Grating Angular Sensor (GAS) does a highly precise angular measurements by using a custom made optical grating surface. GAS is a crucial instrument for the development of the Modular Gravitational Reference Sensor (MGRS). Recently we proposed and demonstrated the use of grating angular sensor can be far more sensitive than a simple reflection scheme for two reasons. First, the diffracted angles can vary more than the incident angle when the grating rotates. The grating thus magnifies the variation of the input angle. Second, the cross section of the diffracted beam is compressed by oblique projection, resulting in higher energy density. These two favourable effects become more pronounced when the normally incident beam diffracts at grazing angles. Our preliminary experiment demonstrated an angular sensitivity around 0.2 nrad/Hz^1/2 by taking advantage of grating angle magnification.

Experimental Data

The two figures below shows the experimental setup of the symmetric grating angular sensor. A Nd: YAG NPRO laser with a wavelength of 1064 nm was used as the light source. The gold-coated grating has a groove density of 935 lines/mm. The grating can be rotated or displaced by driving a pair of piezoelectric transducers (PZTs). For normal incidence, first order (+1, and -1 order) beam symmetrically diffracts at grazing angles of ±84°. The diffraction efficiency is 20% for each beam. As a result of the grating equation, there are no other higher-order diffraction beams. Two identical photodetectors with InGaAs quad-photodiodes were placed symmetrically at both sides of the grating, 6 cm apart from the illumination spot. The quad detectors are connected as a binary detectors sensing the beam linear movement. The differential voltages from the top and the bottom halves were sent to a summing amplifier. In this Arrangement, the output from the summing amplifier should ideally only be sensitive to the differential motion of the two diffracted beams; at normal incidence, it should be zero, because they cancel each other out. Practically, there will be some residual output, which is determined by the common mode rejection ratio (CMRR) of the detector-amplifier chain.


The three plots below shows the result of angular sensitivity measurement. In the plots, the central calibration peak was generated by PZTs rotating the grating with 0.5 µrad of amplitude. In the first plot, where a laser power of 1 mW is used, the noise floor is observed at 2 nrad/Hz^1/2. The frequency of the calibration signal was 1 kHz and the observation bandwidth was 100 Hz. The sensitivity shows no significant frequency dependence. The second plot shows the result when the laser power is increased to 4 mW. The noise floor is below 1 nrad/Hz^1/2 in most regions. A linearity check did not find any detector saturation. The last plot shows the result when laser power is increased to 14 mW, causing detector saturation. The noise floor outside the saturation band is 0.4 nrad/Hz^1/2, which is mostly due to detector system noise. This noise floor actually can be reached before overly saturating the detector. All the measurements are taken at 1 kHz because of environmental noises, such as air flow and vibration. We are planning to reduce the environmental noises by placing the angular sensor and electronics in an isolation chamber, and performing measurements in the LISA detection band, 0.001-1 Hz.


Last modified Mon, 6 May, 2013 at 19:34