Abstract

We report improvements to the integral transform implementation of the Abel inversion.¹ Our experimental data set is the 2-D projection of a 3-D cloud of ionized photofragments of methyl iodide. A typical cloud consists of two thin shells bunched together on the surface of a sphere. These shells correspond to the dissociation channels of iodine. The outer-most shell is much fainter than the inner one. The symmetry of this arrangement is such that any 2-D cross section through the poles of the sphere is the same as any other. Consequently, it is possible to reconstruct the 3-D photofragment distribution by Abel inverting the 2-D projection data line by line. Noise in the data makes it difficult to resolve the two dissociation channels appearing in the Abel inversion. We have therefore concentrated our efforts on the trade-off between resolution and signal-to-noise ratio which inevitably occurs in these reconstruction techniques. Our choice of the integral transform approach to Abel inversion was motivated by computational simplicity and straightforwardness in implementing noise smoothing and data symmetrizing. The transform technique requires a Fourier transform followed by an inverse Hankel transform. We find that presmoothing the projection data with a small 2-D Gaussian convolution mask produces a dramatic enhancement of the final reconstruction. The effects of noise and asymmetric backgrounds are reported.

© 1989 Optical Society of America