Wavefront Analysis and Calibration for Computer Generated Holograms

Abstract

Interferometry with computer generated holograms (CGH) has evolved to be a standard technology for optical testing and metrology. By controlling the phase of the diffracted light, CGHs are capable of generating reference wavefronts of any desired shape, which allows using of interferometers for measuring complex aspheric surfaces. Fabrication errors in CGHs, however, cause phase errors in the diffracted wavefront, which directly affects the accuracy and validity of the interferometric measurements. Therefore, CGH fabrication errors must be either calibrated or budgeted. This dissertation is a continuation and expansion of the analysis and calibration of the wavefront errors caused by CGH in optical testing. I will focus on two types of error: encoding error and etching variation induced errors. In Topic one, the analysis of wavefront error introduced by encoding the CGH is discussed. The fabrication of CGH by e-beam or laser writing machine specifically requires using polygon segments to approximate the continuously smooth fringe pattern of an ideal CGH. Wavefront phase errors introduced in this process depend on the size of the polygon segments and the shape of the fringes. We propose a method for estimating the wavefront error and its spatial frequency, allowing optimization of the polygon sizes for required measurement accuracy. This method is validated with both computer simulation and direct measurements from an interferometer. In Topics two, we present a new device, the Diffractive Optics Calibrator (DOC), for measuring etching parameters, such as duty-cycle and etching depth, for CGH. The system scans the CGH with a collimated laser beam, and collects the far field diffraction pattern with a CCD array. The relative intensities of the various orders of diffraction are used to fit the phase shift from etching and the duty cycle of the binary pattern. The system is capable of measuring variations that cause 1 nm peak-to-valley (P-V) phase errors. The device will be used primarily for quality control of the CGHs. DOC is also capable of generating an induced phase error map for calibration. Such calibration is essential for measuring freeform aspheric surfaces with 1 nm root-mean-square (RMS) accuracy.