A double entrance monochromator for the testing of optical components in the for ultra-violet

Abstract

Due to the lack of highly transparent materials monochromators for the vacuum ultraviolet spectral range are therefore normally equipped with just one optical element, namely a ruled spherical grating. Further, three additionnal properties of such type of mounting would be useful. First would be a single grating motion, an attractive possibility being a simple rotation of the grating. Second, fixed entrance and exit slits would simplify the mechanical aspects of many experimentals set up, particularly when using experimental chambers for optical testing in this spectral range. A last feature would be to use the grating either at normal incidence to avoid an excess amount of astigmatism in the spectral range 4 000 to 500 A either at large angle of incidence, attempting to extend the short wavelenght limit, through the increased reflectivity associated with the total reflection phenomenon. The first order focusing properties of ruled concuve gratings, derived from Fermat's principle, are then well known and various mountings working in the gaussian image plane are currently used in this spectral range. If the well known Seya Namioka monochromator fulfil the two first conditions, the angle 2 Θ between the incident and diffracted beam is a constant equal to 70° 30'. This angle is chosen to minimize the deviations from the rowland conditions and therefere this mounting satisfy approximatively to the condition T + T' = 0 (eq. 3), T and T' being respectively the equation for the object and image tangential focus. In this mounting as in the Rowland circle or Wadsworth mounting the high order terms in the equations of Fermat's principle as well as the possibility of balancing different aberration terms has been ignored. It is well known, however, from lens design studies that a great improvement of an optical element can be achived, by using the phase balancing method and by a proper consideration of the focussing properties in both geometrical and diffraction theories. The principle of this method is to replace the spherical reference sphere centered about the gaussian image by a new reference sphere centred about the brightest part of a line at the best plane of focus. This method involves, then, a change of focus in order to decrease the amount of aberration (eq. 7) and consequently ignores all mathematical solutions of the first order focussing condition. If the wavefront aberration over the pupil is small with respect to the wavelength λ, the diffraction pattern is only slightly modified. Then by using the strehl criterion we obtain first the value of the parameters characterizing the change of focus and second the optimum ruled width W0 for a given height L0 of the ruled area for which the residual aberrations 01 (W2/R2) can be neglected. A generalized focussing condition in which the main aberration terms (except for astigmatism) are balanced by the defocussing term is consequently derived from the Fermat's principle (eq. 4). For large phase-errors we have defined a quality factor Q (eq. 8) characterizing the r. m. s. value of the width of the image pattern which is connected to the slope of the wavefront deviation. Such image evaluation implying an association of ray density and energy flux, the averaging in the image plane uses the geometrical intensity distribution in the image plane as a weighting factor. Using the same procedure as above we have obtained for each value of W0 and L0 the limiting resolution, a second expression for the generalized focussing condition (eq. 5, table 1). Generallly the tilt of defocus coefficients and then the type of correction are different for the physical optics and the geometrical optics limit (fig. 1 to 5). Using an iterative process the equation 5, has been solved for two particular wavelengths λi and λf and for an one meter 1 831,8 lines/mm concave grating. Figure 6 shows in function of θ, the variations of the object and image distance and leads to the design of a two entrance beams monochromator. Indeed to one image distance r' = Re' correspond two θ values θ1 = 10° and θ2 = 49° 48' 45" at which occur a perfect focus. For other λ values the instrumental defocusing (eq. 15) limit the useful spectral range and the practical resolution (fig. 7) which can be obtain. Indeed this defocussing must remain inferior to a tolerated value (equivalent to the deep of the focus of a lens) arising from the quality factor (eq. 16-16'). The A. S. M. 100/2E mounting made by creusot Loire Instrumentation using a single rotation of the grating gives in a fixed direction diffracted beams of spectral width of 3 to 5 A from 256 to 4 000 A. This mounting has been used in particular to test the efficiency of various holographic gratings and some results are summarized on figures 10 to 13.