Wavefront-sensor-induced beam size error: physical mechanism, sensitivity-analysis and correction method

Abstract

When using a commonly-used quadri-wave lateral shearing interferometer wavefront sensor (QWLSI WFS) for beam size measurements on a high power CO2 laser, artefacts have been observed in the measured irradiance distribution. The grating in the QWLSI WFS not only generates the diffracted first orders that are required for introducing the shear, but also diffracts significantly into higher orders. Consequently, in the few millimeters of free space propagation between the QWLSI WFS grating and its imaging device, the beam size may increase significantly (particularly for infrared wavelengths). This error is typically not accounted for in the subsequent processing of measurement data. To gain insight in this undesirable behavior, physical models of the QWLSI WFS using both complex wave propagation and analytic propagation of the D4sigma beam diameter (and its associated M2) throughout the system have been developed. These models show excellent agreement to experimental data, and indicate that in typical situations the sensor-induced beam size error can easily be 40% or more. Although the QWLSI WFS may not originally be intended for beam size measurements, in most industrial applications cost- and volume limitations will often lead to multiple use of sensor data. To aid in the adequate implementation of a QWLSI WFS for determining beam size, the dependence of the sensor-induced beam size error on various system parameters has been determined (e.g. incoming beam size, grating-to-imager distance, grating geometry, wavelength). Using the presented models and guidelines, the sensor-induced beam size error may be minimized and corrected for.