Heated sample
1.6 Review of photo-thermal techniques
1.6.4 Photothermal wavefront deformation measurements
The methods outlined above are limited for my application. Interferometric methods are im- practical for measurements on numerous samples and are unable to exact surface absorptions.
PDSandPCImeasurement systems are capable of this applications goals but impractical due to their extremely long measurement times to measure the entire sample. Instead it is possible to extract absorption over a large area of a sample by imaging the wavefront distortion of a probe beam after passing through the heated sample, using a Hartmann Wavefront Sensors (HWS) [32]–[37].
Differential Hartmann Wavefront Sensors (DHWS) and Shack Hartmann Wavefront Sensors (SHWS), which will be broadly referred to as Hartmann Wavefront Sensors (HWS), use an array of uniformly spaced holes or micro-lenses, respectively, to decompose a beam into rays that propagate normally to the wavefront at that point. The rays are incident on a Charge Coupled Device (CCD) or Complementary Metal–Oxide–Semiconductor (CMOS) sensors creating an array of spots, for which a set of centroids are calculated, as shown in figure Fig.1.11. Changing the shape of the wavefront changes the position of the centroids. The wavefront distortion can be reconstructed from the gradients of the centroid positions before and after the absorption induced distortion using numerical integration or polynomial fitting methods. Consequently, if the sensor is optically conjugate to the sample then the distortion is equivalent to that accumulated through the heated sample and absorption can then be extracted by comparison to a model or via calibration. This method allows a 2D map of the wavefront distortion over a significant portion of a sample, as the probe beam size is only limited by the sample clear aperture. The presence of highly absorbing inhomogeneities in the path of the pump beam are easily identifiable in the map [10].
HWSsystems have been widely applied to measure absorption. The measurement noise floor of theDHWSandSHWScan be dramatically reduced by averaging frames to reduce the effect of shot noise, giving similar sensitivities of ca. 100 pm [36], [38].
HWSabsorption measurement systems with various configurations of the pump and probe beam have been published. Using a co-linear probe and pump beam, bulk absorption has been measured with an uncertainty of 4 ppm cm−1[32]. However, this method did not allow for surface absorption and bulk absorption to be separated from one measurement. Co-linear
1.6 Review of photo-thermal techniques 19
WFprobe WFprobe Centroid map
Centroid map Cool sample
Heated sample
WFprobe WFprobe
Fig. 1.11DHWSmeasure the differential wavefront by decomposing a beam into rays at the Hartmann plate and measuring the change in position of incidence on a sensor. The direction of the rays is defined by the normal to of the wavefront at the plate. This creates a spot pattern on the sensor which is referred to as a centroid map. The effect of the change in wavefront and consequent angle of the rays on the sensor is demonstrated by the position of the centroids measured on the sensor. In this diagram I assume dTdn<0.
measurements also require dichroic mirrors to separate the pump and probe beam which can cause parasitic absorption and distortion as observed in Ingramet al.[33].
Brookset al.[34] first suggested measuring absorption by imaging an off-axis probe beam passing through a centrally heated sample using aDHWSin 2005. In Brooks [35] this archi- tecture was used to measure wavefront distortion in BG20 glass at 1064 nm, and a model predicting the total wavefront distortion due to the thermo-refractive effect was created based on the analytical solution for a temperature distribution from Helloet al.[39]. However, the absorption coefficient of BG20 was not determined.
Fig. 1.12 Optical schematic of a system to measure the wavefront deformation of a probe beam passing off-axis through a sample heated by an on-axis heating beam. [36] .
A similar off-axis probe beam setup has also been used for aSHWSabsorption measurement system using a 248nm pump beam at a 100 ppm cm−1level in fused silica [36], for which the optical schematic is shown in Fig.1.12. The wavefront distortion was then reconstructed as a Zernike polynomial. This study compared two methods of calibrating the absorption measurement. The first was to simulate laser heating using a resistor chain and using the peak-valley temperature change at various electrical powers to determine the calibration factors. The second used a Finite Element Method (FEM) that represented the wavefront distortion as a linear expression in terms of surface and bulk absorption and their respective distortion at each point in the sample. TheFEMwas proven to give a more accurate value, however, it relied upon the assumption that the sample is weakly absorbing and there is negligible power lost over the sample length. The results showed surface absorption could not be extracted due to the small magnitude of the total deformation. While the exact method to determine the deformation was unclear, it was stated that this method considers thermo- expansion and thermo-optic effects.
This system was further modified such that a 50W 1070 nm pump beam and 630 nm probe beam were transmitted through perpendicular faces of the sample, as shown in Fig.1.13. An analytical model was used to estimate the bulk and surface absorption yielding 11±4 ppm and 74±28 ppm cm−1respectively [40]. This model considered thermo-expansion, thermo-optic
1.7 Requirements of system to measure absorption in low-loss glasses 21
Fig. 1.13 The off-axis probe beam, on-axis pump beam set up can be modified such that the probe beam passes through the perpendicular face. In this case aSHWSis used to measure the wavefront deformation [37]
and elasto-optic effects.