**6.1 Experimental details**

318 Advanced Holography – Metrology and Imaging

width. Fig. 10d shows one example of these templates, where the edges of the nanotube in Fig. 10c were blurred by the filtering process. Then the 2-D correlation between all the templates with variable resolution and variable nanotube diameter has been computed resulting in a 2-D correlation map. The global maximum in this map points out to the template that is the most similar to the reconstructed hologram. Both, resolution and nanotube diameter in the reconstructed image are the same as in the template that maximizes the correlation coefficient in the correlation map. Fig. 10e depicts the 2-D correlation map that indicates the CNT diameter equal to 70.6±5 nm and the spatial resolution 47.5±5 nm, where error is assigned as a one step in calculation of the surface

Fig. 10. Procedure to generate the templates with calibrated resolution. Filtered image a) with the low frequency background fluctuations removed. Skeletonizing b) of the image. Binary template c) obtained by convolution of the skeleton template (b) with a circular template. Template with degraded resolution d) obtained by convolution of the binary template (c) with a 2-D Gaussian filter. Correlation coefficients e) of the reconstructed image with different templates plotted as a function of nanotube diameter and template resolution. The nanotube diameter and resolution of the image are determined to be 70.6±5 nm and

The obtained resolution exceeds by ~19-21 nm the best possible obtainable resolution of 27

verified that the spatial and temporal coherence of the laser source is not a limitation in this experiment, because *zp<<lc, Rc* and NA~1. The longitudinal coherence length of the EUV laser is approximately *lc* ~ 470 m, <sup>4</sup> *l l* 10- D » , and the spatial coherence radius is approximately 0.25 mm at the location of the recording, 0.75 m from the source (Liu et al., 2001). With these parameters, the spatial resolution set by the laser coherence properties is approximately 29 nm. Another limiting factor could arise from the digitalization because the AFM maps the hologram into a 1024×1024 matrix over a surface of approximately 9.9×9.9 µm2, giving a pixel size of 9.7 nm. This pixel size sets the maximum spatial frequency that

*l* (Jacobsen et al., 1990). Several factors degrade the resolution. It was

47.5±5 nm by localizing a global maximum in the correlation plot.

shown in Fig. 10e.

nm set by 2 *NA*

The experimental set up is schematically illustrated in Fig. 11. The same source was used in this experiment as in the previous ones. The test object used in holographic volume imaging experiment consisted of a tilted metallic surface covered with opaque spherical markers.

Fig. 11. Diagram of the 3-D EUV holography experimental set up showing details of the test object used.

This test object was fabricated by covering a semicircular hole 1.5 mm in diameter made in an 80 μm thick Mylar sheet with a 100 nm thick aluminum foil. The hole was partially covered

Two and Three Dimensional Extreme

references (Wachulak et al., 2006, 2007, 2008c).

reconstruction of surface of the test object with depth resolution.

reconstruction the expected vertical resolution is δz = 2.12 μm.

Ultraviolet Holographic Imaging with a Nanometer Spatial Resolution 321

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

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

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

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

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 exposure, the photoresist was developed using standard developing procedures.
