A method for the quantitative analysis of two-dimensional (2D) small-angle X-ray scattering (SAXS) patterns with fiber symmetry by successive information filtering is proposed and applied to a series of images recorded during a straining experiment of a two-phase polymer sample at a synchrotron beamline. The studied equatorial scattering is similar to the frequently discussed void scattering, but originates from an ensemble of rodlike soft domains (needles) in the sample, orientated in the direction of strain. The intensity is extracted and projected onto the equatorial plane, the ideal two-phase structure is extracted, and the 2D chord distribution is computed. This curve describes a 2D two-phase morphology made from needle cross-sections embedded in matrix material. Because interparticular correlation is found to be weak in the chord distribution, pure particle scattering is assumed. Modeling the needle cross-sections by circular disks leads to a simple theory, which allows the deconvolution of a disk diameter distribution from the chord distribution. It is shown how parameters of the disk diameter distribution can be computed without deconvolution. For the selected poly(ether ester) thermoplastic elastomer the study of the soft domain needles indicates strain-induced hardening. While for low elongation epsilon the soft needles are more compressible than the microfibrillar matrix, saturation is observed for epsilon > 2.5.