Tomographic Wavefront Sensors For Advanced Gravitational Wave Interferometers

1. Introduction

The international effort to detect gravitational waves (GW) is perhaps the most important and exciting current physics project as it will open a revolutionary new window to the universe. The detection will require the development of advanced laser interferometers that use state-of-the-art optical systems, including ultra-low noise, single frequency, high power CW lasers and optical Fabry-Perot cavities that have stored powers of order 500 kW [1]. At these power levels, usually negligible absorption by the substrates and coatings of the optical components will cause optical path distortions (OPD) that, if uncompensated, will significantly reduce the sensitivity of the detector and potentially cause instrument failure [2]. This problem is being addressed by the development of ultra-low absorption materials for the substrates and coatings, and by the development of high precision optical correction systems.

A practical solution for the latter requires the development of a closed-loop aberration correcting system, including a suitable sensor and actuator, capable of being applied to each optic as required. Numerical modeling suggests that the OPD in each optic should be reduced to less than ?/100 [2] and thus the sensor should have a precision and accuracy significantly better than this. Importantly, the sensor must not interfere with the circulating optical power or cause additional noise, preventing the direct measurement of the on-axis OPD. Hence, the sensor must be able to reconstruct accurately the on-axis OPD using only an off-axis measurement. Furthermore, improved accuracy from a null servo system could be achieved if the sensor could simultaneously measure the aberration and the correction. In this paper, we will discuss the development of a sensor for such a correction system.

We have chosen to develop an off-axis Hartmann sensor as it satisfies all the scientific requirements while also being easy to align and simple to optimize. In section 2, we describe the Hartmann wavefront sensor. Tomographic analysis of the data from the wavefront sensor is used to determine on-axis OPD as described in section 3. The latest results will be shown in Section 4, demonstrating that our sensor can accurately and precisely resolve the spatial distribution of the induced distortion.

2. Hartmann Wavefront Sensor

In a Hartmann sensor, an array of apertures in an opaque plate, referred to as a Hartmann plate, is used to divide a light beam into a set of rays, each of which is perpendicular to the wavefront. An array of spots is formed when these rays are incident on a screen or CCD camera. Initially, the undistorted wavefront spot positions are recorded. The transverse displacement of the spots due to the wavefront distortion are then measured and divided by the distance between the Hartmann plate and the CCD to determine the local gradients or slopes of the wavefront. Numerical integration of this gradient field yields the shape of the distorted wavefront.

The position of each spot is determined using the first moment, or centroid, of the spot intensity profiles recorded by the CCD. Since each spot in a Hartmann sensor occupies many pixels, the centroid can be determined with very high precision and is much less sensitive to variations in pixel responsivity, in contrast to a Hartmann-Shack sensor where the CCD is at the back focal plane of a micro-lens array and each spot consists of very few pixels. We improved the reliability and reproducibility of the centroiding algorithm by subdividing the pixels and iterating to find a self-consistent centroid. Further details of this algorithm will be published elsewhere.

The Hartmann sensor used for this work consists of a Hartmann plate with hexagonally-close-packed circular apertures of 150 ?m diameter and 430 ?m pitch, located 10 mm from a Dalsa 1M60 CCD that has a 12-bit dynamic range. The centroids have a measured reproducibility of about 19 nm.

Publications

[1] A. Weinstein, “Advanced LIGO Optical Configuration and Prototyping Effort”, Class. Quantum Grav. 19, 1575-1584 (2002)

[2] R. Lawrence, D. Ottaway, M. Zucker, and P. Fritschel, “Active Correction of Thermal Lensing Through External Radiative Thermal Actuation”, Opt. Lett. 22, 2635-2637 (2004).

Personnel

Mr Miftar Ganija
Dr Aidan F. Brooks
Prof Jesper Munch
A/Prof. Peter Veitch