DE102014114253A1 - Method for compensating aberrations caused by thermal lens effects in an optic - Google Patents

Abstract

The invention relates to a method for compensating imaging aberrations by effects of thermal lenses in an optics. The object to compensate for aberrations of an optical system, which occur within the optical system in at least one optical element by forming a thermal lens as a result of applied concentrated high-energy radiation, is achieved according to the invention by determining temperature-dependent refractive index inhomogeneities of the optical element as a function of defined operating times Influence of a radiation beam of high-energy radiation applied with predetermined beam parameters and modeling and implementing a proviso of refractive inhomogeneities in the nominal design (zero state) of the optical system without the action of the beam of high-energy radiation such that the effect of the thermally induced refractive index inhomogeneities for defined operating times compensates for the action of the beam become.

Description

The invention relates to a method for compensating aberrations by the effects of thermal lenses in an optics for the application of concentrated high-energy radiation, in particular for focusing or focusing of laser radiation with high beam quality.

In the prior art, the problem of the formation of a thermal lens by the action of high-energy radiation (eg laser radiation) is known and has led to thinking about different compensation measures. A common approach is to compensate for the defocusing caused by the thermal lens in an optics penetrated by the radiation.

So is in the US Pat. No. 6,509,702 B1 discloses a method of correcting for temperature-related focusing errors, in which a head-up display (HUD) is provided with a plurality of lenses made of plastic material and a support of metallic material, taking into account the temperature changes of the environment mechanical measurements of the different coefficients of expansion of plastic and metal and their subsequent use to control the image position. A very similar thermal compensation measure is in the US Pat. No. 6,650,412 B1 discloses in this case, the optics resiliently supported and parallel to the optical axis by a plurality of polymer spacers having a positive linear thermal expansion coefficient, passive (ie without active measuring and control unit) is displaceable, so that with increasing temperature, the optics on a Detector is moved. Yet another method for reducing thermal effects in compact adjustable lenses is the US 8 310 772 B2 has become known, in which for a lens group, a polymer lens body is present, which can be deformed by means of actuators by control signals to adjust the focal length of the lens group.

All of the preceding compensation principles have in common that they take into account only the global warming of the lens or lens group and correct the focus position by axial displacement of the optics, whereby a local formation of a thermal lens in the optics due to bundled radiation exposure is irrelevant and such effects are not compensated ,

A first approach for consideration of local radiation absorption and radial heat conduction with power-dependent temperature distribution and thermal dispersion (for producing a thermal lens) within the optics is in the US 2002/0021724 A1 in particular for laser resonators in which a particularly good beam quality is required disclosed. There, thermal compensation elements with different material properties are brought into direct contact with optical components in order to achieve the same radial temperature distribution as in the adjacent optical element and thus an adapted compensation. The rotationally symmetric compensation units used in the beam path consist of solids and compensation space which is filled with a transparent optical compensation medium which does not transmit any mechanical shear forces. With the same refractive index of optical solid (eg laser rod) and deformable compensation medium, the thermal lensing effect is not effective because no Fresnel reflections occur.

Furthermore, from the US 6 134 039 A It is known to provide a wavelength-dependent thermally compensated optical system for a scanner with a refractive focusing optics and a thermal compensation element, wherein a diffractive optical element (DOE) is arranged in front of the focusing optics, the focus shift due to the thermal expansion of the Refractive focusing optics arises, compensated. To customize and test the design of the DOE, optics design software available from Optical Research Associates, Pasadena, California (USA) was used. For verification, another optical design software ZEMAX ^™ from Focus Software, Inc., Tucson, Arizona (USA) was used.

The last two solutions of the prior art have in common that radially-dependent temperature distributions that cause local thermal lens effects, although locally compensated can be compensated, but for additional, sometimes complex generated or complex held compensating compensation media must be introduced into the beam path, each additional element unwanted radiation attenuation and secondary aberrations generated. In both cases - without any explicit mention - exact measurements are required to determine wavefront aberrations, which were significantly simplified due to the latest optical measurement technology, especially for laser radiation. Such a beam diagnosis is for example of Kunzmann et al. in "Characterization of laser radiation by Hartmann-Shack wavefront sensor" (in: Photonics 1/2005, ISSN 1432-9778) described.

The invention has for its object to find a new way to compensate for aberrations due to thermal lenses in optics for the application of concentrated high-energy radiation, in which caused by locally different temperature fields aberrations of the optics are reduced, without elaborate temperature-controlled corrective measures or additional controlled by the local temperature distribution compensation media are used. An extended object is to provide a method for producing athermal optics, in particular for focusing or focusing laser radiation with high beam quality.

• – Ermitteln von temperaturabhängigen Brechzahlinhomogenitäten des mindestens einen optischen Elements für vorgegebene Betriebsbedingungen des optischen Systems in Abhängigkeit von definierten Betriebsdauern der Einwirkung eines definierten Strahlenbündels der energiereichen Strahlung und
• – Modellieren und Implementieren eines Vorhalts von Brechzahlinhomogenitäten des mindestens einen optischen Elements in einem Nullzustand des Optikdesigns ohne Einwirkung des Strahlenbündels der energiereichen Strahlung derart, dass die Brechzahlinhomogenitäten für definierte Betriebsdauern der Einwirkung des Strahlenbündels minimiert oder kompensiert werden.

According to the invention, the object is achieved by a method for the reduction of aberrations of an optical system that occur within at least one optical element of the optical system by forming a thermal lens as a result of applied concentrated high-energy radiation, with the following steps:

• Determining temperature-dependent refractive index inhomogeneities of the at least one optical element for predetermined operating conditions of the optical system as a function of defined operating times of the action of a defined beam of high-energy radiation and
• Modeling and implementing a Vorhalt of refractive index inhomogeneities of the at least one optical element in a zero state of the optical design without the action of the beam of high-energy radiation such that the refractive index inhomogeneities for defined operating periods of the action of the beam are minimized or compensated.

• – Ermittlung von Bündelparametern des auf das optische System anzuwendenden definierten Strahlenbündels;
• – Berechnung einer Temperaturverteilung im optischen System auf Basis von FEM-Rechnungen für mindestens ein optisches Element des optischen Systems mit mindestens einem verwendeten Optikmaterial;
• – Ermittlung von Referenzbrechzahlen aus Nominalbrechzahlen des verwendeten Optikmaterials bei jeweils einer Referenzwellenlänge und einer Referenztemperatur;
• – Simulation eines Brechzahlprofils durch Anwendung einer analytischen Standardform zur Brechzahlprofilbeschreibung unter Nutzung der simulierten Temperaturverteilung sowie der ermittelten Referenzbrechzahlen und von Koeffizienten thermischer Dispersion des verwendeten Optikmaterials;
• – Modellierung (Programmierung und Nutzung) einer benutzerdefinierten Oberfläche zur Anpassung des simulierten Brechzahlprofils und Umsetzung in Modellparameter zur Optikdesignmodellierung des optischen Systems;
• – Simulation transienter Zustände des Brechzahlprofils im Optikdesign für bestimmte Betriebsdauern und Modellierung angepasste Modelle für unterschiedliche Brechzahlprofile und modifizierte Bündelpropagation mittels Optikdesignmodellierung des optischen Systems; und
• – Auswahl eines angepassten Modells mit einem Brechzahlprofil, bei dem die Simulation der transienten Zustände ein kompensierendes Optikdesign des optischen Systems ergeben hat, bei dem gewünschte Spezifikationen von vorgegebenen optischen Gütekriterien des optischen Systems wenigstens für eine definierte Betriebsdauer erfüllt sind.

The procedure for determining the refractive index inhomogeneities and for compensating their effects is as follows:

• Determination of bundle parameters of the defined beam to be applied to the optical system;
• Calculation of a temperature distribution in the optical system on the basis of FEM calculations for at least one optical element of the optical system with at least one optical material used;
• - Determining reference refractive indices of nominal refractive indices of the optical material used in each case a reference wavelength and a reference temperature;
• - Simulation of a refractive index profile by application of a standard analytical form for refractive index profile description using the simulated temperature distribution and the determined reference refractive indices and coefficients of thermal dispersion of the optical material used;
• - Modeling (programming and usage) of a user-defined interface for adapting the simulated refractive index profile and conversion into model parameters for optical design modeling of the optical system;
• Simulation of transient states of the refractive index profile in optics design for specific operating times and modeling adapted models for different refractive index profiles and modified beam propagation by optical design modeling of the optical system; and
• Selection of an adapted model with a refractive index profile, in which the simulation of the transient states has yielded a compensating optical design of the optical system in which desired specifications of predetermined optical quality criteria of the optical system are satisfied at least for a defined operating period.

Advantageously, a suitable FEM simulation software is used to simulate the temperature distribution or refractive index profile. Preferably, the simulation software ANSYS ^TM is used.

To simulate the refractive index profile, a refractive index profile description using standard GRIN lenses is expediently also applied to any type of refractive optical element as standard form.

For the simulation of transient states of the refractive index profile, a commercially available optical modeling software is preferably used. The optical modeling software ZEMAX ^™ or Code V ^™ is advantageously used for this purpose.

In the modeling of a user-defined surface, a further verification of the modeled optical system by comparison with refractive index profiles, which can be described with GRIN lenses (so-called surface type in ZEMAX ^™ ), is carried out.

To program the user-defined interface, the programming language C ++ is advantageously chosen.

Preferably, the diffraction factor M ^{2 is} used as a quality criterion for the evaluation, optimization and selection of the adapted models of transient states for implementation in the compensated design of the optical system. In addition to this, or only as an alternative, the energy in a defined area (encircled energy - EcE) can be used as the quality criterion. In addition, additionally or alternatively, as the quality criterion, a best focus state or a minimum defocus can be used.

• – die Simulation von Temperaturverteilungen des optischen Systems durch FEM-Rechnungen,
• – die Simulation der Temperaturverteilung im optischen System durch ein analytisches Modell,
• – die Ermittlung des Brechzahlprofils unter Nutzung der simulierten Temperaturverteilung, der ermittelten Referenzbrechzahlen und der Koeffizienten thermischer Dispersion des verwendeten Optikmaterials,
• – Umsetzung des simulierten Brechzahlprofils durch Übergabe der ermittelten Modellparameter an die benutzerdefinierte Oberfläche (UDS);
• – die Simulation des transienten Zustands des optischen Systems mit – einer Ermittlung modifizierter Bündelpropagation in dem optischen System mittels der Optikmodellierungssoftware und – einer Ermittlung modifizierter Ein- und Austritts-Bündelparameter an allen Oberflächen optischer Elemente des optischen Systems

aufeinanderfolgend wiederholt durchgeführt werden, bis vorgegebene optische Gütekriterien des optischen Systems zumindest für eine definierte Betriebsdauer am besten erfüllt sind.Advantageously, the simulation of temperature-dependent refractive index inhomogeneities is carried out iteratively by determining the bundle parameters of the radiating high-energy beam, the determination of free diameters on the surfaces of the optical elements, starting from the simulation of temperature profiles of the optical system by FEM calculations, the adaptation of the state parameters of transient temperature distribution model; Implementation of user-defined surfaces in optics design using these state parameters, the simulation of the bundle propagation in the optical system, determination of the system performance and the thermally modified new bundle parameters are successively applied repeatedly. The temperature-dependent refractive index inhomogeneities are preferably simulated by

• The simulation of temperature distributions of the optical system by FEM calculations,
• The simulation of the temperature distribution in the optical system by an analytical model,
• The determination of the refractive index profile using the simulated temperature distribution, the determined reference refractive indices and the coefficients of thermal dispersion of the optical material used,
• - Implementation of the simulated refractive index profile by transferring the determined model parameters to the user-defined interface (UDS);
• The simulation of the transient state of the optical system with - a determination of modified beam propagation in the optical system by means of the optical modeling software and - a determination of modified input and output beam parameters on all surfaces of optical elements of the optical system

be carried out repeatedly successively until predetermined optical quality criteria of the optical system are best satisfied at least for a defined operating time.

The iterative simulation is preferred for multi-lens optical systems.

The invention is based on the basic idea that optics, due to the influence of different temperature fields as a result of local heating due to the applied beam, form a varying thermal lens and associated wavefront deformations. These depend primarily on the nominal temperature at a time zero (in the cold state) and the temperature after different defined operating periods. The customary in the prior art compensation of thermal effects by mechanical adjustment, which can not compensate locally different temperature fields anyway, or by introducing additional compensation media is inventively improved by performing a simulation of the thermal lens for the thermal operating point of the optical system. The effect of the simulated thermal lens for a given operating state or after a certain period of operation (duration of exposure of the beam of high-energy radiation) can be incorporated into the optical design, which opens up the possibility of the effects of Brechzahlinhomogenitäten, such as defocusing and aperture errors in the optical system to largely compensate for an adapted design. For the verification of the achieved compensation state different optical quality criteria can be used, for. B. Minimization of the diffraction factor M ² (defined by the ray parameter product - SPP = φw ₀ = M ² λ / π), best focus state (minimum defocus - focus shift in z direction), minimum radius of a cross section with given energy content (encircled energy - EcE In other words, according to the invention, for the initial state (zero state or "cold state") of the optical elements of the optical system, wavefront deformations are set as lead by means of aspherical design of the lens surface such that the size of the thermal lens for predetermined operating times - simulated as transient or temporary states taking into account the application-specific temperature fields and modeled in optical design - is calculated in advance, so that optical quality criteria (for collimated or focused laser radiation preferably the diffraction ahl M ^{2 of} the beam parameter product) for one or more desired times or optional time intervals (ie at predetermined operating temperatures T _{i of} the optical system) optimized and thus aberrations due to the thermal lens are largely compensated.

With the present invention, it is possible to compensate for or minimize aberrations due to the refractive incoherence due to the formation of thermal lenses in optics in the application of concentrated high-energy radiation by optical aberrations caused by locally different temperature fields can be reduced without elaborate temperature-controlled corrective measures or additional compensation media controlled by the local temperature distribution are used. In particular, a method for the production of athermal optics is specified in which wavefront deformations by thermal lenses in the "cold state" of the optics are held so that this after the optics, which is particularly intended for focusing or focusing of laser radiation with high beam quality after or are minimized for given operating periods in the thermal operating point of the optics.

The invention will be explained below with reference to exemplary embodiments. The drawings show:

1 : Motivation and schematic outline of the method according to the invention;

2 a preferred embodiment of the simulation of the refractive index inhomogeneities of an optical element based on the computer-aided FEM analysis of the temperature profile as a function of material parameters, the geometry of the applied beam and environmental parameters, such as temperature and thermal conductivity of the element environment;

3 : a temperature simulation based on the finite element method (FEM) after model adaptation for a rotationally symmetrical optics with non-symmetrical beam profile;

4 : a FEM-simulated temperature profile of a lens in axial section for a beam bundle with a limited beam cross-section after 450 s radiation exposure;

5 : a three-dimensional comparison of the FEM-simulated temperature profile of 4 (Points) and the adjusted temperature distribution (area) over the lens diameter (in x-direction) and the lens thickness (z-direction) used for system optimization and performance simulation;

6 : a three-dimensional representation of the residual of the adaptation of the temperature distribution after 450 s of radiation exposure in 5 ;

7 an embodiment with a two-lens projection optics in the original spherical state in a 3D layout;

8th : Representations of FEM-modeled temperature distributions in the axial section of a lens for different beam bundles: a) narrow parallel laser bundle with volume absorption; b) broad, collimated laser bundle with volume absorption, c) broad collimated laser bundle with surface absorption, d) focused laser bundle with volume absorption, e) collimated laser bundle with different surface absorption on top and bottom;

9 an embodiment with a single-lens projection optics in the original spherical state in a 3D layout;

10 : Emigration of focus due to thermal effects over time for an unmodified system 9 ;

11 : a comparison of the temperature at the lens vertex in FEM simulation and temperature distribution model for the transient states between 0.1 s and 900 s for the projection optics of 9 ;

12 : a FEM simulation of the temperature distribution for the projection optics of 9 ;

13 : a representation of defocusing according to three different criteria of the waist position and the bundle quality (diffraction factor M ² ) over time for an original spherical lens (Suprasil);

14 FIG. 3: shows defocusing according to three different criteria of waist position and bundle quality (diffraction factor M ² ) over time for a modeled aspherical lens (Suprasil); FIG.

15 : A graphical comparison of the variation of defocusing and M ² for the original spherical design 13 and the "aspherized" version of 14 over time;

16 : the RMS wavefront error versus exposure time for two design variants of a two-lens optical system with "aspherized" lenses optimized for optimal imaging after 2s and 450s, respectively;

17 : the RMS wavefront error as a function of the exposure time for four variants of a two-lane system with differently aspherized designs, optimized for best performance over different irradiation periods;

18 : a measured intensity cross section of a non-rotationally symmetrical laser beam, the temperature distribution according to 3 generated;

19 : a schematic representation of the fit function for modeling the temperature distribution for a bundle cross-section according to 18 and

20 : a schema of the iterative simulation strategy.

The method for the reduction of aberrations of an optical system, which occur due to refractive index inhomogeneities by forming a thermal lens as a result of applied concentrated high-energy radiation, is basically based on a determination of temperature-dependent refractive index inhomogeneities of the at least one optical element for predetermined operating conditions of the optical system depending on defined Operating times of the action of a defined beam of high-energy radiation on the one hand, the modeling of the effect of these inhomogeneities in the optical system on the other hand, and finally the implementation of a premise for the thermal effects in the design of the system for at least one optical element in a zero state without the influence of the beam of energy Radiation in such a way that the thermal lenses compensate for the action of the beam for defined operating times or at least minimized.

• – Ermittlung von Bündelparametern des auf das optische System anzuwendenden definierten Strahlenbündels,
• – Ermittlung von Referenzbrechzahlen bei einer Referenzwellenlänge und Referenztemperatur sowie den thermischen Dispersionskoeffizienten des verwendeten Optikmaterials,
• – Berechnung einer Temperaturverteilung in mindestens einem optischen Element durch FEM-Simulation unter Nutzung vorbekannter Angaben über das optische System (Daten verwendeter Optikmaterialien und geeignete Annahmen über Wärmekapazität, Wärmeleitfähigkeit und Wärmeübergangskoeffizienten von Strukturen der Optikfassung und angrenzenden Medien),
• – Anpassung eines allgemeinen Temperaturverteilungsmodells mit freien Parametern an die Ergebnisse der FEM-Temperatursimulation zur Erzeugung einer gefitteten Temperaturverteilungsfunktion mit gefittetem Parametervektor und Maßzahlen zur Bewertung der Güte der Anpassung,
• – Berechnung einer Brechzahlverteilung über das Volumen eines optischen Elements, ausgehend von den Referenzbrechzahlen sowie den thermischen Dispersionskoeffizienten des verwendeten Optikmaterials mithilfe der gefitteten Temperaturverteilungsfunktion,
• – Modellierung einer benutzerdefinierten Oberfläche (UDS) mithilfe einer geeigneten Programmiersprache (z.B. C++), die zur Implementierung der allgemeinen analytischen Darstellung der Brechzahlenverteilung und deren räumlichen Ableitungen in ein geeignetes Optikdesignprogramm (bspw. ZEMAX^TM oder Code V^TM) vorgesehen ist und den gefitteten Parametervektor zu einer (ggf. wiederholten) Anpassung an eine vorgegebene Situation der Temperatur- und Brechzahlenverteilung verarbeitet für die Eingabe in das verwendete Optikdesignprogramm, wobei nach Einfügen der UDS in das Optikdesignprogramm und Übergabe der gefitteten Parameter an die UDS eine Repräsentation der thermischen Effekte im Optikdesign des optischen Systems zur Verfügung steht, die die Nutzung aller durch das verwendete Optikdesignprogramm bereitgestellten Analysewerkzeuge ermöglicht,
• – Simulation, Untersuchung und Bewertung von transienten Systemzuständen im Optikdesignprogramm zur Anpassung des optischen Systems als Modelle transienter Zustände für bestimmte Betriebsdauern und
• – Implementierung von ausgewählten angepassten Modellen transienter Zustände als Designvarianten des optischen Systems, für die geforderte optische Gütekriterien für wenigstens eine bestimmte Betriebsdauer am besten erfüllt sind.

The above procedure is broken down into the following more detailed steps:

• Determination of bundle parameters of the defined beam to be applied to the optical system,
• Determination of reference refractive indices at a reference wavelength and reference temperature and the thermal dispersion coefficient of the optical material used,
• Calculation of a temperature distribution in at least one optical element by FEM simulation using previously known information about the optical system (data of used optical materials and suitable assumptions about heat capacity, thermal conductivity and heat transfer coefficients of structures of the optical detection and adjacent media),
• Adapting a general temperature distribution model with free parameters to the results of the FEM temperature simulation to produce a fitted temperature distribution function with fitted parameter vector and measures for assessing the quality of fit,
• Calculation of a refractive index distribution over the volume of an optical element based on the reference refractive indices and the thermal dispersion coefficient of the optical material used by means of the fitted temperature distribution function,
• Modeling of a user-defined surface (UDS) using a suitable programming language (eg C ++) intended to implement the general analytical representation of the refractive index distribution and its spatial derivatives into a suitable optical design program (eg ZEMAX ^™ or Code V ^™ ) and the fitted parameter vector to a (possibly repeated) adaptation to a given situation of temperature and refractive index distribution processed for input into the optical design program used, wherein after inserting the UDS into the optical design program and passing the fitted parameters to the UDS a representation of the thermal effects in the optical design of the optical system that allows the use of all analysis tools provided by the optical design program used,
• Simulation, investigation and evaluation of transient system states in the optical design program for the adaptation of the optical system as models of transient states for certain operating times and
• Implementation of selected adapted models of transient states as design variants of the optical system for which required optical quality criteria are best fulfilled for at least a certain operating time.

1 illustrates the analysis underlying the above procedure. The standard means of describing non-uniform volume fractional refractive index distributions (GRIN surfaces) implemented in optical design software have generally not been suitable for investigating thermal lensing effects after inspection of existing data (FEM-simulated temperature distributions, bundle parameters, and thermal dispersion properties of the materials used) proved. One of the reasons is that the temperature distributions in the optically active elements are very light beam-specific, and are often determined by layer absorption. As an alternative, therefore, the representation of the thermal effects by freely programmable user defined areas (UDS) was chosen. These allow the largely free description of the refractive index distribution as a DLL, for example generated in C ++. The adaptation parameters of the FEM-simulated temperature field to the very general temperature model used are transferred to the UDS and thus determine the refractive index profile in the optical element. In order to verify the software implementation, some practical special cases, which could alternatively be described with standard GRIN surfaces, were examined and the identity of the effect determined.

wobei ∆T die Temperaturdifferenz zur Referenztemperatur des Glases, D₀ bis D₂, E₀ bis E₁ zugehörige Koeffizienten und λ_tk vom Glashersteller bereitgestellte Konstanten sind. Nach Einfügen (Modellieren) der UDS in die Optikdesign-Software und die damit ermöglichte Übergabe der Parameter an die UDS steht eine Repräsentation der thermischen Effekte im Optikdesign zur Verfügung, die die Nutzung aller durch die verwendete Optikdesign-Software (Lens Design Program) bereitgestellten Analysetools ermöglicht. In einem nächsten Schritt wird dadurch in der Optikdesign-Software die Möglichkeit zur Untersuchung und Bewertung der transienten Systemzustände für bestimmte Betriebsdauern des optischen Systems eröffnet. Darüber hinaus werden Designvarianten (angepasste Modelle) des optischen Systems erstellt, die geforderte optische Gütekriterien für vorgegebene definierte Betriebsdauern am besten erfüllen. Diese optischen Systeme mit optimierten Arbeitspunkt, oder athermalisiert über einen weiten Bereich, können dann nach Bedarf gefertigt werden. The simulation of the refractive index inhomogeneities of the optical system includes a simulation of temperature profiles using the finite element method (FEM) as described in 2 is shown schematically. By means of commercially available software (eg ANSYSTM from ANSYS, Inc., Pennsylvania, USA; s. Presentation at ANSYS Conference & 31. CADFEM Users Meeting, Mannheim, 19.-21. June 2013 ) Including diameters and geometrical relationships of the beam used the high-energy radiation (eg collimated or focused laser radiation) as well as material properties from data sheets of the optical material used, eg. B. Suprasil (Suprasil is a product name for a quartz glass of HERAEUS Quarzglas GmbH & Co. KG), as well as using known information of the optical system and appropriate assumptions about heat capacity, thermal conductivity and transition coefficients of the optical material and adjacent media and structures of the optical socket the FEM Calculations of the temperature profiles of the optical elements of the optical system carried out. The result of a performed FEM temperature simulation for an optical component (lens) is in 3 shown as a 3D layer image. From a general analytical representation of the refractive index distribution and its spatial derivatives, a user-defined surface (UDS) can be modeled in a suitable programming language (eg C ++) using suitable optical design software (eg ZEMAX ^™ from Focus Software , Inc., USA, or Code V ^™ of SYNOPSYS Inc., USA) an adaptation to the given situation is achieved by entering a fit parameter vector. Furthermore, nominal reference refractive indices for reference wavelengths and reference temperatures as well as coefficients of thermal dispersion from the data sheets of the optical materials used are to be provided for input into the UDS. The refractive indices n for a specific wavelength λ and temperature T can thus be calculated, for example, according to the following equation (source: SCHOTT Glass Technologies, Inc.):

where ΔT is the temperature difference to the reference temperature of the glass, D ₀ to D ₂ , E ₀ to E _{1 are} associated coefficients, and λ _tk are constants provided by the glass manufacturer. After inserting (modeling) the UDS into the optical design software and allowing the parameters to be transferred to the UDS, a representation of the thermal effects in the optics design is available, using all the analysis tools provided by the Lens Design Program software allows. In a next step, this opens up the opportunity in optics design software to examine and evaluate the transient system states for specific operating times of the optical system. In addition, design variants (adapted models) of the optical system are created that best meet the required optical quality criteria for specified defined service lives. These optical systems with optimized operating point, or athermalized over a wide range, can then be manufactured as needed.

In order to analyze and simulate the refractive index profiles, in addition to the temperature distribution in the optical component, bundle parameters of the high-energy radiation applied to the optical system, such as bundle diameter, focus / waist positions, divergence, astigmatism and mode structure, must be entered. This database forms an input data set for the FEM temperature simulation. A selection of determined 2D temperature profiles in the axial section of an optical component (lens) is available for different beam profiles in 8a to 8e represented, which will be explained in more detail below.

wobei

T_i

– gegebene Werte (FEM-Temperaturen),

T^{^} _i

– zugehörige Modelltemperaturen,

T -

– der Mittelwert der gegebenen Werte (FEM-Temperaturen),

n

– die Anzahl der Messpunkte und

p

– die Anzahl der Anpassungsparameter sind.

A typical temperature profile of a refractive optical element after 450 s exposure time of a beam of high-energy radiation, as calculated by means of the ANSYS software for a selected test object, a biconvex lens, is in 4 shown. In the cross section of the lens, this result of the FEM simulation in 5 as a point cloud compared to the adapted general temperature model (area). In the illustration, the temperature is applied in the vertical direction and the horizontal plane is spanned by lens thickness (z-direction) and lens diameter (x-direction). Clearly visible are the temperature maxima at the entry and exit points of the beam at the lens surface, which lead to the formation of local thermal lenses and thus to refractive index inhomogeneities in the beam passing through the lens. Connected to the point cloud, the temperature distribution according to the fitted general analytical temperature model is shown as the surface. 6 shows the residual between both temperature distributions 5 , To evaluate the quality of the adaptation of the general temperature model to the FEM-modeled temperature field, the adjusted Pearson correlation was used. It is a standard measure for characterizing the quality of a multivariant fit to a set of metric (interval-scaled) variables. The square of the Pearson correlation R ² is a measure of the declared proportion of the variability of a dependent variable by a statistical model. The freedom-adjusted correlation R ² is calculated as follows:

in which

T _i

Given values (FEM temperatures),

T ^{^} _i

- associated model temperatures,

T -

The mean of the given values (FEM temperatures),

n

- the number of measuring points and

p

- are the number of fitting parameters.

In 8th FEM calculations of the temperature in a convex quartz lens are shown taking into account beam profiles and absorption behavior of the optical element. 8a shows the temperature profile for a very narrow radiation beam with dominant volume absorption of the material of the lens. In 8b For example, the temperature distribution that produces a broader bundle is shown to be dominant in volume absorption. In 8c the temperature profile for a broad radiation beam is shown when surface absorption occurs on additionally inserted absorbent layers. In contrast, the temperature profile in the convex lens of 8d again volume absorption with a focused radiation beam. 8e shows again a case of surface absorption with different expression of the absorption at the bundle entry and the bundle exit surface.

First embodiment

9 shows as a test object a single-lens projection optics made of quartz glass (eg HERAEUS [Heraeus Quarzglas GmbH & Co.KG]) with a focal length f '= 54 mm. The original spherical design has an RMS wavefront error of 0.3 λ to 0.6 λ in the apodized integration region up to a radius of 2 · 1 / e ² · 3 · 1 / e ² .

In a focus optimized with respect to the RMS wavefront error, the aperture error (standard Zernike coefficient) is 0.23λ. Thus, the image-side bundle initially has a diffraction factor M ² = 3 (as an optical quality criterion). 10 illustrates the temperature - related emigration of the focus (with respect to a minimized encircled energy value).

To simulate the behavior of well-corrected optics, an opening-error-corrected aspherical variant of the aforementioned projection optics from Suprasil was therefore modeled and generated. The asphere points with a virtually zero corrected aperture error, an RMS wavefront error of 6 μλ to 4 mλ. The result is the quality criterion of the diffraction factor to M ² (t = 0) = 1. In 11 the temperature at the entry vertex is compared with the FEM simulation (solid curve) and the fitted analytical profile (dotted curve) for transient states from 0.1 s to 900 s. The starting temperature was chosen at 22 ° C and then simulated the following temperature evolution: T [° C] @ 10s @ 200s @ 900s T _max 23.0 32.5 43.8 T _min 22.5 31.9 43.2 .DELTA.T 0.54 0.62 0.64

12 shows the result of the temperature simulation for a specific time in perspective view of the projection optics with an axial section.

Table 1 gives for 7 transient system states of a test set the sum of the square deviations of the simulation point of the model (SSE), the classical and adjusted variance explanation (square of the correlation R ² and R ² _adj ) of the FEM simulation by the general analytical model and the RMS Error (RMSE). The variance explanation according to the above equation results for all times t _i to R ² _adj ≥ 99%, which represents a nearly optimal fit. Status SSE R2 R2adj RMSE 100ms .8018 .9941 .9941 0.0095 300ms .8018 .9941 .9941 0.0095 500ms .6562 .9875 .9875 0.0086 2000ms .5498 0.9975 0.9975 0.0079 1000ms .6997 .9939 .9939 0.0089 450000ms .8614 0.9987 0.9987 0.0119 900000ms .9451 0.9986 0.9986 0.0124 Table 1: Variance explanation of the simulated model by means of selected transient states over time

The 13 and 14 show the defocusing of the beam emerging from the optical system (with a lens made of Suprasil) as well as the diffraction factor M ² plotted against time with the original test lens ( 13 ) and "aspherized" test lens ( 14 ) of the projection optics.

The defocusing is given with respect to three different possible criteria: Minimum RMS radius of the point spread image functions (PSF) for two different Gaussian-shaped pupil apodizations and a z-position with minimum circular area with energy content 86.5%, calculated with "Physical Optics Propagation" (POP) in ZEMAX. In addition to the defocusing, the time evolution of the bundle quality (eg diffraction factor M ² ) is also plotted. In 13 FIG. 2 shows the time profiles of the optical quality criteria for the original spherical-shaped optical element, while FIG 14 the courses are recorded for the aspherized lens mold. It can be seen that in the asphere compared to the spherical design on the one hand, the defocusing significantly reduced in amount, and on the other hand, the bundle quality M ² after 2 s slowly approaches a reduced level asymptotically. Table 2 shows the determined data for different quality criteria. TestSet RMS wave front error 0.3λ RMS wave front error 4mλ t [sec] r (EcE) [μm] DefOK. [Mm] M ² r (EcE) [μm] DefOK. [Mm] M ² 0 50.5 0,000 3.1 37.6 0,000 1.0 0.1 50.1 -0.091 2.9 37.6 -0.032 1.0 0.3 49.6 -0,250 2.6 37.6 -0.079 1.2 0.5 49.4 -0.315 2.6 37.6 -0.101 1.3 1 49.2 -0.537 2,4 37.6 -0.155 1.4 2 48.8 -0.648 2,4 37.6 -0.154 1.5 450 48.4 -1.142 2.3 37.7 -0.573 1.6 900 48.4 -1.150 2.3 37.7 -0.572 1.6 Tab. 2: Representation of different quality criteria for the original and the corrected lens model at selected transient states over time and a wavefront error reduced to almost one thousandth

The preference as a quality criterion is obtained in the present projection optics, as is usual for optics for laser material processing, the diffraction factor M ² . However, other optical quality criteria are applicable, such as aperture error or defocusing or encased energy (EcE - encircled energy), for which, in Table 2, the size r (EcE) is a circle radius containing 86.5% of the energy ( Diffration encircled energy) was used.

• – strahlenoptisch: – Schnittpunkt der Strahlen von der Feldachse und mit einem gegebenen Betrag der relativen Pupillenposition;
• – wellenoptisch: “Einzelschritt“: – z-Position mit minimalem RMS-Wellenfrontfehler in der zugehörigen Austrittspupille (AP) oder – z-Position, für die der Defokus-Koeffizient der Zernike-Zerlegung der Wellenfront in der zugehörigen Austrittspupille null ist – z-Position mit maximaler „Diffraction Encircled Energy“ in einem definierten Kreis in der Bildebene – z-Position, an der sich ein minimaler Kreisradius mit gegebenem Inhalt an Diffraction Encircled Energy in der Bildebene ergibt
• – wellenoptische Bündelpropagation: – Taillenlage der Gaußsbündelapproximation im Bildraum – z-Position mit maximaler Encircled Energy in einem definierten Kreis in der Bildebene, berechnet durch wellenoptische Bündelpropagation (POPD40) – z-Position, an der sich ein minimaler Kreisradius mit gegebenem Inhalt an Encircled Energy in der Bildebene ergibt, berechnet durch wellenoptische Bündelpropagation (POPD50)

As a criterion for the defocusing (z-focal position) different definitions are possible:

• - Radiation-optical: - intersection of the rays from the field axis and with a given amount of the relative pupil position;
• - wave-optical: "single step": - z-position with minimal RMS wavefront error in the associated exit pupil (AP) or - z-position for which the defocus coefficient of the Zernike decomposition of the wavefront in the associated exit pupil is zero - z- Position with maximum "diffraction encircled energy" in a defined circle in the image plane - z position, where a minimum circle radius with given content of diffraction encircled energy in the image plane results
• - Wave optical beam propagation: - waist position of the Gaussian beam approximation in the image space - z position with maximum encircled energy in a defined circle in the image plane, calculated by wave optical beam propagation (POPD40) - z position, at which there is a minimum radius of circle with given content of encircled energy in the image plane, calculated by wave-optical beam propagation (POPD50)

The temporal behavior of the quality criteria defocusing and diffraction factor M ² is in 15 plotted again for sphere and modeled asphere of the optical element selected in the example (single-lens projection optics) in direct comparison. For the test lens (from Suprasil), the quality criteria defocusing and diffraction factor M ^{2 are shown} for the models "original spherical" and with "aspherization", whereby the resulting RMS wavefront error is 0.3 λ (spherical) to 0.004 λ (aspherical ) is reduced in the nominal design (cold / t = 0). The Rayleigh length of the working beam is 4.69 mm in this example.

Second embodiment

Heretofore, in order to explain the principle of the invention, the optical system has been limited to a single lens (Suprasil test lens). Subsequently, however, it should be shown that the invention is also applicable to multi-lens optics. In this example, a two-lens optical system is investigated, which is exemplified in 7 is shown. In Table 3, in two differently "aspherized" system variants where the best map (marked) was optimized for each state after 450 s and 2 s, respectively, the quality criteria such as RMS wavefront error (RWCE), circle radius [ r (EcE)], in which 86.5% of the energy (Diffraction Encircled Energy) and defocusing, have been simulated for several transient states t (corr) = 450 sec t (corr) = 2 sec t [sec] RWCE [mλ] r (EcE) [μm] DefOK. [Mm] RWCE [mλ] r (EcE) [μm] DefOK. [Mm] 0 16.7 28.8 0.414 9.2 28.5 0.105 0.1 15.8 28.7 0.404 8.4 28.5 0,095 0.3 14.5 28.6 0.388 7.0 28.5 0.079 0.5 13.7 28.6 0,378 6.2 28.4 0,069 1 11.5 28.5 0.352 4.1 28.4 0.043 2 8.6 28.4 0.309 2.3 28.4 0,000 450 2,4 28.3 0,000 7.9 28.5 -0.311 900 2,4 28.2 -0.023 8.0 28.5 -0.334 Tab. 3: Transient states at operating times between 0 and 900 s calculated for two simulated models with optimized correction for each defined operating time (450 s or 2 s)

In 16 is shown for the two differently "aspherized" models (according to Table 3), the time course of the RMS wavefront error and the Z-position of the best capture level as a function of the exposure time over operating times of 0-900 s. As a result, it can be seen that the wavefront error for the thermal correction for operating times of 450 s already assumes small and still falling values after 2 s, while the wavefront error for the asphere optimized for an operating time of 2 s is very fast in the range up to 2 s small values drops and then increases significantly again. In the interval between 20 and 70 s both modeled system variants are approximately equivalent, but with different tendency of their correction. It depends on the given operating times (exposure to high-energy radiation), which model of "aspherization" should have preference.

In the 16 plotted graphs are based on the values in Table 4 below, where transient states defined in the two columns are simulated for two differently modeled aspheres whose thermal correction is designed for operating times of 450 s and 2 s. The color-coded lines illustrate the state of least defocusing under all transient states between 0 and 900s.

Tab. 4a: Modellrechnungen für verschiedene transiente Zustände bei zweilinsiger Optik mit einer asphärisierten Oberfläche.

Tab. 4b: Modellrechnungen für verschiedene transiente Zustände bei zweilinsiger Optik mit zwei asphärisierten Oberflächen. 17 provides the RMS wavefront error as a function of the exposure time for four variants of the selected two-lane system with differently aspherized designs, optimized for best performance over different irradiation periods. The system variants have either one (Table 4a) or two (Table 4b) aspherized surfaces.

Tab. 4a: Model calculations for different transient states in two-lens optics with an aspherized surface.

Tab. 4b: Model calculations for different transient states in two-lens optics with two aspherized surfaces.

In the 17 solid line indicates a optically optimized for the cold state optical system. In operation, a barely tolerable RMS wavefront error is obtained. On the other hand, the two-surface aspherization for an operating time of more than 2 s already exhibits an acceptable RMS wavefront error, which is significantly better than the one-sphere corrected model for operating times of more than 450 s , The use of 2 aspheres also allows an optimization to an athermal system state, which has an RMS wavefront error <5 mλ over the entire operating time (lower dashed curve in 17 ).

In conclusion, it can thus be summarized that defocusing and aperture aberrations can be compensated to a certain extent by a thermal lens (see r _EcE and M ² in the case of a spherical test set lens), if in the lens design for the "cold state" of the optical system a defined derivative of refractive index inhomogeneity is taken into account for a defined wavefront error, which compensates for the thermally generated wavefront error by the action of the thermal lens (s) after defined operating times (ie the duration of the action of the bundle of high-energy radiation), so that at a given normal operating state with minimum wavefront deformation and thus highest Precision can be worked.

Although the examples chosen so far used a rotationally symmetric beam cross-section, the FEM and model calculations are also suitable for any other beam cross-sections. In particular, laser lasers often use line lasers with a beam profile, as exemplified in US Pat 18 is shown as a profile of the flux distribution over the orthogonal plane of the steel propagation direction (z). For such a beam cross section, the refractive index inhomogeneities occur in the same way and can be taken into account by appropriate provision in the optical design. 19 shows a non-rotationally symmetric temperature distribution function adapted to the FEM calculations described above.

For multi-element systems, thermally modified light propagation in modeled lenses affects the entrance bundle in subsequent elements. On the other hand, simulation results in subsequent lenses can modify the bundle cross-section in predecessor elements in the case of center and rear diaphragms. For such models is - according to the schematic representation of 20 Assume that recursive modeling cycles are required, which use the determined temperature profiles to simulate the temperature distribution in the lenses, calculate free diameters of the lens surfaces from them, and use these results to improve the FEM calculations of the temperature profile, etc.

• – Ermitteln von Bündelparametern des auf das optische System anzuwendenden eingehenden Strahlenbündels,
• – FEM-Simulation von Temperaturprofilen in den optischen Elementen auf Basis der Bündelparameter und der für das (die) optische(n) Element(e) ermittelten Referenzbrechzahlen,
• – Ermitteln von Referenzbrechzahlen bei einer Referenzwellenlänge, einer Referenztemperatur sowie einem zugehörigen Koeffizienten thermischer Dispersion der im optischen System verwendeten Optikmaterialien,
• – Analyse des Brechzahlprofils durch Anwendung einer Standardform zur Brechzahlprofilbeschreibung und jeweilige Anpassung an das FEM-simulierte Temperaturverteilungsmodell durch angepasste Parametervektoren,
• – Einsetzen der angepasste Parametervektoren der Referenzbrechzahlen und der Koeffizienten thermischer Dispersion der verwendeten Optikmaterialien in eine modellierte benutzerdefinierte Oberfläche (UDS);
• – Simulation transienter Zustände des Brechzahlprofils für bestimmte Betriebsdauern des optischen Systems und Anpassen des Brechzahlprofils in Modellen des optischen Designs sowie modifizierter Bündelpropagation an allen Oberflächen des optischen Systems mittels einer Optikmodellierungssoftware,
• – wiederholtes Durchführen der Simulationen von Temperaturprofilen, Brechzahlprofilen und transienten Zuständen sowie Modellieren angepasster Modelle des optischen Designs und modifizierter Bündelpropagation, bis mindestens ein angepasstes Modell des Designs des optischen Systems bei den simulierten transienten Zuständen mindestens für eine definierte Betriebsdauer die gewünschten Spezifikationen vorgegebener optischer Gütekriterien erfüllt,
• – Implementieren wenigstens eines ausgewählten angepassten Modells des optischen Designs, für das bei den simulierten transienten Zuständen die spezifizierten Gütekriterien mindestens erfüllt oder übererfüllt sind, in das optische Design des optischen Systems als kompensierenden Vorhalt für betriebsbedingte (temperaturabhängige) Brechzahlinhomogenitäten.

The iterative simulation of the temperature-dependent refractive index inhomogeneities can be carried out as follows:

• Determining beam parameters of the incoming beam to be applied to the optical system,
• FEM simulation of temperature profiles in the optical elements based on the bundle parameters and the reference refractive indices determined for the optical element (s),
• Determining reference refractive indices at a reference wavelength, a reference temperature and an associated coefficient of thermal dispersion of the optical materials used in the optical system,
• Analysis of the refractive index profile by use of a standard form for the refractive index profile description and respective adaptation to the FEM-simulated temperature distribution model by means of adapted parameter vectors,
• - inserting the adjusted parameter vectors of the reference refractive indices and the coefficients of thermal dispersion of the optical materials used into a modeled user-defined surface (UDS);
• Simulation of transient states of the refractive index profile for specific operating times of the optical system and adjustment of the refractive index profile in models of the optical design as well as modified beam propagation on all surfaces of the optical system by means of an optical modeling software,
• Repeatedly performing the simulations of temperature profiles, refractive index profiles, and transient states, and modeling adapted models of optical design and modified beam propagation until at least one adapted model of the optical system design meets the desired specifications of predetermined optical quality criteria for the simulated transient states for at least a defined operating time .
• Implementing at least one selected adapted model of the optical design for which the specified quality criteria are at least fulfilled or exceeded in the simulated transient states, in the optical design of the optical system as compensating derivative for operational (temperature-dependent) refractive index inhomogeneities.

How many iteration cycles are necessary or useful in order to model the best possible adaptation of the lens design to the thermal lenses to be expected under given operating times is essentially dependent on the optical design (number of optical elements, optical materials and their thermal dispersion , Size of the air spaces and coatings used) as well as the laser intensity (relative refractive power of the thermal lenses in relation to the nominal refractive power of the optical system) dependent.

QUOTES INCLUDE IN THE DESCRIPTION

This list of the documents listed by the applicant has been generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• US 6509702 B1 [0003]
• US 6650412 B1 [0003]
• US 8310772 B2 [0003]
• US 2002/0021724 A1 [0005]
• US 6134039 A [0006]

Cited non-patent literature

• Kunzmann et al. in "Characterization of Laser Radiation by means of Hartmann-Shack Wavefront Sensor" (in: Photonics 1/2005, ISSN 1432-9778) [0007]
• ANSYSTM from ANSYS, Inc., Pennsylvania, USA; s. Presentation at ANSYS Conference & 31. CADFEM Users Meeting, Mannheim, 19.-21. June 2013 [0045]

Claims (12)

 A method for reducing aberrations of an optical system that occur within at least one optical element of the optical system by forming a thermal lens as a result of applied concentrated high-energy radiation, comprising the steps of: Determining temperature-dependent refractive index inhomogeneities of the at least one optical element for predetermined operating conditions of the optical system as a function of defined operating times of the action of a defined beam of high-energy radiation and Modeling and implementing a Vorhalts of refractive index inhomogeneities of the at least one optical element in a zero state without the action of the beam of high-energy radiation such that the refractive index inhomogeneities for defined operating periods of the action of the beam are minimized or compensated.  The method of claim 1, wherein the step of determining the refractive index inhomogeneities further comprises: Simulation of temperature - dependent refractive index inhomogeneities based on Determination of bundle parameters of the defined beam to be applied to the optical system; Calculating a temperature distribution in the optical system based on FEM calculations for an optical material used in the at least one optical element of the optical system; - Determining reference refractive indices of nominal refractive indices of the optical material used in each case a reference wavelength and a reference temperature; Simulation of a refractive index profile by application of an analytical standard form for refractive index profile description using the calculated temperature distribution as well as the determined reference refractive indices and coefficients of thermal dispersion of the optical material used; - Modeling a user-defined surface (UDS) to implement the simulated refractive index profile into model parameters for optical design modeling of the optical system; and the step of modeling and implementing the lead includes: - Simulation of transient states of the refractive index profile for certain operating times as adapted models for different refractive index profiles by optical design modeling of the optical system; and Selection of an adapted model with a refractive index profile, in which the simulation of the transient states has yielded a compensating optical design of the optical system in which desired specifications of predetermined optical quality criteria of the optical system are satisfied at least for a defined operating period.  The method of claim 2, wherein a suitable FEM simulation software is used to simulate the temperature distribution or refractive index profile.  The method of claim 2, wherein for the simulation of the refractive index profile as a standard form a refractive index profile description on standard GRIN lenses is also applied to any type of refractive optical elements.  The method of claim 2, wherein a commercially available optical modeling software is used to simulate transient states of the refractive index profile.  The method of claim 2, wherein the step of modeling a user-defined surface further includes verification of the modeled optical system by comparing refractive index distributions that may be described with standard GRIN lenses.  The method of claim 2, wherein the programming language C ++ is selected for programming the user-defined interface. Method according to claim 2, wherein the diffraction factor M ^{2 is} used as a quality criterion for the evaluation, optimization and selection of the adapted models of transient states for implementation in the compensated design of the optical system. The method according to claim 2, wherein an encircled energy (EcE) is used as a quality criterion for the evaluation, optimization and selection of the adapted models of transient states for implementation in the compensated design of the optical system model selection in the implementation of the adapted models of transient states.  The method of claim 2, wherein a best focus state or a minimum defocus is used as the quality criterion for the evaluation, optimization and selection of the matched models of transient states for implementation in the compensated design of the optical system model selection in the implementation of the adapted models of transient states.  The method of claim 2, wherein the simulation of temperature dependent refractive index inhomogeneities is performed iteratively by: The simulation of temperature distributions of the optical system by FEM calculations, The simulation of the temperature distribution in the optical system by an analytical model, The determination of the refractive index profile using the simulated temperature distribution, the determined reference refractive indices and the coefficients of thermal dispersion of the optical material used, - Implementation of the simulated refractive index profile by transferring the determined model parameters to the user-defined interface (UDS); - The simulation of the transient state of the optical system with A determination of modified beam propagation in the optical system by means of the optical modeling software and A determination of modified input and output beam parameters on all surfaces of optical elements of the optical system be carried out repeatedly successively until predetermined optical quality criteria of the optical system are best satisfied at least for a defined operating time.  The method of claim 11, wherein the iterative simulation is applied to multi-lens optical systems.

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