in column 4 of the US 8,736,827 B2 ). Because of the variable focal length, a relatively complex calibration of the device is required. This limits the accuracy of the method.
  • For variably adjustable lenses, the adjustment range of the focal length is limited by design and fixed to a specific range. The area required to pass through several Rayleigh lengths may be greater than the focal length adjustment range, depending on the parameters of the beam to be measured. Conversely, it is also possible that the Rayleigh length of the focused beam is very short, and therefore the required adjustment range is very short, but a high accuracy and reproducibility of the focal length adjustment in a very small area is required. In both cases, the usability of the in the US 8,736,827 B2 disclosed device to be clearly limited.
  • Consequently, the devices and methods known from the prior art have considerable disadvantages in terms of resolution, accuracy, speed or usability for a large range of parameters.
  • BRIEF DESCRIPTION OF THE INVENTION
  • The invention is therefore based on the object to provide a method and an apparatus for beam analysis, in which several different cross-sectional planes of a light beam can be measured in a very short time, and allow a determination of beam parameters of the light beam with high accuracy.
  • To achieve the object, a device for determining geometric parameters of a light beam is proposed which comprises a variable optical element, an objective, and a spatially resolving detector. At this time, the variable optical element has an adjustable focal length and an image-side major surface, and the objective has a constant focal length and an object-side major surface. The distance between the image-side major surface of the variable optical element and the object-side main surface of the objective is equal to the constant focal length of the objective with a deviation of at most +/- 5%. The objective is connected downstream of the variable optical element in the beam direction. The spatially resolving detector is connected downstream of the objective in the beam direction. By changing the adjustable focal length of the variable optical element and by subsequently focusing the light beam through the objective, a focus position of the focused light beam relative to the spatially resolving detector is variably adjustable in the axial direction.
  • An embodiment of the device is provided in which the relative positions of the light beam, the variable optical element, the objective and the spatially resolving detector are mutually stationary.
  • In one possible embodiment of the invention, the total focal length of the system consisting of the variable optical element and the objective is equal to the constant focal length of the objective with a maximum deviation of +/- 5%.
  • An embodiment of the device is also provided in which the variable optical element comprises a fluid lens.
  • In a further embodiment of the invention, the variable optical element comprises an adaptive lens.
  • In yet another embodiment of the invention, the variable optical element comprises an adaptive mirror.
  • In one possible embodiment of the device, a lens for divergence adjustment in the beam direction is arranged in front of the variable optical element.
  • An embodiment of the device according to the invention is provided in which the Lens comprises a first lens group and a second lens group.
  • In one possible embodiment of the invention with an objective comprising a first lens group and a second lens group, the first lens group of the objective may have a negative refractive power, and the second lens group of the objective may have a positive refractive power, and the objective lens has a constant focal length as a whole a positive value.
  • To solve the problem, a method for the determination of geometric parameters of a light beam is proposed, which comprises the method steps listed below. An opening angle of the light beam is changed by means of a variable optical element having an adjustable focal length and an image-side major surface. The light beam changed by the variable optical element with respect to the opening angle is focused by means of a lens which has a constant focal length and an object-side main surface. The adjustable focal length of the variable optical element is changed. At least three different focal lengths are set in succession. Intensity distributions of the light beam focused by the lens are registered by means of a spatially resolving detector, which is arranged in the beam direction behind the objective. At each of the at least three different set focal lengths, an intensity distribution is registered in each case. Finally, a geometric parameter of the light beam is determined from the registered intensity distributions. Here, the distance between the image-side major surface of the variable optical element and the object-side major surface of the objective is equal to the constant focal length of the objective with a deviation of at most +/- 5%.
  • A method is also provided in which the relative positions of the light beam, the variable optical element, the objective and the spatially resolving detector are stationary relative to each other.
  • In another possible method, determining a geometric parameter of the light beam from the registered intensity distributions comprises determining a beam propagation factor of the light beam.
  • BRIEF DESCRIPTION OF THE FIGURES
  • The invention will be described in more detail with reference to the following figures, without being limited to the embodiments shown. It shows:
  • 1 : A known from the prior art apparatus for beam analysis of a light beam with a variable lens with adjustable focal length, by means of which a beam is focused and an axially adjustable focus position is generated, and with a sensor which is arranged in the region of the adjustable focus position.
  • 2 : A schematic representation of a first embodiment of the invention with a variable optical element, with a lens which is arranged behind the variable optical element, and with a spatially resolving detector. In this embodiment, the lens has a relatively short focal length.
  • 3 : A schematic representation of an embodiment of the invention similar to that in FIG 2 shown embodiment. In this embodiment, the lens has a relatively long focal length. The focus adjustment range is only partially in the real image area of the lens.
  • 4 : A schematic representation of another embodiment of the invention similar to that in FIG 3 shown embodiment. The light beam is not collimated in this example, but has a focus or beam waist in front of the device and then spreads divergently. The focus adjustment range can be completely in the real image area of the lens.
  • 5 : A schematic representation of a second embodiment of the invention, in which a lens for divergence adjustment in the beam direction is arranged in front of the variable optical element. The lens for divergence adjustment has a negative refractive power in this embodiment. This moves the focus adjustment range backwards.
  • 6 : A schematic representation of another embodiment of the invention. In this embodiment, the objective comprises a first lens group and a second lens group which together form a retrofocus-type objective having a rearwardly displaced main surface and thus the focus adjustment range is shifted rearward.
  • 7 : A schematic representation of an embodiment of the second embodiment of the invention, in which a lens for divergence adjustment in the beam direction is arranged in front of the variable optical element. In the embodiment shown here, the lens for divergence adjustment has a positive refractive power and allows the analysis of rays that are not collimated or have a focus or a beam waist relatively close to the device.
  • 8th : A schematic representation of a third embodiment of the invention, in which the original light beam is attenuated by means of a beam attenuation device. By way of example, two beam splitters are shown for this purpose, each of which reflects a small part of the power of the light beam and in each case transmits a larger part of the power of the light beam. The transmitted portion of the power of the light beam is absorbed by absorbers or jet traps.
  • 9 : Representation for determining the position of the main surfaces of a lens composed of two lens groups in retrofocus construction.
  • DETAILED DESCRIPTION OF THE FIGURES
  • 1 shows a schematic representation of a known from the prior art apparatus for beam analysis with a variable optical element 20 , For example, a variable lens LV, and with a spatially resolving detector 50 , The light beam to be measured 10 is focused by the variable lens LV. The focal length of the variable lens LV is adjustable in a range between a minimum focal length f LV, A and a maximum focal length f LV, C. At the in 1 example shown is the light beam to be measured 10 collimates, ie the light beam 10 representing lines are parallel to the optical axis 15 , In this case, the focus is on 18 of the light beam focused by the variable lens LV 17 just at the focal point of the variable lens LV. With the variation of the focal length of the variable lens LV so the focus 18 of the focused light beam 17 within an adjustment range Δs along the optical axis 15 moved axially. In the example shown here, where the light beam 10 is collimated, the focus adjustment range Δs is equal to the focal length adjustment range f LV, A to f LV, C of the variable lens LV. Within this adjustment range Δs becomes the spatially resolving detector 50 positioned, preferably approximately in the middle of the adjustment range .DELTA.s. Thus, the focus or the beam waist can 18 of the focused beam 17 in an axial region on either side of the detector 50 ie before and virtually behind the spatially resolving detector 50 to be positioned. This allows a series of intensity distributions in different cross-sectional planes of the focused beam 17 from the detector 50 to be recorded. Among other things, the beam diameter for each cross-sectional plane can be calculated from the intensity distributions. From the application of the beam diameter above the axial position in the beam, the propagation factor of the beam can be determined.
  • The focused beam 17 has a beam waist 18 , ie an axial position at which the beam diameter is minimal. This axial position can, as in the in 1 shown example, the focus position of the focused beam 17 be. The diameter of the beam waist of the light beam focused by the variable lens LV 17 depends on the respectively set focal length of the variable lens LV, the magnification of the device thus changes over the adjustment range Δs. This manifests itself also at different opening angles of the beam cone of the focused light beam 17 like the three in 1 shown focal length settings is clearly visible. The beam parameters of the focused light beam 17 , in particular the jet waist diameter and the opening angle, are therefore not constant, but change with the set focal length. Because of this varying magnification of the measuring device, the evaluation of the measured beam diameters in different cross-sectional planes for determining a propagation factor can not take place according to the usual formulas described in ISO 11146. Furthermore, a conversion of the measured image-side beam parameters to the searched object-side parameters of the original beam is required. Not only the variable focal length of the variable lens LV, but also the distance of the spatially resolving detector 50 to the variable lens LV influences the measurement results. The exact determination of the beam parameters therefore requires a complex calibration of the device. In many variable lenses is not the focal length, but the refractive power of the lens, so the reciprocal value of the focal length, approximately linearly dependent on a manipulated variable, for. B. an electric current. This has the consequence that the axial focus position depends non-linearly on the manipulated variable. In 1 this is evident from the fact that the focus position B 46 for the average adjustable refractive power 26 is not in the middle of the adjustment range Δs, but much closer to the focus position A, 45 , at the largest adjustable refractive power 25 , The achievable axial resolution is thus not constant within the adjustment range Δs.
  • The varying magnification, the complex calibration, the required conversion to the beam parameters of the original beam to be measured 10 , as well as the fluctuating axial resolution make the in 1 represented, known from the prior art device and the associated methods error prone and limit the achievable accuracy.
  • 2 shows a schematic representation of a first possible embodiment of the invention. The light beam to be measured 10 meets a variable optical element (VOE) 20 with an adjustable focal length. The variable optical element 20 forms the light beam 10 not on a spatially resolving detector 50 but changed adjustable the opening angle, ie the Divergence or the convergence angle of the light beam. Between the variable optical element 20 and the detector 50 is a lens 30 arranged. The objective 30 Focused the beam of light, leaving a beam waist 18 of the focused light beam 17 is generated in a setting range Δs. The spatially resolving detector 50 is arranged within the adjustment range Δs, so that when the focal length of the variable optical element is changed 20 the beam waist 18 in an axial region around the detector 50 can be moved around. In this way, successively several different cross sections of the beam 17 be scanned quickly in quick succession. The distance between the variable optical element 20 and the lens 30 is about the focal length of the lens 30 , More specifically, the distance between the image-side major surface H 'is VOE 22 of the variable optical element 20 and the object-side main surface H obj 31 of the lens 30 approximately equal to the focal length f Obj of the lens 30 , The magnification or the magnification of the beam waist 18 is not of the focal length of the variable optical element 20 dependent. This can be seen from the identical opening angles of the beam cone of the focused light beam 17 at the three in 2 exemplified beams for different focal lengths of the variable optical element 20 , In the in 2 shown embodiment of a first embodiment of the invention is the focal length of the lens 30 chosen relatively short, so that the adjustment range Δs of the beam waist 18 with the positions A, B and C of the focal positions shown by way of example 45 . 46 . 47 completely in the picture space behind the lens 30 lies.
  • 3 shows a further embodiment of the first embodiment of the invention. Unlike the in 2 example shown is the focal length of the lens 30 chosen relatively long. As a result, on the one hand, the setting range Δs is significantly greater than with a short focal length of the objective 30 On the other hand, it may happen that the adjustment range .DELTA.s of the beam waist 18 no longer completely in the picture space behind the lens 30 lies. This can be the one for the detector 50 accessible scanning range of the focused beam 17 to be disabled.
  • In 4 is an embodiment of the first embodiment of the invention similar to in 3 shown. In contrast to 3 is the light beam to be measured 10 but not collimated here, but has a focus or beam waist relatively close to the device 11 and then spread divergently. Such an application is typical for the measurement of a laser beam 10 which was previously focused by a processing optics. The processing optics is not shown here, as this is not part of the measuring device. At the in 4 shown example is due to the divergence of the steel 10 the adjustment range Δs of the beam waist 18 completely in the picture space behind the lens 30 ,
  • At the in 5 shown second embodiment of the invention is in front of the variable optical element 20 a lens for divergence adjustment LD 60 arranged. In the embodiment shown here, the lens has divergence matching 60 a negative refractive power, whereby the previously collimated light beam 10 becomes divergent. As a result, the adjustment range Δs of the beam waist 18 moved backwards and lies completely in the real image space behind the lens 30 ,
  • 6 shows a further embodiment of the first embodiment of the invention. In this embodiment, the lens is 30 composed of a first lens group 35 and a second lens group 36 , In the illustrated embodiment, the first lens group 35 a negative refractive power and the second lens group 36 a positive refractive power. The first lens group 35 and the second lens group 36 Together they form a lens 30 in retrofocus construction, which has a rearwardly shifted main surface. Thus also the adjustment range Δs of the beam waist becomes 18 moved backwards and can be completely in the real image space behind the lens 30 lie.
  • In 7 is shown a further embodiment of the second embodiment of the invention, wherein a lens 60 for divergence adjustment in the beam direction in front of the variable optical element 20 is arranged. If the light beam to be measured 10 a relatively high divergence and a beam waist 11 near the measuring device, the focus adjustment range Δs of the beam waist can be made 18 be moved relatively far to the rear. With the lens 60 for divergence adjustment, a power offset becomes the adjustable power of the variable optical element 20 added, whereby the adjustment range .DELTA.s is axially displaced by a certain amount. In the embodiment shown here has the lens 60 for divergence adjustment a positive refractive power, so that the adjustment range .DELTA.s moved closer to the lens. The analysis of rays 10 that are not collimated and have a focus or beam waist 11 relatively close to the device, so can be done with a compact device whose size is not unnecessarily long.
  • A third embodiment of the invention is in 8th shown schematically. In the measurement of light rays 10 with high light intensity, for example of laser beams, the spatially resolving detector 50 may be overridden. In such situations, it is beneficial to attenuate the beam. The 8th shows an embodiment with a device for beam Slowdown. The device for beam attenuation consists in this embodiment of two beam splitters 70 which are arranged in front of the variable optical element. Each beam splitter 70 reflects a small portion of the light beam 10 , so that after twice reflection of the light beam 10 has a significantly reduced intensity. If the two beam splitters 70 are spatially arranged so that the reflection planes are rotated by 90 ° to each other, a very precise polarization-independent attenuation can be achieved by means of this device. The superfluous beam components transmitted by the beam splitters can be generated by beam traps or absorbers 74 be caught.
  • 9 illustrates the location of major surfaces and foci in one of two lens groups 35 . 36 composite retrofocus lens. Such a lens is in the embodiments of the invention in the 6 . 7 and 8th as a lens 30 exemplified. The object-side main surface 31 is where the focus from the object side 33 outgoing rays with the after picture through the lens 30 parallel rays could be made by extending the rays virtually (shown in the upper part of the 9 ). The image-side main surface 32 lies where the paraxial rays with the after the picture through the lens 30 through the image-side focal point 34 running rays would, if one extends the rays virtually (lower part of the 9 ). The main surfaces 31 . 32 So are the areas where you look at the breaking effect of all the elements of the lens 30 can imagine reduced to an area. In the example shown, the main surfaces 31 . 32 moved very far to the back. This is in the embodiments of the invention in the 6 . 7 and 8th advantageous in spite of a very large focal length of the lens 30 to realize a compact design. Because of the rearward shifted main surface 31 the lens must be very close behind the variable optical element 20 be arranged to the distance condition between the variable optical element 20 and the lens 30 to fulfill (see the 6 . 7 . 8th ). This also contributes to a compact construction.
  • DETAILED DESCRIPTION OF THE INVENTION
  • It is intended to provide a solution to the problem that prior art beam analysis apparatuses require relatively sophisticated multi-level scanning devices, require a long measurement time, have low accuracy, or are susceptible to systematic error sources. In contrast, an apparatus and a method for beam analysis are to be created, which allow a measurement of several different cross-sectional planes of a light beam in a short time and allow determination of beam parameters of the light beam with high accuracy.
  • To solve the problem, a device is proposed which has a variable optical element (VOE). 20 , a lens 30 , and a spatially resolving detector 50 comprising, one behind the other in the beam path of a light beam to be measured 10 are arranged. The variable optical element 20 has an adjustable focal length, which can be changed by means of a manipulated variable between a minimum focal length and a maximum focal length. The refractive power of an optical element is equal to the reciprocal focal length of the optical element, that is, the minimum adjustable focal length corresponds to a maximum refractive power, and the maximum adjustable focal length corresponds to a minimum refractive power.
  • The variable optical element 20 also has an image-side major surface H ' VOE 22 on. It is known from the field of technical optics that the image-side main surface of a lens is a virtual surface on which the refraction of axially parallel rays would take place, if one considers the refraction usually taking place at several optical interfaces of a lens reduced to one surface. The distance of the intersection between the image-side major surface of a lens and the optical axis to the image-side focal point of the lens is therefore equal to the focal length of the subject lens.
  • The objective 30 has a constant focal length f Obj and an object-side major surface H Obj 31 , According to the invention, the lens 30 in the beam direction behind the variable optical element 20 at a defined distance from the variable optical element 20 arranged. The distance H ' VOE H Obj from the image side major surface H' VOE 22 of the variable optical element (VOE) 20 to the object-side main surface H Obj 31 of the lens 30 should be about the same as the focal length f obj of the lens 30 be.
  • The position of the image-side main surface H ' VOE 22 of the variable optical element 20 For example, when using a fluid lens with variable center thickness, can vary in a small range. This variation can typically be from a few 1/10 mm to a few mm. Therefore, it is intended to have a small deviation from the ideal distance condition between the variable optical element VOE 20 and the lens 30 permit. The distance H ' VOE H Obj between the image-side main plane H' VOE 22 of the variable optical element 20 and the object-side main surface H obj 31 of the lens 30 should be in a range of 0.95 * f Obj ≤ H ' VOE H Obj ≤ 1.05 * f Obj . With In other words, the distance between the major surfaces H ' VOE H Obj should be equal to the focal length f Obj of the objective 30 with a maximum deviation of +/- 5%.
  • In the beam direction behind the lens 30 is the spatially resolving detector 50 arranged. The spatially resolving detector 50 is a light-sensitive sensor that can register the local light intensity. The term "local resolution" in this context means that the sensor does not register a single measured value integrally over its entire surface, but has a plurality of cells distributed over the surface and thus can register a two-dimensional lateral light distribution. The spatially resolving detector 50 may be, for example, a CCD camera, a CMOS chip or other pixel-based photosensitive detector. With the spatially resolving detector 50 becomes the intensity distribution of the focused light beam 17 in a cross-sectional plane of the light beam 17 recorded. The spatially resolving detector 50 is at a distance to the lens 30 arranged by varying the focal length of the variable optical element 20 the beam waist 18 of the focused light beam 17 both before (eg front end position A, 45 , the focus adjustment range Δs) as well as virtually behind the spatially resolving detector 50 can be positioned (eg rear end position C, 47 , the focus adjustment range Δs).
  • Due to the features of the invention results in a special operation of the device. The light beam to be measured 10 meets the variable optical element (VOE) 20 , The variable optical element 20 affects the light beam 10 in such a way that the opening angle of the beam cone of the light beam 10 due to refraction by the variable optical element 20 will be changed. Depending on the set focal length of the variable optical element, the opening angle of the beam cone is influenced more or less. In the example shown in 2 is the beam to be measured 10 collimated and is after the influence of the variable optical element 20 convergent, wherein the convergence angle (or opening angle) of the set focal length or refractive power of the variable optical element 20 depends. In 2 By way of example, three rays are shown representing the refracted ray at minimum, average and maximum refractive power. Subsequently, the variable optical element 20 influenced light beam 10 from the lens 30 focused. Due to the adjustable opening angle or convergence angle of the light beam 10 after the variable optical element 20 results after focusing through the lens 30 an adjustable axial position (eg A, B or C) of the beam waist 18 of the focused light beam 17 , After focusing through the lens 30 the angle of aperture or convergence angle of the focused light beam is constant. This is equivalent to saying that the total focal length of the variable optical element 20 and the lens 30 composite system is constant, although the focal length and the refractive power of the variable optical element VOE 20 may have different values.
  • The total focal length f G of a system composed of two lenses 1 and 2 can be determined according to the following formula known from the technical optics: f G = f 1 f 2 / (f 1 + f 2 -e)
  • Here f 1 is the focal length of the first lens 1, f 2 is the focal length of the second lens 2, and e is the distance between the two lenses. Applied to the device according to the invention, corresponds to the variable optical element (VOE) 20 with the focal length f VOE of the first lens 1, the lens 30 with the focal length f Obj corresponds to the second lens 2, and the distance e of the lenses is, optically exactly formulated, the distance of the image-side major surface of the first lens 1 to the object-side major surface of the second lens 2. This distance e is inventively approximately equal to the focal length f Obj of the lens 30 be. It follows: G f = f f VOE Obj / (f + f VOE Obj - e) With e ≈ f Obj follows: f G ≈ f Obj
  • The total focal length f G is thus approximately equal to the focal length of the lens 30 and thus independent of the focal length of the variable optical element (VOE) 20 , Due to the constant total focal length is the diameter of the beam waist 18 constant over the entire adjustment range Δs. The beam parameters of the focused light beam 17 are therefore constant and do not change when adjusting the axial position of the beam waist 18 , The propagation factor or the beam parameter product can therefore be determined from the beam radii in the different cross-sectional planes of the light beam in conformity with the procedure according to ISO 11146.
  • It is provided that the distance H ' VOE H Obj between the image-side main surface of the variable optical element 20 and the object-side main surface of the lens 30 equal to the focal length f obj of the lens 30 with a maximum deviation of +/- 5%. This maximum deviation has only a small effect on the constancy of the total focal length or on the magnification of the system; their fluctuations then typically amount to at most a few percent.
  • Not just the constancy of the focal length of the variable optical element 20 and the lens 30 composite system is a favorable feature. A further advantageous feature results from the fact that the constant focal length of the composite system is equal to the focal length of the objective 30 is. This can be about the appropriate choice of the focal length of the lens 30 the size of the beam waist 18 of the focused beam 17 regardless of the fixed focal length setting range of the variable optical element 20 adjusted to a desired value to the metrological resolution when recording the intensity distributions in the cross-sectional planes of the light beam 17 to optimize.
  • Another favorable property of the device according to the invention is evident when considering the setting range Δs for the beam waist position. A light beam to be measured is simplified 10 considered collimated. In a known from the prior art device as in 1 is then the adjustment range Δs immediately equal to the difference between the maximum focal length and the minimum focal length of the variable optical element or the variable lens LV: Δs = f LV, C - f LV, A. Thus, in the prior art, the adjustment range Δs is determined by the characteristics of the variable optical element.
  • In the case of the device according to the invention, on the other hand, the setting range Δs results from the following formula: Δs = (f Obj ) 2 [(1 / f VOE, min ) - (1 / f VOE, max )]
  • Thus, it is possible to use the selection of a suitable focal length f Obj of the objective 30 the adjustment range Δs can be adjusted to the desired or required range without passing through the fixed focal length adjustment range f VOE, min to f VOE, max of a variable optical element 20 to be limited.
  • For the most accurate determination of the beam parameter product or the beam propagation factor, it is convenient to scan a beam in a range of several Rayleigh lengths around its beam waist. The Rayleigh length is the distance from the beam waist where the beam diameter is √2 times larger than the beam waist diameter. At a distance of a Rayleigh length from the beam waist, the intensity of the beam has fallen by half for Gaussian beams. With a large diameter of the beam waist and a small aperture angle or divergence angle of the beam, the Rayleigh length can be very large. Conversely, the Rayleigh length is very small with a small diameter of the beam waist and a large aperture angle. It is therefore desirable for the most accurate possible measurement of the beam parameters to be able to adapt the setting range Δs of the device to the radiation to be measured. This is in the device according to the invention by selecting the focal length of the lens 30 possible in many areas.
  • In 2 is, for example, the focal length f Obj of the lens 30 chosen relatively short, hence the focus adjustment range Δs is relatively short. In 3 and 4 On the other hand, embodiments are shown in which the focal length f Obj of the objective 30 is chosen much longer. Also, the adjustment range Δs is much larger, although the focal length adjustment range of the variable optical element 20 is just as big as in 2 ,
  • It also follows that the adjustment of the axial position of the beam waist 18 of the focused light beam proportional to the change of the refractive power of the variable optical element 20 is. This is advantageous because with many optical elements or lenses with adjustable focal length not the focal length, but the refractive power is proportionally dependent on a manipulated variable such as an electric current or a pressure. This results in the device according to the invention also a proportional adjustment of the axial position of the beam waist when changing the manipulated variable of the variable optical element 20 ,
  • As a variable optical element 20 For example, a fluid lens may be used. Such a lens is offered for example by the company Optotune AG under the product name EL-10-30 as "Fast Electrically Tunable Lens". In this lens, an electrically controllable actuator presses on a container which is filled with an optical fluid and sealed with a resilient polymer membrane. Depending on the pressure in the container, the elastic membrane is more or less curved. Thus, the focal length of the lens is controlled by the electrical current applied to the actuator. The manufacturer gives an approximate linear relationship between the electric current and the power of the lens.
  • Any other adjustable focus lenses may also be used as the variable optical element 20 be used. For example, adaptive lenses are possible in which the refractive power can be set by means of actuators; Fluid lenses in which an interface can be electrostatically adjusted; or adaptive mirrors in which the curvature can be adjusted by a pressure chamber or by actuators. The list is to be understood as an example; the invention is not limited to the said types of variable optical elements.
  • To determine the beam parameters or the propagation factor of a light beam, it is provided to scan at least three different cross-sectional planes of the light beam. This will be the beam waist 18 of the focused light beam 17 by adjusting the focal length of the variable optical element 20 shifted to three different axial positions, so that at the spatially resolving detector 50 three different cross-sectional planes of the beam 17 to come to rest. The three adjusted positions of the beam waist 18 may be the positions A, B, C shown by way of example in the figures, but any other three positions may be within the adjustment range Δs of the beam waist 18 and more than three positions can be selected. In order to obtain the most accurate results, it is favorable, on the one hand, the setting positions of the beam waist 18 equidistant and on the other hand an approximately equal number of positions in front of and behind the spatially resolving detector 50 to choose. At every approached position of the beam waist 18 becomes the intensity distribution of the focused light beam 17 from the spatially resolving detector 50 registered. From the registered intensity distributions, the respective beam radii or beam diameters can be determined. Plotting the ray radii above the axial position gives the envelope or caustics of the beam 17 , and the propagation factor or the beam parameter product can be calculated therefrom.
  • The objective 30 can consist of a single lens. For example, to minimize aberrations, the single lens may be an aspherical lens. Reduction of aberrations can also be achieved by using multiple lenses. It is therefore also provided that the lens 30 composed of several lenses.
  • Around the beam in a range of several Rayleigh lengths around the beam waist 18 To scan around, it is not necessary that the entire adjustment range Δs in the real image space behind the lens 30 lies. However, at least approximately half of the setting range Δs should be accessible in real terms, so that the spatially resolving detector 50 approximately near the middle focus position B, 46 , can be arranged. From the requirement of a real image position at the middle focus position B, 46 , the beam waist 18 There may be a limitation in choosing the focal length f obj of the lens 30 yield if the lens 30 consists of only a single thin lens in which the object-side major surface is typically within the lens (eg, a biconvex lens). Consequently, the focal length of the lens is likely 30 in this case, not larger than the focal length of the variable optical element 20 at the average adjustable refractive power of the variable optical element 20 , The following numerical example explains the relationship: The focal length of the variable optical element 20 is adjustable, for example, from f VOE, min = 50 mm to f VOE, max = 250 mm. This corresponds to a refractive power of 20 dpt to 4 dpt (dpt: diopter, refractive power in l / m). The average refractive power in this example is about 12 dpt, corresponding to a focal length of 83 mm. If the lens 30 with a single lens then has a focal length of for example 100 mm and therefore would have to be arranged about 100 mm behind the variable optical element, then the image position is at the middle focus position (B) 46 the beam waist 18 not in the real area behind the lens 30 , This in 3 embodiment shown corresponds approximately to the mentioned numerical example. In the present invention, this limitation is for the focal length of the objective 30 overcome, since according to the invention not only single lenses as a lens 30 can be used, but also other types of the lens 30 are provided, in which the main surfaces need not lie within the lens or lenses of the lens.
  • It is also intended that the lens 30 a first lens group 35 and a second lens group 36 includes. Both lens groups 35 . 36 together form the lens 30 , The first lens group 35 may consist of a single lens or comprise multiple lenses. The second lens group 36 may also consist of a single lens or comprise multiple lenses. The first lens group 35 may have a negative focal length, and the second lens group 36 can have a positive focal length, and that of both lens groups 35 . 36 compound lens 30 has a positive focal length. This creates a lens in so-called retrofocus construction. A retrofocus lens has an image section that is larger than the focal length of the lens. The image-side main surface H 'is therefore shifted backwards into the image space. For the device according to the invention, however, the position of the object-side main surface H is essential. The position of the object-side main surface is also shifted to the rear with a retrofocus lens. 9 shows the location of the main surfaces with a lens 30 in retro-focus construction with a first lens group 35 and a second lens group 36 , The 6 . 7 , and 8th show embodiments of the invention with an object designed as a retro-focus lens 30 , The retro-focus construction of the lens 30 can be beneficial in several ways. On the one hand, this allows the position of the adjustment range Δs to be shifted to the rear. Furthermore, this is the distance of the lens 30 to the variable optical element 20 considerably shortened, whereby the size of the device is reduced. Finally, despite the small size of a very large focal length of the lens 30 be realized in order to achieve a large adjustment range Δs.
  • In the following, further embodiments and developments of the invention are shown.
  • When measuring a laser beam with high brilliance, ie with a small beam parameter product or mode factor, it may be desirable, for example, for the lens 30 to choose a very large focal length, around the beam waist 18 of the focused beam 17 as large as possible and to achieve a high lateral resolution. In this case, the situation may occur that part of the focus adjustment range Δs or even the entire focus adjustment range is not in the real image space behind the lens 30 and thus is not available for the survey with the spatially resolving detector. A situation in which only part of the adjustment range lies in the real image space is shown by way of example 3 , In order to be able to completely scan the beam caustic in such situations, further embodiments of the invention are proposed.
  • In a second embodiment of the invention is provided, in the beam direction in front of the variable optical element 20 a lens (LD) 60 to arrange for divergence adjustment. With this lens 60 a refractive power offset is generated and thereby the entire focus adjustment range Δs is axially displaced by a certain amount. Has the lens 60 for divergence adjustment, a negative power, then the focus adjustment range .DELTA.s is shifted in the beam direction to the rear. A corresponding embodiment is in 5 shown.
  • The refractive power of the lens (LD) 60 to divergence adjustment can also be positive. Thereby, the adjustment range Δs of the beam waist becomes 18 forward, closer to the lens 30 postponed. This can be advantageous in the measurement of light rays 10 that have a relatively high divergence and a beam waist 11 have near the measuring device. 7 shows an embodiment with a positive lens 60 for divergence adjustment.
  • The lens (LD) 60 for divergence adjustment may also be a variable lens whose focal length or refractive power can be varied. Thus, a device can be created that is flexible to many geometric configurations of the beam to be measured 10 can be adjusted. This is the measurement of convergent, divergent and collimated rays 10 and rays with different layers of the beam waist 11 possible without having to make a conversion of the device. It only becomes the focal length of the lens 60 for divergence adjustment suitable for the respective beam 10 set, z. B. such that the beam 10 after the lens 60 is collimated to divergence adjustment. During the measurement of the beam 10 is the focal length or refractive power of the variable lens 60 constant for divergence adjustment; for varying the position of the beam waist 18 during the beam measurement, the focal length or refractive power of the variable optical element 20 changed.
  • In a third embodiment, the invention further comprises a device for beam attenuation. The device for beam attenuation may comprise, for example, a filter glass or a neutral density glass, also called gray glass. The device for attenuation may also consist of a pair of polarizing filters with mutually adjustable angle. The device for attenuation may also include one or more beam splitters 70 comprise, which divide the beam into a reflected and a transmitted beam, each having low intensities than the original beam. The beam splitter 70 may be formed by an interface of an optical device such as a plane plate, a wedge plate or a prism. The interface of the optical device may be uncoated or coated, for example provided with a dielectric coating. 8th shows by way of example the device according to the invention with a device for beam attenuation, which consists of two beam splitters 70 exists in front of the variable optical element 20 are arranged. Each beam splitter 70 reflects a small portion of the light beam 10 , so that after twice reflection of the light beam 10 has a significantly reduced intensity. The beam components transmitted by the beam splitters with the majority of the beam power are from beam traps or absorbers 74 collected. The two beam splitters 70 can be arranged spatially so that the reflection planes are rotated by 90 ° to each other. Thus, a very precise polarization-independent attenuation can be achieved, which is also suitable for high beam intensities and high beam powers. The invention is thus also applicable to the measurement of high power laser beams.
  • The invention is not limited to the illustrated and described embodiments. Rather, the features of individual embodiments can also be combined. For example, a device including both a divergence adjustment lens (LD) and a beam attenuation means is within the scope of the present invention.
  • The invention offers numerous advantages over the prior art, which are summarized below:
    • • The device allows the rapid and precise adjustment of the axial position of the image-side beam waist 18 a light beam to be measured 10 relative to a spatially resolving detector 50 , Without elements of the device must be stored axially movable.
    • • The focal length of the overall optical system consisting of the variable optical element 20 and the lens 30 is constant and independent of the focal length of the variable optical element 20 ,
    • • Due to the constant focal length or the constant imaging properties of the overall system of variable optical element 20 and lens 30 the evaluation for the determination of propagation factors or jet parameter products can be carried out according to the formulas of ISO 11146.
    • • By means of a construction of the lens 30 consisting of two lens groups 35 . 36 a compact design with long focal length of the overall system and thus a large axial focus adjustment range Δs can be achieved.
    • The calibration of the device required for the correct determination of the beam parameters and for the conversion of the parameters to the object-side beam parameters is simpler and less error prone than with devices with varying total focal length.
    • • The beam parameter product, which is determined from the beam diameters measured in different cross-sectional planes, is independent of the exact axial positioning of the spatially resolving detector 50 , which reduces the number of potential sources of systematic error.
    • • The focal length of the overall optical system can be independent of the limitations of the variable optical element 20 be selected to the magnification or the diameter of the image-side beam waist 18 to the conditions of the light rays to be measured 10 or to adapt laser beams.
    • • The focal length of the lens 30 may be suitably selected to be independent of the predetermined focal length variation range of the variable optical element 20 a sufficiently large or small adjustment range Δs for the axial position of the image-side beam waist 18 to realize.
    • • The change of the axial position of the image-side beam waist 18 is proportional to the refractive power change of the variable optical element 20 and is thus approximately linearly dependent on the manipulated variable in most variable optical elements 20 ,
  • The determination of a geometric parameter of the light beam from the registered intensity distributions can also be the determination of the axial position of a beam waist or focus position 18 of the focused light beam 17 include. From the position of the image-side focus position 18 can use the mapping equation of the overall system to determine the axial position of the beam waist 11 of the original beam to be measured. The invention is therefore also intended to control or monitor a focus position of a light beam or laser beam. The monitoring of a focus position may be advantageous, for example, in a laser processing system to diagnose changes in the desired focus position of a processing laser beam. Such changes can be caused for example by thermal effects. Changes in the target focus position may also be caused by the laser beam itself due to absorption of the radiation by the processing optics.
  • The invention can be used for example for measuring laser beams. It can be measured laser beams emitted by beam sources. It is also possible to measure laser beams which are emitted by a beam guidance system, such as an optical fiber, or which are imaged or focused by laser processing optics, or which are imaged by beam shaping optics for shaping a desired beam geometry.
  • The invention can also be used for on-line beam diagnosis, for example on a laser processing optical system which decouples a fraction of the laser beam by means of a beam splitter and makes it available at a diagnostic beam output. The device according to the invention can be coupled to the diagnostic beam output of the laser processing optics. The invention can also be integrated as a fixed component in the laser processing optics. The laser processing optics may be, for example, a scanner optics.
  • LIST OF REFERENCE NUMBERS
  • 10
    To be measured light beam
    11
    Beam waist of the light beam to be measured
    15
    Optical axis
    17
    Focused light beam
    18
    Beam waist or focal position of the focused light beam
    20
    Variable optical element with adjustable focal length
    22
    Image-side main surface of the variable optical element
    25
    Image-side focal point of the variable optical element at maximum power
    26
    Image-side focal point of the variable optical element at average power
    27
    Image-side focal point of the variable optical element with the smallest refractive power
    30
    lens
    31
    Object-side main surface of the lens
    32
    Image-side main surface of the lens
    33
    Object-side focal point of the lens
    34
    Image-side focal point of the lens
    35
    First lens group of the lens
    36
    Second lens group of the lens
    45
    Front end position A of the focus adjustment range
    46
    Middle position B of the focus adjustment range
    47
    Rear end position C of the focus adjustment range
    50
    Spatial detector
    60
    Lens for divergence adjustment
    70
    beamsplitter
    74
    Jet trap (absorber)

Claims (12)

  1. Device for determining geometric parameters of a light beam ( 10 ) comprising a variable optical element ( 20 ), a lens ( 30 ), and a spatially resolving detector ( 50 ), wherein the variable optical element ( 20 ) an adjustable focal length and an image-side main surface ( 22 ), wherein the objective ( 30 ) a constant focal length and an object-side main surface ( 31 ), wherein the distance between the image-side main surface ( 22 ) of the variable optical element ( 20 ) and the object-side main surface ( 31 ) of the lens ( 30 ) equal to the constant focal length of the lens ( 30 ) with a deviation of at most +/- 5%, the objective ( 30 ) the variable optical element ( 20 ) is downstream in the beam direction, wherein the spatially resolving detector ( 50 ) the lens ( 30 ) is downstream in the beam direction, and wherein by changing the adjustable focal length of the variable optical element ( 20 ) and by subsequent focusing of the light beam ( 10 ) through the lens ( 30 ) a focus position ( 18 ) of the focused light beam ( 17 ) relative to the spatially resolving detector ( 50 ) is variably adjustable in the axial direction.
  2. Device according to claim 1, wherein the relative positions of the light beam ( 10 ), of the variable optical element ( 20 ), the lens ( 30 ) and the spatially resolving detector ( 50 ) are stationary relative to each other.
  3. Apparatus according to claim 1 or 2, wherein the total focal length of a system consisting of the variable optical element ( 20 ) and the lens ( 30 ) equal to the constant focal length of the lens ( 30 ) with a maximum deviation of +/- 5%.
  4. Device according to one of claims 1 to 3, wherein the variable optical element ( 20 ) comprises a fluid lens.
  5. Device according to one of claims 1 to 3, wherein the variable optical element ( 20 ) comprises an adaptive lens.
  6. Device according to one of claims 1 to 3, wherein the variable optical element ( 20 ) comprises an adaptive mirror.
  7. Device according to one of claims 1 to 6, wherein a lens ( 60 ) for divergence adjustment in the beam direction in front of the variable optical element ( 20 ) is arranged.
  8. Device according to one of claims 1 to 7, wherein the lens ( 30 ) a first lens group ( 35 ) and a second lens group ( 36 ).
  9. Apparatus according to claim 8, wherein the first lens group ( 35 ) of the lens ( 30 ) has a negative refractive power, the second lens group ( 36 ) of the lens ( 30 ) has a positive refractive power, and wherein the constant focal length of the objective ( 30 ) has a positive value overall.
  10. Method for determining geometric parameters of a light beam ( 10 ), comprising the method steps: - changing an opening angle of the light beam ( 10 ) by means of a variable optical element ( 20 ), which has an adjustable focal length and an image-side main surface ( 22 ), - focusing of the variable optical element ( 20 ) with respect to the opening angle changed light beam by means of a lens ( 30 ), which has a constant focal length and an object-side main surface ( 31 ), - changing the adjustable focal length of the variable optical element ( 20 ), in which successively at least three different focal lengths are set, - registering intensity distributions of the lens ( 30 ) focused light beam ( 17 ) by means of a spatially resolving detector ( 50 ), which in the beam direction after the lens ( 30 ), wherein in each case an intensity distribution is registered at each of the at least three different set focal lengths, and - determining a geometric parameter of the light beam ( 10 ) from the registered intensity distributions, wherein the distance between the image-side main surface ( 22 ) of the variable optical element ( 20 ) and the object-side main surface ( 31 ) of the lens ( 30 ) equal to the constant focal length of the lens ( 30 ) with a maximum deviation of +/- 5%.
  11. Method according to claim 10, wherein the relative positions of the light beam ( 10 ), of the variable optical element ( 20 ), the lens ( 30 ) and the spatially resolving detector ( 50 ) are stationary relative to each other.
  12. The method of claim 11, wherein determining a geometric parameter of the light beam ( 10 ) determining from the registered intensity distributions a beam propagation factor of the light beam ( 10 ).
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Citations (2)

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WO2011127400A2 (en) * 2010-04-08 2011-10-13 Scaggs Michael J Laser beam analysis apparatus
US8736827B2 (en) * 2009-04-28 2014-05-27 The Secretary of State for Business Innovation and Skills of Her Majesty's Brittannic Government Method and system for measuring the propagation properties of a light beam

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US5042950A (en) * 1990-05-22 1991-08-27 The United States Of America As Represented By The United States Department Of Energy Apparatus and method for laser beam diagnosis
DE102007053632B4 (en) * 2007-11-08 2017-12-14 Primes Gmbh Method for coaxial beam analysis on optical systems
DE102010053323B3 (en) * 2010-12-02 2012-05-24 Xtreme Technologies Gmbh Method for the spatially resolved measurement of parameters in a cross section of a beam of high-energy, high-intensity radiation

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US8736827B2 (en) * 2009-04-28 2014-05-27 The Secretary of State for Business Innovation and Skills of Her Majesty's Brittannic Government Method and system for measuring the propagation properties of a light beam
WO2011127400A2 (en) * 2010-04-08 2011-10-13 Scaggs Michael J Laser beam analysis apparatus

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Norm DIN EN ISO 11146-1 2005-04-00. Laser und Laseranlagen – Prüfverfahren für Laserstrahlabmessungen, Divergenzwinkel und Beugungsmaßzahlen – Teil 1: Stigmatische und einfach astigmatische Strahlen
Norm DIN EN ISO 11146-1 2005-04-00. Laser und Laseranlagen – Prüfverfahren für Laserstrahlabmessungen, Divergenzwinkel und Beugungsmaßzahlen – Teil 1: Stigmatische und einfach astigmatische Strahlen *

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