Designs for Coherent X-Ray Lasers

The property of coherence is important for many suggested applications of x-ray lasers. For x-ray holography, the longitudinal coherence length is required to be larger than the pathlength difference between the object beam and the reference beam, estimated to be about 5 µm in a Fourier transform holography system. The longitudinal coherence length is related to the line width by Lℓ = λ2/Δλ, where λ is the laser wavelength. Using the thermal Doppler width for an estimate we get Lℓ = 37 µm for a 45Å laser. This estimate is supported by a measurement at 206Å. We therefore expect that longitudinal coherence will not be a problem. The transverse coherence length must be larger than the extent of the sample, typically ≈ 10 µm, and a certain amount of energy must irradiate the sample in order provide a high signal to noise hologram. The coherence length is obtainable straightforwardly by placing a pinhole in front of the laser, or by placing the object far from the laser. The combined requirement of energy and coherence is, however, much more difficult, requiring efficient production of coherent radiation.