Interferometric at-wavelength flare characterization of EUV optical systems

A method of simultaneously measuring flare and test-beam wavefront in an optical element employing a phase-shifting point diffraction interferometer (PS/PDI) that defines an optical path that includes (i) a source of electromagnetic radiation in the optical path that provides an illumination beam, (ii) an optical system under test in the optical path, (iii) a beam divider comprising gratings in the optical path for dividing the electromagnetic radiation from the source into a test beam and a reference beam, and (iv) an irradiance detector in the optical path downstream from the optical element under test, comprising the steps of:

• (a) employing the PS/PDI to collect phase-shifting interferometric data;
• (b) isolating contributions from electronic and photon noise by:
• (i) performing phase-shifting analysis to recover amplitude and phase of the test beam;
• (ii) reconstructing an image-plane point-spread function (PSF) which includes contamination from flare and noise from the wavefront of step b(i);
• and
• (iii) measuring apparent scatter in an area away from the test-beam window to determine electronic and photon noise;
• (c) removing reference-beam flare and noise contribution by:
• (i) employing dual-domain analysis to recover an amplitude and phase of the test beam;
• (ii) reconstructing an image-plane PSF free of the reference-beam flare contribution from the wavefront of step c(i);
• and
• (iii) removing electronic and photon noise determined in step b(iii);
• (d) removing the flare added by remaining PSFs by:
• (i) determining the strengths of the PSFs based on parameters of the grating beam divider, the numerical aperture of the optic under test, and the numerical aperture of the illumination beam;
• (ii) determining the coupling between scatter from the additional image points and the recorded scatter;
• (iii) predicting the spatially-varying-flare contribution from the nonzero order diffraction orders by using the relative strengths determined in step d(i), coupling efficiencies determined in step d(ii), and an initial guess for the scatter-energy-density as a function of radial distance from the image point;
• (iv) removing the spatially-varying-flare contribution predicted in step d(iii) from the image-plane distribution calculated in step c to obtain a PSF free of flare contribution from the reference beam and partially corrected for flare from the other image points;
• (v) calculating scatter-energy-density as a function of radial distance from image point using the approximate result from step d(iv);
• and
• (vi) repeating steps d(iii) through d(v) using the calculated energy density radial dependence until the radial dependence calculated in step d(v) substantially matches that used in step d(iii) from a previous iteration;
• and
• (5) calculating the flare using the final image-plane distribution resulting from step d(iv).

A method for simultaneously measuring flare and test-beam wavefront in an optical element by employing a phase-shifting point diffraction interferometer (PS/PDI) that defines an optical path that includes (i) a source of electromagnetic radiation in the optical path, (ii) an optical system under test in the optical path, (iii) a beam divider comprising gratings in the optical path for dividing the electromagnetic radiation from the source into a test beam and a reference beam, and (iv) an irradiance detector in the optical path downstream from the optical element under test that comprises the steps of:

• (a) using the PS/PDI to collect phase-shifting interferometric data;
• (b) performing phase-shifting analysis to recover a wavefront and calculating from said wavefront the image-plane point-spread function (PSF) which includes contributions from detector and photon noise;
• (c) determining detector and photon noise by measuring the energy density in an area far from the window-limited PSF of step (b);
• (d) performing a dual-domain phase-shifting analysis to reconstruct a wavefront which is free of flare contributed from the reference beam;
• (e) calculating a partially corrected PSF free of reference-beam flare contributions from the wavefront of step (d);
• (f) removing the detector and photon noise determined in step (c);
• (g) determining the strengths of the image points from different grating diffraction orders;
• (h) using predicted phase shifts of image points from each grating diffraction order to determine how flare from said image points will couple to the measurement;
• (i) predicting the spatially varying flare contribution from the non-zero order diffraction points by using the results from steps (g), (h), and an assumed functional form for the scattered-energy-density as a function of distance from the image point;
• (j) removing the flare contribution predicted in step (i) from the dual-domain reconstructed PSF to obtain a PSF free of flare contribution from the reference beam and partially corrected for flare from the other image points;
• (k) using the partially corrected PSF of step (j) to obtain an improved functional form for the scattered-energy-density;
• and
• (l) repeating of steps (i), (j), and (k) until the functional form for the scattered-energy-density converges on a self consistent solution.