DE102021118069B3 - Procedure for energy calibration of a plane grating monochromator - Google Patents

Abstract

The invention relates to a method for the energy calibration of a plane grating monochromator (PGM) which comprises a plane grating and a plane mirror, both equipped with a drive with an angular decoder with an absolute scale. The method comprises the following steps: 1. Provision of the PGM as well as collimated X-rays and an ionization chamber in the beam path behind the PGM and a detector for detecting radiation produced in the ionization chamber. 2. Search for a first extreme value (EW) of the photoionization spectrum of the gas in the ionization chamber by varying the total deflection angle 2θ on the PGM and diffraction angle β of the plane grating and mathematically, based on the energy of the first EW, or geodetic determination of an associated deflection angle θ of the plane mirror and calculation of the associated angular value β of the plane grid and assignment of the angular values to the current tick marks of the decoder as the starting point. Then, in a third step, (i) the plane grating or the plane mirror is rotated until it reaches a second EW of the ionization spectrum that is adjacent to the first EW and (ii) the respective (i) other plane mirror or plane grating is rotated to the first EW of the ionization spectrum rotates back and thereby (iii) pairs of the graduations of the decoder for each partial step (i) and (ii) of the rotations are formed from the read-out initial graduation and graduation when the next EW to be approached is reached and the associated nominal angle differences between the energies of the two EWs of the ionization spectrum assigned to the pairs of tick marks. 4. Repeat 3 at least twice.

Description

technical field

The present invention relates to a method for calibrating the energy of a planar grating monochromator, such as is used for X-ray diffraction, for example.

State of the art

Plane grating monochromators of the type relating to the invention are known from the prior art and are described, for example, in Paper 1 by F. Senf et al. (A plane-grating monochromator beamline for the PTB undulators at BESSY II; Journal of Synchrotron Radiation Vol. 5, 1998, pp. 780-782). They essentially consist of a plane mirror and a plane grating. In the plane grating monochromators, the light or the X-ray radiation is diffracted by means of the plane grating, which can also be designed as a reflection grating, whereby monochromatization is achieved. Monochromatization is to be understood here as a restriction in the spectral width around a specific wavelength for which the diffraction conditions at the plane grating are met. The quality of the monochromatization depends, among other things, on the achievable spectral width of the diffracted X-ray beam. By using a plane mirror, the light is shifted in height in the further beam path or in advance. Due to the line density N (lines/mm) of the planar grating, a specific wavelength λ can be selected from an incident beam by diffraction at the planar grating by setting a corresponding total deflection angle 2θ with the mirror and the angles α and β to the grating normal of the planar grating, whereby this ray is monochromatized in the further beam path. In the case of a plane grating (diffraction grating), ie diffraction of X-rays on a two-dimensional grating, the equation for describing the diffraction conditions is: $$\lambda \ast N\ast m=\left(\text{sin}a-\text{sin}\beta \right)=K,$$

With m = order of diffraction, λ = wavelength, N = number of grating lines per millimeter = line density, α = angle between the incident beam and the grating normal and β = angle between the diffracted (emerging) beam and the grating normal of the planar grating where 2θ = α + β. From the latter relationship, the following relationship can be derived for the diffracted wavelength: $$\lambda =\frac{1}{N\ast m}\ast \left(sin\left(2\theta -\beta \right)-sin\left(\beta \right)\right)=\frac{1}{N\ast m}\ast 2\ast cOs\left(\theta \right)\ast sin\left(\theta -\beta \right)$$

bestimmt bzw. umgekehrt $\lambda =\frac{h\ast c}{E}.$

Es wird nur der gebeugte Anteil des einfallenden Lichts bzw. der einfallenden Röntgenstrahlung im Strahlengang hinter dem Plangittermonochromator weiterverwendet.At the same time, a wavelength λ is always uniquely associated with an energy E according to $E=\frac{H\ast c}{\lambda }$

determined or vice versa $\lambda =\frac{H\ast c}{E}.$

Only the diffracted part of the incident light or the incident X-rays is used further in the beam path behind the planar grating monochromator.

Plane gratings and plane mirrors are usually housed in an evacuable housing with entry and exit windows or slits for the radiation and are each provided with drives with which they rotate about an axis that is perpendicular to the incident beam and in the plane of the plane grating or Plane mirror is rotatable. In order to record the currently set angles of the drives, they are equipped with angle decoders, which can also be provided with absolute scales.

In addition to the alignments or adjustments of the plane grating and the plane mirror to each other and to the beam and possible other optics in the beam path or target locations as well as the resolution to be achieved, the accuracy (also addressable as correctness) of the angle settings with the one is decisive for the quality of the monochromatization Total deflection angle 2θ through the mirror or a specific diffraction angle β through the plane grating, to set a specific wavelength of the monochromatization, on the plane grating and on the plane mirror is adjustable. During operation, a motor position of a plane grating or plane mirror drive is assigned a value for the diffraction angle and thus a specific wavelength or energy via the grating equation (2) by calibration. The accuracy is then the degree of agreement between the displayed (read out) and the "correct value".

A calibration of the energy is usually carried out with reference samples, e.g. metal foils, as described, for example, in Essay 2 by S. Diaz-Moreno (XAFS data collection: an integrated approach to delivering good data, Journal of Synchrotron Radiation, Vol. 19, 2012, pp. 863-868). In the soft range of X-rays, especially X-rays with an energy <1 keV, instead of metal foils, among other things, photoionization spectra of gases are measured, as is described, for example, in article 3 of SI Fedoseenko et al. (Commissioning results and performance of the high-resolution Russian-German Beamline at BESSY II, Nuclear Instruments and Methods in Physics Research A, Vol. 505, 2003, pp. 718-728).

Another method of calibrating the wavelength (energy) of a grating monochromator is to provide a reference beam of emission lines from a gas for comparison with a diffracted beam from the monochromator to be calibrated, as described in US Pat EP 1 120 637 A2 is presented. A determined deviation in the diffraction angle of the two beams provides information about how much the angle setting on the monochromator needs to be changed. A device for comparing the beams (reference and diffracted beam) is also given and is based on gas ionization chambers.

A method for calibrating a grating monochromator, which consists only of a planar grating, is in U.S. 2007/0 258 091 A1 disclosed. The drive for rotating the plane grating is controlled electronically here, with the control working with an equation for correcting an angle to be controlled (and thus also a predetermined wavelength). Various coefficients, which are determined using a calibration method, are taken into account in the equation for correction. In the calibration process, the rays diffracted in the monochromator to be calibrated are compared with reference rays, which here correspond to emission lines of a gas at different energies, and a calibration curve is created that supplies the coefficients.

ergibt, engl. als „constant or fix focal distance“ (konstanter Abstand von der Fokalebene) oder auch als „Plangitter-Fokus Bedingung“ bezeichnet (r = Abstand |Quelle - Gitter|; r'= Abstand |Gitter-virtuelles Bild|). Das betrachtete Verhältnis beeinflusst insbesondere die Fokussierungseigenschaften des Plangitters und ist eine Funktion der Wellenlänge (Energie), der Beugungsordnung und der Gitterperiode. Der Faktor c_ff hat eine in der Entwicklung der Plangittermonochromatoren begründete Bedeutung. Bei der Verwendung eines Plangitters im Monochromator, insbesondere solche, die auch mit Spiegeln ausgestattet sind, wird c_ff durch die Orientierung des Plangitters, in Bezug auf den einfallenden Röntgenstrahl eingestellt und nach Bedarf optimiert. Ebenso von c_ff beeinflusst, sind z.B. Parameter des Monochromators wie die Auflösung und die Transmission. Üblicherweise ist der Parameter c_ff konstant zu halten, um den Strahlengang im Monochromator in Bezug auf Eintritts- und Austrittsspalte in der Monochromatorkammer konstant zu halten. Im Falle, wie in einem Aufsatz 5 von Malcolm R. Howells Nuclear Instruments and Methods 177 (1980)127-139) beschrieben ist, dass der auf den Monochromator einfallende Röntgenstrahl kollimiert ist, z.B. durch einen Spiegel im Strahlengang vor dem Monochromator, entfällt die Bedingung der Konstanz für c_ff, was im Folgenden dadurch ausgedrückt wird, dass der Parameter als C_θ angesprochen wird. An einem Monochromator mit nicht variablem, d.h. durch den Monochromator bestimmten Werten für c_ff kann die erfindungsgemäße Energiekalibrierung nicht angewendet werden.For a consideration of the focusing condition of a plane grating, as it is for example in article 4 by H. Petersen (The plane grating and elliptical mirror: A new optical configuration for monochromators, Optical Communication, Vol. 40, 1982, pp. 402-406) is described, often the parameter c _ff , which is used from the following ratio $$c_{ƒƒ}=\left(cOs\beta /cOsa\right)=\sqrt{\mathrm{right}\text{'}/-\mathrm{right}}$$

yields referred to as "constant or fix focal distance" (constant distance from the focal plane) or also as "planar grid focus condition" (r = distance |source - grid|; r'= distance |grid-virtual image|). The ratio considered particularly affects the focusing properties of the plane grating and is a function of wavelength (energy), diffraction order and grating period. The factor c _ff has a reasoned meaning in the development of the plane grating monochromators. When using a plane grating in the monochromator, especially those that are also equipped with mirrors, c _ff is set by the orientation of the plane grating in relation to the incident X-ray beam and optimized as required. Also influenced by c _ff are, for example, parameters of the monochromator such as resolution and transmission. The parameter c _ff is usually to be kept constant in order to keep the beam path in the monochromator constant in relation to the entrance and exit slits in the monochromator chamber. In the case, as described in an article 5 by Malcolm R. Howells Nuclear Instruments and Methods 177 (1980) 127-139), that the X-ray beam incident on the monochromator is collimated, eg by a mirror in the beam path in front of the monochromator, the Condition of constancy for c _ff , which is expressed in the following by addressing the parameter as C _θ . The energy calibration according to the invention cannot be used on a monochromator with values for c _ff that are not variable, ie values that are determined by the monochromator.

task

The object of the invention is to specify a method for the energy calibration of a planar grating monochromator, with which the energy calibration takes place independently of absolute angular positions and independently of relative positions of the angle decoders to one another.

The object is solved by the features of claim one.

The method for energy calibration of a planar grating monochromator is to be carried out for planar grating monochromators which have at least one planar grating with a first drive, the first drive being equipped with a first angle decoder and also having a plane mirror with a second drive which is equipped with a second angle decoder. Both angle decoders also have absolute scales. All components of a plane grating of the generic type according to claim 1 monochromators are known to the person skilled in the art and are to be selected from the usual points of view or according to the boundary parameters, such as in particular the energy range to be covered.

und $$2\mathrm{\theta }=\text{arcsin}\left(\mathrm{\lambda }\ast \text{N}\ast \text{m}+\text{sin}\left(\mathrm{\beta }\right)\right)+\mathrm{\beta }$$

The method makes use of two angular relationships between half the total deflection angle θ of an X-ray at the plane mirror and an angle of reflection β of an X-ray at the plane grating. The general angle relationships correspond to the following formulas (4) and (5): $$\mathrm{\beta }=\mathrm{\theta -}\text{arcsin}\left(\frac{\mathrm{\lambda }\ast \text{N}\ast \text{m}}{2\text{cos}\left(\mathrm{\theta }\right)}\right)$$

and $$2\mathrm{\theta }=\text{arcsin}\left(\mathrm{\lambda }\ast \text{N}\ast \text{m}+\text{sin}\left(\mathrm{\beta }\right)\right)+\mathrm{\beta }$$

The method has at least the following steps.

In a first step "a.", the plan grating monochromator of the generic type is provided. In addition, collimated X-ray radiation must be provided in order to carry out the method. The x-ray radiation originates in particular from a synchrotron radiation source. The x-ray beam is collimated before it is incident on the plane grating monochromator, in particular by mirrors, such as a toroidal mirror, or parabolic mirrors. The plane grating monochromator is initially aligned to the incident X-ray radiation. The initial alignment of the plane grating monochromator is carried out using surveying methods to the collimated, incident X-ray beam.

Furthermore, an ionization chamber is arranged in the beam path behind the planar grating monochromator, ie in the monochromatized X-ray beam emerging from the monochromator. A gas with a suitable vapor pressure is provided in the ionization chamber, which gas is ionized at an energy of the X-ray beam that matches an ionization energy of the gas provided. In addition to the ionization chamber, a detector is provided with which ionization radiation from the ionization chamber can be detected. Both components are devices familiar to the person skilled in the art, which are to be selected according to the given circumstances and as a function of the energies of the X-ray beam to be examined.

Then, in a second step "b.", a first extreme value of the photoionization spectrum is sought as a starting point by varying the total deflection angle 2θ on the plane grating monochromator and the diffraction angle β of the plane grating. The ionization energies of the gases are known and, for example, in the article 6 by RNS Sodhi and CE Brion (Reference Energies fo inner shell electron energy-loss spectroscopy, Journal of Electron Spectroscopy and Related Phenomena, 1984, Vol 34, pp. 363-372) for some gases listed. Based on the energy-wavelength relationship and the grating equation (Formula 2, see above), the total deflection angle 2θ _x of the planar grating monochromator, which is associated with an energy E _x of a selected extreme value of the ionization spectrum, can be calculated and adjusted accordingly. With the diffraction angle β _x a selected extreme value is then sought by varying the angle. The maxima and minima in an ionization spectrum are to be addressed as extreme values. A maximum is advantageously approached first. In a further advantageous manner, the mirror angle start value θ ₀ is precisely determined at the starting point via collimation with geodetic instruments, as is the case, for example, with the method in FIG DE 10 2018 100 603 A1 he follows. Alternatively, the mirror angle starting value can also be determined by calculation.

In this initial state (starting point) of the angle settings from step "b.", the angle value θ ₀ is assigned to the current graduation t _θ0 on the absolute scale of the first angle decoder of the plane mirror and a current graduation t _β0 on the absolute scale of the second angle decoder with is calibrated to the value for β ₀ of the planar grating that corresponds to θ ₀ according to formula (4). This forms the starting point for the calibration.

• (i) das Plangitter oder der Planspiegel bis zur Erreichung eines nächsten Extremwertes im Photoionisationsspektrum des Gases der Ionisationskammer mit einem Energiewert E₂ rotiert und anschließend
• (ii) das jeweils andere von Planspiegel und Plangitter aus (i) bis zum Wiedererreichen des ersten Extremwertes zurückrotiert.
• (iii) Für jeden Schritt c. (i) und c.(ii) der Rotationen wird ein Wertepaar aus ausgelesenem anfänglichem Teilstrich des zugehörigen Winkeldekodierers und dem Teilstrich bei Erreichen des jeweils als nächstes anzufahrenden Extremwertes gebildet. Zu diesen Wertepaaren wird dann zur Kalibration die jeweils zugehörige nominelle Winkeldifferenz zwischen den Energien der zwei Extremwerte des Photoionisationsspektrums zugewiesen. Die Bestimmung des jeweiligen nominellen Winkelwertes des zuletzt rotierten von Planspiegel oder Plangitter, wird dabei jeweils anhand des nominellen Winkelwertes, für das zuletzt nicht rotierte von Planspiegel oder Plangitter und der Energie des aktuellen Extremwertes des Photoionisationsspektrums gemäß der Formel (4) bzw. (5) bestimmt.

In the following step "c."

• (i) the plane grating or the plane mirror rotates with an energy value E ₂ until a next extreme value in the photoionization spectrum of the gas in the ionization chamber is reached and then
• (ii) the other of the plane mirror and plane grating from (i) rotates back until the first extreme value is reached again.
• (iii) For each step c. (i) and c.(ii) of the rotations, a pair of values is formed from the read-out initial graduation mark of the associated angle decoder and the graduation mark when the respective extreme value to be approached next is reached. The respectively associated nominal angle difference between the energies of the two extreme values of the photoionization spectrum is then assigned to these pairs of values for calibration. The respective nominal angle value of the last rotated plane mirror or plane grating is determined using the nominal angle value for the last non-rotated plane mirror or plane grating and the energy of the current extreme value of the photoionization spectrum according to formula (4) or (5) definitely.

For steps c. (i) and c. (ii) it follows that depending on the selected element of plane mirror or plane grating, with the associated angles θ or β, with the first pass of step c. (i) a rotation is started, the second extreme value is always approached with one of the plane mirrors or plane gratings, or, in a correspondingly complementary manner, the first extreme value.

The next extreme value in the photoionization spectrum with an energy value E ₂ is advantageously an extreme value directly adjacent to the first extreme value, ie if the first extreme value is a maximum, the second extreme value is a directly adjacent minimum.

• Δθ_j = |θ_i-1 - θ_i| und Δβ_j = |β_i-1 - β_i| mit i = Anzahl der Wiederholung des Schritts c. (i) bzw. c. (ii) und j = Anzahl der Wiederholung des Schritts c. (iii). Die Berechnung der Werte für θ_i bzw. β_i erfolgt dabei anhand der Energie des aktuell angefahrenen Extremwertes, E₁ bzw. E₂, und des zuletzt bestimmten Winkelwertes (θ_i-1, β_i-1) für das zuletzt nicht rotierte von Planspiegel oder Plangitter anhand der Formeln (4) und (5).

The nominal angle differences result as follows:

• Δθ _j = |θ _i-1 - θ _i | and Δβ _j = |β _i-1 - β _i | with i = number of times step c is repeated. (i) or c. (ii) and j = number of times step c is repeated. (iii). The values for θ _i and β _i are calculated using the energy of the extreme value currently approached, E ₁ or E ₂ , and the angle value (θ _i-1 , β _i-1 ) last determined for the last non-rotated from Plane mirror or plane grating using formulas (4) and (5).

The angle differences Δθ _j and Δβ _j become the partial distances on the absolute scale of the angle encoders, which result from the pairs of graduation marks t _θi-1 , t _θi and t _βi-1 , t _βi on the absolute scales of the angle decoders, according to Δt _θj = |t _θi-1 - t _θi | and Δt _βj = | _βi-1 - t _βi |, assigned accordingly, whereby the calibration occurs.

Reaching an extreme value in the photoionization spectrum can advantageously be defined as a reversal of the increase or decrease in the signal (or reversal of the sign of the signal change).

Depending on the angular range to be calibrated, step c. repeated at least twice or until a sufficiently large range is covered on the absolute encoder scales. The range is sufficient if it cannot be extended further due to limitations on the device (e.g. limit switches) or if it is assessed as sufficient by the specialist in accordance with the intended use of the planar grating monochromator. This results in a calibration of the absolute scales, starting from a starting point, in angular differences, which is valid regardless of a current angular position. Based on the calibration of the absolute scales, angle values can always be determined, even after the knowledge of the current angle position has been lost, without renewed calibration and independently of a C _θ value. In addition, errors in the absolute scales can be reduced or even almost eliminated with the method according to the invention. Calibration can also be performed in situ, ie while the monochromator is in operation.

character list

• 1: Schematische Darstellung eines nach Anspruch 1 gattungsgemäßen Plangittermonochromators (Stand der Technik).
• 2: Kalibrationskurve für den Winkel θ(a) und den Winkel β (b) gewonnen mit dem erfindungsgemäßen Verfahren (Simulation).
• 3: Abbildung der Fehler der Korrektur der Skala des Winkeldekodierers für den Winkel θ(a) und den Winkel β(b) der durch die Kalibration erfolgt (Simulation).

The invention will be explained in more detail in an exemplary embodiment and with reference to three figures.

• 1 : Schematic representation of a generic plan grating monochromator according to claim 1 (prior art).
• 2 : Calibration curve for the angle θ(a) and the angle β(b) obtained with the method according to the invention (simulation).
• 3 : Illustration of the errors of the correction of the scale of the angle decoder for the angle θ(a) and the angle β(b) made by the calibration (simulation).

In the exemplary embodiment, the plane grating monochromator corresponds to one as described in Article 7 by R. Follath and F. Senf (Nuclear Instruments and Methods in Physics Research A, Vol. 390, 1997, pp. 388-394). The necessary collimation of the incident X-ray beam is effected with a toroidal mirror. The design otherwise corresponds to that in the 1 is shown. Such a monochromator can be operated both with the incident X-ray beam initially on the plane grating (PG) and on the plane mirror (PS). Due to the collimation, c _ff can be freely selected and cannot be kept constant and is therefore noted as C _θ . The rotation through an angle, ie the process of an angle of the planar grating (PG) and the planar mirror (PS) takes place here eccentrically by the drives AG of the planar grating and PS of the planar mirror. The angle decoder SE of the plane mirror and PE of the plane grating are arranged in the axis of rotation of the optical elements. The beam path of an incident, collimated X-ray beam is shown with (h*ν →). The plane grid has a groove density of N = 1200 l/mm. In the exemplary embodiment, the planar grating monochromator is arranged on a synchrotron radiation source (BESSY II, Helmholtz Center Berlin for Materials and Energy GmbH). Something about the ionization chamber and the detector is still missing here. The ionization chamber consists of a vacuum tube with an ionization gas (nitrogen) at a partial gas pressure of a few mbar. This vacuum tube is typographically secured to the ultra-high vacuum section by means of transmission foil. The gas is ionized by the monochromatic synchrotron beam and the number of ions is measured with a sensitive current meter. With different energies of the synchrotron beam, the current measuring device detects minima and maxima or the individual energy states of the gas molecules.

In the exemplary embodiment, two extreme values of a nitrogen ionization spectrum are selected for carrying out the method according to the invention, which, according to article 6, are at E ₁ =400.88 eV, maximum, and at E ₂ =400.99 eV, next minimum.

The starting point of the method is by looking for the first extreme value E ₁ of the photoionization spectrum of nitrogen in the ionization chamber by varying the total deflection angle 2θ on the plane grating monochromator and diffraction angle β of the plane grating and, in the exemplary embodiment, geodetically determining the associated deflection angle θ ₀ of the plane mirror and calculating the associated angle value β ₀ of the plane grid and assigning the angle values to the current tick marks, t _θ0 and t _β0 , the angle decoder determines. In the exemplary embodiment at the starting point: E ₁ = 400.88 eV, λ = 3.0928 nm, K = 0.00371, with a geodetically determined θ ₀ = 87.404° or 2θ ₀ = 174.808°, formula (4) β ₀ = 84.607° calculated for the energy value of E ₁ .

In the exemplary embodiment, the plane grating is then rotated until the next extreme value in the photoionization spectrum of nitrogen, the minimum at E ₂ =400.99 eV, is reached (c. (i)). Using the previously determined nominal value for the angle of the plane mirror that was not rotated last, θ ₀ = 87.404°, and the energy of the second extreme value E ₂ = 400.99 eV, the value for β ₁ is determined using formula (4). . A pair of values is formed from the graduation marks of the angular encoder of the plane grating before the rotation t _β0 and after the rotation t _β1 . The nominal angle difference Δβ ₁ is assigned to this pair of values, which results from the difference for β ₀ and β ₁ according to Δβ ₁ = |β ₀ - β ₁ | gives (c.(iii)).

Then the plane mirror is rotated back until the first maximum of the photoionization spectrum of nitrogen is reached again (c. (ii)). Using the previously determined nominal value for the angle of the plane grating that was not rotated last, β ₁ , and the energy of the first extreme value E ₂ = 400.88 eV, the value for θ ₁ is determined using formula (5). A value pair is formed from the graduation lines of the angle encoder of the plane mirror before the rotation t _θ0 and after the rotation t _θ1 . The nominal angular difference Δθ ₁ is assigned to this pair of values, which results from the difference for θ ₀ and θ ₁ according to Δθ ₁ = |θ ₀ -θ ₁ | gives (c.(iii)).

The plane grating is then rotated again until the second extreme value is reached and the angles are determined accordingly and assigned to the value pairs of the graduations of the angle decoder of the plane grating. Then the plane mirror is rotated back to the first extreme value and immediately until a sufficiently large angular range is covered or the process cannot be carried out further due to external limitations (e.g. limit switches).

In the 2 Calibration curves for the angle encoder of the plane grating (a) and the plane mirror (b) are shown, obtained with the method according to the invention (simulation based on an assumed error of the angle encoder for 40,000 scale steps). The correction of the errors based on the calibration can be seen. In the 3 are shown the errors of the correction made by the calibration for the angular encoder of the plane grating (a) and the plane mirror (b) obtained with the method according to the invention (simulation based on an assumed error of the angle encoder for 400 scale steps). As shown, the remaining errors are small.

This results in a calibration of the absolute scales, starting from a starting point, in angular differences, which is valid independently of a current angular position and a C _θ value, which is continuously changed during the process. Based on the calibration of the absolute scales, angle values can always be determined, even after the knowledge of the current angle position has been lost, without renewed calibration and independently of a C _θ value. In addition, errors in the absolute scales can be reduced or even almost eliminated with the method according to the invention. Calibration can also be performed in situ, ie while the monochromator is in operation.

Claims (1)

Method for the energy calibration of a plane grating monochromator which has at least one plane grating with a first drive with a first angle decoder and a plane mirror with a second drive with a second angle decoder and both angle decoders have absolute scales, at least comprising the steps: a. Provision of the plane grating monochromator and collimated X-rays and an ionization chamber in the beam path of an X-ray beam emerging from the plane grating monochromator and a detector for detecting radiation produced by photoionization of a gas in the ionization chamber; b. Search for a first extreme value of the photoionization spectrum of the gas in the ionization chamber by varying the total deflection angle 2θ on the plane grating monochromator and the diffraction angle β of the plane grating and mathematically, based on the energy E ₁ of the first extreme value, or geodetically determining an associated deflection angle θ ₀ of the plane mirror and calculation of the associated angle value β ₀ of the plane grid and assignment of the angle values to the current tick marks of the angle decoders as the starting point; c. (i) rotation of the plane grating or plane mirror until a second extreme value is reached, which is adjacent to the first extreme value, with an energy E ₂ of the photoionization spectrum and (ii) rotation of the respective (i) other plane mirror or plane grating back to the first extreme value of the photoionization spectrum and thereby (iii) respectively forming pairs of the tick marks of the angle decoders for each step c. (i) and c.(ii) the rotations from the read-out initial graduation and graduation when the next extreme value to be approached is reached and assignment of respectively associated nominal angle differences between the energies of the two extreme values of the photoionization spectrum to the pairs of graduations, with the determination of the nominal angle value of the last rotated plane mirror or plane grating, in each case based on the nominal angle value for the last non-rotated plane mirror and plane grating and the energy of the current extreme value of the photoionization spectrum and d. repeating step c at least twice.

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