Pixel-level interpolation was tested to resolve the centroid shift issue. Pixel alignment worked correctly; however, centroids shift on hundredth of a pixel scales between PSFs of different FRDs in the spectrograph images. Sub-pixel alignment, thus requiring implementation of an interpolator, is thus required. Options for interpolation are currently being investigated. 

To understand the effect of alignment in more detail, simulation images before downsampling were used. One_pixel_offset_simulation.png demonstrates the characteristic residual from centroid misalignment, while One_pixel_offset_spectrograph.png demonstrates the downsampled result (which is a dipole; this is why the FRD image residuals being dipole-dominated indicated centroid misalignment). For comparison, 6mrad_9mrad_simulation.png indicates the residual between images with 6 mrad and 9 mrad FRD. Notably, this structure is different than that of the misalignment residual, giving hope to the prospect of extracting FRD from these images even after centroid alignment. However, the downsampled spectrograph image 6mrad_9mrad_spectrograph.png is also dominated by the dipole shape.

The function scipy.ndimage.interpolation.shift was found to appropriately reproduce pixel-order shifts and also found to successfully interpolate in order to shift sub-pixel distances utilizing third-order spline interpolation. SubpixelScaling.png demonstrates that the subpixel shift gives an appropriate residual magnitude relative to the residual magnitude in the relatively simple pixel shift image. Utilizing this function solves this issue. 

Code that solves this issue has been found and implemented into Brent's FRD analysis.