RSY DEDICATED STIGMATIC MONOCHROMATORS

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RSY DEDICATED STIGMATIC MONOCHROMATORS

M. Pouey

To cite this version:

M. Pouey. RSY DEDICATED STIGMATIC MONOCHROMATORS. Journal de Physique Colloques,

1987, 48 (C9), pp.C9-69-C9-74. �10.1051/jphyscol:1987908�. �jpa-00227203�

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RSY DEDICATED STIGMATIC MONOCHROMATORS M. POUEY

Laboratoire de Physique des Gaz et Plasmas, Universit6 Paris-XI, Bat. 212, F-91405 Orsay Cedex, France

ABSTRACT.

In this paper we describe new STIGMATIC X W monochromators specially designed to fit the "Etendue" of SUPER ACO. Fixed horizontal and vertical diffracted beam divergences, as well as uniform photometric illumination are allowed ; comparison with TGM show the improvements that might be expected from the case of Plane type V grating used in convergent light.

I. INTRODUCTION.

The out'standing properties of synchrotron radiation (Sr) as a light source for spectroscopy in the VUV and XUV spectral range are well known and are described in a number of books [I-31. For the purposes of the present SUPER ACO design we must mention

(i) the tunability over a large range covering the whole V W and XUV part of the electromagnetic spectrum

(ii) the nearly laser-like vertical collimation Rl (3 mrad for the XUV) (iii) a small spot size : 1.2 mm in the horizontal plane and less than 480 pro in the vertical one

(iv) the well defined polarization (100 % linearly polarized within the plane of the orbit, elliptical polarization above and below the plane of the orbit).

For practical resolutions better than 10-2 nm (without any losses in

"btendue"), these characteristics preclude the use of orthodox dispersive devices which was primarily designed for classical laboratory sources.

In the following we describe optimized version of "ULTIMATE" in which : the focusing is achieved by a stigmatic toroidal mirror (unit magnification) : the dispersion of the radiation is achieved by a simple rotation of a plane

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987908

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JOURNAL DE PHYSIQUE

type V holographic grating WORKING AT MINUS ONE MAGNIFICATION 14-63.

In regard to stigmatic diffracted images whose associated wave-fronts are spherical, we have to determine an image distance -and a general configuration as well as the hologram parameters

-

in such a way that the associated reference spherical wavefront osculates with the distorded diffracted ones.In fact distorded diffracted wave-fronts will appear like surfaces of revolution if odd aberration terms are cancelled ; this implies that the plane grating should work at minus one marnification and that the point sources used to record the hologram - -- -- -

are located at the same distance from the grating pole.

11. THE WAVE ABERRATION FUNCTION.

In the following, we adopt classical notation and restrict ourselves to plane type V gratings whose center are located at the origin of a Cartesian coordinate system. We will consider the holographic gratings to be generated by two coherent point sources C[h,q] and D[h,6] of wavelength Ao.

For a point objet A[r,a] and an image point B[r',P], the wave aberration function, expressed as a function of the pupil coordinate w,l, is given by :

where C i J and D i j are respectively the aberration coefficients of the equivalent uniformly-spaced straight-groove grating, and the ones associated with the hologramm. As usual, the grating equation is given by :

(2) sin a + sin P = mNA = mA/Ao (sin 6

-

^{sin q)}⁼^{PN Lo,}

m being the order of diffraction and N the groove density.

For ULTIMATES r' =

-

^{r =}^{d =}kh, and the polar coordinates of points C and D are defined as a whole by

( 3 ) sin F = N A0/2

-

sin 0

*

V, (4) sin q =

-

NAo/2

-

^{sin 0}

*

^V,

V being function of k and of the maximal value of the wavelength reached by the instrument, and 20 = a

-

^p

.

FOR SUCH DEVICES AND SUCH TYPE OF HOLOGRAPHIC GRATING ALL THE ABERRATIONS ARE PROPORTIONAL TO mNA

.

For example the defect of focus reduces to :

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where 7 is the angle of rotation of the grating, 71 being derived from V value.

For grazing incidence (low r values, 7 = 0) the defect of focus given by :

( 6 ) A02 w2 = 2 mN h sin 0 sin2 r/2 w2/d,

is always very low, but the coma terms are only partly balanced.It is then clear that the final design for the system should be obtained by using an rms wave front aberration merit function, giving the FWHM of the LINE SPREAD FUNCTION.

111. THE LINE SPREAD FUNCTION.

To derive the LINE SPREAD FUNCTION we must first calculate the transverse ray aberrations WITH A PUPIL COORDINATE SYSTEM PERPENDICULAR TO THE PRINCIPAL RAY, TO ENSURE THAT THE CORRECT SLOPES OF THE WAVE-FRONT ARE FOUND 17-81. But the wave-front aberration coefficients, as usually, have been derived earlier using a pupil coordinate system lying in the grating plane.

If the principal ray is near the normal these two coordinate systems can be taken to coincide, as generally considered by the quasi totality of designers [9 for example]. But if the principal ray is at an oblique angle to the grating surface, as in most of grating devices except NIM, this approximation remains no more valid. Practically, the exact transverse ray aberration is, in the

dispersion plane, given by :

For the final stages of the optimization the merit function is based on the GEOHETRICAL CRITERION [lo], giving the rms value of the FWHM of the LSF :

with L = 2a, and W = bl+b2. Indeed, for POSITIV orders the solid angle at

aperture stop (plane grating plane) subtended at field stop (entrance slit plane), is VARIABLE, but b, = b2 and W is CONSTANT ; for- NEGATIV orders the solid angle is CONSTANT, but bl # b2, and W DECREASES as the wavelength increases. Then the luminosity-resolution product should be higher for negativ orders than for positiv ones.

The main aberration contribution to the symmetrical broadening of the LSF is, for q = sin &/rl, given by :

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These relation implies that coma terms generate defocusing in so far as the C01 term is not negligible (high slit height in normal incidence and for most of grazing incidence devices except,RS ones). Asymmetrical broadening of the LSF is expressed by :

(10) 9: = B t J biaJ with i+j = 0,4,8 (i+j = 1,2,3,5,6,7 holds from 4:).

Finally, since all the aberrations (C01 terms negligible for RSY) are proportional to mNh, we may write :

the coefficient f characterizing the loss of resolving power, with respect to the theoretical limiting value. In classical devices, f is much less than unity ; but actually, for normal incidence and particular N values the aberrations are s o small that the STREHL CRITERION [lo] is satisfied.

N. GRAZING INCIDENCE ULTIMATE.

At grazing incidence Eq. 2 may be satisfied only for k values larger than 1. The coma terms are then expressed by

For the UGM-86-486 monocromator, the main parameters are the following : TOROIDAL MIRROR : I=86 ; Magnification xl.

Object distance : 4960.79 mm TOROIDAL MIRROR-PLANE GRATING DISTANCE 160.79 mm

PLANE HOLOGRAPHIC GRATING : 0 = 86' ; L = 45 mm : W 6 135 mm.

As shown on Fig. 1, the LSF is mainly determined by the dissymetrical broadening which is lower than 2.5 10-4 nm. To give an idea of the gain in performances over previous design we have optimize a TGM fitted with an available toroidal JOY grating (r = 71.11 m, W , = 150 mm, R1 = 28.79 cm, L = 45 mm). Even for an ETENDUE 1.8 times SMALLER than the UGH, the TGM suffers from a larger

dissymetrical broadening which amounts to 10-2 nm at 6 nm. Consequently the

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distribution don't improve very much thess poor performances (Fig. 8). Of course, since the ultimate performances of the UGH are very high, this device should require a toroidal'blanck of better quality than the one already defined for a TGM

.

V. CONCLUSIONS.

It was well known that the holographic technique may be used to design plane focusing gratings [12]. But until now [13-161 the derived configurations was suffering from astigmatism and comas ; generally, these authors were using the same approximation as Champagne [17] in his non-paraxial theory for point source holograms on plane substrates. All these devices make use of plane grating working on its tangential focus. More recent design 1181 has shown that stigmatism may be allowed in a restricted spectral range.

We consider the sagittal focus condition and we have shown that, even in grazing incidence, astigmatism and comas correction are allowed in a great spectral range.

\ J ~ ~a r - ) ~ ~ ~ E ) L,h.&ab%,2 (--- I

4

Fig. 1

-

A s s y m e t r i c b r o a d e n i n g ( -

-

^{e - 1} o f t h e L i n e S p r e a d F u n c t i o n , L i m i t i n g R e s o l u t i o n (- ) and P r a c t i c a l R e s o l u t i o n

(--- ) a s f u n c t i o n s o f X f o r a 3 0 p m e n t r a n c e s l i t , a n d N = 1 2 0 0 l / m m , type-V p l a n e g r a t i n g

Fig. 2

-

A s s y m e t r i c b r o a d e n i n g ( -

- - 4

. - ) o f t h e L i n e S p r e a d F u n c t i o n , L i m i t i n g R e s o l u t i o n (

-

⁾^,a n d P r a c t i c a l R e s o l u t i o n

(---- ) a s f u n c t i o n s o f X f o r a 4 8 0 p m e n t r a n c e s l i t , a n d a N = 1 2 0 0 l/mm, t y p e

-

^It o r o i d a l g r a t i n g

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Fig. 3

-

A s s y m e t r i c broadening ( - . - * - I of t h e L i n e S p r e a d Function, L i m i t i n g R e s o l u t i o n (- ) , and P r a c t i c a l R e s o l u t i o n

(---- 1 as f u n c t i o n s of 1 f o r a 4 8 0 pm e n t r a n c e s l i t , and a Pi

= 1 2 Q 0 l/mm, t y p e

-

I V toroidal grating.

REFERENCES.

[I] H-Winick, S.Doniach, (eds.), Synchrotron Radiation Research, Plenum Press New-York, 1980.

[a]

C.Kunz (ed.)

,

Synchrotron Radiation, Springer-Verlag Berlin Heidelberg New-York, 1979.

[3] E.E.Koch (ed.), Handbook on Synchrotron Radiation, lA,B, North-Holland, Amsterdam, 1983.

[4] M.Pouey, SPIE 597 (1985) 402.

153 ~.pouey. Nucl. Inst. & Methods, A246 (1986) 256.

[6] B.Lay, F-Cerrina and M-Pouey, Nucl. Inst. & Methods, A246 (1986) [7] E-Ishiguro, R.Iwanaga & T-Oshio, J. Opt. Soc. Am., 69(1979) 1530.

[8] M.P. Chrisp, App. Opt., 22 (1983) 1508.

[9] T. Namioka, M.Seya & H.Noda, Jap. J. of Appl. Phys., 15 (1976) 1181.

[lo] M.Pouey, J. Opt. Soc. Am., 64 (1974) 1616.

[ll] M.Pouey, M.R.Howells & P.Z.Takacs, Nucl. Inst. & Methods, A195 (1986) 223 [la] M.V.R.K.Murty and N.C.Das, J. Opt. Soc. Am., 61 (1971) 1001.

1131 M-Singh, Indian J. of Pure & Appl. Phys., 15 (1977) 338.

[I41 C.H.F.Velze1, J . Opt. Soc. Am., 66 (1976) 346.

1151 Z-Mateeva, J. Optics (Paris), 14 (1983) 209.

[16] H.Petersen, Nucl. Inst. & Methods, A246 (1986) 260.

[17] E-B-Champagne, J. Opt. Soc. Am., 57 (1967) 51.

1181 M.C.Hettrick and S.Bowyer, Appl. Opt., 22 (1983) 3921.