DE2238662A1 - FOCUSING PROCEDURE AND DEVICE FOR ITS IMPLEMENTATION - Google Patents

Description

PATENT LAWYERS

DR .-! NG. BY KREISLER DR.-ING. SCHÖNWALD DRYING. TH. MEYER DR. FÜES DIPL-CHEM. ALEK VON KREISLER DIPL-CHEM. CAROLA KELLER DR.-ING. KLÖPSCH DIPL-ING. SELTING

COLOGNE 1, DEICHMANNHAUS

August 4, 1972 Sg / rcy Is

AGENCE DE VALOISATION DE LA RECHERCHE (ANVAR), Tour Aurore Courbevoie (Hauts-de-Seine) France

Focusing method and device for his execution

The invention relates to focusing by rotating concave gratings. It also affects them Use of such focusing, especially with monochromators en.

We know how a spherical, concave diffraction grating works, which works by reflection to refract the various radiations that form a polychromatic light. The images of the source S (Fig.l), which is located at a distance r, which in the different directions ß. are refracted, are bundled at distances r 'from the vertex of the grating, which are dependent on the wavelength X *; In Fig. 1, the plane adjoining the apex of the lattice - characterized by the radius of curvature R, the number of lines N per mm, the dashed width to 'and the dashed height L - is vertical, and the otrich direction represents the local vertical The axis of rotation of the grid is an axis that runs parallel to the local vertical and

309843/0768. - ² - ■

goes through the crown of the head. It is known that a monochromator, which allows selection of a given wavelength can be realized by providing for a gap at S, which runs parallel to the bars ■ the grating, the so-called entrance slit, and by, at S ¹ a Slit parallel to the direction of the astigmatic, tangential focal lengths attaches, the so-called exit slit. Im -general! the center of the entrance slit is in the horizontal plane that contains the perpendicular to the grid, and the exit slit then runs parallel to the lines of the grid. A focus mechanism generally causes:

- either the displacement of a receiver (in this case, the changes in the direction of the exit blind are important ) _t

- or the rotation and simultaneous displacement of the Grids that also cause changes in the direction of the output beam, which is particularly the case in the case of a grating with a small radius of curvature, which generally shows an opening of interest, are of importance.

It has been recognized that in order to be able to use a monochromator useful, a certain strength of the corresponding Directions of the incoming and outgoing rays was necessary. If you also for reasons the prime cost undertakes to only perform a simple rotation of the grid, then the classic one shows Theory that only moving the exit slit will achieve good focus. In this Case, the tight displacement tolerances of the

■■ ■. '-' 5 -

309843/0768

Grid replaced by those of shifting one of the columns.

From the attempts made about the focusing of concave • ven grids have been carried out, those of

SEYA has shown that with a value of 7Q ⁰ JJO 'for the angle 2 Θ under which you can see the two slits from the vertex of the grid, you get a stationary solution for the values of r and r' equal to R cos θ. The corresponding structure (Fig. 2). provided that he meets the mentioned mechanical loading. conditions, does not offer satisfactory optical qualities. The result is a low resolution and a low brightness, and since the angles of incidence and angles of refraction β are increased, there is also a strong degree of polarization and an increased astigmatism. This result, "confirmed" by the theoretical calculations of NAMIOKA, shows that if one could focus a concave grating "by imparting only one rotation to the grating mentioned, this possibility was imperfect and, as numerous experiments have shown, associated with a very precise value of the angle θ: 'every change in the stated value 2Θ generally causes a substantial deterioration in the resolution, which has been tolerated by certain authors for special reasons.

At low values of 2Θ there was some improvement the image quality achieved at the expense of a shift of the output slit in the grid direction, the size of this The shift is dependent on the value of the wavelength. Considered in the known structures you don't see the aberrations, and so you overlook them important fact that a reasonable choice of reference

_ 4 _ 3098 4.3 / 0768

Sphere, i.e. the position of the initial gap, a compensation sation of the aberrations and an increase in the tolerable line area can allow.

So the search for a general solution, which should be as simple as possible, arose. in view of the numerous practical industrial applications of focusing a spherical, concave grating: in the case of such. Grating allows for Fermat's principle, which allows for the fact that the total optical value L must be fixed with respect to w. Submits the determination of the conditions under which & L ^

which is essentially the sum of the two F
to press.

both functions S ₅ and S « _t as S. + S ₂ » 0

In general, it is found that S ₁ = 0, which leads to writing that the basic equation of focusing T + T '= 0, where T and T ¹ are the equation of the tangential focal length of the object and that of the tantial focal length of the image represents. The term so that represents the aberrations is thus minimized. The inventor was initially of the opinion that the expression S _{2 could be} for a reference sphere which is chosen in a suitable manner

S ₂ = C ₁ W + 1/2 C ₂ w ² + S,

2
where C ₁ W and C ₂ W represent the displacement of the reference sphere and S-. is smaller than S ₂ . Then the inventor had the idea on which the invention is based,

309843/0768 " ⁵ ~.

namely the basic equation for focusing in the form

T + T ¹ = 6

tied to C-, and Cp, where E , which depends on the tolerances in the aberrations of the image on a given line through a concave grating with a right-angled pupil, is fixed. In other words, the inventor has a law of focus _; expressed taking into account the aberrations that allows him to obtain good focus simply by rotating the grating and with fine gaps.

The original equation T + T '= 0 (first-order equation) cannot deliver this result.

In a very general form, the invention thus relates to a method of focusing spherical, concave Diffraction grating that works with dispersion of the various radiations, which is a polychromatic one Form light, with reflection. This method uses an entrance and an exit slit, which are fixed, and the grid is only given a certain rotation. The procedure is marked by the fact that the grating is rotated so that the radiations are in the plane of the exit slit run, and that at a certain wavelength in a certain direction for a certain dashed width of a certain network and a certain resolution is the sum of the equations of the tangential focal lengths of object and image has a value that is different from zero and depends on the Determines aberrations, which according to a right

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angled pupil can be supplied by a concave grating. Said focusing method can by an optical structure can be realized, which is characterized in that the optical parameters such are that the changes in the image distance associated with the first order equation T + T '= 0, be compensated for by the setting error, the must be provided as compensation for the deviations (expression of the second order).

With his suggestion, the inventor accepted which calculations and experience have confirmed - that this expression of the focusing problem greatly facilitate the field of practical applications of focusing the concave gratings would, whereby among other things the resolution and brightness are significantly improved and at the same time the cost price the spectrometers, which are used more and more in industry and in laboratories, to detect monochromatic radiations to deliver in a strictly fixed direction, whereby the incident beam itself is also fixed (monochromator), is reduced.

As part of the new form of the general focusing equation the various conditions have been developed below, which are realized as far as possible need to be in order to achieve the desired result.

a) It is known that every spectrometer is characterized by its practical resolution and its brightness can be.

- 7th 309843/0768

The theoretical resolving power that the Refraction is given is equal to K N W, where K is the order of refraction and W is the dashed width. This resolving power is in fact limited, because as W grows, the aberrations grow, and one must determine a tolerance which is tied to the changes in the image spot. The optimal one The resolving power is therefore equal to K N Wo. A practical resolving power is also generally determined R that of the width f or f 'of the column used

P. . 'r'KKi depends and is expressed by _. _ ,

^p f '* cos ß

In the case of minor aberrations, the practical limit of the resolving power is given by R = 0.8 K NW, the value W _Q of W being calculated according to STREHL's criterion. In the geometric hypothesis (strong aberrations), a quality factor for each value of the pair W, L results in a limit resolution (sj,) * and thus the practical limit resolution force R = / f / ^ SA).

The luminous intensity £ is equal to the flux that occurs when using a standard light source, which is placed in the plane of the entrance slit, exits. Light intensity and resolution are not two independent quantities, because the product s £ R is proportional to NW L

R j>

since the brightness X (geometric hypothesis) is proportional

is " .

309843/0768

b) It is known that, in order ^{to solve the equation T + T 1} * = O, one can consider special mathematical solutions, which corresponds to the known mechanical solution of Rowland's circle or the structure of V / adsworth, ie the equation and above its three partial derivatives are almost zero, which corresponds to the structure of Seya-Namioka. In the latter case, the authors have shown that there is only one possible value (70 ° 3O ^f ) of the angle 2 θ at which the two gaps can be seen from the top of the grid, and that R cos θ for the image position and object distance are equal to.

c) As far as the aberrations are concerned, one can see the enlargement of the image point (and thus the loss of Resolution) depending on the amplitude of the aberrations

to calculate. This calculation is carried out using the STREKL criterion or by examining a Figure of merit that determines the path of the light rays entering the weighted. (weighted) image are characterized by intensity distribution. One looks at it generally only that the quality factor Q is defined as follows (1):

J -W / 2

WL JL / ÖJ-W / 2 VUW _ _co _ _ß

If A (w, Z ) denotes the deviating optical path and Cw and C ₂ w2 denote a shift in the reference sphere, is

Δ '(w, £) given by

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The minimization of the first term of equation 1 results in the values C 1 and C ₂ depending on the deviating coefficients. From this one calculates Q and thus the luminous intensity £ .

d) FIGS. 3 (3a to 3d), which show various asymmetrical, see focusing structures with a simple rotation of the concave grating, indicate the values of the angles of incidence and angles of reflection * C and β. If one makes the distance of the image stationary for a given spectral region, one can write that the deviations given by the "first order equation" are equal to those that one must perform to compensate for the aberrations. According to the invention, this first deviation is derived from the quality factor, which also expresses that the aberrations are compensated for when the reference sphere is shifted with respect to the initial conditions of said first-order equation, that is, the generalized focusing equation (T + T ¹ = £ ) is sufficient, whereby the deviating sizes in these

in this case are equal to C, w + Cp w. Under such conditions The basic focusing equation of a device with simple rotation results in:

I + cos ß + R - * £ = (C ₁ , + C,

Ό4.) + 4. (C ₂₂ + 2 C _ä )% ^? ~ 7 (2), if r = Re and r ¹ = Re ^f ,

and if C _Q ^, C ^, C _{22 are} the 4th order aberration coefficients and? - _o. In the "first order equation"

Where ,

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the second term would be equal to cos «c + cos ß.

For each value of the wavelength X, ie of f or of oi and β, one can calculate the aberration coefficients for a given value e, and e ', of e and e ¹ .

Each value of V / and of 9 corresponds to a V / ert of <like:

Λ T75 ( ^(C 04 ^{+ C} 4> ^{2 +} ^^ 22 ^{+ 2} <V ² ? ² + U

[C ₄ (C _{22 +} 2 c ₄ ) + £ (C _{22 + 2} C ₄ ) ² Jj ⁴ + έ ^c If ⁶ J ^ 4 ² ^

cos ß

where C ₀ -, is a third order coefficient of deviation. The two equations (2) and (3) thus make it possible to determine all optical parameters that characterize a given structure.

On the basis of these results, which demonstrate the justification of the proposal on which the invention is based, the practical implementation of the corresponding procedure must be the representation of a continuous band ΔA, which is as narrow as possible, allow in a given direction given the direction of the incident beam and the position of the slots is fixed. In particular, it must satisfy the condition (2) included in the following Form can be brought

cosffL ₊ cos ² ß. η (/ I).

e ■ e

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309843/0768

This equation can generally be solved by iteration, since H (A) depends on the value of the parameters e and e '. For each value e and e ¹ of e and e ¹ the coefficients Ci j and therefore 4> h A) "and H _n (A) can be calculated.

It must therefore be checked that e ¹ , which is indicated by the designation:

e _n KA) = «es β ι n _n v / l; —— J (p.)

uu «= _n \ ji

is determined is equal to the value e ¹ chosen for the calculation H (X). Otherwise, this would mean that the selected value e ¹ _3, ie the position of the exit slit, is not valid for all wavelengths ces the selected spectral range.

If e ' (X) is very different, the iteration process must be continued, whereby the new

. approximate values of e and e ¹ the values determined from equation (5) for 2 particular values A ι and A _f are used.

Γ 2, 2, cos ² " ^e n ⁺ L ^cos

cos'ß.

2,
cos J

cos ² !

e ' _n + 1. ^ [COS ² BF-COS ² B ₁ ™% * ^F J f

(6)

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309843/0768,

At this point it will be noted that an initial value to be retained for e and e 'is the value e s = e 'cos θ is that by classical theory (T + T '= 0) is given, and that the calculation 2 0 = 70 ° 30' must be carried out before the Calculating the other values of θ goes.

If the differences e - e. and e '- e'. under

_7 ρ P-I P P-I

5 x 10, the aberrations, i.e. the function R (A) for the real end value of the distances between the object and the image, are calculated. The best deviation Ae ■ = e ¹ - e ¹ (Ji) thus becomes a residual error in the

P P

instrumented implementation (the applied The abbreviation inst indicates that it is an instrumental value):

,, Ai W COS'ß ·

Sk inst = A «. _o ( ₇ )

e ^'d RNK

With an object distance r = Re and image distance r ¹ = Re 'and for a given dashed area, one obtains the limit resolution ζό λ) , which would have to be achieved if the image were for all wavelengths in

Distance e 'forms. Since, in general, ^ A inst is not zero, it is necessary to determine a limit on this value. According to the invention, when determining these limits, it can be assumed that everything proceeds as if a non-deviating image were ^{focused at a distance r f} (Λ) = Re '( λ. ), The output slit being at a distance r ^f In other words, = Re 'would find that 0 k is equivalent to a simple mistake in implementation. From the foregoing it can be seen that according to the quality factor defined above, the tolerable

309843/0768

Failure to perform below a trial fourth £ must be like:

W inst <t - ₍₈₎ .

cos ß

For a certain value θ and for each value of the pair W, L, for example using an electronic computer, the values e ″ and e ^f can be determined by iteration, whereby one

- the practical limit resolving power R = the slope ρ of the curve λ / <M inst,

gg ρ \ ,

the corresponding limit value / I j t = receives. V ■?

If the values of e and e '' are positive (the distances Object and image must correspond to real objects and images in the case of an arrangement which is only one Concave grating has to correspond), and if the condition

is satisfied in a given spectral interval, the focusing method can be adjusted by simple rotation of the grating and with fixed slots can be used to create monochromators »

Assuming the Strehl Kriter ium to the properties set to be met by the arrangement, then H (A) has the value

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2
H (A) = cos oC + cos ß + J y (C ₄ + C _o4 )

(10)

where the value of W and of

is calculated with

2205

1620

from the inequality

140

determined according to the 3TREHL criterion. In this case, the value of V / and L is not chosen at the beginning, but is determined on the basis of the values e and e ¹ of condition (11).

The practical limit resolving power is therefore equal to R = 0.8 NW _Q K, and ρ must meet the condition

1.92

meet, where the second term of this inequality is independent of A. Here P represents the maximum slope of the curve X = j (α Α inst).

One or the other structure of FIGS. 3a to 3d is chosen for a given angle θ and results for specific cases that occur, if one considers this If you make a choice, you have to make sure in each case whether the light intensity (i.e. in particular from the value of the dashed area), taking into account the required resolution R, is sufficient. In the borderline case,

309843/0768

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if one assumes very small values for W and L. the condition (8) can still be satisfied, but the corresponding devices then become not practical Be of interest, since their light intensity would be very weak 'which is particularly in the spectral range of the distant Ultraviolet affects where the energies of the light sources generally compare to the others Spectral ranges are not very high »

Special embodiments of the invention for the Realization of single monochromators or double monochromators are characterized by the use of spherical concave diffraction gratings in the Work arrangement "in piano", i.e. in which the centers of the input and output slots are in one plane which contains the grid normal and runs perpendicular to the direction of the lines of the grid, where the entrance and exit slots have a fixed width (i.e. independent of the wavelength Λ) so that there is no loss of flow in the plane of the exit slot.

According to a preferred variant, not only the aberrations of the image plane are used when selecting the image plane Concave grating is taken into account, but also aberrations resulting from the lighting conditions of the grating.

The concave grids used can be those grids which consist of lines applied to glass (or copies of such grids) or in general optical elements that simultaneously ensure the focusing JO and the diffraction of an incident wave,

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regardless of the method by which this refraction is carried out, provided that, v: enn d die The grating division, which is constant over the entire pupil of the optical element, is the basic equation for an arrangement of this type is: ι

sin! Oi + are ß = - KN λ (13)

In this expression, ⁰ C and ß are the angles of incidence and diffraction which are evaluated starting from the grating normal v / earth, N = -r is the number of lines per mm, K is the order of refraction and Λ is the wavelength; the negative sign applies to all refracted rays which lie in the image space and are enclosed between the central spot (i> C = -ß) and the tangent of the grating.

These focusing methods are mainly carried out with holographic gratings of the I-type, in which the lines of the grating generated by a holographic process and for those, as in the case of the classical line gratings, the first-order focusing equation is characterized by the drawing T + T '= 0, T and T'.

Therefore, the corresponding description is only related to the use of spherical concave gratings, their optical features are equivalent to those of the usual gratings. Their lines are defined by overlapping the surface of a concave mirror with parallel planes at the same distance.

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30 984 3/076 8

Above it was stated that if you use the Aberrations taken into account (i.e. expressions of higher Order in the equations, which are derived from the Fermat principle), and if there is a possibility of compensation of these aberrations by shifting the reference sphere, i.e. by a suitable choice of the image distance, monochromators can realize in which the object and image distances are fixed, and this in a larger spectral Interval, with rotation of the grid around an axis that goes through the apex of the grid. It has been found that such arrangements have a low cost price as there is no shifting of the grid, they also have the significant advantage for the user, that the direction of the incident and broken bundle • is absolutely firm. In addition, it has been found that, contrary to the solution proposed by SEYA and then NAMIOKA, the solution for ultraviolet on a single Angle close to 70 ° 30 'is limited, it is possible to make arrangements with any values of 2 θ. The object and image distances are given by a generalized focusing equation in the form of the equation given;

" Η

in which there are higher-order expressions. The equation thus depends on the value of the dashed width W and the dashed height H (or on the relationship 9 - H / W). It must be added that other values of 2 ö have been envisaged by SEYA and NAMIOKA, but these were with a considerable decrease in resolution

309843/0788

(or the light intensity) if the image distance remained fixed, or with an additional one mechanical complication when the value r 'was adjusted experimentally as a function of the wavelength.

From this it can also be seen that a limit resolution is associated with each dashed area, which can only be obtained starting from slots of certain widths f and f '. It has been found experimentally that due to the weak luminosity of the near and far ultraviolet sources used and the poor performance of the gratings commercially available up to now, it was difficult to find slits of widths f and f 'because of the low value of the signal / noise ratio to be used at the exit. So, especially in the case of industrial surveillance, it is important to use wide slots with non-negligible heights, because the outgoing flow is directly proportional to the area of the output slot does not have to vary manually depending on the wavelength. It is, of course, true that automatic arrangements, which are necessarily complex, can be devised to accommodate such width variations, but adjusting the size of the slots, whether automatic or manual, inevitably increases the complexity of the equipment and its cost.

If one uses the method for correcting phase aberrations according to the invention, then first the deviating optical path 4 ¹ (w, £) 'must be taken into account, which is a shift of the reference sphere to that through

309843/0768

First-order theory taken into account. If you have slots with. not negligible, height used and very open superstructures, i.e. for increased values of the relationships H / r 'and w / r', and if (h -2h'L) R is greater than Λ / w, then Δ '( w, Jt) as follows:

Δ '(w, I) = A \ L *. £) = G ₁ W + Δ' ₂ (w, /) + C ₂ W ² + -c _o;

with - ⁰¹

. ι -i 4 A "ZO -

where C.. denotes the coefficient of deviation, with i = 0, 2 ... and i + j = 3 # 5 ·. ·· »where C ₁ W represents the fluctuation of the reference sphere, vjo C, w a function of the height h 'of the slot for

Oil

the exit is, and with
2) Λ '(w, /) «

if i = 0.2 ... and u + j = 4.6,

2 ■ '

if C _o w denotes the displacement of the reference sphere,

2
if C _no w is a function of the height h 'of the exit slit

■ ²⁰ is.

As mentioned above, the coefficients C _{1 and C 2 are} determined by a geometric quality factor Q (or based on the STfIEHL criterion, which was not taken into account here), which allows the aberrations to be included

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the enlargement of the Eildflecks in connection. Corresponds to every value of w and of § = H / W a mean square value of the resolution like:

whereby

With the limit resolution <eiA ^ the slots of width f = r Q and f '= r'Q. Are then connected. In the case of slits of width f.)> F and f '> f ^f and with significant heights h and h', in order to determine the practical resolution, one must first carry out a convolution product of a right-angled function that defines the entrance slit through the intensity distribution in the image plane indicates. This calculation is very complex, on the one hand because of the expression given by the intensity distribution and on the other hand because of the use of straight slits in the arrangements with concave gratings, which causes a strong curvature of the spectral rays, especially in the case of distant ultraviolet. The enlargement of the image follows not only from the enlargement S A _f >, which is tied to the width of the entrance slit, but also from that 6A "* which is tied to a double curvature of the spectral rays (the first curvature RC 1 is due to astigmatism and so stands with the term C ₂₁ ^ w

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309843/0768

in context, the second RC 2 is due
on the deviation from the law of dispersion, namely
associated with the term C _Q , w).

For fourths of f., And f '., Which are much higher
as f and f ', and taking into account the increased
The value of the astigmatism of the structures with concave grids can be shown within the framework of the geometric hypothesis that the practical resolution obtained with a structure "in plane" with a straight exit slot of height h ¹ is essentially the same

p ² ₊ U ₁ ?

In this expression, which has been verified experimentally, the value ^ OÄ) · is derived from equation I ^, in which it is taken into account that the expression C ₀ ^ zero (so one separates the contribution to the enlargement of the image

due to the curvature of the spectral rays from that due to other aberrations). The value of
is equal to

f = r ¹ fi / r di (17)

and the one of ok is the same

C.

($ ■ / = h ^f2 RC / 8 di (18)

where di is the image dispersion of the array.

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This allows the conclusion that if, in an arrangement with a simple rotation of the grating and with fixed distances between object and image, a straight entrance slit of width f ¹ and height h = _ - τ and an exit slit of width f 1, =

ρ di and the height h 'are used, the resulting limit resolution is not ^ o X / , but has the value οAp of equation l6, if oA is in the same order of magnitude as <cίy ^^. The calculation has shown that it is possible ^{to determine non-negligible values of h f} for which this condition is fulfilled if for any values of 2 O between 20 ° and 150 ° to the extent that for 2 θ < h5 ° the curvature RC is assumed to be equal to RCj. (ie the astigmatism is relatively small), and if for 2 G ^ S ⁰ the curvature RC is that which goes back to the astigmatism, and if for 2 θ> -45 ° the values chosen for A ^ and / l _{f cover the} Spectral interval! have been adjusted (the latter obviously depends on the angle 2θ - Equation 13). This applies to the gratings which are generally used in the far ultraviolet and which are currently available on the market. It will be noted that the centers of the entry and exit slots are in the plane containing the grid normals and perpendicular to the direction of the bars. Equation 16 shows in particular that one can increase the flux for the features of the slots under consideration - by increasing f and h and f 'and h' - whereby one loses a little bit of resolution, since (■? /! _ Is always greater as <(ö / X

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309843/0768

After testing the validity of Equation 16 experimentally, it has been found that cfA and f 'are monotonic functions of wavelength decreasing by very small values of θ (e.g. with 'for θ = 10 °, R = 400.7 mm, N = 1200 lines mm, V / = J8 mm, L = 30 mm, h' = 4 mm),

then increase again when θ increases, e.g. θ = 20 °, Q = 30 °, and decrease again, by a very large amount Values of Θ, e.g. θ = 75 °. The conclusion the calculation, which has been confirmed by experiments, shows that it

There are 2 values G * for which the variations of

P. ν

can be neglected depending on the wavelength (the resolution was therefore constant in the entire spectral range investigated, f ¹ ^ generally varies with./O,

2 values of θ and θ are for which the variations from f '. neglected depending on the wavelength (the resolution was therefore variable in the spectral range investigated).

The latter finding was important for the realization of commercial devices, since one is such Can produce monochromator with high flux with slots of fixed width for a low cost price.

The calculation of θ can be carried out in the following way: First, for a given grid and for a given value of f. And h ', the object and image distances for each considered value of θ from equation k' _f in are calculated the

3 0 9 8 4 3/0768 '_ 24 -

H (A) = cos 6i + cos ß + -—- g Y + 4 V §

^{+ 2 C} 02,

where W results from the simplified equation 14 (C ₂₁ = 0).

The final values obtained for r and r ¹ take the aberrations into account and lead to the calculation of <o / {> and δ Λ- (equation 18). One then calculates Oλ * for the value f ₄ and finally SA _n for f \

1 . P 1 ι

the function of / i . The course of the curves f ^ = · $ (Λ.) For each θ thus allows the selection of the values θ of Θ. This can be done automatically by a program in which θ is allowed to vary from minute to minute. The retained value of θ is then that for which

f '( K M) -f * (λ min) ^ y (f (λ M) - tf (A min) ^N (20)

where f '. (A M) the value of vcn f '. for the maximum Is the wavelength of the spectral range under consideration, where f '. (i. min) is the value that corresponds to the minimum wavelength corresponds, while the quantity T ^ defines the desired accuracy, which practically corresponds to the ord-

-2
can reach a value of 10.

Two examples are given in Table 1 below, for which the value of Gp is determined with f ^ = IC / i has been.

309843/0768

RN Wo Lo rr ¹ 2Θ hf * i -Λ pure Ληαχ mm -Str / mia mni now let him be inm mm l \ a

400.7 1200 38 30 152.28 9%, Ψξ 144 ° 52'6 0.195 50 1100 1221.2 54 54 412.08 59 *, 51 30 ° 28 ° 2.8 0.007 350 4000

Outside of the two special applications mentioned above, the focusing method according to the invention for concave grating _a , based on the general focusing equation 4, allows monochromators to be built with an arrangement of simple rotation of the grating around an axis that goes through the vertex. The object distance r = Be and the image distance r ^! = Re ¹ (R is the radius of curvature of the grid) and depends on the angle 2Θ at which the two gaps can be seen from the top of the grid. Such an arrangement provides very bright structures with sufficient resolution for most industrial control work and even for advanced research.

¹ S loop

In addition, the inventor has shown that the best Image plane can be defined if one considers not only the aberrations of the concave grating alone, but also those taken into account resulting from the lighting conditions of the grid in the above-mentioned arrangements. Indeed, it has been shown to either due to the type of source or due to the transmission optics, with which a distant source is focused onto the entrance slit, additional aberrations

occur at the level of the entrance slot can.

Δ tW, I ) i

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Under these conditions, the deviating optical path in the image plane has the total value

As mentioned before, nan can set for A ' (w, 0:

Δ " (w, /) = 4 '} Cw ₁ -f) + C ₁ W +' C ₀₁ W ¹ + C * w 4

+ Λ ' ₂ (W ₁ ^) + ^C 2 ^{w2 + C} o2 ^{w + C} 2 ^W ^ ²² ^

if one separates the even expressions of w and £ from the odd ones, and if one observes that A. (w, <C ) essentially represents an execution error and a tilting of the image.

The odd expressions are defined as follows: ^ ₁ (w, *) = Ei ₀ C ₁ J / V ^ C ₀₃ w ⁵ + C ₂₁ ^ ² W

^C ij ^{are the aberration coefficients of} the concave grating, where i «0, 2 ... and 1 + J = 3.5 ...

C ₀₁ is a functional term for the height h ^{1 of} the exit slit,

C *, w is a first order term related to the exposure mode the device is in communication,

C-W is a term that conveys the tilting of the reference sphere and the position of the maximum intensity determined, which is at a value of the angle of incidence in the direction ß + Aß, where

309843/0768. ₂₇ _

(23) sin ß = - KK λ - sin οί

(24) cos SAß = (1 - m) ~~ (C ₀₃ + C ₂₁ ^ -

2 ^r

W ν !.

₀₃ ^r

if. the geometric criterion defined above considered. The even-order expressions that determine the value of H. (A) are as follows:

, 2 i? 2 _x 2 4
+ (w + £) C

C. »represents the aberration coefficients of the concave grating for which i = 0.2 ... and i + j = K, 6 ...,

C ^ pW is a function of the height h 'of the exit slot,

* 2 ■

C ₂ W is a second order expression that depends on the lighting of the device,

2 ■ '"

C ₂ W characterizes the displacement of the reference sphere in the direction ß, * the value of which, derived from the geometric quality criterion, allows the calculation of H ( A) , which is expressed as follows:

w ^{2 2}

H (Λ) = cos OC '+ cos ß + ^ -

I 5 3 y

+ "2 C ₀₂ + 2 C _2; (25)

^ = ^c o4 ^{+ C} 4 / ^{V = C} 22 ^{+? C} -4 . '■' ■■

■ '■■ -. -28 i

3098A3 / 0768 _r

W is the dashed width and 9 is the ratio h / W, L is the dashed height.

The image focusing plane, ie the value of r ¹ , is thus chosen so that the sum r'er different errors during implementation (the one due to the height of the slits C ₀₂ , the one due to the type of illumination C ₂ * that of the displacement Co sought) so is that the 4th order aberrations are compensated and that the final limit resolution so As is that given by Equation 14.

A particularly important case that the invention can deal with is that in which the rays emitted by the source are enlarged by the Doppler effect, i.e. for the ray particles (ions, atoms or molecules) that are excited by a high velocity ν (with Ψ - - , where c is the speed of light). It is known that if one looks at such a source with an optically corrected monochromator, one obtains an image spot in the image plane, even with a very fine entrance slit, the width of which is at least:

₍₂₆ ) JA _n -Aj * ° - ■ £ cos B ■ ( ⁵ⁱⁿ * + ^Slnß ) ^υ r 'r' KN

for the case of a perpendicular observation to the path of the particles.

It has been found that such a magnification ^ which usually reaches several Ä, can be reduced by shifting the image plane, this shift not only depending * on y, but also on Λ.

309843/0768 _ _2C) _

In practice, the user must ^{change the value r 1} if the spectrum runs in front of the exit slit. In the method for correcting the aberrations by shifting the reference sphere, it can be admitted that this magnification is to a first approximation the same as that which would be observed with a classical source if the execution ^{plane is (r f} + 4r ^f ) instead of r ', where Ar ¹ :

cos ² ß Ag '- L MM ~ κ N ^ ^ - ^ - (sin öC + sin ß)

^w o r '

cos ß - ₍₂₇₎

So everything is done as a first approximation, as if there were an additional instituentelle execution error, how

/ * j -ti-i.1 Jt J / COS ID (J / /. rt s t- <Jo ω

~ - KN Λ j - == - j (sm + sin ß) ^ -— *

In this case, equation (4) Ib'senj is obtained by taking equations 25 and 28 into account in such a way that a pair of values c £, β, r and r ¹ is determined for a considered spectral range in such a way that the values r and r ^{1 are} independent of the wavelength, and that each value of 7 therefore corresponds to a fixed image plane for an extended spectral range.

If one takes into account that such sources are usually not very infectious, one can, as mentioned above, the case of treat straight slots with large dimensions and in particular determine the angle θ * ρ, for which the width

of the exit slot is firm without loss of flow • to effect.

3 0 984 3/0768 _ - 30 -

Finally, the Doppler magnification becomes an im general weak Doppler magnification superimposed, which is always expressed as follows when observing perpendicularly

This means that

ρ

KN d K tv = cos ß 4 ß _n β KN Λ - ^ - a (sin <* + _s i _n ß)

The intensity maximum is thus found in the direction ß 4-Δ ß as

fl 2 ι W

cos ßAß = / C ₀ , + C ₂₁ Λ »-y

309843/0768

The "accompanying drawings show various embodiments of the known art as well as curves and embodiments according to the invention.

Figs. 1 to 3d are schematic representations of appearances and structures according to the known art.

FIG. 4 is a top plan view of a monochromator, partially in section, using the method of FIG Invention with fine, straight or curved gaps.

Fig. 4a is a vertical section.

Fig. 4b shows the control of the wavelength.

FIG. 4c is a diagram corresponding to the monochromator of FIG. 4.

5 shows the values of the reduced object and image distances depending on Θ.

Fig. 6 shows a diagram showing the value ρ for the various Indicates arrangements of Fig. 3 according to the invention (for the case of weak deviations).

Fig. 7 shows the values of the resolving power as a function of θ for a given grating (in the case of stronger Deviations).

8 (8a to 8d) show the basic diagram of the various asymmetrical arrangements for focusing with a simple rotation of the concave grating. The values of the angles α and β for incidence and diffraction can be seen Arrangements M _p and M-, the two '.

30 9 843/0768

are in opposite directions, either of these arrangements is the two preferable to others.

Figure 9 is a top view, partially in section, of a monochromator for using the method of the present invention with straight columns of fixed width.

Fig. 9a shows a partial section (Fig. 4a).

Figures 9b-9b * show the control of the wavelength and their operation (accurate measurement of the wavelength).

10a and 10b are diagrams showing the value of ζ ο Λλ and the value of the practically achieved resolution cfA _D for the two given examples.

Fig. 11 shows schematically a double monochromator with Z-shaped

In the embodiment shown in FIGS. 4, 4a and 4b the monochromator rests on a vacuum stand that carries a plate A on which the various Elements according to FIGS. 4-4a-4b and 4c are arranged.

The vacuum stand, which is not shown, carries a plate A on which, on the one hand, a central block 2 is mounted, in which the concave grating 3 and the rotating mechanism 3 of the grating are arranged. On the other hand, a block 4, which carries the input slot, and finally blocks 5 and 5 'with the output slots are attached to the plate A. The blocks 4, 5 and 5 'are connected to block 1 by pipes 6 which are provided with vacuum-tight bellows membranes 7, for example from 309843/0768

"TOMBAC". These make it possible to adjust the slots by means of the screws 8 which are provided on each block 4 to 5 ¹ and allow the blocks to be displaced accordingly in guides of the plate A, not shown. For each block 4, 5 »5 ¹ , the width of the slots can be adjusted by any suitable device 9.

The disk A also carries a control mechanism 10 for controlling the wavelength, which will be described later will.

In Fig. 4a it can be seen that the block 2, which is fixed in the block by nut screws 1 ', is conical Has part 11 which is arranged with a vertical axial bore, the axis 12 of which is the axis of rotation of the Lattice R forms. At its lower end is the axle 12 firmly connected to the grid R, which is in a bearing 13, which is mounted by suitable means on the block 2, is attached. The axle shaft 12 is kept mechanically precisely aligned by two ball bearings. The first Ball bearing 14, which is pressed onto the axis of rotation, is held in position by a shoulder 15 of the shaft and through a part 16 against an inner shoulder " 17 of the conical part 11 pressed, while the other ball bearing 18 by two intermediate pieces 21 'against a Inner shoulder 19 of part 11 and a shoulder 20 of the Shaft is pressed. The clamping is ensured by the structure 21 with nut and brake 22 * The free end the sleeve 12 protrudes beyond the structure 22 and carries a horizontal arm 23 which is fixed to the Shaft is attached.

The arm 23 here runs parallel to the tangent aiii vertex of the grid R (see Fig. 4b and 4e) * but one kafiri it

309843/0768 ^

give any other desired or advantageous fixed direction with respect to the grid fixed to the plate A. A printing device 24 carries a drive member, which is denoted by 25, to increase the displacement of a roller 26 according to the axis of the printing device before. The roller 26 acts against the arm 23. The contact between the roller and the arm is ensured by a return spring 27 acting on the arm. Under these conditions, the displacement of the roller 26 on its pressure device 24 acts on the arm 23 and causes a rotation γ which allows the wavelengths to pass along the exit slit. In addition, in this way one can measure the wavelength Λ with sufficient approximation, which is expressed in the following formula:

cos θ sin t (32)

The simple movement described results from an impact on the arm 23 by means of the roller 26, which is formed from a ball bearing with the radius u, which moves linearly as a function of time in the direction HoZ and an angle 7 with respect to a parallel to ¹ Forms the direction of the normal for the value j * O of the rotation, ie for the central spot (^ »o).

To get an accurate measure of the wavelength; If Ö5, according to equation (13), it is sufficient that the WeH; Voll sin f * _t which is obtained by a shift Xi ^ JX * »M * a 1 kt (with Sl ₀ H ₉ * al and OH - 1) # tiittä Üit6at * 6 Pühktiöh ** · de * time is.

It can easily throw shown * that

O O

V - a cos J fkt + (l-kt) (l-cos J)] ■

J "1 + a (1-kt) sin \ f

The function sin is generally a complex function. Nevertheless, it is found that at the special value t = - ~ - = t. , V-takes the value y, and sin V *. = a cos ψ = · - Ji- kt
" / 1

For this value t-, of t the wavelength is measured exactly (Effect of roller bearings). ·

When realizing the additional condition at 'sin y = -j- tgjjp ^ f 1, i.e. for small values of ^ and small values of the ratio -j-, one can write:

[l + a (l- kt) sin ψ J ^ ¹ = 1 - a (l- kt) sin ψ From this it follows ■ ■.

sin V '= a cos j kt + b - - ^ r- kt + b b = a (1-kt cos J / "(1-a sin f) (l-cos ^) -a kt sin f' cos

So a non-linear term b is introduced. For a limited spectral range, i.e. for small values from one can simplify b by approximation

1 _ cos -

.- So, the function sin γ takes the following form: sin ψ = X + 0.5 X (X ₁ -X) (1-X ₃ ^ gQ) (XX,)

with ^ X = -j- kt ^x

^x i ⁼ T "

1-X ₁ tg θ

309843/0768

- 56 -

The wavelength is measured precisely for;

= 0

--f- JL

V-jr ™ * Ii "~" * ^% TC ^ 'lit' COS W Λ-j

As a practical example, if you give υ a value of 15 mm / a value of 300 mm and ^ f a value of 4 °, then you can achieve an accuracy of +1 R over a range of 3200 A.

So it can be seen that the very simple mechanism as has been described, it allows the grid rotation to be exploited to be a fairly accurate indication of the value of the wavelength.

In the following, the cases of two grids will be examined in detail, viz

R ₁ (radius R - 500 mm, N = I83I, 8 lines / mm) R ₂ (radius R = 500 mm, N = 1221, 2 lines / mm) The corresponding structures were made with straight slots 10 mm high and wide from

^{= f for the} entrance slot and = f 'for the exit slot

COS 15 * ^ w>

for single monochromators and those with multiple outputs Mistake.

With the simple monochromators you first have the results and conditions according to the STREHL criterion checked.

309843/0768

The values of e and e ¹ are shown in FIG. 5 'as a function of θ. It can be seen that they essentially depend on the value N. But if you double the radius of curvature, the values of 2 and e 'practically do not change.

With a dashed height of 25 mm, the values of W are between 10 and 14 mm for changes in θ between 6 and 45 ° and a reference wavelength of 750 ä. It should be remembered that the STREHL criterion is indeed for any value of K indicates other values of W. For a practical implementation one chooses an average value corresponding to a certain value of the wavelength. It will be found that the STREHL test beyond θ - 50 ° is inadequate for the dotted height considered, and that below 9 = 6 ° the values of e ¹ (structures Fig. 3 "> 3 ^) or of / ( Superstructures

a Q

Fig. 3] - »3 _c ) are too high to lead to practical implementations. Fig. 6 gives the value ρ ~ f (Θ) for the grid R-, and the various arrangements. The solid curve shows R / 1.54, with the broad line determining the range θ for which the limit resolution R is achieved in a spectral range from 200 to 3200 R. In the arrangements of Fig. 3 and ~ 0> _A

CS CS

the range extends approximately from 32 to 36 30 ', while it extends in Fig. 3 and 3 from 26 ° to 36 °. In the case of the grid Rp, the range θ lies between 30 ° and 40 ° for the structures Fig. 3 and Fig. 3 ,.

a et

The condition 12 thus limits the possible range for the angle Θ, which otherwise ^{corresponds to the values of e and e 1} -30, which are completely compatible with the handy realization of a monochromator.

If you deal with a resolution in the

309843/0768

If the order of magnitude of 5000 is sufficient, then the arrangements of FIG. 3 and FIG. (Grid R ₁ ) between 27 30 'and 39 30', the other two between about 20 30 'and 39 are used.

In summary, it can be said that the use * of the grid R ₁ with an optimal dashed area

2
of 11 χ 25 mm makes it possible to obtain a limit resolution of 7,500 for 26 ° <θ <36 ° 30 '. However, it is preferable to consider a figure of merit Q for reasons of brightness.

Therefore, the results and conditions are examined according to the figure of merit Q.

The calculation shows that the values of e and e 'according to FIG. 5 for W = 30 mm and L = 5 ^ mm (f - 1.8) are still practically valid. The limit resolving power R for the various values of ^ is shown in FIG. 7 as a function of θ for the two selected wavelengths λ and Af. Their values result in ÖA inst, minim, in the observed spectral range. For § = 1.8 and for θ between 6 and 50 the practical limit resolving power would be 300 to 750 R and 8000 to 2500 R. As before, the range of validity is limited by the desired value of R. If one wishes to obtain the above values, the calculations show that the interval of θ on the one hand increases when 3k _Q 3 changes from the arrangement of Fig. ^For the arrangement of Fig., And on the other

O el

on the other hand ~ mitf. For § = 1.8 the grid R can be used for values of θ between 22 ° and 40 ° and grid Rg between about 20 and 50. In summary: the use of the grid R ₁ with an optimal dashed

th area of 30 χ 5 ^ mm allows a limit resolution between about 3000 and 8000 to be obtained, 309843/0768

. for 22 ° 4θ £ 4θ °. With the same resolution it turns out the second solution as much more interesting because it corresponds to a brightness gain with a factor of 5.9.

These latter findings, based on the use of Selektionskrlteriüms ρ = f (θ) "shows that the arrangement of Fig. 3 _e alone main-

et

is to be obtained and that there is a limit to the range θ substantially different from the desired value R

■ P ··

depends. The latter will be a maximum for any value of θ between "22 ° and 40 ° for grid R ₁ and 20 ° and 50 ° for grid Rp.

The following table shows the various values of the parameters W, L, e and e 'for the grids R-. and R ₂ and the two particular values of θ
15th

Grid R, ^W o = 50 mm L.
0 == 54 mm θ = 40 ° e = 0.80386 e ' = 0.72306 θ = 30 ° e «0.82789 V «0.91332 Grid R ₂ W.
O = 30 mm L.
0 = 54 mm θ = 50 ° e = 0.76897 e ' = 0.51620 θ = 20 ° e = 0.85117 e. ¹ = 1.0557

The advantages of such a focusing method are numerous: From an optical point of view: the maximum performance of the grid in this arrangement can be achieved? the collapsing and broken bundles are firm, so it is possible to place one in front of or behind the slits to attach additional optics whose axis is not dependent must be changed by the wavelength.

In mechanical terms: A simple rotation is always " - "Easier to do than a translation, especially when the tolerances of the parallelism are tight * as is the case with the diffraction gratings. In particular the structure according to the invention is favorable when

309843/0768

Grids with large radii of curvature can be used.

Since the wavelength ^ = 2 cos θ sin · ^ / N is directly proportional to sin Γ 1st, the direct reading of the value of the wavelength is pleasant. This is not the case with those arrangements in which the value θ is not constant as a function of X when the grating is shifted. This type of monochromator can therefore be realized at a low cost price.

The spectrometers, operating according to the process of this invention are, even if they can be used from the extreme ultraviolet to the far infrared of particular interest for the spectral range 20-3000 Å. ⁵ In the spectral range of the distant violet, the absorption phenomena require, on the one hand, that one works in a vacuum and, on the other hand, that no refractive materials are used which are no longer permeable below 1100 Å. As a result of the relatively low reflectivity values, the use of the concave grating, which simultaneously ensures the diffraction and focusing of electromagnetic rays, is of particular interest in this spectral range.

For monochromators with multiple outputs, i.e. with a fixed direction of the incident beam and several fixed directions that are different at the same time Supply wavelengths, one can ensure that: a) the simultaneous realization of two different

Test types with high resolution in a "* same spectral range is possible, b) the simultaneous execution of the same experiment with variable resolution in different spectral ranges is possible and that

309843/0768

- .41 - "

c) simultaneous photometric measurements in different spectra are possible.

a - Examination of the curves of Fig. 5 shows that two values of 9 correspond to one value of e. A good resolution can be achieved for these two values if the values of the image distances are those given by the curve e '= f (9). If a resolution of 0.3 R is required (grid R ₁ in the arrangement of Fig. 3a), with an object distance of 0.82 R, this object distance can correspond to two outputs, one at an angle of 2 9 = 44 ° (r ¹ = 1.08 R) and the other at an angle of 2 9 = 68 ° (r '= 0.84 R).

b - If one takes an object distance r = Re equal to 0.81 R for the grating R, in the structure according to Fig. 3a, one can choose 9 to obtain a spectral range from 80 to -3400 R for the values dd e, e ', 9 as follows:

dashed

Area 30 χ 54 mm ² 9 =. l4 ° 9 = 35 ° θ = 75 °

_ _, o.8l 0.81 0.81

e ¹ - ■. 1.391 0.833 0.4203

medium resolution 5 R 0.3 R 5 R

Spectral 1500-4300 R 500-3000 R 80-750 R range

c-In the case of photometric reflection or polarization measurements, a resolution of a few R

20- acceptable. On the other hand, it is very often beneficial to have this Make measurements in a wide range of wavelengths, which actually requires the use of two different

^, which requires structures with different characteristics that are difficult to compare. The grid R, in the structure of Fig. 3a, can work between 1500 and 4300 R , 'if 2 9 = 29 ° (r * = 1.44 R) and between 200 and 2000 R, if 2 9 = 100 ° (r = 0.518 R), for a single object

309843/0768

distance equal to 0.77 R. In addition, a similar structure can prove to be interesting, on the one hand for the Measurement of the grating power as a function of the interference order and, on the other hand, for the calibration of the sources and recipient.

Since the values of e in structure 3a (or 3d) are equal to those of e ¹ in structure 3b (or 3c) and are reciprocal to e ¹ , a structure with two inputs and one output can be implemented in the same way.

If the wavelength observed on the first beam

K _{1/1 1} »2 sin γ cos O ₁ ZN

the one on the second bundle must in this case

K ₂ / (2 = 2 sin Jf cos © ₂ / N = K ₁ A ₁ COS Og / eos Q _1. A wavelength 4 can be in order 1 (K ₁ β 1) and in order 2 (Kp = 2 ) can be observed simultaneously when cos θ _? = 2 cos Θ,. The use of the grating fU in the structure of Fig. 3a, with an object distance r = 0.6 R allows the realization of this condition when approximately θ ^ » 60 ° 45 '(r ¹ = 0.38r), and if Q ₂ = 4 ° (r ¹ = 2.1 R), where only a wide continuous (frequency) band (^ 10 i?) is required.

In the example shown in FIGS. 9, 9a, 9b, 9b ', the monochromator rests on a vacuum stand which has a - ». Plate A carries on which the various elements according to FIGS. 9 to 9b 'are arranged. Fig. 9 shows in particular the attachment of a grating of 50Ö Mn, but the construction principle of the various ^{elements shown in Figs. 9 to 9b 1} is for every other value of R gUl-

30 984 3/076 8

tig, - it being understood that in each case the situation of the slot is set to the fixed distance and for the intended angle 2Θ.

On the plate A on the one hand, a central block 1, in which the concave grating R rests, and the system of rotation 5 (Fig. 9a and 9b) are mounted, and on the other hand, the blocks 4 and 4 ^f to the input of valve slit and the exit valve slit. The blocks 4 and 4 'are connected to block 1 by pipes 5 which are provided with bellows diaphragms 6, for example from Tombac. The connection is vacuum-tight and allows the position of the slots to be adjusted. The blocks 4 and 4 'can be moved laterally and in the direction of the grid, being guided in guides which are arranged on the plate A. The guides have a mark that

by suitable optical means with the markings. matched on blocks 4 and 4 '

will. In each block 4 and 4 '. are slits of solid pulp te provided, which are built into a tube that allows adjustment of the slots when rotating. Included the final blocking is done by a group of opposing screws.

In Fig. 9a it can be seen that the block 2, which is fixed in the central block 1 by nut screws, has a conical part 11, 'which is vertically aligned with its axial bore, the axis 12 of which is the axis of rotation of the grid R. At its lower end, the axis 12 is firmly connected to the grid R which rests on a bearing 15 which is fastened to the block 2 by suitable means. The axle shaft 12 is held in a precisely defined direction by means of a group of ball bearings. The first ball bearing 14 is pressed onto the rotation axis _r, held by a shoulder 15 of the shaft in position and with a part 6 with respect an inner

309843/0768

_ 44 -

shoulder 17 of the conical part 11 pressed. The second ball bearing 18 is within the piece 11 of a Shoulder 19 and a shoulder 20 of the shaft held by two intermediate pieces 21, the clamping by a unit with screw and brake 22 takes place.

The free end of the axis 12 protrudes beyond the complex 2 and carries a horizontal arm 23 which is fixedly seated on the shaft, the role of which will be described.

The arm 23 runs parallel to the tangent in the oitter apex R (FIGS. 9 and 9b ¹ ), but it can also be given any other desired or advantageous fixed direction with respect to the grid. A printing device 24 firmly connected to the plate A carries a drive device 25 in order to move a roller 26 along the axis of the printer. The roller, which can in particular be a ball bearing, is mounted on the arm 23 by means of a slider, so that the distance Ji between the lattice apex, which is embodied by the center of the axle shaft 12 and the center of the roller, can be adjusted. The roller is placed on one of the generatrices of the horizontal axis cylinder 27, which runs perpendicular to the direction of displacement of the printing device. The contact between the roller and the cylinder is ensured by a return spring 28 which:

acts on the arm 23. Under these conditions, the movement of the roller 26 takes place on one of the generators of the Cylinder 27, the displacement of which is effected by the pusher 24, the arm 23 a rotation, which the passage of the wavelengths along the exit slit.

In addition, one can measure the wavelength k , which is expressed as follows, with a fairly high degree of accuracy.

- 45 -309843/0768

^{cos θ} ρ ^sin r

According to this equation 33, the wavelength is only a linear puncture of time if the value of sinj ^ (t) can be obtained by measuring the displacement D of a pusher element. This shift can easily be made time-proportional if the speed of the motor connected to the ram remains constant (D = vt). It can be seen in Fig. 9b ¹ that when the arm 23 is rotated, the displacement D = C _o C '= C' _o e of the cylinder 27 in the direction perpendicular to the arm 23 has the following value:

D = H ₀ H = / sin f (t) = vt, (j4) if / = OH = 'OH. Equation 33 can be written accordingly

λ (t) - -4j cos θ _ρ -p - Et '05) E can be an integer (which can be obtained by choosing the value of £ ), which facilitates the evaluation of the recordings. In the case of the grid with 1221.2 lines / mm, which works in the first order (K = 1), the value of / if one wants to sweep 10 R in one minute and if the speed ν of the displacement of the plunger is 24 den Wsrt of 1/5 mm per minute, derived from equation / = 317.807 mm.

It can thus be seen that the mechanism described, in spite of its simplicity, makes it possible to use the rotation of the grating to give a fairly precise measure of the value of the wavelength: an accuracy of the order of a few tenths of a ³ can easily be obtained. ■

Below are some results obtained with single and double monochromators that

309843/0768 - "46 -

with the mechanisms described and input and output columns fixed width are provided.

1.) Single monochromators

In FIGS. 10a and 10b, for the two cases under consideration (Table 1), on the one hand, the value f 'as a function of the wavelength and, on the other hand, the values of
theoretical resolution ^ cT X} and the practical resolution SX .

With the grid of 500 mm (Fig. 10b), the one with 2Θ = 28
works, the interval between and cfA- is negligible for the heights considered, although the opening is large.

In the case of the grid of 400.7 mm (FIG. 10a), although it is between (SA) and oX, the distance is and

larger is (^ 0.5 ^) only about a tenth that

Limit resolution, whereby the arrangement realized in this way is open to f / 4 ... This opening is for the most considered Spectral range very large compared to that of the currently commercially available devices, where it is the same f / 75 is. So you can see that it is possible to realize simple monochromators in which

the incident and flexed bundles are firm,

the entry and exit slots firmly in place
and width are

the grid from a rotational movement through one

Mechanism is stimulated, which at the same time the
Wavelength measurement enables.

^ With a rotation V ^ of the grating one obtains the width f 'at the exit slit. continuous bands OA * whose length is f '. and whose maximum intensity is in the direction of ß + A ß:

309843/0768

C ^ = cos ß A ß = - (C ₀₃ + j f) —J- = K Ν 'which corresponds to a wavelength K (/ j + / dl).

In practice one cannot observe Δ Λ in the structures with weak dispersion, and according to Equation 33 one observes wavelengths A, - ^ -> ~ 4r- first, second and third order for a given rotation Ϋ- of the grating This results in a superposition of the orders in the plane of the exit slit "This phenomenon, which is known, can only be avoided either by using filters or by a structure that ensures pre-filtering, ie in particular with double monochromators"

2.) Double monochromators

Since one has to ultraviolet only a limited number of filters, it is necessary to separate the orders to realize double monochromators. Included . the output slot S of the first structure plays the role of the input slot of the second. This clearly reveals the interest shown for the single monochromators in such a structure in which the intermediate slot S ^ is fixed in position and width. You can therefore implement structures in "Z" shape (Fig. 11), adding a structure M (Fig. 8a) - to a structure WL (Fig. 8c), or by adding a structure Mp (Fig. 8b ) connects to a structure M. (Fig. 8d).

It is thus possible to build double monochromators by the inventive process, wherein the separation "^ is ensured of the trims and the spectral purity is increased This is carried out at very high brightness -. Resistance and increased resolution and at an angle of 2Θ between the both angles considerably below 70. Furthermore, extensive intensity ^λ losses due to astigmatism and polarization are avoided.

309843/0768 _ ₄₈ _

Claims (1)

Expectations (1.yFocusing method using concave spherical diffraction gratings, in which the dispersion of the various radiations forming a polychromatic light is caused by reflection, and in which the radiation passes through a fixed slit before and after hitting the rotating diffraction grating It is calculated that the diffraction grating is given such a rotation that the radiations pass through in the plane of the exit slit, and that at a given wavelength, in a given direction, with a certain dashed "width of the diffraction grating and a certain resolution, the sum of the equations of tangential object and image focal lengths assumes a value S which is different from zero and which is determined as a function of the aberrations supplied by a concave grating corresponding to a right-angled pupil. 2. Apparatus for performing the method according to claim 1, characterized in that the optical parameters are chosen so that those changes in the image distance which are related to the first order equation (T + T ¹ = 0) are compensated for by the Error in focusing which must be provided to compensate for the aberrations (terms of the second order). J. Device according to claim 1 or 2, characterized in that each value of θ and each value of the pair W and L is assigned a value of £ 309843/0768 - 49 - is ordered as T + T '= S , and that there is also a practical resolving power associated with any value of f' of the output glitz «P - · -«. - ^ -> A ' X inst. 4. Monochromator for performing the method according to claim 1 with a device according to the claims 2 and 3, characterized in that that it satisfies the following equations: ή \ cos ß _R 2 ΥΊΓ ^p wherein the entrance slot has a width of r K N COS O <R COS c < R. and the exit slot has a width of f - r 'KN <cM> r NK cos ß cos ET so that the practical limit resolution R is achieved. 5 · Monochromator to carry out the procedure according to Claim 1 with a device according to Claims 2 and 3 »characterized in that ^that R wherein the entrance slot has a width of R λ : cosoi 0, b W ₀ - and the exit slot has a width of. - 50 3098 4 3/0768 F ' - 50 - cos ß 0.0 W so that the practical limit resolution of R «0.8 nK W is achieved. 6. Multiple monochromator for carrying out the procedure according to claim 1, characterized in that the rotating diffraction grating has several Output slots are assigned which are arranged at angles and spacings in such a manner with respect to the grid are that each of them satisfy the conditions according to any one of claims 2 to 5. 7. The method according to claim 1, characterized in that the choice of the image plane not only is taken in consideration of the aberration of the concave diffraction grating, but also taking into account the aberrations resulting from the lighting conditions of the diffraction grating result. 8. Monochronator according to claims 1 and 2, characterized in that the centers of the entrance and exit slits lie in a plane which contains the grating normal and is perpendicular to the direction of the lines of the diffraction grating, and that the entrance and exit slits have fixed widths, which are independent of wavelength \, which is determined so that 'there is no loss of flux is produced in the plane of the exit slit. 9. Monochronator according to claims 1 and 6, characterized in that "that the value of the angle θ of each grid is determined such that for a given grid and for object and image distances according to the relationship T + T ¹ = £ the value the 30 984 3/0768 " - 51 - Width f ', of the exit slit , which is necessary to capture the flow according to the practical resolution οAp, is independent of the wavelength. 10. Double monochromator according to claim 9 »thereby characterized in that the two devices with a simple rotation of the grid together are connected in a Z-shaped structure, the exit slot being the first as the entrance slot for the second device is used, and that the rotation of the first grid in the direction of the entrance slot and the rotation of the second takes place in the opposite direction (direction of the exit slot of the second Contraption). 309843/0768