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letters to nature 344 NATURE | VOL 400 | 22 JULY 1999 | www.nature.com discrete Bragg peaks. This continuous pattern can therefore be sampled on a finer scale. That sufficient oversampling can lead to a reconstruction was pointed out by Bates 4 . To perform such a reconstruction, Chapman 2 devised a Fienup-type 17 iterative algorithm. Using a strengthened form of this, Miao et al. 5 were able not only to perform reconstructions of model data in two and three dimensions, but also to show that the degree of oversampling called for by Bates 4 can be relaxed somewhat for the higher-dimensional cases.In our experiment we made use of this reconstruction algorithm. The reconstruction from the diffraction pattern of Fig. 2 is shown in Fig. 4. Our phasing algorithm uses knowledge of a finite support which is defined as an enclosing boundary of the specimen. In this reconstruction, we chose a 5:7 m ϫ 5:7 m square as the finite support which is larger than the size of the image itself. The initial input to the iterative algorithm was a random phase set and, after about 1,000 iterations, a good reconstruction (Fig. 4) was obtained. The computing time of 1,000 iterations is ϳ30 min on a 450-MHz Pentium II workstation. Details of the reconstruction procedure are given elsewhere 5,16 . The reconstructed image is consistent with the resolution limit, ϳ75 nm, set by the angular extent of the CCD detector. The inner portion of the diffraction pattern could also be filled by Fourier processing of a moderate-resolution image of the specimen made with a scanning transmission X-ray microscope 1 , whereupon a reconstruction with an almost perfectly clean background was obtained.We believe that the successful recording and reconstruction of the test pattern reported here is the critical step that will open the way to high-resolution three-dimensional imaging of such structures as small whole cells, or large sub-cellular structures, in cell biology. Extension from two to three dimensions requires that a series of diffraction patterns be recorded as the specimen is rotated around an axis perpendicular to the beam. We have take the first steps in this direction. Model calculations indicate that the iterative algorithm used in this work is able to reconstruct such a data set 5 . To be able to collect the data set from a biological (or other radiation-sensitive) specimen, it would be necessary to keep the specimen near the temperature of liquid nitrogen. Experiments show that specimens at this temperature can withstand a radiation dose up to 10 10 Gy without observable morphological damage 18,19 . Finally, to improve the resolution without sacrificing specimen size, a CCD detector with more pixels would be needed: such detectors are now commercially available. Ⅺ