incoherent and coherent illumination. The optical transfer function is a function of the wavelength of light and changes with the coherence of the light. Hence images that contain the information we are seeking are influenced by the coherence or non coherence of light. 4.0 Fundamental parameters common to all the techniques Spatial frequency is a fundamental concept that applies to all the OTD methods, Figure 2. Utilizing nomenclature of the Fourier transform (FT), there is two spaces the physical space and the frequency space that are related by the reciprocal relationship. Through the Fourier analysis we know that to any configuration in the physical space corresponds a configuration in the frequency space through the FT. To extend this concept to image formation through a projection center it is necessary to introduce an angular variable [3], Figure 3. The angle θ=X/R is the variable that relates the fundamental frequency X to the process of projection from a center and it is possible to define the angular frequency ξang=R/X. The laws of projective geometry provide the means of extracting information from the 2-D image that pertains to the 3-D object. Added to this aspect of the process of gathering information through a projecting center is the fact that there is a lens system that has its own laws of transferring information. If one wants to get mathematical we can say that we have a set of points in S3 space that is converted into a set in the S2 space, through the recording of a 2D matrix of rows and columns that contain positive integers coded into a set of gray levels. Because of the presence of pupil apertures in the lens system the geometrical ideal point is transformed due to diffraction effect of the pupil into a distribution of intensities that depends on the particular pupil that controls the image, in the simple case of a circular pupil is an Airys’ intensity distribution. . Figure 2.Spatial and inverse space frequencies 5.0 The sensitivity vector Figure 4 brings us to another important concept that is common to all the techniques, the sensitivity vector [4]. Although it was originally introduced in holography it applies to all the OTD methods since it defines the displacement components that the optical set up is sensitive to. In the original developments of moiré there was a separation between two forms of moiré, moiré that is sensitive to in-plane displacements, called intrinsic moiré and the moiré sensitive to out-of-plane displacements called shadow moiré. Figure 3.Angular space frequency ξang=R/X. 156
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