John E. Greivenkamp

Generalized data reduction for heterodyne interferometry

A generalized algorithm for use with digital heterodyne or fringe- scanning interferometers was developed that removes many of the restrictions that had previously applied to the data collection scheme. The required phase steps may be chosen with unequal spacing and to extend over a range greater than 2w. The integrating-bucket and phase-step approaches produce identical results.

Sub-nyquist interferometry

The primary limitation of conventional phase-shifting interferometry (PSI) is its inability to measure surfaces with large aspheric departures. A new method of data analysis, sub-Nyquist interferometry (SNI), is described and demonstrated to overcome this problem. SNI is an extension of PSI, and it preserves the measurement precision that is inherent to PSI. For some types of wavefronts, measurement range improvements of more than 2 orders of magnitude are shown, and these improvements result from the utilization of a priori knowledge about the wavefront. Simple and reasonable assumptions are found to be very powerful for improving the aspheric measurement capability of the interferometer system.

Representation of videokeratoscopic height data with Zernike polynomials

Videokeratoscopic data are generally displayed as a color-coded map of corneal refractive power, corneal curvature, or surface height. Although the merits of the refractive power and curvature methods have been extensively debated, the display of corneal surface height demands further investigation. A significant drawback to viewing corneal surface height is that the spherical and cylindrical components of the cornea obscure small variations in the surface. To overcome this drawback, a methodology for decomposing corneal height data into a unique set of Zernike polynomials is presented. Repeatedly removing the low-order Zernike terms reveals the hidden height variations. Examples of the decomposition-and-display technique are shown for cases of astigmatism, keratoconus, and radial keratotomy.

Field guide to geometrical optics

This Field Guide derives from the treatment of geometrical optics that has evolved from both the undergraduate and graduate programs at the Optical Sciences Center at the University of Arizona. The development is both rigorous and complete, and it features a consistent notation and sign convention. This volume covers Gaussian imagery, paraxial optics, first-order optical system design, system examples, illumination, chromatic effects, and an introduction to aberrations. The appendices provide supplemental material on radiometry and photometry, the human eye, and several other topics.

Using corneal height maps and polynomial decomposition to determine corneal aberrations

Purpose. To review the use of corneal videokeratoscopic height data, elaborate on the advantages and disadvantages of such data, describe techniques for overcoming the limitations of height data, and demonstrate its use in quantifying the optical properties and aberrations of the cornea. Methods. The steep sag of the cornea hides fine variations in corneal height that arise naturally or due to disease or surgery. The dynamic range, or ratio of the overall sag to the feature height, is the primary limitation of videokeratoscopic height data. Techniques for removing single or multiple reference surfaces are described in detail, and applications of the methodology to wavefront and raytracing analysis of corneal aberrations arising from radial keratotomy (RK), photorefractive keratectomy (PRK), and keratoconus are described. Results. Removing a single reference surface from the raw corneal height data begins to reveal subtle variations in corneal height. However, expansion of surface height data into a complete set of basis functions provides a sophisticated method for extracting high-order corneal variations. Choosing an orthogonal basis set provides a robust least-squares fit and forms unique expansions of the surface. The resulting coefficients are uncorrelated and form a simple measure of the optical quality. Conclusion. Videokeratoscopic height data are useful for analyzing and quantifying corneal deformity arising from disease or refractive surgery and they provide a sophisticated alternative or complement to dioptric power maps.

Visual acuity modeling using optical raytracing of schematic eyes

PURPOSE We developed a methodology to predict changes in visual performance that result from changes in the optical properties of the eye. METHODS Exact raytracing of schematic eyes was used to calculate the point spread function and the modulation transfer function of the visual system. The Stiles-Crawford effect, photopic response, diffraction, and the retinal contrast sensitivity are included in the model. Visual acuity was predicted by examining the modulation of the resultant retinal image of a bar target and by determining when the modulation falls below a threshold value. Visual acuity was predicted for refractive errors ranging from 0 to 5 diopters and for pupil diameters ranging from 0.5 to 8 mm. RESULTS Visual acuity predictions were compared to clinically found Snellen visual acuities and were found to be highly correlated (r2 = .909). CONCLUSIONS This modeling technique shows promise as a means of evaluating clinical and surgical procedures before undertaking clinical trails.

Keratoconus detection based on videokeratoscopic height data

Purpose. To develop a videokeratoscopic-based keratoconus detection scheme that avoids the ambiguity of dioptric power definitions and videokeratoscope design. Methods. Corneal height data obtained with a commercial videokeratoscope are decomposed into the set of orthogonal Zernike polynomials. Expansion coefficients of a “normal” group and a keratoconus group are compared to find significant differences. Elevated Zernike terms are used to detect the disease in these populations. The performance of this detection scheme is compared to other videokeratoscopic keratoconus indices. Results. Two low-order Zernike polynomial terms are identified as being elevated in keratoconus patients and combined to form a new detection index. This index performed at least as well as keratoconus detection schemes based on the inferior- superior (I-S) value, the steepest radial axes (SRAX), and the Surface Asymmetry Index (SAI) for the samples studied. Conclusion. The proposed Zernike scheme offers a potentially viable algorithm for detecting keratoconus that avoids the ambiguities of dioptric power definitions and is independent of videokeratoscope design.

Color dependent optical prefilter for the suppression of aliasing artifacts

Optical prefilters, which make use of the double-refraction effect in crystalline quartz, reduce the amount of aliasing artifacts in the displayed image of a video system. This paper describes anew class of optical prefilter that produces different amounts of blur for different colors. The chromatic variation is obtained by placing a polarization retarder between two quartz crystals. This type of filter is useful with sensors that have unequal pixel densities in the three sensed colors.

Lateral-shift variable aberration generators

We describe and analyze an optical device capable of generating tilt, defocus, astigmatism, coma, and spherical aberration wave-front deformation. This optical device consists of a pair of aspheric plates that produce aberrations by laterally shifting one plate relative to the other. The surface descriptions of these optical plates are provided, and their aberration-inducing properties are verified with ray-tracing software. In addition, we examine the versatility and the limitations of using variable aberration generators and provide insight into how aberrations may be controlled by a simple lateral shift. The device may find application in aberration control in lens systems that are nonrotationally symmetric.

Interferometer errors due to the presence of fringes

Phase-shifting interferometry permits analysis of complex interferograms. However, the measurement accuracy is reduced as the number of fringes is increased. The wave-front from a defocused spherical surface is used to demonstrate this degradation for several different transmission reference objectives.