I have heard about many new developments in radiotherapy for treating cancer/tumors such as hadron therapy but why can't we use wave interference for it? Incoming waves could interfere destructively on healthy tissues and constructively at the tumour site so that distribution of the total energy of the waves is concentrated at the tumour. According to the concept of Fourier series every periodic function can be approximated by an infinite weighted sum of sines and cosines, this corresponds to each wave being in a superposition of infinite number of different waves. A light wave packet localised at the site of the tumour can theoretically be obtained by interfering a large number of waves. This could also mean that the tumour could be destroyed by only using low energy light waves as the combined energy of the large number of waves distributed at the tumour would account for not using high energy x-ray beams. Please don't hesitate to point out any stupid mistakes I've made.
1 Answer
The soft tissue penetration depth of visible light is just a few mm, in the best case (red light). And the penetration through bones (like skull for example) is practically zero. However, versions of your idea are used with ultrasound. However is not interference that is used to localize the target area but focusing of multiple beams in the tumor area. Each beam has intensity low enough to avoid damage to the tissue. But when all the beams overlap the total intensity is high enough to burn the tumor. This technique id called HIFU (High intensity focused ultrasound) and is relatively new procedure. Now you can say that interference has a hand of it as the focusing of the each beam may be done by using linear arrays of transducers emitting beams with phases electronically controlled to add constructively in the target area. The same focusing and scanning method is used in conventional ultrasound imaging.
As for EM, I think the x-ray therapy also uses multiple beams converging on the target area.
