On-axis conoscopic holography without a conjugate image

Abstract

We present a method for removing the conjugate image in an incoherent-light holographic technique, namely, on-axis conoscopic holography. The point-spread function that we obtain is that of a complex Gabor zone pattern, which thus should allow good-quality reconstructions of objects. Experimental results are also presented, which confirm the validity of this method.Conoscopic holography is a recent incoherent-light holographic technique first presented in 1985 (Ref. 1) that is based on the propagation of light in a birefringent medium. The basic setup is shown in Fig. 1: a uniaxial crystal (C) is sandwiched between two circular polarizers (P1, P2). A lens images the object-here a point source-into the system. When the monochromatic light from the image (S) of the point source passes through the crystal and the two polarizers, a Gabor zone pattern (GZP) is observed at the output; it is the result of the velocity disparity between the ordinary and the extraordinary waves in the crystal. This interference pattern can be recorded on a photographic plate and reconstructed optically' both coherently and incoherently. It can also, as in Ref. 2 and this Letter, be recorded on a CCD camera and digitized in a microcomputer for a numerical reconstruction of the image and the shape of the object. Such patterns thus are referred to as holograms.In the on-axis (or in-line) configuration, the crystal axis is parallel to the geometrical axis, Oz, of the system, and the point-spread function (PSF), say H +, is a real GZP plus a bias. For a complete object, the hologram is the incoherent superposition of the GZP of each point.The two major problems in the reconstruction of the original object are the bias and the conjugate image. The bias is a usual drawback of incoherent holography; this problem has been solved 2 ' 3 by inserting an electrically driven half-wave plate [a liquid-crystal light valve (LCLV)] after the first circular polarizer so as to change its handedess (e.g., from right to left handed), thus providing us with a second PSF, which we denote Hcg. By calculating numerically the difference between the holograms obtained with each impulse response, we obtain a real GZP without bias, Hc = H+ -Hc. These H-(xy) = COS[fr(Xwhere x and y are the coordinates in the recording plane and fr is the Fresnel parameter, a scale factor that depends on the distance between the point and the recording plane. The exact expression of fr can be found in Ref.4, but it is not needed here. It is well known that the cosine in Hc can be decomposed into two exponentials, corresponding to the virtual image and to the conjugate real image of the point, 5 which, from an algorithmic point of view, is due to the fact that the real GZP Hc has zeros in the Fourier domain, whereas a phase GZP has none. We address here the remaining problem, namely, the elimination of the conjugate image. The configurations used until now to remove it are (i) the quasi-complex configuration, 2 3 in which one of the polarizers is changed from circular to linear, whose...

Conoscopic holograms analysis using variations of the Hough transform

“…The image is processed using a Gaussian low pass filter, which reduces smoothens out the present noise. The filtering process replaces the liquid crystal light valve used to produce a conjugate image for noise elimination (Mugnier and Sirat, 1992). Histogram equalization: The image resulting from application of the Gaussian filter has grey levels that require readjustment.…”

Conoscopic holography: toward three-dimensional reconstructions of opaque objects

“…8,9 In conoscopic holography, there are efficient ways to remove both the bias 5,10 and the conjugate image. 11 These improvements are based on numerical combination of different system PSF's, each of them being obtained by an adequate change in the input polarization state 1with a liquid-crystal light valve2 and modulation of the amplitude of the incident light field 1with a rotating mask; see Ref. 112.…”

Analysis of Effect of Phase Error Sources of Polarization Components in Incoherent Triangular Holography

“…Mugnier and Sirat [4] suggested the use of a liquid-crystal light valve and a mask to resolve the bias and twin images. Recently, Poon et al [ 5] proposed a technique that can simultaneously obtain sine and cosine Fresnel holograms to remove twin images.…”