= Solution
The $x$ axis lies along the mean <Poynting vector>. A two-dimensional <optical camera> sensor intended to sample many $x$ positions at once would have to lie along the <energy> flow, where it receives no normal flux in the ideal geometry; a side-view <optical camera> also sees no light from an empty nonscattering propagation region. Putting a detector normal to $x$ measures one transverse section instead, and absorbs the light before a downstream detector can sample the same rays.
One could translate a detector to successive $x$ positions or introduce a scattering screen, but that is a different measurement. Moreover the ideal result here is already the constant $I(x)=2I_0$, so it contains no longitudinal <optical coherence> structure for the <optical camera> to resolve. The difficulty is the longitudinal sampling geometry, rather than a hidden $x$-fringe period.
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