Bob F. Oreb

Phase-shifting algorithms for nonlinear and spatially nonuniform phase shifts

In phase-shifting interferometry spatial nonuniformity of the phase shift gives a significant error in the evaluated phase when the phase shift is nonlinear. However, current error-compensating algorithms can counteract the spatial nonuniformity only in linear miscalibrations of the phase shift. We describe an error-expansion method to construct phase-shifting algorithms that can compensate for nonlinear and spatially nonuniform phase shifts. The condition for eliminating the effect of nonlinear and spatially nonuniform phase shifts is given as a set of linear equations of the sampling amplitudes. As examples, three new algorithms (six-sample, eight-sample, and nine-sample algorithms) are given to show the method of compensation for a quadratic and spatially nonuniform phase shift.

Measurement of transient deformations with dual-pulse addition electronic speckle-pattern interferometry

We describe an electronic speckle-pattern interferometry system for analyzing addition fringes generated by the transient deformation of a test object. The system is based on a frequency-doubled twin Nd:YAG laser emitting dual pulses at a TV camera field rate (50 Hz). The main advance has been the automatic, quantitative analysis of dual-pulse addition electronic speckle-pattern interferometry data by the introduction of carrier fringes and the application of Fourier methods. The carrier fringes are introduced between dual pulses by a rotating mirror that tilts the reference beam. The resulting deformation-modulated addition fringes are enhanced with a deviation filter, giving fringe visibility close to that of subtraction fringes. The phase distribution is evaluated with a Fourier-transform method with bandpass filtering. From the wrapped phase distribution, a continuous phase map is reconstructed with an iterative weighted least-squares unwrapper. Preliminary results for a thin plate excited by an acoustic shock show the suitability of the system for the quantitative evaluation of transient deformation fields.

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.

Ultraviolet laser-induced damage on fused silica substrate and its sol-gel coating

A comparative study of the laser-induced damage thresholds (LIDTs) of fused silica substrates and their sol-gel silica coatings was carried out with 355 nm laser irradiation. Chemical etching and superpolishing were employed in different ways to improve the substrate. The laser damage tests showed that the coated substrate was no more susceptible to laser damage than the bare substrate, showing that the substrate quality was the dominant factor limiting the LIDT for UV irradiation. In addition, it was found that high value of substrate microroughness was more harmful to the LIDT of the coated than the bare substrate, and that a proper combination of etching and superpolishing can optimize the LIDT.

Fabrication and testing of a high-precision concave spherical mirror

CSIROs Australian Centre for Precision Optics has recently finished the production of a high-precision concave spherical mirror. The specifications were very ambitious: numerical aperture 0.75; asphericity below 5.5 nm rms and 27.3 nm P-V. The available reference transmission sphere had to be calibrated to enable adequate accuracy. Due to the high numerical aperture of the mirror, sub-aperture measurements had to be stitched together to form a complete surface map of the mirror. Phase-shifting interferometry at high numerical aperture suffers from phase-step non-uniformity because of the large off-axis angles. We present what we believe to be a new interpretation of this phenomenon as a focus error, which clarifies where in the interferometer the phase-shift error occurs. We discuss the ball-averaging method for calibrating the reference transmission sphere and present results from the averaging process to ensure an uncertainty commensurate with the certification requirement. For carrying out the sub-aperture measurements, we constructed a two-axis gimbal mount to swivel the mirror around the focus of the test wavefront. If the centers of curvature of the transmission sphere and the mirror coincide, the mirror can be tilted without losing the interferogram. We present a simple and effective alignment method, which can be generally applied to optical tests where the wavefront comes to a focus. The mirror was coated with protected aluminum and tested in its mount. No effect on the sphericity error from the coating was found, and the specifications were exceeded by approximately 30%. We discuss subtleties of the stitching process on curved surfaces and report final results.

Certification of the full size double corner cube fiducials for the Space Interferometer Mission-PlanetQuest test bed

A full size Double Corner Cube (DCC) assembly was delivered recently to NASAs Space Interferometer Mission (SIM) PlanetQuest testbed at JPL. The DCC was developed at CSIROs Australian Centre for Precision Optics (ACPO) to demonstrate the fabrication of the flight size DCC fiducials. The DCC was assembled from three 30°, high precision ULE glass wedges and a 132 mm diameter base plate. After alignment to sub arc-second angular tolerances, the three wedges were chemically bonded to the base-plate. Comprehensive testing was performed on the assembly to certify the compliance of several parameters including the dihedral angle errors, figure of all reflecting surfaces and the Non Common Vertex Error (NCVE) of the DCC. This paper elaborates on some of the metrology and the certification results of the delivered DCC assembly as well as the chemical bond strength tests.

Position magnifying sensor

This paper describes the application of multiple beam shearing interferometry to a position magnifying sensor. A multiple beam shearing interferometer (MBSI) with a shear plate wedged in the vertical direction produces sharp multiple beam fringes. When the lateral displacement of a point source (which gives rise to the input beam of the MBSI) or its image occurs in the horizontal direction, these fringes move vertically in a magnified manner. This characteristic was used in a position magnifying sensor to detect the displacement of a point image. The advantages of the sensor include a large displacement magnification (more than a hundred times) and a large working distance.

Phase Shifting Algorithms for Non-Sinusoidal Waveforms with Phase Shift Errors

In phase shifting interferometry, phase errors due to harmonic components of a fringe signal can be minimized by applying synchronous phase shifting algorithms with more than four samples. However, when the phase shift calibration is inaccurate, these algorithms cannot eliminate the effects of a non-sinusoidal waveform. It is shown that by taking a number of samples beyond one period of the fringe pattern, phase errors due to the harmonic components of the fringe signal can be eliminated, even when there exists a constant error in the phase shift interval. A general procedure for constructing phase shifting algorithms that eliminate these errors is derived. A seven-sample phase shifting algorithm is derived as an example, in which the effect of the second harmonic component can be eliminated in the presence of a constant error in the phase shift interval.