Methods and software for capturing three-dimensional digital images using spatial demodulation

Abstract

The paper proposes the generalized technique of demodulation, which can be applied for capturing digital three-dimensional images in optical microscopes. This technique allows the calculation of the contrast of harmonic spatial modulation with any values of phase angles. The input data is a stack of digital images with harmonic spatial modulation. Three digital images with different phases of modulation captured in the same focus position are processed to get one data set about the contrast distribution. This data makes it possible to compose the three-dimensional images by the selection of the maximal values of the contrast in three-dimensional space. The paper contains the analytical solution of the system with three linear equations that helps to identify the principal parameters of harmonic spatial modulation, including its average value and contrast. As a result, the expression for contrast calculation is present in an analytical form. This expression is valid for any modulation phase angles that do not coincide. The paper contains MathCAD modeling, which illustrates the procedure of composing the three-dimensional images.
 The modeling confirms the correctness of described calculations and demonstrates the built of the three-dimensional surface image as a composition of the contrast distribution map and the corresponded height map. The advantage of the proposed technique is the possibility to apply the economical units for the formation of a harmonious spatial modulation. These units can be installed on most optical microscopes with digital cameras and motorized focusing drives without purchasing expensive commercial software. It significantly reduces the price of transforming these optical microscopes into instruments for capturing digital three-dimensional images.