Analysis of voltage effect on holographic gratings by modulation transfer function

Spectacle lenses performance is simulated based on the eye model system. The modulation transfer function (MTF) curve of spherical lens, aspheric lens and optimized lens is analyzed, and the results are compared and analyzed non-curved lenses were found to be more effective in improving image quality. For free-form lenses, we measured the far-field, progressive corridor and near-field in the simulated optical system, and studied the relationship between the face matching angle and the tilt of the endoscope and the MTF of the conventional spectacle lens and the free-form lens. The experimental results show that when the face fitting angle and the inclination of the endoscope inclination increase, the MTF decreases and the imaging quality deteriorates. The tilt of the endoscope has the greatest influence on the MTF value, followed by the face fitting angle, where the influence of the spatial frequency is negligible, but as the spatial frequency increases, the MTF also decreases. Therefore, for the free-form surface, when the face fitting angle and the inclination of the endoscope are different, the image quality is easily affected, so these two factors must be fully considered in the design.

For the image quality analysis of photogrammetrical systems using the Modulation Transfer Function (MTF), the edge gradient analysis (EGA), using a Hanning function, and the grating pattern method are compared. Artificial edge and grating patterns were photographed from an airplane and were analyzed to determine the quality of the photogrammetric system. The pictures were scanned with a microdensitometer. For comparison with the artificial patterns, a natural roof edge was examined. Good agreement of all MTF measurements was found. Furthermore, the resolution found from MTF curves agreed well with the resolution obtained from three-bar targets. Generally, the MTF curves obtained from patterns in the flight direction were lower than the MTF's perpendicular to the flight direction due to airplane movement. The influence of linear image motion and its compensation was examined and is discussed. N PHOTOGRAMMETRY the image quality of photographs is of great importance. With digital image processing the image quality can be improved under certain conditions. Flight con­ ditions usually lead to reduced image quality (Holdermann, 1976). The optical transfer function (OTF) and especially the modula­ tion transfer function (MTF) are useful techniques for measuring the image quality of photographs. The MTF is the result of -the contributions of the links in the image transfer forming chain, namely, the camera, the film, image motion (in systems without forward motion compensation, FMC), vibrations, and the at­ mosphere (Tiziani, 1977). Artificial or natural edges are used for the edge gradient analysis (EGA), and varying spatial frequency patterns are used for the grating pattern technique. The aim of this paper is to compare both methods and to test their reliability. Results are shown and discussed. Furthermore, the influence of linear image mo­ tion on image quality is examined.

Objective: To optimize the spherical aberrations of toric intraocular lens (IOL): to design toric IOLs with different spherical aberrations, and to study the rotation, the tolerance to decentration, and imaging rules. Methods: In this experimental study, the spherical aberrations of toric IOLs were optimized in the Hwey-Lan Liou model eye. The spherical structure, the curvature radius, and the thickness of the anterior and posterior surfaces of the toric IOLs, and the aspheric coefficients of the anterior surface of toric IOLs were optimized respectively. The targets was optimized to produce IOLs with -0.26 μm, -0.1 μm and 0 μm spherical aberrations. In the computer optical simulation system, the effect on the modulation transfer function (MTF) was evaluated when spherical and aspherical IOLs were decentrated in the horizontal direction with 0.25 mm, 0.50 mm and 0.75 mm at 3- and 5-mm pupil diameters. The effect on MTF was also evaluated when the two types of IOLs were rotated by 3°, 5° and 10° at 4-mm pupil diameter. Results: At the center, the aspherical toric IOL displayed a better image performance with the increased pupil diameter. When the decentration was 0.5 mm at 3-mm pupil diameters, the imaging quality of the -0.26 μm toric IOL decreased and was worse than that of 0 or -0.1 μm IOL. At 5-mm pupil diameter, when the decentration was 0.75 mm, the MTF of -0.26 μm toric IOL was close to that of the spherical toric IOL, while the MTF of toric IOL with 0 μm and -0.1 μm spherical aberration was slightly better than that of the spherical toric IOL. The MTF of aspherical toric IOLs was better than that of the spherical toric IOL with 3° to 5° rotation, but the curve was equal or even worse than that of the spherical toric IOL with 10° rotation in high spatial frequency. Conclusions: Toric IOLs with a spherical aberration of -0.26 μm have good imaging quality at the center but lower tolerance to decentration. The proper optimization of the spherical aberration of toric IOLs can improve the imaging quality of the model eye, while maintaining the tolerance for decentration and rotation errors. Optimized toric IOLs can attain better optical quality under comprehensive conditions. Key words: cataract; artificial lenses; astigmatism; cornea; decentration; rotation; modulation transfer function; model

Analysis of angular dependent spatial frequency response of Digital Coplanar Translational Laminography

Objective To measure and compare the visual quality in myopic patients corrected by laser in situ keratomileusis (LASIK) and rigid gas permeable contact lens (RGPCL) by using point spread function (PSF).Methods This was a prospective study.There were 2 groups of patients with middle-high myopia corrected using either LASIK or RGPCL:44 eyes of 22 patients received LASIK (group A),with the spherical equivalent (SE) (-6.84±1.65)D,while 49 eyes of 25 patients corrected by RGPCL (group B),with the SE(-6.43±1.59)D.The changes of the modulation transfer function (MTF) in their eyes were evaluated before and 3 months after LASIK in group A,before and after the fitting of RGPCL in group B by using the PSF examination under conditions of 3 mm and 6 mm pupil diameters respectively.The changes of PSF in each group before and after correction were compared and the differences between groups were statistically analyzed with paired samples t test and analysis of covariance.Results ① The MTF values at low-middle spatial frequencies were decreased 3 months after LASIK (3 nun pupil diameter,2.98～23.81 cpd; 6 mm pupil diameter,2.98～9.42 cpd,P＜0.01),which was a statistically significant decrease,whereas the changes of MTF at high frequencies were not significant.②Under the condition of 3 mm pupil diameter,the MTF values at high spatial frequencies were increased after fitting of RGPCL (18.85～37.70 cpd,P＜0.05),whereas at low-middle frequencies the difference was not significant.Under the condition of 6 mm pupil diameter,the MTF values were improved at all spatial frequencies after RGPCL (2.98～37.70 cpd,P＜0.05).③The changes of MTF values at all spatial frequencies in the RGPCL group were better than those in the LASIK group (P＜0.05).Conclusion LASIK can deteriorate the visual quality of myopic patients in the early stage after surgery,whereas RGPCL can improve it.The visual quality of myopic patients corrected by RGPCL is better than that of the early stage after LASIK. Key words: Myopia; Keratomileusis,laser in situ; Contact lenses,rigid gas permeable; Point spread function

Objective To study tilt and decentration of spherical and aspheric IOL implantation after phacoemulsification surgery and effect on higher-order aberrations （HOAs） and visual quality. Methods It was a prospective clinical study. A total of 60 eyes （50 patients） were divided into 2 groups randomly, of 30 eyes in each group, one group with Sensar AR40e （AMO）, one group with Tecnis ZA9003 （AMO）. Three to four months after surgery, higher-order aberrations （HOAs） and modulation transfer function （MTF） at six spatial frequencies （5, 10, 15, 20, 25, 30 cpd） were measured in 5.0mm pupil size. Tilt and decentration of the IOLs were measured using Scheimpflug photography. The tilt and decentration, HOAs and subtracted lower order aberration MTF （MTF（HOA）） were compared. The effect of tilt and decentration on HOAs and visual quality was assessed using multiple regression analysis. Results The mean optic tilt was （2.99± 0.94）° for AR40e group and （2.98± 1.15）° for the ZA9003 group. The mean optic decentration was （0.30± 0.13）mm, （0.31± 0.14）mm,respectively. No significant differences in IOL tilt or decentration were found （Z= -0.044, -0.525, P =0.965,0.600, Mann-Whitney U test）. The total 4th order spherical aberration in AR40e group was larger than it was in ZA9003 group and the differences were statistically significant （t = -10.386, P =0.000）. In 5.0mm pupil size,MTF （HOA） at all spatial frequencies in ZA9003 group were larger than they were in AR40e group and the differences were statistically significant （P 〈0.05）. Tilt and decentration did not significantly affect HOAs and MTF （HOA） with either IOL. Conclusions When IOL tilt and decentration are within normal limits, hey do not compromise the correction of spherical aberration by the aspheric IOL and the amounts of tilt and decentration of both IOLs are not large enough to cause deterioration of visual quality. Key words: IOL; Tilt; Decentration; Aberration; MTF

The authors describe a new technique to determine the system presampled modulation transfer function (MTF) in digital radiography using only the detector noise response. A cascaded-linear systems analysis was used to develop an exact relationship between the two-dimensional noise power spectrum (NPS) and the presampled MTF for a generalized detector system. This relationship was then utilized to determine the two-dimensional presampled MTF. For simplicity, aliasing of the correlated noise component of the NPS was assumed to be negligible. Accuracy of this method was investigated using simulated images from a simple detector model in which the "true" MTF was known exactly. Measurements were also performed on three detector technologies (an x-ray image intensifier, an indirect flat panel detector, and a solid state x-ray image intensifier), and the results were compared using the standard edge-response method. Flat-field and edge images were acquired and analyzed according to guidelines set forth by the International Electrotechnical Commission, using the RQA 5 spectrum. The presampled MTF determined using the noise-response method for the simulated detector system was in close agreement with the true MTF with an averaged percent difference of 0.3% and a maximum difference of 1.1% observed at the Nyquist frequency (fN). The edge-response method of the simulated detector system also showed very good agreement at lower spatial frequencies (less than 0.5 fN) with an averaged percent difference of 1.6% but showed significant discrepancies at higher spatial frequencies (greater than 0.5 fN) with an averaged percent difference of 17%. Discrepancies were in part a result of noise in the edge image and phasing errors. For all three detector systems, the MTFs obtained using the two methods were found to be in good agreement at spatial frequencies less than 0.5 fN with an averaged percent difference of 3.4%. Above 0.5 fN, differences increased to an average of 20%. Deviations of the experimental results largely followed the trend seen in the simulation results, suggesting that differences between the two methods could be explained as resulting from the inherent inaccuracies of the edge-response measurement technique used in this study. Aliasing of the correlated noise component was shown to have a minimal effect on the measured MTF for the three detectors studied. Systems with significant aliasing of the correlated noise component (e.g., a-Se based detectors) would likely require a more sophisticated fitting scheme to provide accurate results. Results indicate that the noise-response method, a simple technique, can be used to accurately measure the MTF of digital x-ray detectors, while alleviating the problems and inaccuracies associated with use of precision test objects, such as a slit or an edge.

The pixel array of BSI CMOS image sensor is a kind of photoelectric device to obtain 2D image information. The image quality was evaluated by the modulation transfer function (MTF) of BSI CMOS image sensor pixel at Nyquist frequency. With the decreasing pixel size of BSI CMOS image sensor and the increasing spatial resolution, it is more and more difficult to improve the MTF at Nyquist frequency. According to the theoretical analysis, MTF is composed of aperture MTF and diffusion MTF, the comprehensive MTF function is usually obtained by the multiplication relationship between the two MTFs in the frequency domain. Aperture MTF and diffusion MTF have different influence factors and calculation functions, but they are related to the size of the opening. The opening here represents the sensitivity aperture and photo-sense region respectively. The smaller the opening of the detector pixel, the larger MTF will be. In this paper, the theoretical mechanism of MTF function is analyzed in detail, and the calculation results of MTF of BSI CMOS image sensor pixel under 8 typical optical wavelengths in 300nm-1000nm spectral band are listed.

The ability to improve visualization of structural information in digital radiography without increasing radiation exposures requires improved image quality across all spatial frequencies, especially at high frequencies. The detective quantum efficiency (DQE) as a function of spatial frequency quantifies image quality given by an x-ray detector. We present a method of increasing DQE at high spatial frequencies by improving the modulation transfer function (MTF) and reducing noise aliasing. The Apodized Aperature Pixel (AAP) design uses a detector with micro-elements to synthesize desired pixels and provide higher DQE than conventional detector designs. A cascaded system analysis (CSA) that incorporates x-ray interactions is used for comparison of the theoretical MTF, noise power spectrum (NPS), and DQE. Signal and noise transfer through the converter material is shown to consist of correlated an uncorrelated terms. The AAP design was shown to improve the DQE of both material types that have predominantly correlated transfer (such as CsI) and predominantly uncorrelated transfer (such as Se). Improvement in the MTF by 50% and the DQE by 100% at the sampling cut-off frequency is obtained when uncorrelated transfer is prevalent through the converter material. Optimizing high-frequency DQE results in improved image contrast and visualization of small structures and fine-detail.

Our work is to investigate and understand the factors affecting the imaging performance of amorphous selenium (a-Se) flat-panel detectors for digital mammography. Both theoretical and experimental methods were developed to investigate the spatial frequency dependent detective quantum efficiency [DQE(f)] of a-Se flat-panel detectors for digital mammography. Since the k-edge of a-Se is 12.66 keV and within the energy range of a mammographic spectrum, a cascaded linear system model was developed which takes into account the effect of k-fluorescence on the modulation transfer function (MTF), noise power spectrum (NPS) and DQE(f) of the detector. This model was used to understand the performance of a prototype detector with 85 mm pixel size. The presampling MTF, NPS and DQE(f) of the prototype were measured, and compared to the theoretical calculation by the model. The calculation showed that k-fluorescence reduces the MTF by 15% at the Nyquist frequency (f<SUB>NY</SUB>) of the prototype detector, and the NPS at f<SUB>NY</SUB> was reduced to 82% of that at zero spatial frequency. Because of the decrease in both MTF and NPS at high spatial frequencies, k-fluorescence only has a small degradation effect on DQE(f) for mammography. The measurement of presampling MTF of the prototype detector revealed an additional source of blurring, which was attributed to the blocking layer at the interface between a-Se and the active matrix. This introduced high frequency drop in both presampling MTF and NPS, and reduced aliasing in the NPS. As a result, the DQE(f) of the prototype detector at f<SUB>NY</SUB> approaches 50% of that at zero spatial frequency.

The Modulation Transfer Function (MTF) is a major parameter for high resolution optical remote sensing systems, indicating how spatial frequencies are transmitted and weakened by the imaging global chain. Assessing MTF is thus a very important task during both the in-flight commissioning period and the routine monitoring phases. Classical in flight MTF measurement methods are based upon devoted well known patterns such as knife edge patterns. These techniques induce heavy constraints upon satellite payload programming taking into account nebulosity conditions and pattern ground maintenance. Moreover, for high MTF systems, MTF assessment proves to be difficult because the point spread function has a too reduced extension. Another solution consists in taking two images of the same scene, one in a high resolution mode and the other one in a lower resolution mode. When the resolution ratio is high enough (typically higher then 3), it is possible to simulate the lower resolution image through convolution with a filter and undersampling. The least square method consists in an iterative process, according to which the convolution filter evolves in order to minimize a least square criterion measuring the difference between the simulation and the low resolution image. Once the process has converged, taking the Fourier Transform of the convolution filter gives an estimation of the ratio between low resolution image MTF versus high resolution image MTF. This method may be successfully applied to remote sensing systems such as Quickbird, Ikonos, SPOT5 and future PLEIADES-HR to assess MTF in the multispectral mode. The goal of this paper is to present the MTF assessment method, the way it was validated through simulations and its application within SPOT5 context.

Background Cornea astigmatism can be effectively corrected by implanting Toric intraocular lens (IOL) during cataract surgery and therefore improve visual acuity of patients.However, the decentration and rotation position errors were inevitable sometime.What's the difference of effect of position errors on quality of image between spherical IOL and Toric IOL needs further research. Objective This study was to evaluate the optical performance and wavefront with rotation and decentration of Toric IOL. Methods Different decentration for SN60AT IOL(spherical IOL) and Toric IOL in Hwey-Lan Lion model eyes was set with the role as follows: decentration 0.25 mm to 0.75 mm in a 5°-interval from 0° to 90°.Furthermore, Toric IOL was rotated at 5° and 10°, respectively.Then the image performances of SN60AT IOL and Toric IOL at different decentration distances and rotated degrees were evaluated with modulation transfer function (MTF) and value of wavefront aberration under all conditions. Results At the centration, the MTF curves of spherical IOL and Toric IOL were similar under 3, 4 and 5 mm pupil diameter at each spatial frequency.Under the condition of 4 mm pupil diameter, when the decentration was 0.25 mm, the MTF values of SN60AT IOL at 6 c/d and 12 c/d were 0.581 087 and 0.411 960, respectively.T3 IOL were 0.454 259 and 0.382 313, T4 IOL were 0.426 020 and 0.360 490, T5 IOL were 0.425 606 and 0.359 877.When the decentration was 0.50 mm, the MTF values of SN60AT at 6 c/d and 12 c/d were 0.573 073 and 0.412 787, respectively.T3 IOL were 0.450 943 and 0.379 481, T4 IOL were 0.423 153 and 0.356 664, T5 IOL were 0.422 881 and 0.356 230.When the decentration was 0.75 mm, the MTF values of SN60AT at 6 c/d and 12 c/d were 0.560 038 and 0.413 624, respectively.T3 IOL were 0.445 597 and 0.374 322, T4 IOL were 0.418 522 and 0.350 087, T5 IOL were 0.418 468 and 0.349 976.When the IOL decentralized along 0°, 5°, 10°, 90°meridian line, the MTF values were almostly same.The root mean square (RMS) of spherical IOL and Toric IOL was increased when the IOL decentralized from 0 mm to 0.75 mm, with the most increasing level in coma aberration and slight increase in trefoil aberration.When the T4 IOL decentralized from centre to 0.75 mm, the coma increased from 0 to C(3, -1) -0.049 79 μm, C(3, 1) -0.037 59 μm and the trefoil aberration increased from 0 to C(3, 3) 0.005 72 μm, C(3, -3) 0.004 64 μm.With the increase of rotation degrees (from 5°to 10°) of Toric IOL, the MTF was worse at high spatial frequency.Toric IOL rotation caused the increase of astigmatism and residual astigmatism and spherical error, but not high order aberration. Conclusions The tolerance of Toric IOL to decentration is very close to the spherical IOL, and optical performance is only associated with the amount of decentration but not direction.The aberration caused by Toric IOL decentration is mainly coma.The rotation of Toric IOL causes astigmatism error but not high order aberrations. Key words: Lenses, intraocular; Refraction, ocular/physiology; Astigmatism/physiopathology; Lens implantation, intraocular; Decentration; Optical performance; Visual acuity/physiology; High order aberrations

Thinned aperture optical systems (including phased telescope arrays) pose unique problems in specifying or characterizing image quality. Traditional image quality criteria such as "resolution" and encircled energy are woefully inadequate for many thinned aperture applications. Variations in the subaperture geometry that produce only subtle effects upon the core of the point spread function may produce highly undesirable artifacts or spurious images as well as a modulation transfer function (MTF) that exhibits zero (or negligible) values over substantial regions within the cut-off spatial frequency of a filled aperture circumscribing the array. Clearly, some minimum value of the MTF exists below which spatial information cannot be retrieved in the presence of noise. An MTF property called the "practical resolution limit," defined as the reciprocal of the maximum spatial frequency within which no zeros occur in the MTF, thus becomes the image quality criterion of choice for those applications in which fine detail is required from extended objects. This practical resolution limit and its effect upon subaperture configuration will significantly impact the telescope mechanical architecture, stowage and deployment techniques, and perhaps even the booster vehicle selection for future large space telescopes.

In this chapter, we consider the imaging properties of a system with a circular exit pupil by applying the general formulas derived in Chapter 1. We derive expressions for its point-spread function (PSF), optical transfer function (OTF), and encircled, ensquared, and excluded powers. The effect of aberrations on a PSF is first studied in terms of its central value, i.e., its Strehl ratio. An exact expression is obtained for the Strehl ratio and the results for primary aberrations are compared with those obtained from the approximate expressions based on the phase variance of the aberration across the pupil derived in Chapter 1. The tolerances for primary aberrations are given for a certain value of the Strehl ratio. Balanced primary aberrations are also discussed and they are identified with the Zernike circle polynomials. A defocused PSF is considered next, and it is shown that systems with large Fresnel numbers, such as photographic systems, have a very small depth of focus. However, systems with small Fresnel numbers, e.g., a laser transmitter, have a large depth of focus. Focused and collimated beams are discussed, and the concept of near- and far-field distances is introduced. It is shown that if the Fresnel number of the beam focused on a target is small, the axial irradiance is maximum at a point that is closer to the focusing optics. However, maximum central irradiance on a target at a given distance is obtained when a beam is focused on it, even though a larger irradiance is obtained at a closer point. Aberrated PSFs for rotationally symmetric aberrations are considered, and numerical results are obtained that show that the size of their central spot is practically independent of the aberration. Symmetry properties of the aberrated PSFs are considered next. Full PSFs for primary aberrations are shown graphically and pictorially. A brief comparison of the diffraction and geometrical PSFs is also given. The line of sight of an optical system is identified with the centroid of its PSF and discussed for aberrated systems. It is shown that only coma-type aberrations change the line of sight. The OTFs for primary aberrations are discussed, and the concept of contrast reversal is described. The OTF aberrated by coma is complex, and we give its real and imaginary parts as well as its modulus and phase. Aberration tolerances are given for a certain value of the Hopkins ratio. The geometrical OTF is also discussed and approximate expressions for it are obtained for the primary aberrations. It gives reasonably accurate results in the region of very low spatial frequencies, a region of practical interest when the MTF of an aberrated system at high frequencies is practically negligible. It is shown that the MTF averaged over all angular orientations of a spatial frequency vector is maximum when the standard deviation of the ray aberration [i.e., the root mean square (rms) radius of the spot diagram with respect to its centroid] is minimum. The diffraction OTF is shown to approach the geometrical OTF in the limit of zero wavelength. The differences between the diffraction and geometrical OTFs are summarized. The incoherent line- and edge-spread functions are discussed, and numerical results for both the aberration-free and the aberrated systems are given. The aberration tolerances for a certain value of the Struve ratio are also given.

Objective To evaluate the parallactic unsharpness caused by flat panel detector in digital radiography using different incident angle of central ray. Methods R-1 square-wave phantom was exposed by Kodak DR3000 system with X-ray tube angled 0°, 10°, 20°, 30°, and 40° respectively. Then,presampled modulation transfer function (MTF) was calculated for each case above. Subsequently,experimental data were processed and Wilcoxon signed ranks test were performed by statistic software SPSS 10. 0, in which P ＜ 0. 05 was considered as statistically significant difference. Results The presampled MTF curves of incident angle of 0°-40° degree, were presented orderly from top to bottom, especially the incident angle of 40° was obviously the lowest. The incident angle of 0° was considered as a control group and other groups were compared against it. There was no statistically significant difference for MTF of incident angle of 10°( Z = - 1. 893 ,P = 0. 058 ), while there were significant difference for MTF of incident angle of 20°, 30°, and 40° ( Z = - 2. 547, - 2. 666, - 2. 666, P ＜ 0. 05 ). Conclusions For flat panel detector in digital radiography, the bigger the incident angle of central ray, the larger the parallactic unsharpness. In addition, this effect has less influence on structures of low spatial frequency than those of high spatial frequency. Key words: Radiography; Evaluation studies; Quality control