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Using Multivariate Statistics

A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

A self-scanned 1024 element photodiode array and minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100. The photodiode array samples intensities over a 32 x 32 matrix in the interference pattern as the length of the reference arm is varied piezoelectrically. Using these data the minicomputer synchronously detects the phase at each of the 1024 points by a Fourier series method and displays the wavefront in contour and perspective plot on a storage oscilloscope in less than 1 min (Bruning et al. Paper WE16, OSA Annual Meeting, Oct. 1972). The array of intensities is sampled and averaged many times in a random fashion so that the effects of air turbulence, vibrations, and thermal drifts are minimized. Very significant is the fact that wavefront errors in the interferometer are easily determined and may be automatically subtracted from current or subsequent wavefrots. Various programs supporting the measurement system include software for determining the aperture boundary, sum and difference of wavefronts, removal or insertion of tilt and focus errors, and routines for spatial manipulation of wavefronts. FFT programs transform wavefront data into point spread function and modulus and phase of the optical transfer function of lenses. Display programs plot these functions in contour and perspective. The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.

Digital wavefront measuring interferometer for testing optical surfaces and lenses

Approaches to learning

Biomechanics and wound healing in the cornea

PURPOSE: The goal of this study was to determine age-related variation in the elasticity of the human cornea using nondestructive means METHODS: Organ cultured human corneoscleral buttons were studied Changes in strain were measured with a radial shearing speckle pattern interferometer after an increase in intraocular pressure from 150 to 155 mm Hg Changes in central corneal displacement were calculated by integration, and a bulk corneal Young's modulus was derived by mathematical analysis RESULTS: Fifty corneas, including 17 pairs, were studied Donors were aged between 24 and 102 years (mean, 731); 29 (58%) specimens were from male donors and 21 from female donors Young's modulus of the cornea increased with age, with the line of best fit indicating an approximate doubling from 027 MPa at age 20 years (95% confidence interval, 022-031) to 052 (050-054) MPa at age 100 years (R² = 070) CONCLUSIONS: The stiffness of the human cornea increases by a factor of approximately two between the ages of 20 and 100 years This variation is relevant to the algorithms used to predict the response to incisional and ablative refractive surgery and will also affect the formulas used to calculate intraocular pressure by applanation

Age-related differences in the elasticity of the human cornea.

Purpose To develop a technique to quantify biomechanical changes in the cornea after microkeratome incisions as would be performed in laser in situ keratomileusis. Setting St Thomas' Hospital, London, and the Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, United Kingdom. Methods Corneal displacements of whole sheep eyes were studied under hydrostatic loading using electronic speckle pattern interferometry before and after microkeratome incisions. Results After hydrostatic loading, there was a 20.7% increase in corneal displacement in corneas with microkeratome incisions compared to unoperated corneas; this was statistically significant ( P  = .0068, unpaired t test). Conclusions Results show that in the formation of the microkeratome flap, collagen fibers are severed and minimal biomechanical loading is distributed through the flap. Corneal biomechanical integrity is compromised after microkeratome incisions.

Interferometric technique to measure biomechanical changes in the cornea induced by refractive surgery.

Measurement of plane-strain surface displacement with ESPI requires at least two in-plane illumination geometries. For static loading conditions it is acceptable to record these two interferograms sequentially. However, for time-dependent strain fields, it is necessary to use both illumination geometries simultaneously so that a recording is made with identical strain conditions existing for both. The authors describe a new interferometer that has been devised to measure two in-plane interferograms at the same time. The determination of the method of operation and experimental verification of the technique are given.

https://iopscience.iop.org/article/10.1088/0957-0233/1/10/006/pdf

An electronic speckle pattern interferometer for complete in-plane displacement measurement

Purpose To study the corneal biomechanical effects of varying LASIK flap depth and side cut angulations and evaluate the relative contribution of the lamellar and side cuts using a femtosecond laser and radial shearing speckle pattern interferometry (RSSPI). Methods Forty-two organ-cultured human corneas were divided into a control group and three investigative groups, each undergoing different incision types at both 90- and 160-μm depth using a femtosecond laser. In the first group, typical LASIK flaps were created; in the second group, only the bed was cut (delamination); and in the third group, side cuts alone were affected. Corneal strain was measured using RSSPI before and after treatment following an increase in hydrostatic pressure from 15.0 to 15.5 mmHg and again after 1 week of incubation in culture medium. Results The flap group demonstrated a weakening of strength related to the depth of cut, with strain increasing by 9% and 32% at 90 and 160 μm, respectively. Similar changes, 9% and 33%, were observed following execution of side cuts to the same depths. By contrast, strain increase following delamination showed no relationship with depth, increasing by 5% in both instances. When the side cut angle was made more acute, strain decreased with a 2% strain increase being measured after a 90-μm, 150° side cut was created. No significant changes occurred during the period of organ culture. Conclusions Vertical side cuts through corneal lamellae rather than horizontal delamination incisions contribute to the loss of structural integrity during LASIK flap creation. Angulating side cuts such that the stromal diameter of the flap exceeds its epithelial diameter can decrease this effect.

John R. Tyrer

Papers

Age-related differences in the elasticity of the human cornea.

Interferometric technique to measure biomechanical changes in the cornea induced by refractive surgery.

An electronic speckle pattern interferometer for complete in-plane displacement measurement

Effects of Variation in Depth and Side Cut Angulations in LASIK and Thin-flap LASIK Using a Femtosecond Laser: A Biomechanical Study

Two-dimensional strain measurement with ESPI