An adaptive constraint algorithm for image understanding of digitally reconstructed in-line holograms

Abstract

Accurate quantitative decoding of the 3D information encoded in in-line holograms, at best difficult optically, may be achieved by A/D sampling of the hologram followed by digital reconstruction. Using standard reconstruction technique, the resulting image bandwidth is limited by the size of the hologram. In addition, the phase ambiguity inherent in magnitude-only hologram recording yields, along with the desired object reconstruction, an out-of-focus conjugate artifact called the twin image. Both limited bandwidth and twin image restrict the available resolution well below the theoretical diffraction limit. In this paper an algorithm is presented which addresses both problems by iteratively combining phase retrieval and spectrum continuation to produce estimates of the phase of the recorded hologram, and both magnitude and phase of the hologram beyond its physically recorded boundaries.Since algorithms based on spectral continuation are sensitive to the constraints imposed on the extent of the objects being imaged (which must be space limited), a method for selecting these constraints adaptively was developed. Effective use of adaptive constraints greatly accelerates convergence of the algorithm compared to fixed constraints. The chosen adaptive constraint selection rule is shown to have an error-cmecting property in which over-constraint is naturally corrected and the constraint set boundaries stably relax toward the actual object boundaries. Examples demonstrate the degree of improvement in resolution over conventional reconstruction, and over reconstruction with phase retrieval only. This algorithm suggests the possibility of super-resolution holography, in which the diffraction limit is exceeded. While difficult to achieve in practice, super-resolution has been demonstrated for other kinds of imaging but not heretofore considered for holography.

Orientation and Pair Correlation at High Density by Superresolution Holography

“…For a full derivation and description of ACT, the reader is directed to references [7] and [8]. We conclude this section with two examples illustrative of the relative performance of ACT compared to previous algorithms in the case of closely juxaposed particles.…”

“…As density increases, since the region of significant suport of each particle extents many times farther than the real image of the particle, images on the hologram plane begin to encroach upon one another. At high density it becomes impossible to resolve individual particles using conventional optical technique, or even using the more accurate digital techniques developed previously in the Principal Investigator's laboratory [2]- [7], with accuracy commensurate with the quantitative high density configurational studies whose feasibility is the subject of this investigation.…”

“…As density increases, since the region of significant suport of each particle extents many times farther than the real image of the particle, images on the hologram plane begin to encroach upon one another. At high density it becomes impossible to resolve individual particles using conventional optical technique, or even using the more accurate digital techniques developed previously in the Principal Investigator's laboratory [2]- [7], with accuracy commensurate with the quantitative high density configurational studies whose feasibility is the subject of this investigation.Thus the present effort was focused on prototyping of digital hologrammetry technique permitting the enhanced suppression of twin image artifact in the high density regime where both optical technique and previous algorithms fail. Algorithms which iteratively combine phase retrieval and spectral continuation are sensitive to the constraints imposed on the physical extents of the objects (particles) being imaged.…”

“…Though not without its limitations, this algorithm succeeds in extending the quantitative usefulness of in-line holography to the desired regime. Moreover, by careful selection of the parameters of the algorithm the computational costs associated with the resolution enhancement are small.For a full derivation and description of ACT, the reader is directed to references [7] and [8]. We conclude this section with two examples illustrative of the relative performance of ACT compared to previous algorithms in the case of closely juxaposed particles.…”

Direct Measurement of Pair Correlation in Model Aerosols

“…Under a variety of conditions a multidimensional signal may be reconstructed from partial information about its transform, for instance its Fourier or Fresnel transform [1][2][3][4]. While the ability to reconstruct a signal from magnitude information only would be useful in several applications settings,[ 5 -91 magnitude alone is not in general sufficient to reconstruct a signal.…”