Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating

The overall goal of this procedure, is to measure the transverse coherence of the X-ray beam, at a synchrotron beamline, using grading interferometery. The main advantage of this technique, is that it can measure the coherence property of X-ray beam, in multiple directions, simultaneously, by using 2D gradients. Though, the method was demonstrated at the 1-BM beamline, at the Advanced Photon Source, it can be applied to any synchrotron beamline.

The manufacture of a 2D gratings, is critical to measure different beamline coherent conditions. The creation of the phase grating, first requires fabrication, of an electroplating mold. The starting point for this demonstration, is a prepared piece of silicon wafer.

This, is the gold layer on the working face of the 15 millimetre by 15 millimetre sample. On the opposite side of the sample, there is a 5 millimetre by 5 millimetre silicon nitride window. More detail of the sample, is in this schematic cross-section.

A layer of silicon, that has been etched, is at the core of the sample. The working side of the sample has a layer of low stress silicon nitride, covering the silicon. On top of the silicon nitride, is a five nanometre layer of chromium, and then a 30 nanometre layer of gold.

At the bottom, silicon nitride has been etched away to create a window to the working surface. Begin by taking the sample to a resist spin coater, and loading it. Deposit PMMA resist solution, on the gold chromium side of the sample.

Run the spin coater, to form a resist film, of the desired thickness. When done, remove the sample from the spin coater. Place it on a hot plate, held at 180 degrees celsius, for one minute, to remove residual solvent, from the film.

After the baking is complete, take the sample to a 100 kiloelectron volt electron beam lithography system, and load it, into the apparatus. Use the lithography system to expose the PMMA, to the grading pattern. In the pattern for this protocol, the red areas will be exposed, and become soluble to the developer.

When done, retrieve the sample, and prepare to develop it. Move the sample to a fume hood. There, have ready a solution of isopropyl alcohol, and deionized water for the developer, and a beaker of isopropyl alcohol for rinse.

Put the sample in the developer, and allow it to sink, before gently swirling the container, for 30 to 40 seconds, to circulate the solution. As the development process proceeds, the grading pattern on the working surface becomes visible. After the development step, remove the sample, and submerge it in a beaker of isopropyl alcohol.

Keep it there for 30 seconds, while gently swirling the beaker. Remove the sample, and dry it with flowing nitrogen gas. When the sample is fully developed and cleaned, proceed to the electroplating the gold grating.

This requires an electroplating setup, with a beaker, filled with a gold sulphite based electroplating solution, heated to 40 degrees celsius, a platinum mesh anode in the solution, and a direct current power supply. Submerge the sample into the gold sulphite solution, to act as a cathode. Then turn on the DC power supply, set-up the appropriate current, to electroplate gold at the desired plating rate.

When the desired thickness is reached, stop the electroplating, and rinse the sample in deionized water. Remove the sample from the rinse, and dry it with flowing nitrogen. Next, prepare a heated solvent on a hot plate, to remove the polymer mold.

Submerge the sample in the solvent, and let it remain there for 15 to 30 minutes. Remove the sample, and proceed to rinse it in isopropyl alcohol, and dry it. This is the sample, after the steps to add the two dimensional checkerboard phase grating have been completed.

Take scanning electron microscope images, of the sample as part of an inspection, to confirm the desired grating period, duty cycle and grating thickness, have been achieved. In this image, the same grating is tilted backward 35 degrees, to provide additional perspective. Continue to prepare for the coherence measurements, in the experiment hutch of the facility.

In this demonstration, the beam will pass through the phase grating, and fall onto this CCD detector. The object lense for the detector, is behind a panel. This setup, uses a 10 times objective, which helps to resolve the smallest interference pattern.

Next, position the detector scintillator, for rough focusing. Place the detector scintillator, at the working distance from the lense, here about 5.2 millimetres. Close all panels, before proceeding to the control room.

In the control room, begin to set the focus, by remotely adjusting the position of the object lense. With ambient light in the hutch, view the control room monitors, to observe the focus. After the focus is set, return to the experiment hutch.

Move the two dimensional detector, into the X-ray beam path, which is indicated here, with a laser beam. Centre the beam, using the vertical and horizontal translation stages. In order to perform fine focusing, place a phase sample in the X-ray beam path.

A piece of styrofoam, placed on the grating stage, is adequate. In the control room, observe the X-ray scattering pattern, and adjust the objective lense position, until the highest image sharpness is achieved. It is now time to mount the grating, for the coherence measurements.

This is the 2D checkerboard phase grating, once it is mounted in the grating stage stack. Move the 2D checkerboard phase grating, to where the beam coherence, is to be measured. From the control room, adjust the plane of the phase grating, to be perpendicular, to the X-ray beam.

Then, monitor the images, and use the motorized translation stages, to centre the grating, in the X-ray beam line. Next, rotate the grating, around the direction of the X-ray beam. The goal, is to have the diagonal of the checkerboard pattern, along the transverse beam direction of interest.

In this case, along the vertical and horizontal directions. Continue fine tuning, by rotating about axis perpendicular to the X-ray beam, to maximise the interferogram periods, in the horizontal, and vertical directions. From the control room, engage the translation stage, to move the detector.

The motion, should place the detector as close as possible to the phase grating, along the direction of the beam. Once it is in place, record an interferogram, with the appropriate exposure time, here four seconds. Next, engage the translation stage again, to move the detector.

Using the translation stage controls, move it by an increment along the beam path, chosen to generate sufficient data. Continue recording interferograms, and moving the detector, until the maximum grating to detector distance. For this system, the final grating to detector distance is about 750 millimetres for the last interferograms.

To complete data collection, turn the X-ray beam off. Then, using the same exposure time, as for the interferograms, acquire a dark frame image. These interferograms were measured, using the 2D checkerboard phase grating, described in the text protocol.

This interferogram, corresponds to visibility measurements, at the first talbot distance along the line of propagation, at a value of grating to detector distance, of 83 millimetres. This pattern, is for the fourth talbot distance, at 579 millimetres. A fast fourier transform of the data in the interferograms, produces harmonic peaks, which provide information on the periodic nature of the interferogram.

The zeroth order peak, is at the centre of the image, at the centre of a red square. A first order peak at zero degrees, is at the centre of a green square. There are four independent first order peaks, at zero, 45, 90, and 135 degrees, from which the visibility along each direction can be obtained.

Here is the evolution of the visibility, for zero degree, as a function of the grating to detector distance. The experimental data, are plotted with blue circles. The red circles, are data selected around talbot distances, for gaussian envelope fitting.

Analysis, gives a coherence link, of 3.6 micrometers. Similar analysis of the visibility data, along all four directions, provides this estimate of the coherence map. Only the interferograms, at the self imaging distances, are needed to obtain the coherence links.

Once mastered, this technique can be done within a couple of hours, if it is performed properly. While attempting this procedure, it is important to choose the grating, with the optimized period for each measurement. After its development, this technique paved a way for researchers, in the field of X-ray optics, to develop coherence preserving optics, for next generation, light sources.