Digitally enhanced spatial heterodyne interferometry is a new technique which transfers the identification of wavefront information from analogue analysis tools to digital pro- cessing. It senses the wavefront phase using a single diode, a spatial light modulator and digital interferometry. It provides an alternative way to measure wavefront tip and tilt with comparable accuracy to conventional approaches based on a quadrant photodiode. The approach is immune to various sources of low-frequency noise that affect quadrant diode techniques because all measurements share a common analogue signal chain. In the implementation presented here, the noise performance above 5 Hz was limited by noise from the segmented mirror, but this could be avoided using a non-mechanical SLM or an optical phased array. This technique is likely to find application in alignment systems for satellite interferometers.
5.9 Conclusion
=
+
Mirror with Hadamard Code
Mirror with Number Offset
Mirror with Hadamard Code and Number Offset
Figure 5.19: An illustration of how a DC offset and a Hadamard code could be added on the surface of the SLM so that both act together to change the shape of the wavefront. The Hadamard code cycles many times for each DC offset and disappears during the demodulation process resolving the shape defined by the DC offset, in this case a 5.
Figure 5.20: Demonstration of higher-order spatial phase manipulation. The blue rectangle shows the individual phases across a 9 by 7 matrix of elements each of which has been spatially tagged with an orthogonal code. The numbers are created by adding a fixed offset to the code modulation on some of the segments of the SLM.
Furthermore, we have shown that the technique can measure phase at many points and so sense and manipulate higher-order spatial modes, limited only by the resolution of the SLM and the capabilities of the digital signal processing hardware. Potential applications include isolating different spatial modes in an interferometer or continuously maximizing input coupling to an optical cavity.
Chapter 6
Controlling Wavefronts in Real
Time
6.1
An Overview of the Experiment
The goal of the experiment reported in this chapter was to maximise the amount of light transmitted through a cavity by reshaping the laser wavefront so that its mode matches the mode of the cavity as closely as possible. The goal of the second experiment, reported in section 6.5, was to harness these wavefront shaping techniques to select a specific,
higher order mode (the T EM10 mode) and have this preferentially transmitted through
the cavity.
The work has been reported in a draft paper ’Automatic alignment of a Fabry-P´erot cavity
using two spatial light modulators, a single photodiode and digitally enhanced heterodyne
interferometry’, submitted for publication and is currently undergoing peer review. I
designed, set-up and ran the experiment on my own. This included building the software and resolving the issues associated with running two spatial light modulators from the same PC with Boston Micromachines. Dr Paul Altin, helped me align the cavity for the first time and provided advice throughout as requested. Professor Daniel Shaddock reviewed my progress and suggested that I run the sensing routine in LabVIEW asynchronously, which saved a lot of coordination work.
There have been previous attempts to optimise transmission through a cavity automat- ically but these have been focused on physically moving optical components. To date approaches have relied on the differential wavefront sensing outlined in subsection 2.2.1 which uses one or more multi-element photodiodes to measure the varying phase difference between two beams and derive an error signal to improve alignment, see Ref [26]. In 2005 a group at ANU developed a system which used galvanometer actuated mirrors driven by an error signal to control the tilt and offset of the signal beam and optimised them to maximise cavity transmission. The optical arrangement used a Gouy phase invariant telescope to decouple these actuators as far as practicable so that tilt and offset could be controlled separately Ref [101]. In 2010 another group, based in Colorado, developed a simplified actuator with a flat amplitude and phase response to frequencies above 200
kHz, which stabilised the lock of a Fabry-P´erot to a continuous wave laser, see Ref [102].
The cavity was locked using PDH locking.
This experiment includes not only tilt and offset but also waist size and position and, to a degree, beam shape. At first sight it is quite straightforward. The essential optical arrangement is shown in figure 6.1. A laser was directed onto two spatial light modulators and thence along the optical axis of a cavity from which the transmitted power was meas- ured. The surfaces of the SLMs were dithered using predetermined shapes, variations in
6.1 An Overview of the Experiment
transmitted power measured and an algorithm applied to determine the direction in which each movement increased transmission. This information was used to develop an error sig- nal which was multiplied by a gain and applied to make small, automated adjustments to the surfaces of the SLMs and so reshape the wavefront accordingly. The transmitted power was incrementally increased until the maximum value was reached. The individual shapes were dithered with orthogonal codes using the techniques demonstrated in chapter 5 so that their individual contributions could be isolated and evaluated simultaneously. The first experiment focusses on adjusting beam tilt and offset and waist size and position. This is accomplished by dithering tilts and curves in both the horizontal and vertical planes (see figure 6.8), a total of four degrees of freedom for each mirror. Tilting the surfaces of the SLMs as planes affects the tilt and offset of the beam while curving them, either positively or negatively, changes the incident beam’s waist size and position. More complex patterns are introduced later in this chapter in section 6.5.
Cavity Laser
Beam Splitter
Figure 6.1: A simplified schematic of the essential experimental optical arrangement.
Section4.3 identified some of the factors that had to be optimised to maximise cavity transmission. The first two were physical attributes of the cavity - the quality of its construction and the degree to which it was impedance matched - and these were accepted as given for the cavity used in this experiment. The cavity was of high quality and nearly impedance matched (see its detailed specifications in figure 6.4).
Factor three - the continual match of laser frequency to cavity resonance - was accom- plished using PDH locking although future work might assign this work to the SLMs as well. As the cavity was fixed, the PDH error signal was used to feed back to the laser piezo.
The last five - tilt, offset, waist size and waist position and beam quality (the degree to which the beam has a Gaussian profile) - are all qualities of the laser wavefront and were controlled using the two SLMs.
Chapter 6 Controlling Wavefronts in Real Time