Design of variable line-space plane gratings with holographic recording

Variable Line-Space gratings play an important role in focusing and aberration-reduced. They are widely used in spatial spectrum and synchrotron radiation facilities. However the design and fabrication methods of them are difficult. The problem is to be able to record holographically the expected grooves distribution. The geometric theory of aspheric wave-front recording optics is briefly described. We introduce the genetic algorithm to the parameters optimization of holographic variable line-space gratings. In order to obtain a steady set of recording parameters, we propose that the objective function of the genetic algorithm should consider the effect of the recording parameters errors. The integral expression of the objective function is also derived to improve the efficiency of calculation. Design example of holographic variable line-space plane gratings for a position sensor is given to demonstrate the capability of this method. The line-profiles of variable line-space plane gratings with different recording parameters are also compared in this paper.