Strehl Intensity Ratio Research Articles

Clinical use of the ocular point spread function for retinal image quality assessment

The purpose of this study is to demonstrate the clinical use of the point spread function (PSF) as metric for the assessment of retinal image quality in eyes with different ocular conditions. The PSF was computed from the wavefront aberrations obtained in seven eyes with different ocular conditions: emmetropia, myopia, hyperopia, post-myopic laser in situ keratomileusis (LASIK), post-hyperopic LASIK, keratoconus, Intacs® in keratoconus, radial keratotomy (RK), LASIK after RK, cataract, phacoemulsification after cataract surgery, and LASIK after astigmatic keratotomy. The Strehl intensity ratio was calculated for all the PSFs computed. The PSF was correlated with the change in the optical elements of the eye: cornea and lens. Corneal refractive surgery, keratoconus, Intacs insertion and cataract surgery induce different changes in the optics of the eye which were well reflected by the PSF and the Strehl intensity ratio. Spread of the PSF in each case was caused by optical aberrations and/or scatter. The PSF measurement and the Strehl intensity ratio calculation is useful for the qualitative assessment of the retinal image and for quantifying optical degradation imposed by different optical conditions.

Simulation of Eye-tracker Latency, Spot Size, and Ablation Pulse Depth on the Correction of Higher Order Wavefront Aberrations With Scanning Spot Laser Systems

The aim of this theoretical work was to investigate the robustness of scanning spot laser treatments with different laser spot diameters and peak ablation depths in case of incomplete compensation of eye movements due to eye-tracker latency. Scanning spot corrections of 3rd to 5th Zernike order wavefront errors were numerically simulated. Measured eye-movement data were used to calculate the positioning error of each laser shot assuming eye-tracker latencies of 0, 5, 30, and 100 ms, and for the case of no eye tracking. The single spot ablation depth ranged from 0.25 to 1.0 microm and the spot diameter from 250 to 1000 microm. The quality of the ablation was rated by the postoperative surface variance and the Strehl intensity ratio, which was calculated after a low-pass filter was applied to simulate epithelial surface smoothing. Treatments performed with nearly ideal eye tracking (latency approximately 0) provide the best results with a small laser spot (0.25 mm) and a small ablation depth (250 microm). However, combinations of a large spot diameter (1000 microm) and a small ablation depth per pulse (0.25 microm) yield the better results for latencies above a certain threshold to be determined specifically. Treatments performed with tracker latencies in the order of 100 ms yield similar results as treatments done completely without eye-movement compensation. CONCWSIONS: Reduction of spot diameter was shown to make the correction more susceptible to eye movement induced error. A smaller spot size is only beneficial when eye movement is neutralized with a tracking system with a latency <5 ms.

A method to predict refractive errors from wave aberration data.

We explored the impact of the eye's higher-order aberrations on subjective refraction comparing two classes of methods for estimating refractive state, one based directly on the wave aberration defined in the pupil plane and another based on the retinal image plane. The method defined in the pupil plane chose the sphere and cylinder that either minimized the wave aberration root mean square or minimized the sum of all the spherical and cylindrical components in the wave aberration. The method defined in the image plane chose the sphere and cylinder that optimized an image-quality metric such as the Strehl intensity ratio, the entropy and the intensity variance of the point-spread function, the volume under the modulation transfer function, or the volume under the contrast-sensitivity function. All these methods were compared in a population of six eyes for which we measured both the wave aberration with a Shack-Hartmann wavefront sensor and the subjective refraction under identical conditions. Pupil plane methods predicted subjective refraction poorly. The mean absolute error of the prediction, in spherical equivalent, was about 0.5 D (range, 0.1 to 0.8 D) and increased with increases in higher-order aberrations. However, for all the retinal image plane methods, the mean error between predicted and subjective refraction was about 0.1 D (range, 0 to 0.25 D). The reliability of the method based on the image-quality optimization was further confirmed in a large population of 146 eyes. In conclusion, higher-order aberrations influence the amount of sphere and cylinder required to correct vision. The results indicate that subjective refraction can be predicted from the eye's optics alone by optimizing computed retinal image quality.

Selection of glasses for achromatic doublets with reduced secondary spectrum I Tolerance conditions for secondary spectrum, spherochromatism, and fifth-order spherical aberration

We describe a way of selecting pairs of glasses for both thin cemented achromatic doublets and thin aplanatic achromatic doublets with a reduced secondary spectrum. By taking one pair of glasses at a time, we can compute and display the secondary spectrum in increasing value. The number of solutions based on the magnitude of the secondary spectrum alone is huge: 40,804 pairs. Some tests are applied at different stages of the design procedure to reduce the number of acceptable solutions. Aberrations that cannot be corrected, namely, spherochromatism and fifth-order spherical aberration, are further calculated to reduce drastically the number of acceptable solutions. To do this, we establish tolerance conditions based on the relationship between the Strehl intensity ratio and the rms wave-aberration error so that the rms wave error is minimized in the presence of the secondary spectrum, spherochromatism, and the fifth-order spherical aberration.

Diffraction losses of high power solid state lasers

A uniform pumping distribution is very important in a side pumped rod geometry. Based on space-dependent rate equations, the threshold pump power and the TEM 00 mode output power of a solid state laser with a uniform pump are obtained. The diffraction losses arising from thermally induced spherical aberration have been estimated by the Strehl intensity ratio. The diffraction losses may prevent the solid state laser from ultrahigh power levels before the thermal fracture limitation. The diffraction losses for different sizes of laser beams and the laser rods are discussed. A significant increase in average power and a great decrease in thermal distortion and birefringence at cryogenic temperature have been analyzed in cooperation with thermal induced diffraction losses.

Influence of the thermal effect on the TEM_00 mode output power of a laser-diode side-pumped solid-state laser

A fraction of pump power has been converted to TEM00 mode laser power for a side-pumped solid-state laser by use of a space-dependent rate equation. We investigated the pump-to-mode (TEM00) ratio when scaling laser-diode side-pumped solid-state lasers to high-power levels by including the thermal effect in the space-dependent rate equation. Based on the assumption that Gaussian pump power is the same at any cross section of a laser rod, we resolved the output power with a space-dependent rate equation; temperature distribution in the laser rod was obtained; the optical path difference distribution was derived, and we estimated the diffraction losses that result from thermally induced spherical aberration by use of the Strehl intensity ratio. We determined that thermally induced diffraction losses are strongly dependent on pump power and on the pump-to-mode ratio.

Optimization in scaling fiber-coupled laser-diode end-pumped lasers to higher power: influence of thermal effect

The optimum mode-to-pump ratio in scaling fiber-coupled laser-diode end-pumped lasers to higher power has been investigated by including the thermal effect into the space-dependent rate equation analysis. The optical path difference (OPD) distribution has been derived as a function of the pump-beam quality, focus position of pumping light, and pump radius at the focal plane under the assumption that the end faces of the crystal are thermally insulated. The diffraction losses arising from thermally induced spherical aberration have been estimated by the Strehl intensity ratio. The present results for the optimum mode-to-pump ratio are markedly different from previous analyses in which thermal effects are neglected. Here, the optimum mode-to-pump ratio is a decreasing function of input pump power, and is less than unity in the case of a slightly high pump power. The practical example of a Nd:YAG laser pumped by a 13-W fiber-coupled laser diode is considered to confirm our physical analysis.

Influence of thermal effect on output power optimization in fiber-coupled laser-diode end-pumped lasers

A general model has been developed for the output power optimization of fiber-coupled laser-diode end-pumped lasers by including the thermal effect into the analysis. The optical path difference (OPD). Distribution has been derived as a function of the pump-beam quality, focus position of pumping light, and pump radius at the focal plane under the assumption that the end faces of the crystal are thermally insulated. With the derived OPD, the diffraction losses arising from thermal-induced spherical aberration have been estimated by the Strehl intensity ratio. The practical example of an Nd:YVO/sub 4/ laser pumped by a 1.2-W fiber-coupled laser diode is considered to illustrate the utility of the present model. Experimental results have shown a fairly good agreement with the theoretical predictions.

Renormalization of the Buchdahl-Rimmer Third- and Fifth-order Geometric Aberration Coefficients to Rms Wave Aberration Function Expressions

The Buchdahl-Rimmer third- and fifth-order geometric aberration coefficients are converted or renormalized to a rms value of the wave aberration function. The purpose of this is to make it possible to compare different aberration coefficients directly since any aberrations which have the same renormalized coefficients will have the same effect on the image quality in terms of the Strehl intensity ratio. This is an advantage which, until now, has only been obtained using the renormalized Zernike coefficients.

Psychometrically appropriate assessment of afocal optics by measurement of the Strehl intensity ratio

Several different performance criteria have been proposed for assessing the quality of visual afocal sights. Earlier research by one of the authors (Haig) has shown that a high degree of correlation exists between a subjective assessment of performance and the Strehl intensity ratio of the optical system. We discuss some of the problems in choosing an objective performance criterion for visual sights and describe equipment that has been developed for measuring the line Strehl ratio of binoculars, both on and off axes. The equipment can be modified for testing other types of visual sight. It can also be used for measuring several additional performance parameters such as the modulation transfer function, transmission, and field curvature.

The Solution of Some Inverse Diffraction Problems in Terms of the Diffraction Coefficients

The form of the recently developed series representation of the axially symmetrical diffraction fields enables us to establish the pupil function from the series coefficients γk (u). A new interpretation of the Strehl intensity ratio is given. It represents the ratio of the energy coming to the image focus and that coming to the other foci of the filter. Further, by the use of the three-term approximation, the transmissivity of the filter giving the desired two-point resolution and attaining the maximum value of the Strehl criterion is found and compared with the exact solution proposed by Luneberg. Finally, it is shown that the Luneberg filter transmissivity represents a common approximative solution of the apodization problems that utilize the integral criteria of apodization.