In holography, spatially dependent amplitude and phase information about an unknown signal is encoded in an intensity image by means of interference with a known reference wave. In analogy with methods developed for radar, we introduce synthetic optical holography (SOH) for quantitative, phase-resolved imaging. In SOH, the reference wave of a digital hologram is defined point by point, uniquely combining technical simplicity, fast phase imaging and broadband operation from visible to terahertz frequencies within a single setup. To illustrate the advantage of SOH, we use it in conjunction with a scattering-type near-field optical microscope to perform near-field holography, improving the speed of operation by more than an order of magnitude while significantly simplifying the experiment. OCIS codes: (090.1995) Digital holography; (170.5810) Scanning microscopy.
BackgroundHolography [1] provides a straightforward way to encode amplitude and phase information about an unknown field in an intensity measurement. In digital Fourier holography, [2] the image of an unknown object field is superimposed on a known planar reference wave of the form U r = Ae ik·r on a CCD, where k is the wavevector with magnitude k = 2π/λ . The intensity on the CCD can then be expressed in the spatial Fourier domain aswhere the tilde indicates the Fourier transform with respect to position, δ is the Dirac delta function, C = |Ũ S | 2 , and k is the in-plane component of the wavevector. The first two terms of this equation are centered at q = 0, and contain no phase information. The last two terms are offset from the origin by q = ± k respectively. Either of these terms may be filtered out, shifted to the origin, and inverse Fourier transformed to retrieve the object field with reduced spatial bandwidth compared to the original intensity data. This holographic technique constrains us to use plane wave references that can be physically produced using far-field optics. The radar community developed an analogous concept [3] that instead assembles a hologram pointwise using a local electronic oscillator as a reference to avoid the impossible task of physically interfering the object field with a similarly scaled reference. We here introduce synthetic optical holography (SOH) [4], which uses a similar concept to produce an optical digital hologram. This is desirable in cases where an appropriate reference field is inconvenient or impossible to produce using conventional optics.
Synthetic Optical HolographyFigure 2(a) is a sketch of a basic synthetic optical holography setup. Coherent light is focused on a sample, which back-scatters light with unknown amplitude and phase into a Michelson interferometer, where it is combined with a planar reference to give a single intensity measurement on a point detector. As the sample is translated to address each transverse coordinate, the reference phase is changed linearly, typically by translating the reference mirror with a peizoelectric device. The resulting equivalent reference field can be described as a...