**6.2 Results of 3-D holographic imaging with EUV laser**

Digitized hologram is shown in Fig. 12a. The digital reconstruction of the hologram digitized with the AFM is based on a numerical Fresnel propagator. Fig. 12a shows a small (4242 μm2) section of the hologram. The numerical reconstruction of the hologram provided images of the object described above and shown in Fig. 12b.

Fig. 12. Hologram of 3-D sample a) recorded in the photoresist surface and digitized with the AFM with a random distribution of 465nm diameter latex spheres - markers over tilted surface of Al foil. Numerical reconstruction b) of the hologram using Fresnel propagator algorithm. Intensity cuts in vertical direction of one marker that is "in focus" (c) and one "out of focus" (d). The white dotted lines indicate region in the reconstruction that is "in focus".

<sup>2</sup> *from CXRO database, "http://www-cxro.lbl.gov/".* 

<sup>3</sup> *From Polysciences Inc.*

with a second Mylar sheet 80 μm thick, as schematically indicated in Fig. 11. The aluminum foil contours over the semicircular aperture to produce a variable height surface with desirable characteristics for this test and has a transmittance of approximately 35% at λ=46.9 nm limited mainly by a layer of native oxide 2. The Al filter also suppresses lower photon energy plasma

The object was prepared by placing a drop of water with heavily diluted latex spheres (2.62% solution in water) 465 nm in diameter, 3 on top of Al foil. Evaporation of the water left a random distribution of latex spheres (markers) deposited over the partially transparent tilted Al foil membrane. These spheres are completely opaque to 46.9 nm EUV laser radiation. With this deposition procedure, the markers are randomly distributed over the supporting Al foil and at predictable distances to the photoresist (heights) imposed by the foil profile. To activate the PMMA with 46.9 nm radiation requires exposures of 240 laser shots, 4 minutes exposure time at the repetition rate employed in this experiment. After

Digitized hologram is shown in Fig. 12a. The digital reconstruction of the hologram digitized with the AFM is based on a numerical Fresnel propagator. Fig. 12a shows a small (4242 μm2) section of the hologram. The numerical reconstruction of the hologram

Fig. 12. Hologram of 3-D sample a) recorded in the photoresist surface and digitized with the AFM with a random distribution of 465nm diameter latex spheres - markers over tilted surface of Al foil. Numerical reconstruction b) of the hologram using Fresnel propagator algorithm. Intensity cuts in vertical direction of one marker that is "in focus" (c) and one "out of focus"

(d). The white dotted lines indicate region in the reconstruction that is "in focus".

<sup>2</sup> *from CXRO database, "http://www-cxro.lbl.gov/".* 

<sup>3</sup> *From Polysciences Inc.*

exposure, the photoresist was developed using standard developing procedures.

emission (i.e., long wavelength background) from the Ar laser source.

**6.2 Results of 3-D holographic imaging with EUV laser** 

provided images of the object described above and shown in Fig. 12b.

One of the critical parameters in the reconstruction code is a distance between the recording medium and the object, indicated in the diagram in Fig. 11 as *zp*. Small changes in *zp* reconstructs slightly different images. To determine the value of *zp* corresponding to the optimum reconstruction, a 2-D image correlation was used and is described in details in references (Wachulak et al., 2006, 2007, 2008c).

To demonstrate retrieval of the depth information from the hologram the numerical reconstruction of the digitized hologram, shown in Fig. 12a, has to be performed for different values of distance *zp*. The different runs produced different reconstructed images in which the latex spheres - markers located at the correct *zp* generated a sharper image than those markers "out of focus". Fig. 12b shows one of these reconstructed images. In this case the reconstruction is optimum for *zp* that matches height of a central part of the hologram, indicated in the figure by white dotted rectangle. In this region the height is such that the markers located there are reconstructed "in focus", while the latex spheres above and below this level are reconstructed blurred. This can be observed in Fig. 12c,d where the intensity profiles obtained in a vertical cut of one "in focus" marker (c) and one "out of focus" marker (d) are plotted. By changing *zp* in the reconstruction code only the latex sphere markers located at the height equal to *zp* produce sharper reconstruction images as compared to those markers out of focus. This is a similar effect to optical sectioning, however, performed on a digitally reconstructed image. The depth information in the hologram can finally be retrieved varying the reconstruction parameter *zp*. To determine a value of *zp* corresponding to the best reconstruction the reconstructed image was correlated with a template of the marker consisting of a circular mask with known size representing the latex sphere. Finding the maximum value of correlation between the reconstructed image of each marker and the mask determines corresponding optimum height. Combining this information with *x-y* coordinates of each marker allowed for placing each marker uniquely in a 3-D space and the reconstruction of surface of the test object with depth resolution.

Fig. 13a,c show the surface topography obtained from the reconstructed images in two different regions of the hologram. In case of Fig. 13a, the AFM scan was performed in region of the test object close to edge of Mylard spacer, where the slope of the Al foil is expected to be high. A similar scan performed at distance approximately 200 μm away from this edge, produced image with smaller slope, as shown in Fig. 13c. Fig. 13b,d show reconstructed heights for all markers as a function of transversal coordinate *x* in the same two regions of the object plotted in Fig. 13a,c. The surface plot from *xyz* space was projected into *xz* plane. These plots give a measure of spread of the calculated heights for all the markers and also show, as indicated by the best linear fit, different slopes in these two regions. The statistical dispersion of data points relative to the best linear fit are Δz = 2.64 μm for the region with high slope, Fig. 13b, and Δz = 1.32 μm for the region with lower slope Fig. 13d. This spread in the measured heights of markers compares well with expected accuracy in *z* direction determined by the NA of the hologram. As pointed out by Rogers, if one assumes the hologram as a superposition of Fresnel Zone Plates (FZPs) (Rogers, 1950), the resolution in *z* coordinate can be related to its depth of focus. For a FZP the depth of focus is given by δz = λ / NA2 (Attwood, 1999). The NA corresponding to higher slope region, where zp = 160 μm, is NA = 0.13, yielding a depth of focus δz = 2.77 μm. In region, where the Al foil has a lower slope, the latex markers were closer to the hologram, at a distance zp = 140 μm. For this reconstruction the expected vertical resolution is δz = 2.12 μm.

Two and Three Dimensional Extreme

**8. Acknowledgements** 

imaging techniques.

**9. References** 

Ultraviolet Holographic Imaging with a Nanometer Spatial Resolution 323

single shot recording, permitting full field time resolved holographic imaging. This imaging method allows hologram recording without any previous object preparation, as required in electron microscopy, and free of any interaction with a probe that may occur in scanning microscopes. Photon based imaging systems also allow spectroscopic contrast, an important characteristic in imaging with shorter wavelength radiation. It also opens the possibility to study specimens in different environments, for example in the presence of external magnetic or electric fields. Moreover detailed processing of the reconstructed holographic images, performed by changing object-hologram distance in the reconstruction code was presented. It enables retrieving the depth information from a single high NA hologram. Using a specially fabricated 3-D object the numerical reconstruction and analysis of the hologram

This work was supported by the National Science Foundation ERC for Extreme Ultraviolet Science and Technology, Award Number EEC-0310717. The authors thank to Prof. Randy Bartels, Prof. Carmen Menoni and Prof. Jorge Rocca for their constructive comments and

First author would also like to acknowledge the support from Foundation for Polish Science, Homing 2009 Program, award number HOM/2009/14B, related to novel, high resolution

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Fig. 13. Surface topographies obtained from reconstructed images and heights of the markers in different regions of the object. a), b) show the region close to the edge of the spacer where high slope is revealed in the Al foil while c), d) show region approximately 200 μm away from the edge with lower Al foil slope. b), d) are the projections of the 3-D plots on x-z plane to better visualize the slopes.
