The invention comprises a method and apparatus for probing a tumor of a patient using positively charged particles, comprising the steps of: (1) sequentially delivering sets of varied and known positively charged particles to a patient; (2) after transmission through the patient, sequentially detecting a residual energy of each of the sets of positively charged particles; and (3) determining a water equivalent thickness of a probed path of the patient using a plot of the detector response as a function of residual energy that is fit with a curve. The analyzer relates a half maximum of the fit curve, such as a Gaussian curve, to the water equivalent thickness of the sampled beam path. Repeated measurements as a function of incident angle and/or position of the incident charged particles allows generation of an image of the sample, such as a computed tomography image.