Thomas H. Barnes

Determination of interferometer phase distributions by use of wavelets

A new technique for directly extracting phase gradients from two-dimensional (2-D) interferometer fringe data is presented. One finds the gradients by tracking the maximum modulus of the continuous wavelet transform of the fringe data and the phase distribution that is obtained, with a small error, by integration. Problems associated with phase unwrapping are thereby avoided. The technique is compared with standard methods, and excellent agreement is found. In common with Fourier-transform methods, the technique is capable of extracting the full 2-D phase distribution from a single image.

Phase-only modulation using a twisted nematic liquid crystal television

We used a commercially available liquid crystal television display unit as a spatial optical phase-only modulator. To do this, we removed the integral polarizers from the unit and double passed the light under modulation through it. We found that it was possible to obtain continuous phase modulation from 0 to PI with essentially no change in the state of polarization of the output light and absorption changes of <2.5%. We wrote computer-generated phase-only holograms on the LCTV and reconstructed them optically.

Adaptive wave-front correction by means of all-optical feedback interferometry

A novel adaptive wave-front correction system based on an all-optical feedback interferometer is described. In this system the two-dimensional output fringe intensity from a Mach-Zehnder interferometer with large radial shear is optically fed back to an optically addressed phase-only liquid-crystal spatial light modulator. Consequently, without a separate aberration-free reference wave, the modulator phase approximates the conjugate of the interferometer phase that is directly related to the phase of the input aberrated wave front, so this system is applicable in adaptive optics. We successfully achieved real-time correction of aberrated wave fronts: A diffraction pattern that was seriously distorted because of aberrations was transformed into a diffraction-limited spot immediately after the feedback loop was closed.

Reconfigurable free-space optical interconnections with a phase-only liquid-crystal spatial light modulator

A range of space-invariant and space-variant holographic optical interconnections are demonstrated with the aid of a nematic liquid-crystal panel that is capable of nearly continuous phase modulation. Results on fan-out, nearest-neighbor/next-nearest-neighbor interconnects, and 8-bit perfect shuffle are presented. The diffraction efficiencies are close to 15% of incident light in all cases.

Surface-profile measurement by means of a polarization Sagnac interferometer with parallel optical feedback.

We describe a novel feedback interferometer for real-time, unambiguous measurement of surface profiles that consists of a polarization Sagnac interferometer and an optically addressed phase-only spatial light modulator. In this system the output intensity from the Sagnac interferometer is optically fed back to the phase modulator placed in one arm of the interferometer, which produces a sawtooth fringe intensity profile (instead of the conventional cosinusoidal one) that is directly and unambiguously related to the surface profile. Preliminary experimental results demonstrate the feasibility of applying this system to surface-profile measurement.

Focal-length measurement by multiple-beam shearing interferometry.

The application of multiple-beam shearing interferometry to lens focal-length measurement is described. A coated shearing plate interferometer was used in transmission to produce sharp multiple-beam fringes that rotate as the collimation of the incoming wave front from the lens under test changes. The test lens was used to collimate light from a point source that was translated longitudinally, and the focal length was determined from the rate of rotation of the fringes as the source moved. This method is simple, accurate, and lends itself to automatic determination of focal length.

Analysis of a joint transform correlator using a phase-only spatial light modulator

A theoretical analysis of a joint transform correlator that uses a phase-only spatial light modulator to input joint transform plane intensity data into the second Fourier transform system is presented. It is shown that this correlator produces signals that differ from, but are related to, the mathematical correlation between the test and reference input images. An undesirable characteristic of the correlator is that the form of the output signals depends on both the intensity-to-phase transfer characteristic of the phase modulator and the intensities of the input images. However, apodization of the joint transform intensity distribution by the reciprocal of the intensity distribution of the reference image Fourier transform can overcome this problem, and results in a correlator with narrow matching output peaks and high discrimination, in which the autocorrelation peak can be eliminated. Theoretical results are demonstrated by computer simulation.

Grating interferometer with extremely high stability, suitable for measuring small refractive index changes.

We describe here a grating interferometer with extremely high stability and which can be used as a differential refractometer. The instrument uses heterodyne techniques to achieve high sensitivity. We present an analysis of the operation of the system and results which show that it has a long term stability of the order of 1/1500 wavelength over 2 h.

Adaptive restoration of a partially coherent blurred image using an all-optical feedback interferometer with a liquid-crystal device

A liquid-crystal adaptive optics system using all-optical feedback interferometry is applied to partially coherent imaging through a phase disturbance. A theoretical analysis based on the propagation of the cross-spectral density shows that the blurred image due to the phase disturbance can be restored, in principle, irrespective of the state of coherence of the light illuminating the object. Experimental verification of the theory has been performed for two cases when the object to be imaged is illuminated by spatially coherent light originating from a He-Ne laser and by spatially incoherent white light from a halogen lamp. We observed in both cases that images blurred by the phase disturbance were successfully restored, in agreement with the theory, immediately after the adaptive optics system was activated. The origin of the deviation of the experimental results from the theory, together with the effect of the feedback misalignment inherent in our optical arrangement, is also discussed.

Joint Transform Correlator Using a Phase Only Spatial Light Modulator

A Joint Transform Optical Correlator is described which uses a phase only spatial light modulator for input of the Joint Transform plane information into the second stage of the correlator. This, combined with suitable apodizing of the Joint Transform plane intensity distribution, brings several advantages including high optical efficiency, good signal-to-noise ratio, and the ability to correct system aberrations.