2.3
More Complex Wavefront Sensing Using Hartmann Sensors
Description
The Hartman sensor provides an alternative and now very accurate method of sensing a wavefront Ref [15], Ref [16] and Ref [30]. It was developed in 1900 by Johannes Franz Hartmann Ref [31] and works because a light wave always travels perpendicularly to its wavefront. A Hartmann sensor is a screen of very precisely arrayed holes through which a beam is shone onto a Charge-Coupled Device (CCD) camera figure 2.6).
Hartmann Plate
Hartmann Sensor
CCD Camera Wave front
Figure 2.6: The Hartmann sensor allows a user to sense the shape of a wavefront from the distortion caused in the image of a regular array of holes projected onto a CCD camera.
If the wavefront striking the screen is a plane wave, the image of the holes on the CCD camera is a precise recreation of the screen. If the wavefront is curved or irregular, the image is distorted, figure 2.7). Algorithm can then be used to infer the shape of the wavefront from these distortions Ref [15].
Hartmann sensors are being used in the most demanding sensing application on the planet, the Laser Interferometer Gravitational Wave Observatory (LIGO). LIGO comprises two Michelson interferometers with 4 kilometre arms, separated by about 4,300 km. The two interferometers are one instrument as it is only by comparing signals received at both and matching them (with appropriate delays) that observers can be certain that any signal is a gravitational wave and the product of not some local, unsuppressed noise source. Further it allows observers to estimate the direction from which the gravitational wave originated and this can be enhanced by adding data from the Virgo interferometer in Europe. In each observatory, a high quality, high power laser beam is split, injected into the arm and then recombined to look for tiny changes in relative arm length. The precision of the
measurement is breathtaking. LIGO can measure a strain of 10−22 which is equivalent
to measuring a change the width of a human hair in the distance between Earth and the second nearest star (that is, not the Sun)! Obviously any source of extraneous noise can
Chapter 2 Current Wavefront Sensing Techniques
Figure 2.7: The picture on the left represents the regular image produced by a Hartmann sensor sensing a plane wave. The middle picture shows how this pattern changes as the wavefront changes; these changes can be used to infer the wavefront’s shape. On the right is a photograph of one of the Hartman sensors being installed in the Gin Gin Gravitational Wave facility in Western Australia.
ruin the measurements and one noise source that must be managed is the distortion of the large mirrors (the test masses) at the end of each cavity by the large amounts of heat that the circulating lasers create. This is accomplished by the Thermal Compensation System (TCS) which uses Hartmann sensors to infer thermal distortion from wavefront distortion and ring heaters to try to correct it.
LIGO has put new demands on the accuracy of Hartmann sensors and the team at the University of Adelaide reported in 2016 that they had achieved a wavefront sensitivity of 1.35 nm RMS Ref [32], within the tolerances required for LIGO.
Currently LIGO requires that the Hartmann sensors use laser light of a different frequency (532nm and 800 to 840 nm) from that used in the interferometer (1064nm) and some scatter loss from defects may be wavefront dependent. Like any sensor, the Hartmann sensors only provide measurements can cannot actively correct any wavefront aberrations. Nonetheless they represent a remarkable achievement and were able recently to detect wavefront distortions in one of the test masses that were not visible to human observers, see Ref [33].
Great care is taken to ensure that the light injected into the main interferometer arm
in LIGO is coherent, monochromatic and Gaussian. Wavefront distortions that arise
therefore, tend to come from two sources:
1. Defects in the optics, such as the spot found on one of the test masses, or
2. Distortions of the optics caused by expansion and absorption due to the high optical powers resident within the cavity.
There is little that can be done to correct defects of the first type other than the reworking or replacing the optic. Defects of the second type can be mitigated using the active half of the Thermal Compensation System (TCS) which attempts to compensate for low order distortions in the test masses using ring heaters, Ref [32].
The Shack-Hartmann Sensor
The Shack-Hartmann sensor is a variant of the Hartmann sensor which grew out of a demand for better satellite imaging during the Cold War, see Ref [34] and Ref [31]. The
2.3 More Complex Wavefront Sensing Using Hartmann Sensors
traditional Hartmann sensor suffered from two disadvantages when it came to satellite imaging, see Ref [35]:
1. The sensor was in line with the imaging beam, blocking it, and
2. The sensor blocked a large proportion of the light falling on on it, allowing only that fraction passing through the holes in the sensor to create an image.
Image
Figure 2.8: The Shack-Hartmann Sensor. A variant of the Hartmann sensor, the Shack-Hartmann sensor uses a beam splitter to divert a small proportion of the incoming light onto a lenslet array which intensifies the pattern of spots it produces. The bulk of the beam is free to pass through to a CCD camera and produce a high resolution image. The control system analyses displacements in the positions of the spots and produces an error signal. This in turn can adjust a deformable mirror which then adjusts the incident wavefront in real time.Of course, the feedback from the control system must be faster than the rate of change aberrations being corrected. This image is taken from Ref [36]
After an approach from the military, Dr Aden Meinel and the Optical Sciences Center (OSC) at the University of Arizona devised an approach which involved tapping off a small part of the image beam, using a beam splitter, and intensifying the images of spots produced using a lenslet array. This left the bulk of the beam free to produce an image while the lenses focused the tapped portion into a series of spots. It was Roland Shack, whom Dr. Meinel had recruited to OSC, who was given the task of determining whether this technique was feasible, see Ref [35].
Figure 2.8 shows a typical adaptive optics system based on a Shack-Hartmann sensor using in astronomy. The incoming light strikes a deformable mirror (initially set flat) and then a beam splitter. A small proportion is diverted to the Shack-Hartmann sensor and produces an image of an array of dots. Their deviation from the expected regular array is used by the control system to create an error signal which is fed back to the deformable mirror, which in turn modifies the next part of the incoming light. Provided the response of the
Chapter 2 Current Wavefront Sensing Techniques
control system is faster than changes due to turbulence in the atmosphere, the main part of the beam passes to the CCD camera where it produces a corrected, high resolution image, see Ref [36].
The Shack-Hartmann sensor is now a well proven and well used part of adaptive optics being employed for everything from reducing distortions due to atmospheric turbulence for astronomical observations to making detailed assessments in ophthalmology, see Ref [37] and Ref [31]. Figure 2.9 shows the type of correction possible. The figure on the left is the uncorrected image, while that on the right is the corrected image. This figure is reproduced from Ref [37].
Figure 2.9: A demonstration of image Correction Using a Shack-Hartmann Sensor. The figure on the left is the uncorrected image, while that on the right is the corrected image. This figure is reproduced from Ref [37].