Optimal conditions for using the binary approximation of continuously self-imaging gratings

Abstract

Diffractive Optical Elements (DOE), that generate a propagation-invariant transverse intensity pattern, can be used for metrology and imaging application because they provide a very wide depth of focus. However, exact implementation of such DOE is not easy, so we generally code the transmittance by a binary approximation. In this paper, we will study the influence of the binary approximation of Continuously Self-Imaging Gratings (CSIG) on the propagated intensity pattern, for amplitude or phase coding. We will thus demonstrate that under specific conditions, parasitic effects due to the binarization disappear and we retrieve the theoretical non-diffracting property of CSIG's.

Regularized image reconstruction for continuously self-imaging gratings

“…For practical implementation of a CSIG, binary approximations of the transmittance function have been considered [24]. But even with a binary-coded CSIG, the OTF is composed of sparse delta functions, as shown in Fig.…”

“…In [24], it has been demonstrated that, for an ideal CSIG, the OTF is composed of a central peak of relative weight N, where N is the number of diffracted orders, N peaks of relative weight 1 are located on the cutoff frequency ring, and N 2 ∕2 − N other peaks of relative weight 2 are located inside the cutoff frequency ring. If the CSIG is implemented with a binary grating, the relative weights of all peaks are slightly different from those ideal values.…”

“…This model is an approximation of the sampling process realized by the CSIG, and it allows us to get an estimation of the FOV inside which the image of an object is well sampled by the CSIG. We consider that the mean area around an OTF peak is approximately the area of the OTF divided by the number of OTF peaks [24]. The mean sampling pitch in the FD, represented by b mean , is also defined as the square root of this mean area, which is the mean distance between the neighboring delta functions of the OTF shown in Fig.…”

“…Their imaging properties, such as a large angular tolerance, and implementations with binary gratings have been demonstrated [16][17][18][19][20][21][22][23][24]. It has been shown that one of the advantages of CSIGs compared with diffractive axicons is noise robustness, because the optical transfer functions (OTFs) of CSIGs are composed of multiple delta functions whose heights are larger than that of an axicon's OTF [25].…”

Design rules for IR micro cameras based on a single diffractive optical element

“…8(b), we can deduce that this global intensity pattern is composed by a propagation-invariant term and a propagation-dependant term under monochromatic illumination. Under incoherent and polychromatic illumination, it has been shown, for other self-imaging objects 8,9 , that the propagation-dependant term decreases because of a visibility factor due to the spectrum's width, and can be neglected after the panchromatic distance defined by:…”