Optics

In the ILT experiment an amplitude grating is used in plane z = 0. The derivative I/ z is estimated by taking the difference between the illuminations measured in plane z = 0 and in plane z = z at some distance z downstream. From this difference both the wavefront local slopes W and the wavefront local curvatures 2W are uniquely determined. This experiment opens new prospects. Indeed it can be interpreted in different ways: (1) The grating with period a diffracts light producing waves propagating at angles multiple of λ/α. The illumina­ tion in plane Z = z is the result of interference between these waves. In their data reduction technique ILT isolate the first harmonic produced by waves interfering at an angle λ/α. These waves are copies of the original wave laterally sheared by an amount x = (λ/a) z. Their phase difference is therefore Δφ = ( φ/ x)Δx = ( φ/ x)(λ/a) z or in terms of the wavefront surface W = (λ/2π)φ: which is exactly the phase shift given by the transport equa­ tion as described by the imaginary part in ITL Eq. (9). Hence this experimental setup can be described as a lateral shear interferometer although the authors claimed they had no recourse to interferometry. (2) The grating may be considered as a 1-D Hartmann mask. Light rays going through the slits propagate at an angle W/ x which over a distanceΔZproduces a shift of the periodic pattern by an amount ( W/ x) z, i.e., a phase shift given by Eq. (2). This shows that there is no real difference between Hartmann sensor and a lateral shear interferometer other than in the interpretation. An important consequence is that Fourier transform tech­ niques developed by Takeda et al.5 and Roddier et αl.6,7 to process interferograms and used in the ILT experiment also apply to Hartmann data. Such an application would consid­ erably increase the dynamic range—hence the spatial resolu­ tion—of Hartmann sensors. Indeed current centroiding methods require the absolute displacement of Hartmann spots to be...