Angular dependence of sampling modulation transfer function

Sampling modulation transfer function (MTF) as defined in Park et al. [Appl. Opt. 23, 2527-2582 (1984)] as an x and y sampling can be generalized for image data not along x and y directions. For a given sampling lattice (such as in a laser printer, a scene projector, or a focal-plane array), we construct a two-dimensional sampling MTF based on the distance between nearest samples in each direction. Because the intersample distance depends on direction, the sampling MTF will be best in the directions of highest spatial sampling and poorer in the directions of sparse sampling. We compare hexagonal and rectangular lattices in terms of their equivalent spatial frequency bandwidth. We filter images as a demonstration of the angular-dependent two-dimensional sampling MTF.     

Conjugate phase plate use in analysis of the frequency response of imaging systems designed for extended depth of field

We unveil a relationship between generating a point spread function with a pair of conjugate phase elements and visualizing the modulation transfer function (MTF) of a single phase element for a variable focus error, at a tunable spatial frequency. We show that the defocused MTF of a pair of conjugate phase elements can be expressed as the modulus of the second order ambiguity function of a single phase element. Finally, we propose a tunable wavefront coding technique with a pair of quartic (4th power) conjugate phase elements.     

Modulation transfer function evaluation of linear solid-state x-ray-sensitive detectors using edge techniques

The exact determination of the modulation transfer function (MTF) of a physical system is a persistent problem. We present a practical method of measuring numerically the MTF of linear solid-state x-ray-sensitive detectors. The method is based on the use of edge techniques and allows us to obtain the MTF of a linear detector from its edge-spread function (ESF). ESF measurement techniques are discussed in detail, and calculation of the corresponding MTF's are shown.     

Modulation transfer function measurement of sparse-array sensors using a self-calibrating fringe pattern

A simple method for the measurement of the pixel modulation transfer function (MTF) of sparse-array (extended MTF) sensors has been developed. We use a phase-shifting Twyman-Green interferometer to generate a series of single spatial-frequency fringe patterns incident on the sensor The resulting signal modulation is measured. We achieve self-calibration by restricting the measured spatial frequencies to multiples of the Nyquist frequency. The aliased patterns at these frequencies are unique and easily identifiable. Spatial frequencies of 480 cycles/mm are generated and measured. This frequency value is more than ten times that of the sensor sampling frequency. The expected MTF shape is obtained at multiples of the sampling frequency. At odd multiples of the Nyquist frequency, the MTF's are affected by the electronic bandwidth and cross talk in the charge-injection device sensor.     

A Review of Current Image-Evaluation Techniques

The characteristics of image-evaluation techniques are reviewed in relation to their use in the design and testing of photographic systems. Each technique has advantages and limitations; no one technique can serve all purposes. Resolving power takes account of many factors that affect image quality, hence it can be a significant measure of system performance; for the same reason it is inaccurate and inherently unsuitable for measuring the performance of lenses. The MTF is potentially more accurate than resolving power, but by itself lacks significance because it omits important factors in the system. Nevertheless the MTF is an invaluable aid in design and analysis as well as in research. The importance of adequate calibration of MTF equipment and of standardization of resolving power targets is stressed. The possibilities of a calculated resolving power based on the MTF and a signal to noise ratio are mentioned. Problems of evaluating the MTF in practically significant ways, and the advantages of the single bar target for interpreting it in spatial terms, are discussed.     

Modulation transfer function measurement method for electrically addressed spatial light modulators

The modulation transfer function (MTF), when used with amplitude modulation (m(A)) data, is a vital coherent optical performance measure for a spatial light modulator (SLM). A new image plane amplitude MTF (MTF(A)) measurement method is presented for electrically addressed SLMs. It involves digital analysis of the output image of a square-wave pattern written onto the SLM. Modulation-level effects are also addressed. Optical laboratory results are presented for two liquid-crystal SLMs. The need to consider amplitude rather than intensity modulation (when coherent optical processing applications are considered) is noted in terms of SLM biasing.     

Best Focal Planes Determined by Different Image Quality Criteria

Relative contrast values that correspond to the best focal planes defined by minimizing the different image quality criteria are examined in the whole frequency range. The quality criteria are those commonly employed as merit functions in automatic optical design: the wavefront variance, the variance of the difference function and the geometrical r.m.s. spot size. Analogous results obtained when the diffraction-based modulation transfer function (MTF) is directly maximized by numerical searching for the true best focal plane at a given spatial frequency, are also computed. The results show how the image quality criteria correlate with the true frequency response for different states of correction at various spatial frequencies. Since odd aberrations do not change the localization of the best focal places defined by the three criteria chosen for consideration, the spherical aberration case is selected for detailed investigations. A number of conclusions of direct importance in optical design and testing are made.     

Analytical optimal solution of the extension of the depth of field using cubic-phase wavefront coding. Part I. Reduced-complexity approximate representation of the modulation transfer function

In this paper we derive an approximate analytical representation for the modulation transfer function (MTF) of an imaging system possessing a defocused cubic-phase pupil function. This expression is based on an approximation using the Arctan function and significantly reduces the computational time required to calculate the resulting MTF. We derive rigorous bounds on the minimum and average accuracy of our approximation. Using this approximate representation of the MTF, the analytical solution of the problem of calculating the extension of the depth of field for a circular aperture with a cubic phase mask becomes possible. We also comment on how one can modify our method to construct a lower-bound or an upper-bound approximate analytical expression for the MTF.     

Modulation transfer function of antenna-coupled infrared detector arrays

Individual antenna-coupled IR bolometers have recently been demonstrated at wavelengths near 10 μm. If focal-plane arrays (FPA's) of antenna-coupled detectors can be fabricated, enhancement of IR-imager performance is possible. A first step in the design process is to analyze the image-quality potential of antenna-coupled, FPA-based imagers in terms of the modulation transfer function (MTF). The key step in our analysis is development of a cross-talk MTF that accounts for the electromagnetic coupling between adjacent antennas in the FPA. We find that electromagnetic cross talk will not be a significant image-quality factor in antenna-coupled IR FPA's.     

用CCD测量光学系统OTF的研究

线性光学系统的光学传递函数可由线扩散函数的付立叶变换求出。本文研究了用电荷耦合器件测量光学系统OTF的系统,用CCD作为光电转换器件,对CCD接收到的LSF的光强信号进行视频放大,采样一保持、A/D转换接口到计算机,可方便而精确地测得光学系统的OTF。为了避免采用高速A/D和DMA方式,对CCD的信号处理采用分时处理。用CCD测量MTF的误差为3%,不重复性为1%,能在2分钟之内测试出物镜的10种空间频率的MTF值。     

Atmospheric modulation transfer function in the infrared

In high-resolution ultranarrow field-of-view thermal imagers, image quality over relatively long path lengths is typically limited by atmospheric degradation, especially atmospheric blur. We report our results and analyses of infrared images from two sites, Fort A. P. Hill and Aberdeen Proving Ground. The images are influenced by the various atmospheric phenomena: scattering, absorption, and turbulence. A series of experiments with high-resolution equipment in both the 3-5- and 8-13-microm regions at the two locations indicate that, as in the visible, image quality is limited much more by atmosphere than by the instrumentation for ranges even of the order of only a few kilometers. For paths close to the ground, turbulence is more dominant, whereas for paths involving higher average elevation, aerosol modulation transfer function (MTF) is dominant. As wavelength increases, turbulence MTF also increases, thus permitting aerosol MTF to become more dominant. A critical role in aerosol MTF in the thermal infrared is attributed to absorption, which noticeably decreases atmospheric transmission much more than in the visible, thereby reducing high-spatial-frequency aerosol MTF. These measurements indicate that atmospheric MTF should be a basic component in imaging system design and analysis even in the infrared, especially as higher-resolution hardware becomes available.     

An Afocal-system OTF Test Standard

Several standard test lenses for evaluating the accuracy of OTF measuring equipment have been described in the literature. However, these are not generally suitable for evaluating the equipment and test procedures used for afocal systems which differ from those used with normal lenses in several significant ways. A special afocal system in the form of a straight-through telescope has been designed and built for this purpose. The paper describes the design and construction of this telescope and compares the calculated and experimentally measured values for the MTF of the system. A particular feature of the MTF calculations is that they have been carried out, not only for the usual radial and tangential azimuths, but also for several intermediate azimuths. Thus it has been possible to determine the value of a range of different MTF-based criteria which relate to measuring equipment where the MTF is measured at a single spatial frequency in all azimuths.     

Interferometric measurement of the modulation transfer function of a spectrometer by using spectral modulations

We present our results on measurement of the modulation transfer function (MTF) of a given spectrometer by using the sinusoidally modulated spectrum from a Michelson interferometer with white light. We studied the MTF by varying the periodicity of the spectral fringes produced by the interferometer. Experimental data are fitted to a theoretical model to derive the spectral slit width from the measured MTF of the spectrometer.     

Analysis of MTF degradation in the imaging of cells in a flow system

The time-delay and integration method can be used with a charge-coupled device array to acquire images of cell in a flow cytometer. The loss of high spatial frequency components in images acquired with this technique is studied by deriving the modulation transfer function (MTF) for each of the main causes of image degradation: finite sampling aperture, nonsynchronism between image movement and charge transfer rate, discrete charge motion, transfer inefficiency, and axis misalignment. The system MTF and resolution in the horizontal and vertical directions are then examined.©1994 John Wiley & Sons Inc     

Novel approaches to the design of halftone masks for analog lithography

We report novel approaches to the design of halftone masks for analog lithography. The approaches are derived from interferometric phase contrast. In a first step we show that the interferometric phase-contrast method with detour holograms can be reduced into a single binary mask. In a second step we introduce the interferometric phase-contrast method by interference of the object wavefront with the conjugate object wavefront. This method also allows for a design of a halftone mask. To use kinoform holograms as halftone phase masks, we show in a third step the combination of the zeroth-order phase-contrast technique with the interferometric phase-contrast method.     

Making optical low-pass spatial filters by thin-film phase grating

A modified rule was applied to design a grating optical low-pass spatial filter (GOLF) with a thin-film phase grating. This filter differed from the crystal type of optical low-pass spatial filter (OLPF). The fabrication method of the thin-film phase GOLF was also different from the conventional lithographic process. A new fabrication method utilizing a metal mesh mask and a thin-film coating process was applied to make the GOLF. The process had the advantages of being simple and cheap, and would thus be good for mass-production. The modulation transfer function (MTF) of the device was measured and the results agree well with the theoretical calculations. Finally, the GOLF was installed on a digital camera which was used to capture images of the circular zone plane (CZP), to show the Moiré pattern suppression ability.     

Comparison of Sagnac and Mach-Zehnder ultrafast all-optical interferometric switches based on a semiconductor resonant optical nonlinearity

We present a theoretical analysis of recently demonstrated ultrafast all-optical interferometric switching devices (based on Sagnac and Mach-Zehnder interferometers) that use a large optical nonlinearity in a resonant regime. These devices achieve ~10-ps switching windows and do not require high-energy optical control pulses. We theoretically analyze and compare one Sagnac and two Mach-Zehnder switching configurations.     

Investigations Regarding the Measurement of the Modulation Transfer Function and Possibilities for its Designation by a Numerical Value

A step by step analysis of the photographic image forming process is used to explain the possible restrictions on the range of validity of the modulation transfer function (MTF). In general the MTF characterizes a film-developer-system within a given range of exposure and contrast. Other functions to describe the spatial frequency response are discussed. The use of photographic film as a photometer is distinguished from the use as image reproducer on behalf of the use of the proper signal functions. The interaction between the aperture of the exposing pencils and the thickness of the coating is investigated experimentally and a simple formula is proposed to describe it. The possibilities of characterizing the MTF by one single numerical value are discussed.     

圆孔阵列对“猫眼”目标成像质量的影响分析

利用圆孔阵列光强调制作用可以有效减弱光学窗口的“猫眼”效应,同时也会对“猫眼”目标成像质量产生一定不利影响.考虑到利用调制传递函数(MTF)可对光电仪器成像质量进行综合评价,分别给出了测试望远系统和微光夜视系统MTF的数学模型,利用自行研制的光学仪器MTF数字化检测系统,实现了这两种典型“猫眼”目标MTF的数字化检测.结果表明,圆孔阵列在全空间频率上均使“猫眼”目标的MTF有所下降,且孔径较小、孔阵较密的圆孔阵列对“猫眼”目标MTF的影响较小,这为合理设计圆孔阵列结构以减小对“猫眼”目标成像质量的影响提供了可靠的实验数据.     

Assessment of a CRT Display System

The use of cathode ray tube (CRT) monitors and graphics cards for the display of pictorial images is common. Certain applications require the characteristics of the display device or medium to be accurately understood. One such application is the use of CRT based displays in experiments involving subjective analysis of viewed images. In this paper we describe a series of experiments performed to characterize a display device used in our laboratories prior to its use in a subjective assessment experiment. The tone reproduction characteristics are studied using transfer functions and gamma. Colour reproduction is studied in temporal and spatial dimensions. Finally, spatial effects are characterized by use of modulation transfer function (MTF) analysis.