Design of Cascaded Diffractive Optical Elements for Optical Beam Shaping and Image Classification Using a Gradient Method

Abstract

We present a gradient method for designing cascaded diffractive optical elements (DOEs) consisting of several sequentially located phase DOEs. Using the unitarity property of the operator of light propagation through the cascaded DOE, we obtain explicit expressions for the derivatives of the error functional with respect to the phase functions of the cascaded DOE. We consider the application of the gradient method to the problem of focusing different incident beams to regions with different intensity distributions and to the problem of optical image classification. The presented description of the gradient method treats the problems of designing cascaded DOEs for focusing laser radiation and for image classification within a unified approach reducing the calculation of the derivatives of the error functionals to the same formula. We present examples of the calculation of single and cascaded DOEs for focusing different incident beams to different regions and for classifying handwritten digits, which demonstrate the high performance of the proposed method. The presented results may find application in the design of diffractive neural networks and systems for focusing laser radiation.

Keywords

• diffractive optical element
• phase function
• scalar diffraction theory
• gradient method
• image classification