Polychromatic Modulation Transfer Function Research Articles

Correlation between Contrast Sensitivity and Modulation Transfer Functions.

Previous studies found no correlation between visual acuity and optical quality in a population of young subjects with good vision. Using sinusoidal gratings, we systematically investigate the correlation between contrast sensitivity and optical quality as a function of spatial frequency. This study describes the correlation between the contrast sensitivity function (CSF) and the modulation transfer function (MTF) in a sample of young and informed subjects. Our results are compared with prior studies on the correlation between visual acuity and metrics of image quality. We also compare our results with previous studies that compare the CSF, the MTF, and the neural contrast sensitivity function (NCSF). The CSF of 28 informed subjects is measured in photopic conditions. The polychromatic MTF is computed from the measurements of monochromatic aberrations. The (CSF, MTF) correlation is estimated as the Pearson correlation coefficient, at each spatial frequency. The NCSF of each subject is estimated as the ratio of CSF to MTF. We obtain high correlation coefficients (0.8) in the range of spatial frequencies of 3 to 6 cycles per degree, which also corresponds to high NCSF. Correlation decreases with increasing spatial frequency in the range of 6 to 18 cycles per degree (down to 0.0 at 18 cycles per degree). In that range, optical and neural contrast sensitivities are both approximately reduced by factor 4. In our sample of young subjects with good vision, the CSF with sinusoidal gratings better differentiates eyes of good optical quality at intermediate spatial frequencies (3 to 6 cycles per degree) than at higher spatial frequencies (12 to 18 cycles per degree). At the highest tested spatial frequency of sinusoidal gratings (18 cycles per degree), there is no significant correlation between optical quality and contrast sensitivity.

Modulation transfer function of a fish-eye lens based on the sixth-order wave aberration theory.

A calculation program of the modulation transfer function (MTF) of a fish-eye lens is developed with the autocorrelation method, in which the sixth-order wave aberration theory of ultra-wide-angle optical systems is used to simulate the wave aberration distribution at the exit pupil of the optical systems. The autocorrelation integral is processed with the Gauss-Legendre integral, and the magnification chromatic aberration is discussed to calculate polychromatic MTF. The MTF calculation results of a given example are then compared with those previously obtained based on the fourth-order wave aberration theory of plane-symmetrical optical systems and with those from the Zemax program. The study shows that MTF based on the sixth-order wave aberration theory has satisfactory calculation accuracy even for a fish-eye lens with a large acceptance aperture. And the impacts of different types of aberrations on the MTF of a fish-eye lens are analyzed. Finally, we apply the self-adaptive and normalized real-coded genetic algorithm and the MTF developed in the paper to optimize the Nikon F/2.8 fish-eye lens; consequently, the optimized system shows better MTF performances than those of the original design.

Differences of Longitudinal Chromatic Aberration (LCA) between Eyes with Intraocular Lenses from Different Manufacturers.

Several researchers have studied the longitudinal chromatic aberration (LCA) of eyes implanted with an intraocular lens (IOL). We investigated the LCA of eyes implanted with yellow-colored IOLs from three different manufacturers: Alcon Inc., HOYA Corp., and AMO Inc. The number of subjects was 11, 16, and 16, respectively. The LCA of eyes implanted with SN60WF and SN60AT (Alcon Inc.), and with XY-1 (HOYA Corp.), was the same as that of phakic eyes. The LCA of eyes with ZCB00V (AMO Inc.) was smaller than that of phakic eyes. The LCA of eyes implanted with Alcon’s and HOYA’s IOLs, but not the LCA of eyes implanted with AMO’s IOLs, was positively correlated with the powers of the IOLs. We also performed simulations to verify the impacts of LCA on visual performance for 4-mm pupil diameter; the simulations were a polychromatic modulation transfer function (MTF) and a visual Strehl ratio computed on the basis of an optical transfer function (VSOTF). We concluded that the differences between the LCA of different manufacturers do not affect visual performances when some extent of higher-order aberration (HOA) exists. The smaller HOA of AMO IOLs may enhance visual performance.

The Effect of Corneal Wavefront Aberrations on Corneal Pseudoaccommodation

To determine the effect on corneal pseudoaccommodation of anterior corneal wavefront aberrations in normal corneas and corneas with prior myopic or hyperopic photorefractive keratectomy (PRK) or laser-assisted in situ keratomileusis (LASIK). Theoretical study. In 220 normal eyes, 102 myopic-PRK eyes, and 106 hyperopic-LASIK/PRK eyes, anterior corneal higher-order aberrations (HOAs, third to sixth order, 6- and 4-mm pupils) were computed from the Atlas corneal elevation data using the VOL-CT program. Using the ZernikeTool, corneal optical image quality was evaluated by the polychromatic modulation transfer function with Stiles-Crawford effect. Defocus from -3.0 diopters (D) to +3.0 D was added to corneal HOAs, and depth of focus was defined as the ranges over which the polychromatic modulation transfer function maintains 80% of the peak value (DOF80) and 50% of the peak value (DOF50). The depth of focus values between groups were compared, stepwise multiple regression was used to assess if any Zernike terms significantly contributed to the depth of focus, and correlation analysis was performed to evaluate the correlation between depth of focus and corneal HOAs. The depth of focus varied widely between corneas, especially in corneas with prior hyperopic-LASIK/PRK. For 6-mm pupil, mean depth of focus values in myopic-PRK and hyperopic-LASIK/PRK corneas were significantly greater than those for normal corneas, and for 4-mm pupil, depth of focus values in hyperopic-LASIK/PRK corneas were greater than those in normal and myopic-PRK corneas. Zernike terms significantly contributing to both DOF80 and DOF50 were fourth- and sixth-order spherical aberration and fourth- and sixth-order astigmatism in normal corneas, third-order vertical coma and fourth-order tetrafoil in myopic-PRK corneas, and third-order vertical coma and fourth-order astigmatism in hyperopic-LASIK/PRK corneas. Depth of focus had weak to moderate positive correlation with HOAs (Pearson correlation coefficient r ranged from 0.300 to 0.583). These theoretical calculations suggest that certain corneal wavefront aberrations affect corneal pseudoaccommodation. To predict corneal pseudoaccommodation, the most important Zernike term is spherical aberration in normal eyes and coma in eyes with prior laser corneal surgery.

Theoretical Performance of Intraocular Lenses Correcting Both Spherical and Chromatic Aberration

To assess the performance and optical limitations of intraocular lenses (IOLs) correcting both longitudinal spherical aberration (LSA) and longitudinal chromatic aberration (LCA) compared to standard spherical and aspheric IOLs. Using a set of 46 white light, pseudophakic eye models representing a population of cataract patients, retinal image quality was assessed for three IOL designs-standard spherical IOLs; aspheric IOLs, correcting a fixed amount of LSA; and aspheric refractive/diffractive IOLs, correcting a fixed amount of LSA and LCA. Depth of field and tolerance to IOL misalignments were also assessed. The improvement factor, based on the area under the radial polychromatic modulation transfer function (pMTF) curve of the IOL, correcting both average LSA and LCA over the aspheric IOL was 1.19±0.12, and over the spherical IOL was 1.43±0.29. Within the range of ±1.00 diopter of defocus, pMTF of the IOL correcting both LSA and LCA was equal or higher than both the spherical and aspheric IOLs. The IOL could be decentered up to 0.6 to 0.8 mm before the performance degraded below that of a spherical IOL. This is the first study that evaluates IOLs correcting both LSA and LCA in the presence of corneal higher order aberrations. Intraocular lenses that correct both LSA and LCA improve simulated retinal image quality over spherical IOLs and IOLs that correct LSA alone, without sacrificing depth of field or tolerance to decentration. Correction of LCA in combination with LSA shows the potential to improve visual performance.

Residual higher-order aberrations caused by clinically measured cyclotorsional misalignment or decentration during wavefront-guided excimer laser corneal ablation

To evaluate the impact of residual wavefront aberrations on optical image quality induced by cyclotorsional misalignment and centration error. Cullen Eye Institute, Baylor College of Medicine, Houston, Texas, USA. Cyclotorsional misalignment and decentration were measured in 58 eyes of 38 patients using an iris-registration system. To calculate residual wavefront aberrations if iris registration was not engaged, each eye's preoperative wavefront map was rotated or decentered by the amounts calculated by iris registration; this wavefront was subtracted from the preoperative wavefront (6.0 mm pupil). The impact of the residual wavefront aberrations on optical quality were analyzed by (1) the root mean square of the total aberrations (2nd to 6th orders), lower-order aberrations (LOAs) (2nd order), and higher-order aberrations (HOAs) (3rd to 6th orders); (2) normalized polar Zernike coefficients; (3) polychromatic modulation transfer function (PMTF) with the Stiles-Crawford effect. On average, centration error induced 4.9 times, 2.8 times, and 8.7 times higher values of total aberrations, LOAs, and HOAs, respectively, than cyclotorsional misalignment. For all Zernike terms except 2nd-order astigmatism, centration error produced significantly higher values than cyclorotational misalignment (all P<.05 with Bonferroni correction). Compared with the PMTF value with perfect alignment, cyclotorsional misalignment decreased the PMTF values slightly whereas centration error reduced the PMTF values by 31% to 66%. Theoretically, image quality was reduced more by clinically measured decentration than by cyclotorsional misalignment.

White-light imaging with fractal zone plates

We report the achievement of the first images to our knowledge obtained with a fractal zone plates (FraZPs). FraZPs are diffractive lenses characterized by the fractal structure of their foci. This property predicts an improved performance of FraZPs as image forming devices with an extended depth of field and predicts a reduced chromatic aberration under white-light illumination. These theoretical predictions are confirmed experimentally in this work. We show that the polychromatic modulation transfer function of a FraZP affected by defocus is about two times better than one corresponding to a Fresnel zone plate.

New intraocular lens for achromatizing the human eye

To describe the design of a new intraocular lens (IOL) capable of correcting spherical and chromatic aberrations when implanted in the human eye. University of Murcia, Murcia, and University of Valencia, Valencia, Spain. A hybrid singlet achromatic IOL was designed. The IOL has a combination of a refractive and a diffractive surface, with 1 of the surfaces being aspherical. Optical simulations were used to model the polychromatic modulation transfer function (MTF) in pseudophakic eyes to explain the differences in optical quality afforded by the achromatic IOL. Parameters such as focus shift, optical path difference, through-focus, and robustness to tilt and decentering of achromatic IOLs were obtained. The polychromatic MTF in an eye with a centered, not tilted achromatic IOL was near the diffraction-limited MTF. The focus shift change for the achromatic IOL through the visible spectrum was approximately 0.1 diopter. The polychromatic MTF in an eye with the achromatic IOL would be similar to that in an eye with a spherically centered IOL if the achromatic IOL were decentered 1.0 mm or tilted 4 degrees. The range of centration and tilt error for the achromatic IOL to obtain an optical benefit in the polychromatic MTF was larger than the typical postoperative IOL decentration and tilt errors. The hybrid singlet achromatic IOL design resolved the chromatic aberration problem, improving the overall optical quality in the human eye.

Theoretical Comparison of Aberration-correcting Customized and Aspheric Intraocular Lenses

To assess the performance and optical limitations of standard, aspheric, and wavefront-customized intraocular lenses (IOLs) using clinically verified pseudophakic eye models. White light pseudophakic eye models were constructed from physical measurements performed on 46 individual cataract patients and subsequently verified using the clinically measured contrast sensitivity function (CSF) and wavefront aberration of pseudophakic patients implanted with two different types of IOLs. These models are then used to design IOLs that correct the astigmatism and higher order aberrations of each individual eye model's cornea and to investigate how this correction would affect visual benefit, subjective tolerance to lens misalignment (tilt, decentration, and rotation), and depth of field. Physiological eye models and clinical outcomes show similar levels of higher order aberration and contrast improvement. Customized correction of ocular wavefront aberrations with an IOL results in contrast improvements on the order of 200% over the control and the Tecnis IOLs. The customized lenses can be, on average, decentered by as much as 0.8 mm, tilted > 10 degrees , and rotated as much as 15 degrees before their polychromatic modulation transfer function at 8 cycles/degree is less than that of the Tecnis or spherical control lens. Correction of wavefront aberration results in a narrower through focus curve but better out of focus performance for +/- 0.50 diopters. The use of realistic eye models that include higher order aberrations and chromatic aberrations are important when determining the impact of new IOL designs. Customized IOLs show the potential to improve visual performance.

Comparative assessment of contrast with spherical and aspherical intraocular lenses

To analyze the contrast differences between spherical and aspherical intraocular lenses (IOLs) using polychromatic modulation transfer function (MTF) computations. Oto-Neuro-Ophthalmological Department, Eye Institute, University of Florence, Florence, Italy. A questionnaire evaluating patients' subjective perception of halos, glare, and contrast sensitivity in different lighting conditions was administered to 2 groups of pseudophakic patients. In the first group, a spherical IOL (AR40e, AMO) had been implanted and in the second group, an aspherical IOL (Tecnis Z9000, AMO). The optical performances of the 2 IOLs were analyzed with ray-tracing software. The overall MTF of an electro-optical system and the polychromatic MTF were evaluated. The questionnaire analysis, confirmed with ray-tracing analysis, showed that patients with an aspherical IOL do not present with all the expected advantages. Even if there are differences in the monochromatic MTF curve computation, there is not a significant difference in the results obtained in the polychromatic MTF computation. The aspherical IOL anterior surface resolved the spherical aberration problem, but the longitudinal chromatic aberration must still be resolved.

다색광전달함수를 사용한 컬러 LCD 모니터의 광학적 상평가법

컬러 LCD(liquid crystal display) 모니터의 광학적 상에 대한 성능을 평가하기 위하여 LCD 모니터를 포함한 모든 광학계의 파장별 공간주파수 반응에 가중치를 부여한 진폭전달함수(modulation transfer function ; MTF)를 이용한 다색광전달함수(polychromatic modulation transfer function ; PMTF)를 제안한다. 서로 다른 진폭들을 갖는 적색(R), 녹색(G), 청색(B)의 3개의 막대형 LCD 단위물체를 이용한 컬러 LCD의 PMTF의 시뮬레이션 결과와 실험적 결과가 잘 일치하며, 이 결과 컬러 LCD의 결상성능은 단색으로 측정하는 MTF 및 가시광의 전파장대를 사용하는 백색광 MTF와는 다른 R, G, B의 3색에 대한 PMTF로 측정하늘 것이 보다 적절하다. We propose a method for evaluating the image quality of color liquid crystal display(LCD) monitors by using the polychromatic modulation transfer function(PMTF), which is calculated from the modulation transfer function(MTF) weighted by the overall color response of the system including the test LCD monitor. We confirm that experimental results using the PMTF agree well with simulated results of the PMTF of a color LCD monitor by using three bar targets with different amplitudes and three elementary colors such as red(R), green(G), and blue(B). As a results, we should choose the PMTF instead of the white color MTF or monochromatic MTF in order to evaluate correctly the image quality of color LCD monitors.

Eye models for the prediction of contrast vision in patients with new intraocular lens designs.

Theoretical calculations of the polychromatic modulation transfer function (MTF) and wave-front aberration were performed with physiological eye models. These eye models have an amount of spherical aberration that is representative of a normal population of pseudophakic eyes implanted with two different types of intraocular lens (IOL) made from high-refractive-index silicone. These theoretical calculations were compared with the measured contrast sensitivity function (CSF) under mesopic lighting conditions and with wave-front aberration (obtained with a Hartmann-Shack wave-front sensor) collected from 37 patients bilaterally implanted with the same types of lens. The relationships between the ocular wave-front aberration and the MTF predicted by the eye models and the CSF and the ocular wave-front aberration measured in eyes implanted with IOLs were investigated. The predicted improvements in MTF and wave-front aberration correlated well with the improvements measured in practice. Physiological eye models are therefore useful tools for IOL design.

Design of a multiple-field-of-view optical system for 3- to 5-μm infrared focal-plane arrays

The design of a triple-field-of-view optical system for 3- to 5-μm infrared focal-plane arrays is described. Preliminary calculations are done to determine the first-order parameters of the narrow-, medium-, and wide-field-of-view modes. An optical configuration based on the combination of axial motion of a lens group and the rotate-in motion of two separated lens groups is used. Diffractive and aspheric surfaces are employed to control the color and monochromatic aberrations, thereby decreasing the total number of lenses used. Paraxial and real-ray modeling of the narcissus effect, which plays an important role in the optical design of infrared systems, is explained. The final optical designs along with their aberrations curves and polychromatic modulation transfer function plots are presented, showing acceptable performance in all fields of view.

A design study of dual-field-of-view imaging systems for the 3 5 m waveband utilizing focal-plane arrays

In this work, a design study of switchable dual-field-of-view (FOV) optical systems for 3– 5 µm imaging using infra-red focal-plane arrays is presented. In order to switch the FOV, two different optical configurations are explored and compared for their merits and demerits. The first scheme is based on the axial motion of a lens group and the second is based on a rotate-in motion of two widely separated lens groups. It is found that the rotate-in scheme achieves better optical performance in both narrow-and wide-FOV modes due to its improved colour correction. Moreover, this scheme can achieve very wide FOV (up to 90° full diagonal coverage) with good optical performance using fewer lenses. Diffractive and aspheric surfaces are utilized to control colour and monochromatic aberrations, reducing the total lens count. The final optical designs along with their aberration curves and polychromatic modulation transfer function plots are presented, showing excellent performance in both FOVs.

Retinal image quality in myopic subjects after refractive surgery

In the present work, we offer a theoretical analysis of retinal image quality for different groups of myopes (-2D, -4D, -8D, -12D) subjected to refractive surgery. For this, the polychromatic optical MTF (modulation transfer function) corresponding to the far point of a myopic eye was compared with the image for the infinity point after refractive surgery. The optical quality of the retinal image was studied, considering the defocusing corresponding to chromatic aberration and the spherical aberration. The results for retinal image quality show a general deterioration, which was accentuated with the degree of myopia. The results suggest that refractive surgery could be improved by modifying the asphericity of the anterior surface of the cornea, which, in addition to making the eye emetropic, would optimize the MTF of the subjects. We also present a theoretical analysis involving non-spherical surfaces before and after operation, testing the influence of corneal asphericity in this case, as well as the possible optimization of the polychromatic MTF.

Image quality in pseudophakic eyes with two different types of intraocular lenses ranging in the degree of high myopia

The image quality of pseudophakic eyes with intraocular lenses in high myopia was studied by applying geometric and wave optics. Two types of intraocular lenses (IOL) were compared—one that was meniscus shaped and the other either planoconcave or planoconvex [bending factor (X)511]. A geometric study of image quality was used to analyze the transverse spherical aberration (TA) and the chromatic aberration (chromatic difference of the blur circles, CDBC). The loss of image quality and visual acuity increases as the TA and CDBC increase. The polychromatic modulation transfer function (MTF) was obtained using the point-spread function (PSF), taking into account spherical aberration and defocus coefficients. Finally, for chromatic and spherical aberrations and polychromatic MTF, the type of IOL that would best improve image quality for a given patient can be established.

Achromatizing the human eye: the problem of chromatic parallax

Attempts to correct the chromatic difference of focus of the human eye will introduce unwanted chromatic parallax if the eye is misaligned with the optical axis of the achromatizing system. Using geometrical optics, we show that the amount of parallax is approximately proportional to the amount of misalignment of the eye, with the constant of proportionality equal to the eye's chromatic difference of refractive error. This prediction was confirmed by the experimental determination of chromatic parallax for two commercially available achromatizing lenses. On the basis of these results, we calculated that anticipated improvements in the polychromatic modulation transfer function of the eye offered by achromatizing lenses will be canceled by approximately 0.4 mm of the misalignment between the lens and the eye. Our prediction that further misalignment would severely reduce image quality of the achromatized eye was verified by psychophysical measurements of contrast sensitivity.

A simple method of evaluating the polychromatic modulation transfer function for photographic systems

A rapid method of the measurement of the polychromatic optical transfer function (POTF) of a total system-optics plus reversal colour film is described, based on the scanning and Fourier analysis of the photographic image of a slit. This scanning is carried out through a microdensitometer with a spectral response that has been adapted to be analogous to the human eye in photopic vision. The results of the curves calculated in different positions of the image plane by this method are compared with the curves calculated according to the integral extended to various monochromatic wavelengths. The values of the PMTF calculated by the proposed method are on average lower over the whole range of frequencies than those calculated by several wavelengths. In order to analyse the implications of these differences in image quality the authors have applied a numerical criterion of image quality to both methods, based on the area of the PMTF. The results indicate a strong statistical dependence between the two methods.

Evaluation of polychromatic image quality by means of transfer function

The polychromatic optical transfer function requires a considerable amount of time for measurement and calculation, which reduces the possibilities of its being applied to the evaluation of opto-photographic systems. As a simplification the authors have suggested defining the polychromatic modulation transfer function (PMTF) as a relation of contrasts for sinusoidal tests of several spatial frequencies measured by means of a microdensitometer whose spectral chromatic response is analogous to the human eye. Criteria of quality were defined based on the PMTF and in order to study their efficiency in the evaluation of the image quality of colour opto-photographic systems the orders given by the criteria and by the eight observers were compared over a group of images corresponding to different conditions of aberrations. The criterion which gave the best evaluation of image quality was the integral of the product of the PMTF by the transfer function of the eye and by the weight function f( nu )= nu .

MTF of Proximity-Focused Image Tube in Polychromatic Light

The effect of different conditions of illumination and the spectral sensitivity of the detector on the performance of proximity-focused image tube has been evaluated in terms of the polychromatic modulation transfer function. The physical efficiencies of sources commonly used in the infrared image conversion system have been compared for a Corning glass 2540 glass filter and a GaAs filter having antireflection coatings on both sides.