Katherine Creath

Phase-shifting speckle interferometry

Speckle patterns have high frequency phase data, which make it difficult to find the absolute phase of a single speckle pattern; however, the phase of the difference between two correlated speckle patterns can be determined. This is done by applying phase-shifting techniques to speckle interferometry, which will quantitatively determine the phase of double-exposure speckle measurements. The technique uses computer control to take data and calculate phase without an intermediate recording step. The randomness of the speckle causes noisy data points which are removed by data processing routines. One application of this technique is finding the phase of deformations, where up to ten waves of wavefront deformation can easily be measured. Results of deformations caused by tilt of a metal plate and a disbond in a honeycomb structure brazed to an aluminum plate are shown.

Extended averaging technique for derivation of error-compensating algorithms in phase-shifting interferometry

Phase-shifting interferometry suffers from two main sources of error: phase-shift miscalibration and detector nonlinearity. Algorithms that calculate the phase of a measured wave front require a high degree of tolerance for these error sources. An extended method for deriving such error-compensating algorithms patterned on the sequential application of the averaging technique is proposed here. Two classes of algorithms were derived. One class is based on the popular three-frame technique, and the other class is based on the 4-frame technique. The derivation of algorithms in these classes was calculated for algorithms with up to six frames. The new 5-frame algorithm and two new 6-frame algorithms have smaller phase errors caused by phase-shifter miscalibration than any of the common 3-, 4- or 5-frame algorithms. An analysis of the errors resulting from algorithms in both classes is provided by computer simulation and by an investigation of the spectra of sampling functions.

Step height measurement using two-wavelength phase-shifting interferometry

Two-wavelength phase-shifting interferometry is applied to an interference phase-measuring microscope enabling the measurement of step features. The surface is effectively tested at a synthesized equivalent wavelength lambda(eq) = lambda(a)lambda(b)/| lambda(a) - lambda(b)| by subtracting phase measurements made at visible wavelengths lambda(a) and lambda(b). The rms repeatability of the technique is lambda/1000 at the equivalent wavelength. To improve the precision of the data, the phase ambiguities in the single-wavelength data are removed using the equivalent wavelength results to determine fringe orders. When this correction is made, a measurement dynamic range (feature height/rms repeatability) of 10(4) is obtainable. Results using this technique are shown for the measurement of an optical waveguide and a deeply modulated grating.

Basics of Interferometry

Chapter 1: Introduction Chapter 2: Interference: A Primer Chapter 3: Two-Beam Interferometers Chapter 4: Source-Size and Spectral Effects Chapter 5: Multiple-Beam Interference Chapter 6: The Laser as a Light Source Chapter 7: Photodetectors Chapter 8: Measurements of Length Chapter 9: Optical Testing Chapter 10: Digital Techniques Chapter 11: Macro- and Micro-Interferometry Chapter 12: White-Light Interference Microscopy Chapter 13: Holographic and Speckle Interferometry Chapter 14: Interferometric Sensors Chapter 15: Interference Spectroscopy Chapter 16: Fourier-Transform Spectroscopy Chapter 17: Interference with Single Photons Chapter 18: Building an Interferometer Appendix A: Monochromatic Light Waves Appendix B: Phase Shifts on Reflections Appendix C: Diffraction Appendix D: Polarized Light Appendix E: The Pancharatnam Phase Appendix F: The Twyman-Green Interferometer: Initial Adjustment Appendix G: The Mach-Zehnder Interferometer: Initial Adjustment

Vibration-observation techniques for digital speckle-pattern interferometry

Vibration observation is a major application of digital speckle-pattern interferometry (DSPI), which is a variation on electronic speckle-pattern interferometry (ESPI). DSPI processes speckle patterns in a computer rather than with a frame grabber and analog electronics as in ESPI. A new method of observing vibration fringes is presented and compared with existing techniques as well as some variations on them. Fringe contrast and signal-to-noise ratio are used as a means of comparison since these quantities are dependent on the techniques used. This new technique involves continuously subtracting a reference frame containing only self-interference terms and no cross interference term from the time-averaged data frames of the vibrating object. This reference frame is created by vibrating a reference mirror at a high amplitude while the object is at rest. Comparisons of calculated fringe contrast with four other observation methods show that this method yields extremely good fringe contrast. Experimental results are shown for this new technique as well as for the most commonly used vibration-observation technique. These results show that the new technique is far superior to all the other methods for moderately unstable objects, which may slowly drift or deform in time.

Window function influence on phase error in phase-shifting algorithms

We present five different eight-point phase-shifting algorithms, each with a different window function. The window function plays a crucial role in determining the phase (wavefront) because it significantly influences phase error. We begin with a simple eight-point algorithm that uses a rectangular window function. We then present alternative algorithms with triangular and bell-shaped window functions that were derived from a new error-reducing multiple-averaging technique. The algorithms with simple (rectangular and triangular) window functions show a large phase error, whereas the algorithms with bell-shaped window functions are considerably less sensitive to different phase-error sources. We demonstrate that the shape of the window function significantly influences phase error.

Calibration of numerical aperture effects in interferometric microscope objectives

The numerical aperture (N.A.) of a microscope objective can affect the measurement of surface profiles. Large N.A. objectives measure smaller heights than the actual values. An experiment to calibrate these effects on objectives with N.A.s of 0.1-0.95 is described using four traceable step height standards and a computer-controlled interferometric optical profiler utilizing phase-measurement interferometry techniques. The measured N.A. scaling factors have good agreement with a theory developed by Ingelstam. N.A. scaling factors are determined to an uncertainty of +/- 1% for N.A.s </=0.5 and +/- 2% for N.A.s >/=0.9.

Contouring Aspheric Surfaces Using Two-wavelength Phase-shifting Interferometry

Two-wavelength holography and phase-shifting interferometry are combined to measure the phase contours of deep wavefronts and surfaces, such as those produced by aspherics, with a variable sensitivity. When interference fringes are very closely spaced, the phase data contain high frequencies where 2 ~ ambiguities cannot be resolved. In this technique, the surface is tested at a synthesized longer equivalent wavelength. The phase of the wavefront is calculated modulo 2φ using phase-shifting techniques at each of two visible wavelengths. The difference between these two phase sets is the phase of the wavefront as it would be measured at λeq=λ1λ2/|λ1 − λ2 |, assuming that 2π ambiguities can be removed at λeq. This technique enables surfaces to be contoured to an accuracy of λeq/100.

Comparison Of Phase-Measurement Algorithms

Phase-measurement algorithms for calculating the phase of a wavefront from interference fringe data are compared. Experimental data show that different algorithms yield different phase values when using the same intensity data. A computer simulation of errors due to phase-shifter miscalibration and nonlinearity, as well as detector nonlinearity is performed to show that certain algorithms are more sensitive to some errors than others. Dependences of each of these errors is found versus percent of error over a 2ic range of phase values. These results enable the determination of what system errors are present in a phase-measurement interferometer.

Liquid-Crystal Point-Diffraction Interferometer for Wave-Front Measurements

A new instrument, the liquid-crystal point-diffraction interferometer (LCPDI), is developed for the measurement of phase objects. This instrument maintains the compact, robust design of Linniks point-diffraction interferometer and adds to it a phase-stepping capability for quantitative interferogram analysis. The result is a compact, simple to align, environmentally insensitive interferometer capable of accurately measuring optical wave fronts with very high data density and with automated data reduction. We describe the theory and design of the LCPDI. A focus shift was measured with the LCPDI, and the results are compared with theoretical results.