## 3 Results  
The experiments with a copper TEM mesh (SPI, West Chester, PA, USA) with 1000 lines/inch (bar width 6 \(\upmu\)m, hole width 19 \(\upmu\)m) were performed to determine the spatial resolution of the microscope. The measured and calculated magnification was around 340\(\times\) for this microscope layout, and, thus, the corresponding field of view is -80 \(\times\) 80 \(\upmu\)m. The image of Cu mesh shown in Figure 4a was acquired with an exposure time of 3 min and the repetition rate of the capillary discharge source  
Figure 3: Photographs of the soft X-ray (SXR) imaging system: (**a**) The “source” view showing plasma driver and vacuum chamber with imaging optics, (**b**) the internal photograph of a vacuum chamber with sample and zone plate holder, (**c**) photograph of the “imaging” part of the SXR microscope.  
Figure 2: Schematic of a water-window microscope based on a nitrogen plasma capillary discharge source.  
of 2 Hz, which allowed the acquisition of 360 SXR pulses. The spatial resolution was calculated via a knife-edge test across a sharp edge. A 10-90% intensity transition, corresponding to the Rayleigh resolution limit, is equal to 150 nm; a half-pitch spatial resolution is equal to 75 nm (Figure 4b), measured from the image of the mesh and highlighted by a red, dashed rectangle. The spatial resolution was calculated from the average of many pixels along the edge to remove the effect of noise.  
To compare the quality of soft X-ray images of Cu mesh, several images were taken with different exposure times. Figure 5 depicts the outcome of this experiment, demonstrating the differences among the soft X-ray images of Cu mesh taken with 10, 30, 60, and 180 SXR pulses, respectively, at a 2 Hz repetition rate of the source. Some imperfections of the Cu mesh are still visible down to a 5 s exposure time.  
Finally, the green algae-_Desmodesmus communis_ was imaged. Cells were deposited onto an Si\({}_{3}\)N\({}_{4}\) membrane (see Section 2.3 \"Sample Preparation\"). The soft X-ray image (Figure 6a) was taken with a 390\(\times\) magnification and an exposure time of 12 min with a 2 Hz repetition rate of the source. The inner structure (organelle) of the cell is visible and distinguishable. No post-processing was made with a  
Figure 4: (**a**) Soft X-ray image of copper mesh 1000 lines/inch acquired with 3 min exposure time (360 SXR pulses). A red, dashed rectangle highlights a sharp edge representing the place where the spatial resolution was calculated. Scale bar is 6 μm. (**b**) Knife-edge resolution test results showing normalized intensity profile across a sharp edge. A 10–90% intensity transition corresponding to Rayleigh resolution is equal to 150 nm, half-pitch spatial resolution equal to 75 nm, measured from the image of the Cu mesh.  
Figure 5: Comparison of soft X-ray images of copper mesh (1000 lines/inch) with different exposure times. The scale bar is 6 μm and is the same for each image.  
soft X-ray image except for CCD background removal and brightness adjustment. For comparison, an image of the same sample was taken with the visible light microscope (Figure 6b), the image was captured with a 400\(\times\) magnification, and the white, dashed rectangle represents the field of view in Figure 6a. The SXR image exhibits a superior spatial resolution compared to visible light microscopy (Figure 6b), owing to a much shorter wavelength beyond the capabilities of diffraction-limited visible light microscopes. Small features in the order of hundreds of nanometers can be easily observed, as demonstrated in a zoomed view in Figure 6a.