Short pulses used by traditional time-of-flight mass spectrometers limit their duty cycle, pose space-charge issues, and require high speed detectors and electronics. The motivation behind the invention of continuous time of flight mass spectrometers was to mitigate these problems, by increasing the number of ions reaching the detector and eliminating the need for fast data acquisition systems. The most crucial components of these spectrometers are their modulators: they determine both the maximal modulation frequency and the modulation depth. Through these parameters they limit the achievable mass resolution and signal-to-noise ratio. In this paper, a new kind of setup is presented which modulates the beam by deflecting it in two perpendicular directions and collects ions on a position sensitive detector. Such an Lissajous time of flight spectrometer achieves modulation without the use of slits or apertures, making it possible for all ions to reach the detector, thereby increasing the transmission and signal-to-noise ratio. In this paper, we provide the mathematical description of the system, discuss its properties, and present a practical demonstration of the principle.