H. Philip Stahl

Sensitivity of two-channel Ronchi test to grating misalignment

The Ronchi test is performed by placing a periodic grating at or near the focus of an optical system. Like most geometric tests, the Ronchi test measures wavefront slope instead of the contour of the wavefront like conventional interferometry. A two-channel Ronchi test with a horizontal and a vertical grating can be used to reconstruct a non-symmetric test surface. This paper investigates the errors introduced by different rotational and translation misalignments of the gratings in the two-channel Ronchi test relative to one another. The Ronchigrams are analyzed with a modal technique based on Zernike polynomials. The severity of each misalignment is dependent upon the frequency of the gratings used and on the f/# of the system.

Systematic errors of a projection-moire contouring system

Projection moire techniques are useful tools for the determination of surface contour features. They can provide interferometric type fringe patterns showing regions of equal height on the surface. The difference between moire and interferometry appears in the spacing of the equal height contours lines. In an interferometric fringe pattern, the height difference between consecutive fringes is equal to the wavelength of the illumination source and is a constant over the entire pattern. For a projection moire contour pattern the height difference between consecutive fringes is determined by illumination geometry parameters and is not constant; it changes as a function of the objects out of plane height. This variation in fringe spacing causes a misrepresentation of the surfaces shape if the pattern is analyzed as a traditional interferogram. This paper discusses the types of aberrations generated by this process and the dependence of aberrations on the geometry of the object.

Design review of an infrared phase-shifting interferometer

The design and system performance of an infrared phase-stepping interferometer is reviewed. This instrument is capable of measuring rms surface roughness with a repeatability of 0.02 waves. The instrument uses a 4-bucket unwrapping algorithm. Calibration of the interferometer and removal of inherent system aberrations are discussed along with the system performance, including repeatability and accuracy. The interferometer is an all-reflective optics design to permit use at any wavelength, accommodating both far- (10.6 micron) and near- (5 micron) infrared sources. Testing applications include infrared windows and surface testing.

Vector formulation for Ronchi shear surface fitting

Ronchi interferometry is an optical testing technique similar to shearing interferometry. A coherent wavefront is interfered with a sheared form of itself by placing a periodic grating at, or near, the focus of an optical system. The resultant interference pattern contains information about the wavefronts slope in a direction perpendicular to the grating structure. The wavefront can be reconstructed from two orthogonal slope data sets via the process of sampling, ordering, and fitting. This paper develops a linear-algebra vector notation model of the interferogram sampling and fitting process.

Vector formulation for interferogram surface fitting

Interferometry is an optical testing technique based on the interference of light. Fringes are formed when the optical path difference (OPD) between a reference beam and an object beam is an integral multiple of the illuminating wavelength. This OPD is extracted through the process of sampling, ordering, and interpolating. This paper develops a linear-algebra vector notation model of the interferogram sampling and interpolation process.

Feasibility of using the Hartmann test for contouring an automotive headlamp parabolic reflector

This paper presents the results of a feasibility study to determine the suitability of using Hartmann screen techniques to measure the surface shape of reflection-coated automotive headlamp parabolic reflectors.

Mechanism for surface fitting of interferometric slope data

One approach for obtaining a surface representation is to fit Zernike polynomials (in a least squares sense) to discrete data points in the full aperture. The mathematics for this have been described using both matrix and vector notation. Additionally, vector notation has been used to describe how to obtain a surface representation from orthogonal (x, y) slope data. The result of that paper was a matrix operator for linearly combining the first eight Zernike polynomial coefficients fit to x- and y-slope data to produce a Zernike polynomial surface representation. This paper extends that process by presenting a systematic approach for obtaining the linear relationship between slope and surface using the first 49 Zernike polynomials.

Projection moire technique for contouring injection-molded parabolic reflectors

Testing injection molded aspheres, with large deviations from spherical is difficult. One solution is to use a long wavelength interferometer, such as an infrared interferometer. Another solution is to use moire. This paper presents the use of a projection moire system to test the surface shape of an injection molded f/0.1 parabolic reflector. The theory of moire and its effective wavelength is presented. A projection system is constructed and data taken for a reflector is shown. Finally, some alignment errors associated with the system and how to correct them is presented.

Polariscope testing of plastic eyeglass frames to predict stress-induced fracture points

Partially transparent plastic eyeglass frames are susceptible to fracture due to stress from oversized lenses. Using a dark field polariscope, likely fracture points can be predicted.

Contouring of a free oil surface

A non-contact (i.e., optical) technique is required to measure the deformation of a free oil surface under the influence of a localized thermal load. This deformation is caused by surface tension driven thermal convective flow inside the fluid, and can be as large as 250 micrometers . Therefore, conventional interferometry is not possible. Instead, a Ronchi technique is proposed for contour mapping the oil surface. This paper presents a design concept for a two channel Ronchi instrument and some preliminary results from a feasibility study using a single channel Ronchi instrument.