288Chapter 5Decadic RMS Density (RMSD)LSFRMSFRHSFR110-Example "best"-Example "mean"100-Example"worst"Example "power-2"90801001.E+041,E+031.E+021,E+011.E+001E-02spatial wavelength A [um]310+1+2decadic number aFigure 5.51 Isotropic 2D PSDs in Fig.5.50 represented as decadic RMSD.RMS valuesare given in Fig.5.53.One can compare the different PSDs continuously over all spatial frequenciesin a quantifiable manner on a linear scale in terms of TIS per decade or RMSper decade.One can even quantitatively guess the band RMS or band TISvalues for the different decadic intervals of spatial wavelengths.5.6.4.4 The stray light point spread function:the link between the surfacePSD and the flare distribution at the waferIn the foregoing sections,the relationships between the mirror surfaceroughness (PSD,RMS,and decadic RMSD)and the amount andcharacteristics of the light scattered off the mirror surface (BSDF,TIS,anddecadic TISD)were discussed.Now we describe how this stray light is thendistributed in the image plane at the wafer level.Therefore,the imaging of aperfect point source is being considered.This image is the so-called pointspread function (PSF).The PSF of an ideal projection optics without anyaberrations and without stray light is determined by the diffraction of light onOptical Systems for EUVL289Decadic TIS Density (TISD)LSFRMSFRHSFR-Example"best"0,90%-Example "mean"Example"worst"0,80%-Example "power-2"0,60%0,40%0,00%1,E+031,E+021,E+001,E-011,E-02spatial wavelength A[um]432-1+1+2decadic numberaFigure 5.52 Isotropic 2D PSDs in Fig.5.50 represented as decadic TISD.TIS values aregiven in Fig.5.53.the aperture stop that defines the NA of the projection optics.In this case,thePSF is the well-known Airy function PSFo(r)(see Ref.136):where J is the Bessel function of the first kind.The diameter of this Airy disk,which is defined by the radial distance of the first zero of the Airy function,isdetermined by the NA:(5.32)Any aberration in the wavefront of the exit pupil causes a redistribution oflight within or outside of the Airy disk;low-pupil-frequency aberrations dueto figure errors of mirrors cause a coherent redistribution of light within the290Chapter 510mm-1mm1mm-100μm100μm-10μm10μm-1μm1μm-100nm100nm-10nmExample "best"243830233871Example "mean"446548404875Example "worst"578461515678Example "power-2"505050505050Example-best”0,12%0,08%0,05%0,12%0,44%Example "mean"0,17%0,37%0,20%0,14%0,20%0,49%Example"worst"0,28%0,61%0,33%0,23%0,27%0,53%Example "power-2"0,22%0,22%0,22%0,22%0,22%0,22%Figure 5.53RMS and TIS values of the various PSDs in Figs.5.50-5.52 for six differentintervals of spatial wavelengths,each representing one decade.Airy disk (