Lensless Diffractive Imaging Using Tabletop Coherent High-Harmonic Soft-X-Ray Beams Richard L. Sandberg, * Ariel Paul, Daisy A. Raymondson, Steffen Ha ¨drich, David M. Gaudiosi, Jim Holtsnider, Ra’anan I. Tobey, Oren Cohen, Margaret M. Murnane, and Henry C. Kapteyn JILA and Department of Physics, University of Colorado and NSF Engineering Research Center in Extreme Ultraviolet Science and Technology, Boulder, Colorado 80309, USA Changyong Song and Jianwei Miao Department of Physics and Astronomy, University of California, Los Angeles, California 90095, USA Yanwei Liu and Farhad Salmassi Center for X-Ray Optics, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA (Received 18 April 2007; published 29 August 2007) We present the first experimental demonstration of lensless diffractive imaging using coherent soft x rays generated by a tabletop soft-x-ray source. A 29 nm high harmonic beam illuminates an object, and the subsequent diffraction is collected on an x-ray CCD camera. High dynamic range diffraction patterns are obtained by taking multiple exposures while blocking small-angle diffraction using beam blocks of varying size. These patterns reconstruct to images with 214 nm resolution. This work demonstrates a practical tabletop lensless microscope that promises to find applications in materials science, nanoscience, and biology. DOI: 10.1103/PhysRevLett.99.098103 PACS numbers: 87.59.e, 61.10.i, 41.50.+h, 42.65.k Microscopy has been a critical enabling technology for understanding materials and biological systems since its invention. Using innovative imaging and labeling tech- niques, visible light microscopes can image living cells with a resolution as high as 200 nm [1]. However, this resolution is fundamentally limited by the wavelength of light in the visible to near-UV range. To further increase resolution, the much shorter wavelength of moderate- energy electrons can be used, and atomic level resolution has been demonstrated in electron microscopy [2]. However, electron microscopes are limited by the mean- free-path of the charged particles, and therefore this tech- nique is restricted to imaging thin samples, typically <500 nm. Many biological specimens, as well as samples of interest for materials science, are too thick for electron microscopy. Furthermore, low contrast in electron micros- copy also requires sophisticated labeling techniques. Thus, new techniques for nanomicroscopy are of great interest. One of the most promising alternative approaches for high-resolution imaging of thicker samples is to use shorter wavelength light, in the extreme ultraviolet (EUV) or soft- x-ray (SXR) regions of the spectrum [3]. EUVor SXR light can be used for nondestructive imaging applications re- quiring high resolution in thick samples [4]. Furthermore, numerous core-level absorption edges and widely varying elemental absorption cross sections provide excellent in- herent image contrast, particularly for biological imaging in the ‘‘water window’’ (300 eV–500 eV) region of the spectrum, or for magnetic domain imaging around 800 eV [3 – 6]. Successful soft-x-ray imaging techniques use dif- fractive or reflective optics such as Fresnel zone plates or multilayer mirrors, since the very strong absorption by matter and low index contrast of materials at short wave- lengths precludes the use of refractive optics. Zone-plate imaging has been demonstrated at resolutions as high as 15 nm using state-of-the-art diffractive optics at syn- chrotron sources [7], while zone-plate imaging with tab- letop high harmonic sources can achieve resolutions of  200 nm [8]. Zone plates require very careful manufac- turing, with feature sizes equal to the desired resolution, and dimensional tolerances several times smaller. Fur- thermore, microscopes based on zone-plate optics have a relatively short depth of field. Lensless imaging is a relatively new coherent imaging technique that is complementary to zone-plate imaging [9 – 13]. This technique requires spatially coherent beams and eliminates imaging elements in the optical system by replacing them with a computerized phase retrieval algo- rithm. By obviating the need for an imaging system, lens- less imaging is well-suited to x rays, and it was first demonstrated in 1999 using spatially filtered light from a synchrotron source [9]. In lensless imaging, the x-ray beam illuminates an object, and the scatter pattern (diffracted light) from the object is collected on an x-ray CCD camera. For this technique to work, the diffraction pattern must be oversampled, i.e., the diffraction peaks coming from the highest spatial frequency of interest must be sampled at a higher rate than the Nyquist criterion [14]. If a sharp diffraction pattern has been obtained and the oversampling requirement is met, the image can be reconstructed using iterative algorithms that retrieve both its amplitude and phase [15]. Given the need for coherent illumination, most small- scale EUV=SXR sources are not suitable for lensless imag- PRL 99, 098103 (2007) PHYSICAL REVIEW LETTERS week ending 31 AUGUST 2007 0031-9007= 07=99(9)=098103(4) 098103-1  2007 The American Physical Society