Abstract
We introduce a generalization of Fourier transform holography that allows the use of the boundary waves of an extended object to act as a holographic-like reference. By applying a linear differential operator on the field autocorrelation, we use a sharp feature on the extended reference to reconstruct a complex-valued image of the object of interest in a single-step computation. We generalize the approach of Podorov et al. [Opt. Express 15, 9954 (2007)] to a much wider class of extended reference objects. Effects of apertures in Fourier domain and imperfections in the reference object are analyzed. Realistic numerical simulations show the feasibility of our approach and its robustness against noise.
Highlights
Techniques that are able to form images without the use of lenses or mirrors have been developed and have found a wide range of applications in the optical regime
Fourier transform holography is a non-iterative lensless imaging technique in which a complex-valued image may be reconstructed in a single-step deterministic computation [1, 2]
Let us assume that we selected an extended reference and a linear differential operator, L (n) {·}, such that when we apply the latter onto r(x, y) we get the sum of a point Dirac delta function at (x0, y0) and some other function, namely, L (n) {r(x, y)} = Aδ (x − x0)δ (y − y0) + g(x, y), (4)
Summary
Techniques that are able to form images without the use of lenses or mirrors have been developed and have found a wide range of applications in the optical regime. Fourier transform holography is a non-iterative lensless imaging technique in which a complex-valued image may be reconstructed in a single-step deterministic computation [1, 2] This is achieved by placing a coherent point source at an appropriate distance from the object and having the object field interfere with the reference wave produced by this point source at the detector plane. For x-ray applications, the resolution for holography is typically limited by the size and quality of the point-like source that needs to be placed in the vicinity of the object [10, 18, 19] This approach requires a higher transverse coherence on the illuminating beam than phase retrieval, since the object field and the point-like source have to satisfy the holographic separation condition and still interfere [2]. Received 5 Oct 2007; revised 29 Nov 2007; accepted 1 Dec 2007; published 11 Dec 2007 24 December 2007 / Vol 15, No 26 / OPTICS EXPRESS 17595
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