A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

We designed an optical‐digital system that delivers near-diffraction-limited imaging performance with a large depth of field. This system is the standard incoherent optical system modified by a phase mask with digital processing of the resulting intermediate image. The phase mask alters or codes the received incoherent wave front in such a way that the point-spread function and the optical transfer function do not change appreciably as a function of misfocus. Focus-independent digital filtering of the intermediate image is used to produce a combined optical‐digital system that has a nearly diffraction limited point-spread function. This high-resolution extended depth of field is obtained through the expense of an increased dynamic range of the incoherent system. We use both the ambiguity function and the stationary-phase method to design these phase masks.

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Extended depth of field through wave-front coding

Generation of high-order Bessel beams by use of an axicon

Despite the rapid progress in optical imaging, most of the advanced microscopy modalities still require complex and costly set-ups that unfortunately limit their use beyond well equipped laboratories. In the meantime, microscopy in resource-limited settings has requirements significantly different from those encountered in advanced laboratories, and such imaging devices should be cost-effective, compact, light-weight and appropriately accurate and simple to be usable by minimally trained personnel. Furthermore, these portable microscopes should ideally be digitally integrated as part of a telemedicine network that connects various mobile health-care providers to a central laboratory or hospital. Toward this end, here we demonstrate a lensless on-chip microscope weighing ∼46 grams with dimensions smaller than 4.2 cm × 4.2 cm × 5.8 cm that achieves sub-cellular resolution over a large field of view of ∼24 mm2. This compact and light-weight microscope is based on digital in-line holography and does not need any lenses, bulky optical/mechanical components or coherent sources such as lasers. Instead, it utilizes a simple light-emitting-diode (LED) and a compact opto-electronic sensor-array to record lensless holograms of the objects, which then permits rapid digital reconstruction of regular transmission or differential interference contrast (DIC) images of the objects. Because this lensless incoherent holographic microscope has orders-of-magnitude improved light collection efficiency and is very robust to mechanical misalignments it may offer a cost-effective tool especially for telemedicine applications involving various global health problems in resource limited settings.

/pdf/compact-light-weight-and-cost-effective-microscope-based-on-5ei326xa63.pdf

Compact, light-weight and cost-effective microscope based on lensless incoherent holography for telemedicine applications

Publisher Summary This chapter describes the self-imaging phenomenon and its applications. The self-imaging phenomenon requires a highly spatially coherent illumination. It disappears when the lateral dimensions of the light source are increased. When the source is made spatially periodic and is placed at the proper distance in front of the periodic structure, a fringe pattern is formed in the space behind the structure. The chapter discusses the theoretical and applicational aspects of the self-imaging phenomenon—that is, the property of the Fresnel diffraction field of some objects illuminated by a spatially coherent light beam. The applications of self-imaging are summarized in four main groups—namely, (1) image processing and synthesis, (2) technology of optical elements, (3) optical testing, and (4) optical metrology. The chapter describes the double diffraction systems using spatially incoherent illumination. The first periodic structure plays the role of a periodic source composed of a multiple of mutually incoherent slits. Depending on whether the periods of two periodic structures are equal, the Lau or the generalized Lau effect is discussed. Various applications of incoherent double-grating systems are described in the fields of optical testing, image processing, and optical metrology. After examining some cases of coherent and incoherent illumination, the general issue of spatial periodicities of optical fields and its relevance to the replication of partially coherent fields in space is discussed.

I The Self-Imaging Phenomenon and its Applications

The ambiguity function as a polar display of the OTF

We propose a method for designing apodizers that increase the depth of focus and reduce the influence of spherical aberration. These two properties are explicitly manifested in computer-generated pictures and values of the Strehl ratio for variable spherical aberration.

Annular apodizers for low sensitivity to defocus and to spherical aberration.

We show that a zone plate with a prespecified number of foci, which are separated axially by Rayleigh’s limit of resolution, can create an arbitrarily high focal depth when used as an apodizer over an otherwise clear aperture. We discuss the resolution and light gathering power of this method.

Zone plate for arbitrarily high focal depth

We present a family of asymmetric phase masks that extends the depth of field of an optical system. To verify our proposal, we compute several modulation transfer functions with focus errors, and we report numerical simulations of the images that can be achieved by use of our proposed procedure.

Asymmetric phase masks for extended depth of field

We explore the use of phase profiles with fractional power for tailoring modulation transfer functions with high focal depth at high pupil apertures. We present numerical simulations of the images that can be obtained with certain fractional-power profiles.

Jorge Ojeda-Castaneda

Papers

The ambiguity function as a polar display of the OTF

Annular apodizers for low sensitivity to defocus and to spherical aberration.

Zone plate for arbitrarily high focal depth

Asymmetric phase masks for extended depth of field

High focal depth with fractional-power wave fronts