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Electrons in a standing electromagnetic wave—an optical lattice—tend to oscillate due to the quiver and ponderomotive potentials. For sufficiently intense laser fields (lλ2≤5×1017 W cm-2 µm2) and in plasmas with sufficiently low electron densities (n≤1018 cm-3), these oscillations can occur faster than the plasma can respond. This paper shows that these oscillations result in Thomson scattering of light at both the laser and ponderomotive bounce frequencies and their harmonics as well as at mixtures of these frequencies. We term this mixing ponderomotive intermodulation. Here, the case of counterpropagating laser beams creating a one-dimensional (1D) optical lattice is analyzed. The near-equilibrium electron orbits and subsequent Thomson scattering patterns are computed in the single-particle limit. Scaling laws are derived to quantify the range of validity of this approach. Finally, collective plasma and laser focusing effects are included by using particle-in-cell (PIC) techniques. This effect resulting in light-frequency conversion has applications both as an infrared light source and as a means to diagnose high laser intensities inside dense plasmas.