Several integrated optics solutions currently exist to develop monolithic, robust, and lightweight high-resolution spectrometers for spatial applications. An interesting option is generating a stationary wave inside a single-mode waveguide, and sampling the interference fringes using dielectric discontinuities on the surface of the waveguide. This allows the recording of the signal on a detector on top of the waveguide, and using dedicated Fourier transform methods to recover the spectrum of the source. All the difficulty is then linked to the length of the interferogram that is sampled. This determines the spectral resolution and the spacing between sampling centers, which are ultimately limited by the pixel pitch, and that will determine the spectral range of the spectrum. In addition, the dielectric discontinuities that will extract the flux from the waveguide have a relatively wide angular emission, resulting in crosstalk between pixels, and reducing the effective sampling step. Finally, the optical sensitivity of these systems is limited since the waveguides are single mode. Therefore, improving the efficiency of stationary wave Fourier transform spectrometers will require reducing the angular divergence of the sampled signal, reducing the sampling step, and increasing the optical input collection capacity. To achieve the two latest conditions, one interesting approach is spatial multiplexing. In this paper, we present the proof of concept of a multiplexed integrated optics Fourier transform spectrometer based on lithium niobate waveguides, using focused ion beam nanogrooves as sampling centers. The spatially shifted position of the antennas between consecutive waveguides will allow us to determine an unknown wavelength with tens of picometer resolution. The extraction efficiency and bandwidth of the antennas will be theoretically studied to optimize their periodicity and match a given pixel pitch. Finally, the ability to develop this concept on an electro-optic material will be of great interest to achieve further active phase modulation and increase the spectral bandwidth.