Harmonics in Quantal Histogram
The key problem with this histogram is that it looks more like a collection of impulses rather than a "waveform" and this "shows" at the output of the Discrete Fourier Transform (DFT).

If you have to use the DFT then you need to preprocess the histogram so that it becomes smoother. You can do this with a moving average filter that will effectively integrate the impulses into smooth "humps". The downside of this is that you will have to tune the integrating period of the moving average filter to something that makes sense for your problem. And while doing this you will also notice that the waveform might change a bit from the expected depending on the time scale (or in the case of the histogram the resolution) that results from the use of a filter.

You can then pass the smoothed waveform to the FFT or, if your objective is to determine modes occuring at regular intervals, pass the smoothed histogram "waveform" to something like Kernel Density Estimation which seems more suited to your application.

Kernel Density Estimation will try to approximate the smoothed histogram output as a sum of gaussians with different widths and centers. Ideally, if these modes resemble gaussians, you might get one gaussian per mode you are trying to locate and then the regularity of the modes will show up in the centers of the fitted gaussians.

Hope this helps