An improved two-dimensional phase unwrapping procedure is discussed that uses a weighted least-squares algorithm, a congruence operation, and a filter to unwrap the phase distribution of an electromagnetic beam. These improvements make possible several advances for mirror designs used in gyrotron quasi-optical mode converters. The improved phase unwrapping procedure is demonstrated by applying it to a measured beam and a simulated beam that are used to design mirrors. The unwrapping procedure produces a smooth unwrapped phase that does not change the characteristics of the beam. The smooth unwrapped phase distribution is also used to find an estimate for the wavenumber vector distribution that is needed to design the mirrors.

An iterative planar-and cylindrical-based mirror design procedure is discussed for use in a gyrotron quasi-optical mode converter. The planar-based mirrors were designed using the iterative Katsenelenbaum-Semenov phase corrector procedure with an input beam obtained from a planar phase reconstruction. Many improvements were made to the design procedure including the use of an advanced phase unwrapping technique. The more robust design procedure resulted in smooth mirror surfaces. It was found that the fraction of power coupled between the target beam and the output of the planar-based mirrors measured in a cold test setup was 0.982. A similar design process was used for a cylindrical-based mirror pair. This design was performed using a simulated output of the launcher. It was found that the fraction of power coupled between the target beam and the theoretical output of the system was 0.990. The fraction of power coupled between the target beam and the phase-reconstructed beam at the output of the second mirror was 0.961. By using a cylindrical phase reconstruction, it was found that the reason for the slightly degraded performance of the cylindrical-based mirrors tested in the low power test setup was due to inaccuracies in modeling the field radiated from the launcher. These inaccuracies are presumed to come from impurities in the mode generator. The techniques discussed in this article can be used to improve the efficiency of quasi-optical mode converters and thus improve the operation of gyrotrons.Index Terms-Gyrotrons, millimeter wave antennas, multireflector antennas, phase estimation, phase shifters.

We describe an experimental method to measure the gate profile of an x-ray framing camera and to determine several important functional parameters: relative gain (between strips), relative gain droop (within each strip), gate propagation velocity, gate width, and actual inter-strip timing. Several of these parameters cannot be measured accurately by any other technique. This method is then used to document cross talk-induced gain variations and artifacts created by radiation that arrives before the framing camera is actively amplifying x-rays. Electromagnetic cross talk can cause relative gains to vary significantly as inter-strip timing is varied. This imposes a stringent requirement for gain calibration. If radiation arrives before a framing camera is triggered, it can cause an artifact that manifests as a high-intensity, spatially varying background signal. We have developed a device that can be added to the framing camera head to prevent these artifacts.

Some gyrotrons use an internal launcher and a series of mirrors to shape the cavity mode into a Gaussian beam at the output. We will discuss the design and cold testing of a pair of iteratively designed cylinder-based heamshaping mirrors to transform the launcher output into a Gaussian beam at the output. One additional weakly curved planar-based mirror would direct the beam out of the gyrotron window.