Fresnel incoherent correlation holography (FINCH) records holograms under incoherent illumination. FINCH was implemented with two focal length diffractive lenses on a spatial light modulator (SLM). Improved image resolution over previous single lens systems and at wider bandwidths was observed. For a given image magnification and light source bandwidth, FINCH with two lenses of close focal lengths yields a better hologram in comparison to a single diffractive lens FINCH. Three techniques of lens multiplexing on the SLM were tested and the best method was randomly and uniformly distributing the two lenses. The improved quality of the hologram results from a reduced optical path difference of the interfering beams and increased efficiency.
We propose and demonstrate a new concept of incoherent digital holography termed coded aperture correlation holography (COACH). In COACH, the hologram of an object is formed by the interference of light diffracted from the object, with light diffracted from the same object, but that passes through a coded phase mask (CPM). Another hologram is recorded for a point object, under identical conditions and with the same CPM. This hologram is called the point spread function (PSF) hologram. The reconstructed image is obtained by correlating the object hologram with the PSF hologram. The image reconstruction of multiplane object using COACH was compared with that of other equivalent imaging systems, and has been found to possess a higher axial resolution compared to Fresnel incoherent correlation holography.
We present a new method for recording digital Fourier holograms under incoherent illumination. A single exposure recorded by a digital camera is sufficient to record a real-valued hologram that encodes the complete three-dimensional properties of an object. © 2012 Optical Society of America OCIS codes: 090.0090, 090.1995, 110.6880, 100.3010, 070.6120. In recent years we have witnessed noteworthy achievements of incoherent holography techniques such as optical scanning holography [1] and Fresnel incoherent correlation holography (FINCH) [2,3]. The latter has fundamental system robustness since it is based on a single channel incoherent interferometer and because it does not require any scanning or mechanical movement. However, though a single FINCH image contains the complete three-dimensional (3D) information of an object, at least three images are required to solve the twin image problem [4]. In this Letter, we present a new method for recording digital Fourier holograms under incoherent illumination. Fourier holograms [5,6] possess some advantages over Fresnel holograms including, but not limited to, increased space-bandwidth product performance [7,8] and the relatively easy ability to process and manipulate the hologram, since it is captured in the spatial frequency domain. In addition, the hologram is more robust to information loss, as each object point is distributed over the entire hologram plane. Moreover, by recording a Fourier hologram of a half plane (or space), the twin image problem is avoided and the object can be reconstructed from a single exposure. Still, the proposed method maintains many other advantageous characteristics of FINCH [9]. We coin our method Fourier incoherent single channel holography (FISCH). The FISCH system is shown in Fig. 1. A white-light source illuminates a 3D object. Light scattered from the object passes through a band pass filter (BPF), becomes partially temporally coherent, and continues to propagate through a single channel incoherent interferometer. Eventually, interference patterns are captured by the CCD. Consider a point source object of complex amplitude A s positioned at the coordinate x s ; y s ; z s , a distance z s from the lens L 0 . A tilted diverging spherical wave of the form Tx; y; ⃗r s ; z s A s c ⃗r s ; z s L−⃗r s ∕ z s Q1 ∕ z s is induced over the L 0 plane, where ⃗ r s x s ; y s , c ⃗ r s ; z s is a complex valued constant dependent on the position of the point source, and L⃗ s expi2πλ −1 s x x s y y and Qs expiπsλ −1 x 2 y 2 are the linear and the quadratic phase functions, respectively, in which λ is defined as the central wavelength. A diffractive optical element of the form Q−1 ∕ f 1 is displayed on the spatial light modulator (SLM), positioned at a small angle relative to the optical axis. The SLM is polarization sensitive, so by introducing the linear polarizer P1 the single channel optical apparatus is effectively split into two beams (see [10] for a detailed explanation). With one beam the SLM functions as a converging diffractive lens wi...
Abstract:The Lagrange invariant is a well-known law for optical imaging systems formulated in the frame of ray optics. In this study, we reformulate this law in terms of wave optics and relate it to the resolution limits of various imaging systems. Furthermore, this modified Lagrange invariant is generalized for imaging along the z axis, resulting with the axial Lagrange invariant which can be used to analyze the axial resolution of various imaging systems. To demonstrate the effectiveness of the theory, analysis of the lateral and the axial imaging resolutions is provided for Fresnel incoherent correlation holography (FINCH) systems.
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