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A lateral-shearing interferometer with a pair of double Fresnel rhombs is proposed. Use of Fresnel rhombs enables us to accomplish simultaneously lateral shearing and achromatic nulling. Nulling interferometry with lateral shearing is one of the basic methods for searching directly for extrasolar planets with a segmented-mirror telescope. Here the Thirty-Meter Telescope is considered as a model of a segmented-mirror telescope. Our computer simulations show high extinction for the K-band (2.0-2.4 μm). Optical experiments are conducted to verify the lateral shearing and nulling with a pair of double Fresnel rhombs.

We propose a common-path lateral-shearing nulling interferometer for direct detection of exoplanets. A Savart plate is placed between crossed polarizers to produce a lateral shear and realize fully achromatic and highly stable nulling interference for starlight. We construct a double-shearing interferometer using two Savart plates for implementing orthogonal x and y shears. A laboratory demonstration is carried out using a broadband light source with a bandwidth of Δλ/λ(0)=0.33 (Δλ=0.2 μm and λ(0)=0.6 μm). As a result, achieved extinction levels are 4 × 10(-4) at peak and 4 × 10(-7) at 10λ(0)/D(L) (D(L) is the diameter of a Lyot stop).

A shift-and-add (SAA) method is used to restore atmospherically degraded images. The operation of the SAA method is simple, but the deconvolution method of SAA images remains to be developed, especially for extended objects. We propose to deconvolve a SAA image of an extended object by use of a self-deconvolving data reconstruction algorithm (SeDDaRA). Computer simulations show the effectiveness of the SeDDaRA to SAA images. It is also shown that use of the SAA method after each data frame is self-deconvolved leads to a better reconstruction.

A nulling stellar coronagraph based on polarization interferometry is proposed that has achromatic characteristics. The principle and the optical setup of the nulling stellar coronagraph are described. Experimental results with monochromatic and white light show the usefulness of the proposed method. A liquid-crystal device is used as a four-quadrant polarization mask, which is the key element of a polarization interferometric stellar coronagraph.

Nulling interferometry is a method of detecting a faint source near a bright one, in which destructive interference is realized for the light from the bright source. A nulling interferometer that makes use of geometric phase (Pancharatnam phase) is proposed. An experimental setup is constructed to simulate a stellar interferometer with geometric-phase modulation. We attained extinction of 6 x 10(-5) in white light.

A superresolution method is presented with a conjugate-gradient procedure under a nonnegativity constraint. The method is based on the property of a nonnegative object that its band-limited spectrum is the autoconvolution of a spectrum with a half-band limit, and the method is capable of doubling the band limit of an image. Computer simulations are conducted to investigate the performance of the present method.

It is shown that a band-limited spectrum of a nonnegative object can be represented as the autoconvolution of a spectrum whose cutoff frequency is half of the band limit. This permits spectral-magnitude-only reconstruction with a nonnegativity constraint without a support constraint. A magnitude-only reconstruction method using a conjugate-gradient procedure is developed and is investigated by computer simulations.

Projected specklegrams are used for spectroscopy with high spatial resolution under atmospheric turbulence. One-dimensional peak tracking allows one to realize high throughput and simple real-time operation for speckle spectroscopy. Results of simulation experiments are presented, and they confirm the usefulness of the proposed method.

High-resolution imaging with reference to a widely separated star is examined. Peak tracking of the specklegram in the reference channel results in a high-resolution image in the observational channel. A binary star with angular separation of 30.5 arcsec is examined in white light, and the resultant image of the primary star obtained with reference to the secondary star is shown to have better resolution than the centroid tracking image by a factor of 3.

A stellar speckle spectrometer with tip-tilt operation is proposed for high-spatial-resolution spectroscopy under atmospheric turbulence. A specklegram is used to drive a tip-tilt mirror for real-time shift-and-add operation to its dispersed specklegram. The proposed speckle spectroscopy attains a long exposure for the spectrum and a slit spectrometer. Several simulation experiments confirm the effectiveness of our method.

Stellar specklegrams at different wavelengths are examined. The position of the brightest speckle at one wavelength is shown to coincide nearly with that at a widely separated wavelength. The shift-and-add operation for specklegrams at one wavelength produces a high-resolution stellar image at the other wavelength. We show that the shift-and-add operation at 450 nm results in a high-resolution image at 800 nm by use of observational speckle data from which specklegrams at these wavelengths are taken simultaneously.

For restoration of an image degraded with a shift-invariant point-spread function (PSF), partial images segmented from the degraded image are blind deconvolved in parallel for estimation of the common PSF in each partial image. An object function is reconstructed by deconvolution of the whole image with the PSF. A technique for calibrating contamination caused by the segmentation is developed. Results for a computer-generated image and an atmospherically degraded solar image are presented.