Phase-Shifting Liquid Crystal Point-Diffraction Interferometry
Microgravity fluid physics experiments frequently measure concentration and temperature. Interferometers such as the Twyman Green illustrated have performed full-field measurement of these quantities. As with most such devices, this interferometer uses a reference path that is not common with the path through the test section. Recombination of the test and reference wavefronts produces interference fringes. Unfortunately, in order to obtain stable fringes, the alignment of both the test and reference paths must be maintained to within a fraction of the wavelength of the light being used for the measurement. Otherwise, the fringes will shift and may disappear. Because these interferometers are extremely sensitive to bumping, jarring and transmitted vibration, they are typically mounted on optical isolation tables. Schlieren deflectometers or the more recent Shack-Hartmann wavefront sensors also measure concentration and temperature in laboratory fluid flows. Ray optics describe the operation of both devices. In a schlieren system, an expanded, collimated beam passes through a test section where refractive index gradients deflect rays. A lens focuses the beam to a filter placed in the rear focal plane of the decollimating lens. In a quantitative color schlieren system, gradients in the index of refraction appear as colors in the field of view due to the action of the color filter. Since sensitivity is a function of the focal length of the decollimating lens, these systems are rather long and filter fabrication and calibration is rather difficult. A Shack-Hartmann wavefront sensor is an array of small lenslets. Typical diameters are on the order of a few hundred microns. Since these lenslets divide the test section into resolution elements, the spatial resolution can be no smaller than an individual lenslet. Such a device was recently used to perform high-speed tomography of heated air exiting a 1.27 cm diameter nozzle. While these wavefront sensors are very compact, the limited spatial resolution and the methods required for data reduction suggest that a more useful instrument needs to be developed. The category of interferometers known as common path interferometers can eliminate much of the vibration sensitivity associated with traditional interferometry as described above. In these devices, division of the amplitude of the wavefront following the test section produces the reference beam. Examples of these instruments include shearing and point diffraction interferometers. In the latter case, shown schematically, a lens focuses light passing through the test section onto a small diffracting object. Such objects are typically either a circle of material on a high quality glass plate or a small sphere in a glass cell. The size of the focused spot is several times larger than the object so that the light not intercepted by the diffracting object forms the test beam while the diffracted light generates a spherical reference beam. While this configuration is mechanically stable, phase shifting one beam with respect to the other is difficult due to the common path. Phase shifting enables extremely accurate measurements of the phase of the interferogram using only gray scale intensity measurements and is the de facto standard of industry. Mercer and Creath 2 demonstrated phase shifting in a point diffraction interferometer using a spherical spacer in a liquid crystal cell as the diffracting object. By changing the voltage across the cell, they were able to shift the phase of the undiffracted beam relative to the reference beam generated by diffraction from the sphere. While they applied this technology to fluid measurements, the device shifted phase so slowly that it was not useful for studying transient phenomena. We have identified several technical problems that precluded operation of the device at video frame rates and intend to solve them to produce a phase-shifting liquid crystal point-diffraction interferometer operating at video frame rates. The first task is to produce high contrast fringes. Since the diffracted beam is much weaker than the transmitted beam, interferograms have poor contrast unless a dye is added to the liquid crystal to reduce the intensity of the undiffracted light. Dyes previously used were not rigorously characterized and suffered from hysteresis in both the initial alignment state of the device and the electro-optic switching characteristics. Hence, our initial effort will identify and characterize dyes that do not suffer from these difficulties and are readily soluble in the liquid crystal host. Since the ultimate goal of this research is to produce interferometers capable of phase shifting at video frame rates, we will quantify the difference in switching times between ferroelectric and nematic liquid crystals. While we have more experience with nematic crystals, they typically switch more slowly than ferroelectric cells. As part of that effort, we will investigate the difference in the modulation of the interferograms as a function of the type of liquid crystal in the cell. Because the temporal switching response of a liquid crystal cell is directly related its thickness, we intend to explore techniques required to produce cells that are as thin as possible. However, the cells must still produce a total phase shift of two pi radians.