Notes on van der Meer Scan for Absolute Luminosity Measurement

An absolute luminosity can be measured in an accelerator by sweeping beams transversely across each other in the so called van der Meer scan. We prove that the method can be applied in the general case of arbitrary beam directions and a separation scan plane. A simple method to develop an image of the beam in its transverse plane from spatial distributions of interaction vertexes is also proposed. From the beam images one can determine their overlap and the absolute luminosity. This provides an alternative way of the luminosity measurement during van der Meer scan.