Non-uniform optical transfer functions in particle imaging: calibration and application to tomographic reconstruction

Abstract

A new approach to the weighting function, which describes particle imaging in tomographic reconstruction, is introduced. Instead of assuming a spatially homogeneous mapping function of voxels to the images, a variable optical transfer function (OTF) is applied. By this method, the negative effects of optical distortions on the reconstruction can be reduced considerably. The effects of these improvements in reconstruction quality on the methods of tomographic particle imaging velocimetry, as well as 3D particle tracking are investigated. A method to calibrate the OTF to experimental circumstances is proposed as an additional step to the volume self-calibration. It is shown that this kind of calibration is able to capture the predominant particle imaging both for simulated as well as experimental data. The most common distortions of particle imaging are blurring due to a small depth of field and astigmatism due to imaging optics. The effects of both of these distortions on reconstruction and correlation quality are investigated via simulated data. In both cases, a strong influence on relevant parameters can be seen. Reconstructions using a spatially varying OTF, calibrated to the imaging conditions, show a significant improvement in reconstruction quality and the accuracy of the particle peak position, as well as in the accuracy of the gained displacement vector field when using two time steps. Evaluation of experimental data by PTV methods shows a reduction in ghost particle intensity and improvements in peak position accuracy. A computationally efficient method of applying the OTF to tomographic reconstruction is introduced.