feed probe to backshort distance for wideband waveguide?

assume we want to feed waveguide or horn for wideband usage. For narrowband distance from probe to backshort is about quarterwave. What can be used in wideband case. Probe is microstrip wideband monopole on pcb.

Generally the distance can be the quarter-wave of a center wavelength. Specifically, this distance must be fine-tuned in a real transition given that the probe is not a thin line.
Wideband commercial transitions are expensive due to that company know-how is used for best results.
If you do not agree, design your device to see how complex the task is.