Olof Bryngdahl

Single-Sideband Holography*

In making in-line holograms of amplitude objects with a strong background, the single-sideband technique can be used to improve the quality of the reconstruction. The main advantage of this method is the suppression of the twin image. Modifications of the same technique are also presented for making holograms of complex objects and objects with a weak background.

Nonlinear Effects in Holography

The ideal photographic material in holography would have a linear relationship between amplitude transmittance and exposure. Here we study the case where this relationship can be described instead by a polynomial. This nonlinearity in reconstruction gives rise to some extra images, autocorrelations, autoconvolutions, and ambiguity functions of the object, which may be found superposed on normal images, or spatially separated both laterally and in depth.

Holography with Evanescent Waves

Information contained in evanescent wave fields was recorded by holographic techniques. Internal reflection within a highly refractive liquid was used to create evanescent surface waves in the emulsion of immersed high-resolution photographic plates. The holograms have unique properties. When reconstructed by an evanescent wave, two mirror images of the same kind were formed; however, two conjugate images were obtained by reversing the direction of the surface wave. Although the holograms are very thin with fringes confined to the surface of the emulsion, they reconstruct in white light and exhibit frequency-selection properties similar to thick holograms.

Shearing Interferometry by Wavefront Reconstruction

Lately, practical applications for holographic techniques have been found in interferometry. These techniques are usefully applied to shearing interferometry. Different kinds of shear are treated, and in several cases the optical system is significantly simplified, compared to the corresponding conventional setups. Both zero-order (no tilt) and multiple-fringe (tilt between wavefronts) interferograms can he achieved, as well as a simple method for displaying the second derivative of phase variation in an object. Experimental results of holographic shearing interferometry are shown.

A Lateral Wavefront Shearing Interferometer with Variable Shear

A lateral wavefront shearing interferometer is presented. Two diffraction gratings are used as beam splitters in the Fraunhofer planes of two successive image forming systems. Each diffraction order of the first grating forms an image of the object in an intermediate image plane. These are completely separated from each other, so that all but two can be blocked out. Then the second grating, together with the second image forming system, creates two partially overlapping sets of images of the two passing intermediate images. A variable lateral shear between these two sets is achieved by rotation of the gratings in opposite senses. The principle of this shearing interferometer has been experimentally verified. It can be simplified by folding so that only one grating and one image forming system are needed. Furthermore, a sine wave generator using an generator using an extended, polychromatic source is presented which is built on this principle.

Shearing Interferometry with Constant Radial Displacement

A type of shearing interferometry is presented in which a constant shear is introduced in the radial direction. For small shear, the interferogram displays the radial phase derivative of the wave front under test. The interferometer can be realized with axicon or circular-grating arrangements and seems useful for studying objects with cylindrical or circular geometry.

One-Dimensional Holography with Spatially Incoherent Light*

In previous attempts to record holograms of incoherent objects, the fringe contrast has been quite low, often barely exceeding the photographic grain noise. A method is presented which improves the fringe contrast by allowing only a limited number of object points to contribute to any local fringe pattern in the hologram. The number of object points is reduced by taking the holographic transformation in only one direction while imaging the object onto the hologram plane in the orthogonal direction, using an astigmatic lens system. An interferometric device divides the wavefront and inverts one leg about a line in the imaging direction. The interference patterns from corresponding points are then incoherently superimposed on the hologram. Some experimental results are shown. The objects were illuminated with spatially incoherent light; a rotating diffuser was introduced in a laser beam.

Reversed-Radial-Shearing Interferometry*

A type of shearing interferometry is presented in which the wave front under test interferes with a radially reversed replica of itself. The radial reversal of the wave front can be achieved either by an axicon–lens system or by use of a circular grating. Experimental verification is shown.

Holographic Compensation of Motion Blur by Shutter Modulation

Ordinarily, in photographic recording, the shutter is opened for a finite time which can be described by a rectangular shutter function (= flux as a function of time). Such a shutter function, in connection with linear image motion, creates a degradation due to motion blur. If the shutter modulates the flux by a function cos2 (t2), a recording is obtained that has the properties of an incoherent one-dimensional hologram. Hence, compensation of motion blur is achieved by reconstructing a sharp image from the hologram. This method can be modified in order to cope with harmonic vibrational or random translational motion.

Multiple-Beam Interferometry by Wavefront Reconstruction

A method is presented for producing multiple-beam interferograms by using holographic techniques. A conventional image hologram of the object under test is processed in such a way that nonlinearities are introduced. Then, in the reconstruction process, several reconstructed images of the object with successively amplified phase will arise from the consecutive diffraction orders. These images are made to superpose and form the multiple-beam interferogram by illuminating the hologram with an appropriate set of illuminating beams. The method is useful for testing optical surfaces and systems as well as in studies of refractive-index variations in transparent objects. One of the advantages of the method is that multiple-beam Fizeau fringes can be obtained from a non-reflecting object with a single light passage through the object.