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Simplified model of image forming in spaceborne linear array sensors at arbitrary sight angles is proposed in this paper. On basis of evaluation of system "lens - linear array detector" modulation transfer function (MTF), the equations were obtained that allow you to determine spatial resolution on Earth’s surface. An example of pushbroom imager’s MTF determination at sight of Nadir and with different slopes of lens optical axis is given. Image quality changes, which accompany lens optical axis angular inclination were studied. More research needed to determine the impact of lens aberrations on imager’s MTF with arbitrary viewing angles.

The applications of fluorescence microscopy span medical diagnostics, bioengineering and biomaterial analytics. Full exploitation of fluorescent microscopy is hampered by imperfections in illumination, detection and filtering. Mainly, errors stem from deviations induced by real-world components inducing spatial or angular variations of propagation properties along the optical path, and they can be addressed through consistent and accurate calibration. For many applications, uniform signal to noise ratio (SNR) over the imaging area is required. Homogeneous SNR can be achieved by quantifying and compensating for the signal bias. We present a method to quantitatively characterize novel reference materials as a calibration reference for biomaterials analytics. The reference materials under investigation comprise thin layers of fluorophores embedded in polymer matrices. These layers are highly homogeneous in their fluorescence response, where cumulative variations do not exceed 1% over the field of view (1.5 x 1.1 mm). An automated and reproducible measurement methodology, enabling sufficient correction for measurement artefacts, is reported. The measurement setup is equipped with an autofocus system, ensuring that the measured film quality is not artificially increased by out-of-focus reduction of the system modulation transfer function. The quantitative characterization method is suitable for analysis of modified bio-materials, especially through patterned protein decoration. The imaging method presented here can be used to statistically analyze protein patterns, thereby increasing both precision and throughput. Further, the method can be developed to include a reference emitter and detector pair on the image surface of the reference object, in order to provide traceable measurements.

Increasing challenges of the industry to improve camera performance with control and test of the alignment process will be discussed in this paper. The major difficulties, such as special CFAs that have white/clear pixels instead of a Bayer pattern and non-homogeneous back light illumination of the targets, used for such tests, will be outlined and strategies on how to handle them will be presented. The proposed algorithms are applied to synthetically generated edges, as well as to experimental images taken from ADAS cameras in standard illumination conditions, to validate the approach. In addition, to consider the influence of the chromatic aberration of the lens and the CFA’s influence on the total system MTF, the on-axis focus behavior of the camera module will be presented for each pixel class separately. It will be shown that the repeatability of the measurement results of the system MTF is improved, as a result of a more accurate and robust edge angle detection, elimination of systematic errors, using an improved lateral shift of the pixels and analytical modeling of the edge transition. Results also show the necessity to have separated measurements of contrast in the different pixel classes to ensure a precise focus position.

Optical components in large aperture optical imaging system are susceptive to intense laser radiation. Optical band pass filter for spectra selection and nonlinear filter for intense laser blocking, are usually focal or near focal elements in imaging system, will more likely to be permanently damaged by high intense unwanted laser irradiating. In order to relate the optical imaging performance degradation to laser irradiating parameters, characteristics of the damage sites and so on, a test facility consisting of scaled electro-optical imaging system and standard imager evaluation system was constructed, and the linear spread function, modulation transfer function, signal transfer function, and noise power spectrum were obtained. Experimental imaging performance degradation law of damaged fused silica and colored glass filters were analyzed. Furthermore, some brief discussions on the imaging performance degradation mechanisms are also presented.

As pixel sizes reduce in the development of modern High Definition (HD) Mid Wave Infrared (MWIR) detectors the interpixel cross-talk becomes increasingly difficult to regulate. The diffusion lengths required to achieve the quantum efficiency and sensitivity of MWIR detectors are typically longer than the pixel pitch dimension, and the probability of inter-pixel cross-talk increases as the pixel pitch/diffusion length fraction decreases. Inter-pixel cross-talk is most conveniently quantified by the focal plane array sampling Modulation Transfer Function (MTF). Cross-talk MTF will reduce the ideal sinc square pixel MTF that is commonly used when modelling sensor performance. However, cross-talk MTF data is not always readily available from detector suppliers, and since the origins of inter-pixel cross-talk are uniquely device and manufacturing process specific, no generic MTF models appear to satisfy the needs of the sensor designers and analysts. In this paper cross-talk MTF data has been collected from recent publications and the development for a generic cross-talk MTF model to fit this data is investigated. The resulting cross-talk MTF model is then included in a MWIR sensor model and the impact on sensor performance is evaluated in terms of the National Imagery Interoperability Rating Scale’s (NIIRS) General Image Quality Equation (GIQE) metric for a range of fnumber/ detector pitch Fλ/d configurations and operating environments. By applying non-linear boost transfer functions in the signal processing chain, the contrast losses due to cross-talk may be compensated for. Boost transfer functions, however, also reduce the signal to noise ratio of the sensor. In this paper boost function limits are investigated and included in the sensor performance assessments.

An objective performance of the reflective-band imaging systems is required in order to provide the warfighter with the right technology for a specific task. Various methods to measure and model performance in the visible (Vis) spectral regions have been proposed in the literature. This correspondence shows the influence of the spectral region averaging on the monochromatic modulation transfer function (MTF). This works unequivocally shows that the illumination source plays a crucial role in the accurate predictive analysis of the system performance. For accurate analysis the illumination sources need to be carefully considered for the atmospheric conditions. This work shows the possibility of using an LED configuration in the system performance analysis. Such configurations need rigorous calibration in order to become a valuable asset in system characterization.

The critical dimension(CD) is main factor to determine the line width of semiconductor equipment fabricating ability for the smallest line width of produced electronic components. Modulation transfer function(MTF) has been popularly used to evaluation the optical system, due to the contrast of each line-pair in dimension analytically, however, while the light source is coherent or near coherent for the small dimension near the optical diffraction limit, the MTF is hard to achieve consistently. The study of ultra-violet partial coherence modulation transfer function is to calculate the 1-D and 2-D the line with anoptical design program, to estimate the MTF near the size of diffraction limit. It provides fabricating parameter for a 1-to-1 TSV lithographic system. By applying partial coherence analysis, the optimized relative numerical aperture (RNA) has found. As the system is built, the optimized performance should be expected.

An imaging system’s spatial quality can be expressed by the system’s modulation spread function (MTF) as a function of spatial frequency in terms of the linear response theory. Methods have been proposed to assess the MTF of an imaging system using point, slit or edge techniques. The edge method is widely used for the low requirement of targets. However, the traditional edge methods are limited by the edge angle. Besides, image noise will impair the measurement accuracy, making the measurement result unstable. In this paper, a novel measurement method based on the support vector machine (SVM) is proposed. Image patches with different edge angles and MTF levels are generated as the training set. Parameters related with MTF and image structure are extracted from the edge images. Trained with image parameters and the corresponding MTF, the SVM classifier can assess the MTF of any edge image. The result shows that the proposed method has an excellent performance on measuring accuracy and stability.

We have presented the plastic based ultra-compact aspheric lens for disposable epidural spinal endoscope. We have also showed the analysis of the stray light distribution on the image plane using optical illumination system design software (Light Tools). The optical system consists of the aspheric lens with a size of 1.4mm (total track of optical system). The effective length and field of view (FOV) is 0.66mm and 90 degrees. The distortion of the optical system is below 25%. The curves of modulation transfer function (MTF) are higher than 0.3 at 80 line pairs/mm (lps/mm) in image space. For the analysis of stray light, we assumed that the 98 percent of incident light is absorbed inside lens barrel and the rest is scattered on the inner surfaces of the lens barrel. The average value of stray light is 0.16% in the image intensity. The maximum stray light and minimum stray light of the proposed optical system is 0.57% and 0.0005% in the image intensity, respectively. The effective transmission rate of the proposed optical system is 89.6%.

The need for stability of aberration and correction of images for a zoom lens system should be considered during zooming process. Our work presents detailed theoretical and experimental analysis of multiple moving zoom optical systems. In our work we propose methods to determine the basic parameters of such optical system, the focal lengths of each element of the objective lens and their mutual axial separation. Introduce two different image stability equation and cam curve design method to calculate basic parameters. This type of optical system is widely spread in practice mainly in the field of photographic lenses and in surveying instruments (theodolites, leveling instruments, etc.). Furthermore, the detailed analysis of aberration properties of such optical systems is performed and methods for measuring the focal lengths of individual elements and their mutual distance without the need for disassembling the investigated optical system are presented. Finally according to theoretical and experimental analysis of zoom lens system, a zoom optical system with effective focal length 27-220mm has been design, the first element of such system is fixed, and the other groups can move during zoom process to get a continuity consecutiveness effective focal length (EFL). Using the powerful optimization capabilities of optical design software CODE V; we get the imaging quality analysis such as the modulation transfer function (MTF) etc. © 2017 SPIE.

The off-axis parabolic collimator with eccentric pupil has the advantages of wide spectrum, simple structure, easy assembly and adjustment, high performance price ratio. So, it is widely used for parameters testing and image quality calibration of ground-based and space-based cameras. In addition to the Strehl ratio, resolution, wavefront aberration, modulation transfer function, the general evaluation criteria on the imaging quality of the optical system, the beam parallelism characterize the collimator angle resolving capability and collimation condition of the collimator with the target board, can be measured easily ,quickly and operation process is simple, but the study mainly focus on how to measure it so far. In order to solve Quantitative calculation of this problem, firstly, the discussion of aberration condition of the off- axis parabolic is carried out based on the primary aberration theory. Secondly, analysis on the influencing factor on collimator optical properties is given, including the geometrical aberrations of spherical aberration, coma, astigmatism , the relation between the position of the eccentric pupil and the aberration and optical element surface wavefront aberration, after that, according to the basis of diffraction and wavefront aberration theory, the paper deduced calculation method of the beam parallelism, at last, an example of a 400mm diameter off-axis parabolic collimator with eccentric pupil is given to calculate, the practical results shows that calculation data is well in accordance with actual measurement data and results can meet the demand and has a guiding significance to the actual project manufacture and the theory analysis.

For 640 pixel×512 pixel cooled staring focal plane array detector, a VisSWIR wideband continuous zoom optical system with 7X zoom range is presented based on the pattern of the negative zoom group and compensating lens group. The zoom system provides continuous changed in the field of view from narrow to the wide. The zoom optical system works in the range of 0.4μm~1.7μm, F number is 4, the pixel of the detector is 15μm. It realizes 20mm~140mm continuous zoom with a smooth zoom path and provided high image quality with the whole zoom range, the zoom ratio is 7:1. The modulation transfer function(MTF) for the system is above 0.5 within the whole focal length range at spatial frequency of 34lp/mm and it almost approaches the diffraction limit. RMS value of spot diameter was investigation, the maximum distortion value is less than 5% and the surface type of all lens applied is spherical. Moreover, the cam curve after optimization is given by the optical design software Code V macro. The design results provide that the zoom system has the small size, high resolution, excellent image quality and the smooth cam curve etc.

Optical system alignment has a great influence on the whole system accuracy. In this paper, the processing of optical system alignment was mainly studied, the processing method of optics on the primary and secondary mirrors, front correction lens group and behind correction lens group with high precision centering lathe and internal focusing telescope. Then using the height indicator complete the system alignment of the primary mirror, secondary mirror, front correction group and behind correction group. Finally, based on the zygo interferometer detect the wavefront information. Using this alignment program for catadioptric optical system, the wavefront aberration of optical system, focal length, modulation transfer function (MTF) and other technical indicators have reached the requirements.

With the increasing demand of the high-resolution remote sensing images by military and civilians, Countries around the world are optimistic about the prospect of higher resolution remote sensing images. Moreover, design a visible/infrared integrative optic system has important value in earth observation. Because visible system can’t identify camouflage and recon at night, so we should associate visible camera with infrared camera. An earth observation optical system with dual spectral and high resolution is designed. The paper mainly researches on the integrative design of visible and infrared optic system, which makes the system lighter and smaller, and achieves one satellite with two uses. The working waveband of the system covers visible, middle infrared (3-5um). Dual waveband clear imaging is achieved with dispersive RC system. The focal length of visible system is 3056mm, F/# is 10.91. And the focal length of middle infrared system is 1120mm, F/# is 4. In order to suppress the middle infrared thermal radiation and stray light, the second imaging system is achieved and the narcissus phenomenon is analyzed. The system characteristic is that the structure is simple. And the especial requirements of the Modulation Transfer Function (MTF), spot, energy concentration, and distortion etc. are all satisfied.

We propose using the time multiplexing super resolution method in order to extend the depth of focus of an imaging system. In standard time multiplexing the super resolution is achieved by generating duplication of the optical transfer function in the spectrum domain by using moving gratings. By changing the grating's frequency, and by that changing the duplication positions, it is possible to obtain an extended depth of focus. Using the same concept, it is also possible to correct geometrical aberrations of the imaging lens. The proposed method is presented analytically, demonstrated via numerical simulations, and validated by a laboratory experiments.

X-ray phase contrast imaging (XPCI) is a novel method that exploits the phase shift for the incident X-ray to form an image. Various XPCI methods have been proposed, among which, in-line phase contrast imaging (IL-PCI) is regarded as one of the most promising clinical methods. The contrast of the interface is enhanced due to the introduction of the boundary fringes in XPCI, thus it is generally used to evaluate the image quality of XPCI. But the contrast is a comprehensive index and it does not reflect the information of image quality in the frequency range. The modulation transfer function (MTF), which is the Fourier transform of the system point spread function, is recognized as the metric to characterize the spatial response of conventional X-ray imaging system. In this work, MTF is introduced into the image quality evaluation of the IL-PCI system. Numerous simulations based on Fresnel - Kirchhoff diffraction theory are performed with varying system settings and the corresponding MTFs were calculated for comparison. The results show that MTF can provide more comprehensive information of image quality comparing to contrast in IL-PCI.

Due to the exotic freeform surface exhibited by Progressive Addition Lenses, a new characterization approach that takes into account the projection of the eye pupil over the lens is required. In this work, a locally resolved description of the performance of the lens has been obtained by calculating the Modulation Transfer Function (MTF) for uniformly spaced subaperture positions. This quality metric is conveniently suitable to characterize imaging systems, because it describes the contrast resolving capabilities of the lens as a function of the spatial frequency. In addition, it is independent of the eye perception of the test engineer. The MTF has been indirectly calculated using Experimental Ray Tracing, by extracting the values of the ray slopes of each subaperture from the complete ray traced data. By following this procedure, two-dimensional maps are generated using two different criteria. The first criterion is based on the determination of the normalized spatial frequency where the MTF has declined by 50 %. The second one uses a simplified Strehl ratio. Also, the results for different subaperture diameters are obtained without the need for changing the setup or repeating the measurements.

We have presented a novel Single Snapshot Multiple Frequency Demodulation (SSMD) method enabling single snapshot wide field imaging of optical properties of turbid media in the Spatial Frequency Domain. SSMD makes use of the orthogonality of harmonic functions and extracts the modulation transfer function (MTF) at multiple modulation frequencies and of arbitrary orientations and amplitudes simultaneously from a single structured-illuminated image at once. SSMD not only increases significantly the data acquisition speed and reduces motion artifacts but also exhibits excellent noise suppression in imaging as well. The performance of SSMD-SFDI is demonstrated with experiments on both tissue mimicking phantoms and in vivo for recovering optical properties. SSMD is ideal in the implementation of a real-time spatial frequency domain imaging platform, which will open up SFDI for vast applications in, for example, mapping the optical properties of a dynamic turbid medium or monitoring fast temporal evolutions.

We present a novel approach for single snapshot determination of absorption coefficient based on multi-frequency modulation transfer function (MTF) characterization from measurement in spatial frequency domain. The adopted Fourier transform domain analysis enables simultaneous extraction of information at multiple applied frequencies and excellent reduction of noise. Simulations were conducted for respectively verifying the feasibility of the MTF based approach and the performance of single snapshot determination of absorption coefficient using multi-frequency measurements. Phantom experiments without reference measurement demonstrated the high accuracy of absolute absorption coefficient determination with a maximum reconstruction error of 0.002 mm-1.

In order to improve the remote target detection ability of infrared (IR) images effectively, an infrared telephoto objective for 3μm~5μm and 8μm~12μm dual wave-band is designed for 640 pixel×512 pixel infrared CCD detector. The effects of the surrounding environmental temperature are analyzed and the refractive diffractive hybrid thermal compensation is discussed. The focal length of the system is 200mm, the relative aperture is 1:2.2 and the field of view is 7°. The infrared dual band telephoto system with small volume and compact structure is designed in a large range of temperature. The system is composed of four lenses with only three materials of zinc sulfide, zinc selenide and germanium to compensate for the temperature. The image quality of the system is evaluated by ZEMAX optical design software. The results show that the modulation transfer function (MTF) for each field of view at cut-off frequency of 17 lp/mm are respectively greater than 0.6 and 0.4 which approaches the diffraction limit. The telephoto objective has favorable performance at the working temperature of -40°C~+60°C. The relative aperture, field of view, and focal length are same for both spectral regions. The system meets the requirements of technical specification.

As athermal design is an important issue in the field of infrared optical system design, this paper originated a test procedure on athermal design effect based on optical transfer function gauge. In this procedure, we let the optical system under test automatically focus first, then record its focus position under different temperatures, finally get the relative defocusing amount of the optical system under test under different temperature. This paper also developed a test system of a kind of athermal design effect, introduced its system composition and its working principle of measuring the defocusing amount, and gave the experiment results. The results suggest that it can focus fast, its repeatability is good, and it can resist noise interference with high precision.

Traditional slanted knife-edge method experiences large errors in the camera modulation transfer function (MTF) due to tilt angle error in the knife-edge resulting in non-uniform sampling of the edge spread function. In order to resolve this problem, a non –uniform sampling knife-edge method for camera MTF measurement is proposed. By applying a simple direct calculation of the Fourier transform of the derivative for the non-uniform sampling data, the camera super-sampled MTF results are obtained. Theoretical simulations for images with and without noise under different tilt angle errors are run using the proposed method. It is demonstrated that the MTF results are insensitive to tilt angle errors. To verify the accuracy of the proposed method, an experimental setup for camera MTF measurement is established. Measurement results show that the proposed method is superior to traditional methods, and improves the universality of the slanted knife-edge method for camera MTF measurement.

Modulation Transfer Function(MTF) is an important imaging quality indicator of optical system, in order to evaluate the imaging quality for a space remote sensing TDICCD camera, the MTF testing system，including hardware components and software components, was established based on refocusing system. Firstly, the design of Three Mirror Anastigmatic (TMA) optical system and the long interlace assemble TDICCD focal plane were introduced. Secondly, the construction and the schematic diagram of the refocusing system was presented in detail, as well as the relationship between refocusing range and position encoder for interlace assemble TDICCD focal plane. Thirdly, the schematic diagram of the MTF testing system was given, and the relationship between MTF and contrast transfer function(CTF) was discussed. Finally, on the basis of the schematic diagram of CTF, the transfer process of a square wave target was investigated. The testing results indicate that the MTF testing system can measure the CTF of every TDICCD on the focal plane in the focusing range, which meet the requirement of evaluation of imaging quality for a space TDICCD camera.

Due to the loss of the flexibility of the crystalline lens, presbyopia is the most common vision dysfunction for adults after 40. To correct presbyopia, this paper presents a design of a MIOL, which can give extended clear vision range both in photopic vision(3mm pupil diameter) and in the mesopic vision(4.5mm pupil diameter). With a pseudophakic eye model, a multi-configuration with object distance covering a full range of normal visual from 8m to 0.4m was applied. The surfaces of MIOL were aspherical diffractive surface. MIOL was divided into two regions: the inner zone was optimized when the pupil diameter was 3mm and the outer zone was optimized when the pupil diameter was 4.5mm. Finally, we got a 22 diopters (D) MIOL with a central thickness of 0.652mm and an optical diameter of 4.5mm. By evaluating the modulation transfer function, we got optical performance of the pseudophakic eye with this MIOL. When the pupil diameter of pseudophakic eye was 3mm, MTF at 50c/mm and 100c/mm was respectively above 0.4 and 0.15 for the object distance from 8m to 0.4m. When the pupil diameter of pseudophakic eye was 4.5mm, MTF at 50c/mm and 100c/mm was respectively above 0.25 and 0.09 for the object distance from 8m to 0.4m.The visual acuity was above 0.9 for the whole visual range at both of two pupil diameters. Therefore it is safe to say that the new MIOL design provides good optical performance for whole visual range under both of the photopic vision and the mesopic vision.

When the environment temperature has changed, then each parameter in infrared lens has also changed, thus the image quality became bad, so athermal technology is one of key technology in designing infrared lens. The temperature influence of each parameter in infrared lens is analyzed in the paper. In the paper, an athermal mid-wave infrared optical system with long focal length by Code-v optical design software was presented. The parameters of the athermal infrared system are 4.0 f/number, 704mm effective focal length (EFL) , 1° field of view and 3.7-4.8 μm spectrum region 100% cold shield efficiency. When the spatial frequency is 16lp/mm, the Modulation Transfer Function (MTF) of all the field of view was above 0.5 from the working temperature range -40℃ to 60℃. From the image quality and thermal analysis result, we knew that the lens had good athermal performance.

High-resolution remote sensing satellites (HRRSS) that use time delay and integration (TDI) CCDs have the potential to introduce large amounts of image smear. Clocking and velocity mismatch smear are two of the key factors in inducing image smear. Clocking smear is caused by the discrete manner in which the charge is clocked in the TDI-CCDs. The relative motion between the HRRSS and the observed object obliges that the image motion velocity must be strictly synchronized with the velocity of the charge packet transfer (line rate) throughout the integration time. During imaging an object off-nadir, the image motion velocity changes resulting in asynchronization between the image velocity and the CCD’s line rate. A Model for estimating the image motion velocity in HRRSS is derived. The influence of this velocity mismatch combined with clocking smear on the modulation transfer function (MTF) is investigated by using Matlab simulation. The analysis is performed for cross-track and along-track imaging with different satellite attitude angles and TDI steps. The results reveal that the velocity mismatch ratio and the number of TDI steps have a serious impact on the smear MTF; a velocity mismatch ratio of 2% degrades the MTF smear by 32% at Nyquist frequency when the TDI steps change from 32 to 96. In addition, the results show that to achieve the requirement of MTF smear ≥ 0.95 , for TDI steps of 16 and 64, the allowable roll angles are 13.7° and 6.85° and the permissible pitch angles are no more than 9.6° and 4.8°, respectively.

Development and operational planning for ocean color satellite requires lots of careful consideration of the spatial and radiometric performance, which are represented by modulation transfer function (MTF) and signal-to-noise ratio (SNR) respectively. Those representative values are crucial indicator of sensor performance so that small changes of ocean properties (e.g., remote sensed reflectance (Rrs), surface chlorophyll-a concentrations (Chl-a), and so on) can be quantified and directly related with those values. MTF is affected from a performance of instrument itself and environmental conditions, and its variation leads to change the final products. The goal of this study is to simulate and to analyze the relationship between MTF parameter and ocean product variations, and then to provide a reference for the design of future ocean color sensors. In this study, we used the Geostationary Ocean Color Imager (GOCI) data to generate the simulated atmospheric correction band image. And then Rrs data and ocean products were generated with imagery from two different locations and acquisition times, and we analyzed and compared the statistical results with study area having different characteristics. For ocean products relationships, we notify the linear variation of the absolute percentage difference (APD) according to the changeable MTF value. Especially, Case-II water (turbid water) area shows more sensitive variation than Case-I water (clear water) area. Even though the same area was applied in the simulation, it was 1-2 times higher sensitivity of variation when a specific ocean phenomena such as red tide. The suggested simulation can be confirmed the relationship between blurred NIR band image and ocean products. And statistical results with MTF values were able to help estimating ocean product precision and designing a future mission such as the Geostationary Ocean Color Imager-II (GOCI-II) mission currently being progressed.

This paper presents an optical design for the all-reflective dual-channel imaging system based on freeform surfaces. This system may be useful in remote sensing where coarse searching and fine observation are both needed. For this system, an off-axis three-mirror system with a middle image is chosen to design and the uniform stop is placed before the first optical surface. Meanwhile, beam splitter can be placed between secondary mirror and the location of the middle image to obtain multiple paths and the different curvatures of the tertiary mirrors can be used to differentiate the focal lengths of two channels and then get a zoom ratio of this system. One channel with a wide FOV of 3×1.5° but a small focal length of 700 mm can be used for searching, while the other one with a long focal length of 1480 mm but a narrow FOV of 0.5×0.5° can be used for fine reconnaissance. Furthermore, An XY polynomial, established as an even function of x, was employed to improve imaging quality, so we obtained a system of the symmetry about the YOZ plane, which can bring considerable convenience to alignment and testing for the system. The modulation transfer function curves of both channels are above 0.3 at 50 line pairs per millimeter, which indicates a good imaging quality.

According to the large aperture, long focal length zoom system design, the structure of the optical system based on the modular concept is proposed. The structure is constituted of an afocal compression telescope and a zoom system. The parts of each other are individually designed. The aberrations of them are independently. Because of this, the alignment of the system and the difficulty of test are greatly reduced. It is easily replaced by changing the zoom system parts, which can achieve other different focal length and ratio. Using afocal compression telescope greatly reduces the radial aperture of the zoom group, simplifies the system structure and reduces the cost. Meanwhile, the variable stop is placed in the vicinity of the primary mirror. It is instead of the zoom system used in floating variable stop. In addition, the problem about large aperture zoom system pupil matching is solved perfectly. In this article, four methods of pupil matching are given and the advantages and disadvantages of them are analyzed. Using this optical structure, a zoom system is designed, which is working in the visible wavelength band with variable focal length between 900mm and 4500mm, 500mm maximum aperture. The axial dimension of the system is less than 650mm. The maximum diameter of zoom system parts is less than 40 mm. Moreover, the distances of the zoom group and compensating group are all less than 60 mm. Besides, the motion curves of each other are given in the article. The Modulation Transfer Function (MTF) values of the system are greater than 0.3 at 48lp/mm across different focal length and field pointing on the axis. The design results show that the imaging quality is excellent, the structure is compact, and the alignment and test are easy. The imaging requirements of zoom system are all satisfied.

Wavefront Coding is a new method to extend the depth of field, which combines optical design and signal processing together. By using optical design software ZEMAX ,we designed a practical wavefront coded imaging system based on a conventional Cooke triplet system .Unlike conventional optical system, the wavefront of this new system is modulated by a specially designed phase mask, which makes the point spread function (PSF)of optical system not sensitive to defocus. Therefore, a series of same blurred images obtained at the image plane. In addition, the optical transfer function (OTF) of the wavefront coded imaging system is independent of focus, which is nearly constant with misfocus and has no regions of zeros. All object information can be completely recovered through digital filtering at different defocus positions. The focus invariance of MTF is selected as merit function in this design. And the coefficients of phase mask are set as optimization goals. Compared to conventional optical system, wavefront coded imaging system obtains better quality images under different object distances. Some deficiencies appear in the restored images due to the influence of digital filtering algorithm, which are also analyzed in this paper. The depth of field of the designed wavefront coded imaging system is about 28 times larger than initial optical system, while keeping higher optical power and resolution at the image plane.

Retinal images are obtained by simultaneously illuminating and imaging the retina, which is achieved using a fundus camera. This device meets low light illumination of the fundus with high resolution and reflection free images. Although the current equipment presents a sophisticated solution, it is complex to align due to the high number of off-axis components. In this work, we substitute the complex illumination system by a ring of LEDs mounted coaxially to the imaging optical system, positioning it in the place of the holed mirror of the traditional optical design. We evaluated the impact of this substitution regarding to image quality (measured through the modulation transfer function) and illumination uniformity produced by this system on the retina. The results showed there is no change in image quality and no problem was detected concerning uniformity compared to the traditional equipment. Consequently, we avoided off-axis components, easing the alignment of the equipment without reducing both image quality and illumination uniformity.

Based upon the empirical observation that BRDF measurements of smooth optical surfaces exhibited shift-invariant behavior when plotted versus    o , the original Harvey-Shack (OHS) surface scatter theory was developed as a scalar linear systems formulation in which scattered light behavior was characterized by a surface transfer function (STF) reminiscent of the optical transfer function (OTF) of modern image formation theory (1976). This shift-invariant behavior combined with the inverse power law behavior when plotting log BRDF versus log   o was quickly incorporated into several optical analysis software packages. Although there was no explicit smooth-surface approximation in the OHS theory, there was a limitation on both the incident and scattering angles. In 1988 the modified Harvey-Shack (MHS) theory removed the limitation on the angle of incidence; however, a moderate-angle scattering limitation remained. Clearly for large incident angles the BRDF was no longer shift-invariant as a different STF was now required for each incident angle. In 2011 the generalized Harvey-Shack (GHS) surface scatter theory, characterized by a two-parameter family of STFs, evolved into a practical modeling tool to calculate BRDFs from optical surface metrology data for situations that violate the smooth surface approximation inherent in the Rayleigh-Rice theory and/or the moderate-angle limitation of the Beckmann-Kirchhoff theory. And finally, the STF can be multiplied by the classical OTF to provide a complete linear systems formulation of image quality as degraded by diffraction, geometrical aberrations and surface scatter effects from residual optical fabrication errors.

Previous research on optical surface scatter either assumed for the ACV (Auto-Covariance function) a simple analytical but unrealistic Gaussian form or depended on intensive numerical integrations. Measurements of polished optical surfaces indicate they accurately follow a simple inverse power law for the BSDF (Bi-directional Scatter Distribution Function) and the related PSD (Power Spectral Density) of their random height variations, i.e. they are fractal-like. By applying the appropriate limits to the scale-invariant (no intrinsic correlation length) PSD, a general analytic form for the corresponding ACV and STF (Surface or Scatter Transfer Function) can be derived. Combined with other Fourier-Bessel transform pairs, it’s possible to accurately simulate the effect of not only diffraction and aberrations such as defocus (via the system OTF or Optical Transfer Function) but also surface and particulate scatter on the incoherent imaging of highcontrast fine-detail scenes. Simple examples of Gaussian and point objects are first presented followed by application to digital cameras that require integrating the aerial image over each pixel’s active area. The needed subsampling for a camera with over ten million pixels (each only few microns in size) requires two-dimensional FFTs (Fast Fourier Transforms) of many gigabytes to accurately perform the detailed imaging calculations.

Following the successful operations of the first Visible Infrared Imaging Radiometer Suite (VIIRS) instrument on-board the Suomi National Polar‐orbiting Partnership (SNPP) spacecraft since launch in October 2011, a second VIIRS instrument to be on-board the first Joint Polar Satellite System (JPSS-1) satellite has been fabricated, tested and integrated onto the spacecraft, readying for launch in 2017. The ground testing, including geometric functional performance testing and characterization, at the sensor level was completed in December 2014. Testing at the spacecraft level is on-going. The instrument geometric performance includes sensor (detector) spatial response, band-to-band coregistration (BBR), scan plane and pointing stability. The parameters have been calibrated and characterized through ground testing under ambient and thermal vacuum conditions, and numerical modeling and analysis. VIIRS sensor spatial response is measured by line spread functions (LSFs) in the scan and track directions for every detector. We parameterize the LSFs by: 1) dynamic field of view (DFOV) in the scan direction and instantaneous FOV (IFOV) in the track direction; and 2) modulation transfer function (MTF) for the 17 moderate resolution bands (M-bands) and for the five imagery bands (I-bands). We define VIIRS BBR for M-bands and I-bands as the overlapped fractional area of angular pixel sizes from the corresponding detectors in a band pair, including nested I-bands within the M-bands. The ground tests result in static BBR matrices. VIIRS pointing measurements include scan plane tilt and instrument-to-spacecraft mounting coefficients. This paper summarizes the pre-launch test results along with anomaly investigations. The pre-launch performance parameters will be tracked or corrected for as needed in on-orbit operations.

Recently, an original method for the statistical modeling of surface topography of state-of-the-art mirrors for usage in xray optical systems at light source facilities and for astronomical telescopes [Opt. Eng. 51(4), 046501, 2012; ibid. 53(8), 084102 (2014); and ibid. 55(7), 074106 (2016)] has been developed. In modeling, the mirror surface topography is considered to be a result of a stationary uniform stochastic polishing process and the best fit time-invariant linear filter (TILF) that optimally parameterizes, with limited number of parameters, the polishing process is determined. The TILF model allows the surface slope profile of an optic with a newly desired specification to be reliably forecast before fabrication. With the forecast data, representative numerical evaluations of expected performance of the prospective mirrors in optical systems under development become possible [Opt. Eng., 54(2), 025108 (2015)]. Here, we suggest and demonstrate an analytical approach for accounting the imperfections of the used metrology instruments, which are described by the instrumental point spread function, in the TILF modeling. The efficacy of the approach is demonstrated with numerical simulations for correction of measurements performed with an autocollimator based surface slope profiler. Besides solving this major metrological problem, the results of the present work open an avenue for developing analytical and computational tools for stitching data in the statistical domain, obtained using multiple metrology instruments measuring significantly different bandwidths of spatial wavelengths.

In this paper we describe a cryogenic testbed designed to offer complete characterisation-via a minimal number of experimental configurations— of mercury cadmium telluride (MCT) detector arrays for low-photon background applications, including exoplanet science and solar system exploration. Specifically, the testbed offers a platform to measure the dark current of detector arrays at various temperatures, whilst also characterising their optical response in numerous spectral bands. The average modulation transfer function (MTF) can be found in both dimensions of the array along with the overall quantum efficiency. Working from a liquid-helium bath allows for measurement of arrays from 4.2 K and active-temperature control of the surface to which the array is mounted allows for characterisation of arrays at temperatures up to 80 K, with the temperature of the array holder known to an accuracy of at least 1 mK, with the same level of long-term stability.

The differential Optical Transfer Function (dOTF) is a focal plane wavefront sensing method that uses a diversity in the pupil plane to generate two different focal plane images. The difference of their Fourier transforms recovers the complex amplitude of the pupil down to the spatial scale of the diversity. We produce two simultaneous PSF images with diversity using a polarizing filter at the edge of the telescope pupil, and a polarization camera to simultaneously record the two images. Here we present the first on-sky demonstration of polarization dOTF at the 1.0m South African Astronomical Observatory telescope in Sutherland, and our attempt to validate it with simultaneous Shack-Hartmann wavefront sensor images., 11 pages, 9 figures, Proc. SPIE Vol. 9912

Euclid is the name of a space telescope currently being developed in the framework of the ESA Cosmic Vision 2015- 2025 Program [1], [2]. It addresses cosmological questions related to dark matter and dark energy. The lens system of one of the two scientific key instruments on board of Euclid (a combined near-infrared spectrometer and photometer) is designed and tested at the Max Planck Institute for Extraterrestrial Physics. In this paper, we compare two complementary approaches to determine the imaging quality of the photometer. The first approach is based on a direct camera measurement of the point-spread function (PSF) while the second approach uses a Shack-Hartmann sensor to reconstruct the wave front of the system. Both methods yield in principle largely overlapping information in terms of e.g. modulation transfer function (MTF), encircled energy (EE) or spot shape. However, the experimental requirements are quite different. Details like the spatial extent and coherence properties of the object have different impact and are essential for the degree of agreement between both approaches. Moreover, the disturbance due to measurement noise is quite unequal and requires different evaluation steps. The pros and cons of both methods that actually complement one another are investigated and discussed.

Computational efficiency and accuracy of wave-optics-based Monte-Carlo and brightness function numerical simulation techniques for incoherent imaging through atmospheric turbulence are evaluated. Simulation results are compared with theoretical estimates based on known analytical solutions for the modulation transfer function of an imaging system and the long-exposure image of a Gaussian-shaped incoherent light source.

Using the brightness function imaging approach we analyze the impact of the desert and ocean type inverse temperature layer (ITL) on the modulation transfer function (MFT) of an incoherent imaging system. It is shown that an ITL located in vicinity of an imaging path can result in nonlinear deviation in imaging of an object spatial spectrum. Using periodical (sine) patterns of different spatial frequencies as an object, we show that presence of an ITL leads to formation of images with a broadened spatial spectrum with shifted frequency of the sine pattern image in respect to object frequency. The image spectrum shift and width depend on the ITL characteristics and its location in respect to optical wave propagation path. The observed changes in the sine pattern spectral content represent a challenge for analysis of imaging systems performance using conventional MTF based framework. We also analyzed impact of atmospheric turbulence on imaging of periodical (sine) patterns and compared this with the known theoretical results.

Point spread function (PSF) is a very important indicator of the imaging system; it can describe the filtering characteristics of the imaging system. The image is fuzzy when the PSF is not very well and vice versa. In the remote sensing image process, the image could be restored by using the PSF of the image system to get a clearer picture. So, to measure the PSF of the system is very necessary. Usually we can use the knife edge method, line spread function (LSF) method and streak plate method to get the modulation transfer function (MTF), and then use the relationship of the parameters to calculate the PSF of the system. In the knife edge method, the non-uniformity (NU) of the detector would lead an unstable precision of the edge angle; using the streak plate could get a more stable MTF, but it is only at one frequency point in one direction, so it is not very helpful to get a high-precision PSF. In this paper, we used the image of the point target directly and combined with the energy concentration to calculate the PSF. First we make a point matrix target board and make sure the point can image to a sub-pixel position at the detector array; then we use the center of gravity to locate the point targets image to get the energy concentration; then we fusion the targets image together by using the characteristics of sub-pixel and get a stable PSF of the system. Finally we use the simulation results to confirm the accuracy of the method.

Emerging underwater optical imaging and sensing applications rely on phase-sensitive detection to provide added functionality and improved sensitivity. However, underwater turbulence introduces spatio-temporal variations in the refractive index of water which can degrade the performance of these systems. Although the influence of turbulence on traditional, non-interferometric imaging has been investigated, its influence on the optical phase remains poorly understood. Nonetheless, a thorough understanding of the spatio-temporal dynamics of the optical phase of light passing through underwater turbulence are crucial to the design of phase-sensitive imaging and sensing systems. To address this concern, we combined underwater imaging with high speed holography to provide a calibrated characterization of the effects of turbulence on the optical phase. By measuring the modulation transfer function of an underwater imaging system, we were able to calibrate varying levels of optical turbulence intensity using the Simple Underwater Imaging Model (SUIM). We then used high speed holography to measure the temporal dynamics of the optical phase of light passing through varying levels of turbulence. Using this method, we measured the variance in the amplitude and phase of the beam, the temporal correlation of the optical phase, and recorded the turbulence induced phase noise as a function of frequency. By bench marking the effects of varying levels of turbulence on the optical phase, this work provides a basis to evaluate the real-world potential of emerging underwater interferometric sensing modalities.

Standard methods for improved imaging system performance under degrading optical turbulence conditions typically involve active adaptive techniques or post-capture image processing. Here, passive adaptive methods are considered where active sources are disallowed, a priori. Theoretical analyses of short-exposure turbulence impacts indicate that varying aperture sizes experience different degrees of turbulence impacts. Smaller apertures often outperform larger aperture systems as turbulence strength increases. This suggests a controllable aperture system is advantageous. In addition, sub-aperture sampling of a set of training images permits the system to sense tilts in different sub-aperture regions through image acquisition and image cross-correlation calculations. A four sub-aperture pattern supports corrections involving five realizable operating modes (beyond tip and tilt) for removing aberrations over an annular pattern. Progress to date will be discussed regarding development and field trials of a prototype system.

Measuring the Modulation Transfer Function (MTF) of a display monitor is necessary for many applications such as: modeling end-to-end systems, conducting perception experiments, and performing targeting tasks in real-word scenarios. The MTF of a display defines the resolution properties and quantifies how well the spatial frequencies are displayed on a monitor. Many researchers have developed methods to measure display MTFs using either scanning or imaging devices. In this paper, we first present methods to measure display MTFs using two separate technologies and then discuss the impact of a display MTF on a system’s performance. The two measurement technologies were scanning with a photometer and imaging with a CMOS based camera. To estimate a true display MTF, measurements made with the photometer were backed out for the scanning optics aperture. The developed methods were applied to measure MTFs of the two types of monitors, Cathode Ray Tube (CRT) and Liquid Crystal Display (LCD). The accuracy of the measured MTFs was validated by comparing MTFs measured with the two systems. The methods presented here are simple and can be easily implemented employing either a Prichard photometer or an imaging device. In addition, the impact of a display MTF on the end-to-end performance of a system was modeled using NV-IPM.

Since launch, both Terra and Aqua MODIS instruments have continued to operate and make measurements of the earth's top of atmospheric (TOA) radiances and reflectance. MODIS collects data in 36 spectral bands covering wavelengths from 0.41 to 14.4 microns. These spectral bands and detectors are located on four focal plane assemblies (FPAs). MODIS on-board calibrators (OBC) include a spectro-radiometric calibration assembly (SRCA), which was designed to characterize and monitor sensor spatial and spectral performance, such as on-orbit changes in the band-to-band registration (BBR), modulation transfer function (MTF), spectral band center wavelengths (CW) and bandwidths (BW). In this paper, we provide a status update of MODIS spatial and spectral characterization and performance, following a brief description of SRCA functions and on-orbit calibration activities. Sensor spatial and spectral performance parameters derived from SRCA measurements are introduced and discussed. Results show that on-orbit spatial performance has been very stable for both Terra and Aqua MODIS instruments. The large BBR shifts in Aqua MODIS, an issue identified pre-launch, have remained the same over its entire mission. On-orbit changes in CW and BW are less than 0.5 nm and 1 nm, respectively, for most VIS/NIR spectral bands of both instruments.

The paper presents the scheme for improving the image contrast in the remote sensing images and highlights the novelty in hardware & software design in the test system developed for measuring image contrast function. Modulation transfer function (MTF) is the most critical quality element of the high-resolution imaging payloads for earth observation consisting of TDI-CCD (Time Delayed Integration Charge Coupled Device) image. From the mathematical model for MTF Smear MTF of 65% (35% degradation) is observed. Then a operating method for TDI-CCD is developed, using which 96% of Motion Smear MTF will occur within the imaging operation. As a major part of the validation, indigenously designed and developed a test system for measuring the dynamic MTF of TDI Sensors which consists of the optical scanning system, TDI-CCD camera drive & video processing electronics, thermal control system and telecentric uniform illumination system. The experimental results confirm that image quality improvement can be achieved by this method. This method is now implemented in the flight model hardware of the remote sensing payload.

Chest digital tomosynthesis (CDT) is a new 3D imaging technique that can be expected to improve clinical diagnosis over conventional chest radiography. We investigated the effect of the angular range of data acquisition on the image quality using newly developed CDT system. The four different acquisition sets were studied using ±15°, ±20°, ±30°, and ±35° angular ranges with 21 projection views (PVs). The point spread function (PSF), modulation transfer function (MTF), artifact spread function (ASF), and normalized contrast-to-noise ratio (CNR) were used to evaluate the image quality. We found that increasing angular ranges improved vertical resolution. The results indicated that there was the opposite relationship of the CNR with angular range for the two tissue types. While CNR for heart tissue increased with increasing angular range, CNR for spine bone decreased. The results showed that the angular range is an important parameter for the CDT exam.

This study compares the spatial resolution in step-and-shoot and continuous motion acquisition modes of digital tomosynthesis using a bench-top prototype designed for breast phantoms imaging. The prototype employs a flat panel detector with a 50 μm pixel pitch, a micro focus x-ray tube and a motorized stage. A sharp metal edge with a thickness of 0.2 mm was used to measure the modulation transfer function (MTF). The edge was rotated from −7.5° to +7.5° with 1.5° increments to acquire 11 angular projections using 40 kVp, 500 μA with 5.55 s per projection. In continuous motion mode, the motorized stage moved the test object for the whole exposure time at a speed of 0.377 mm/s. The impact of acquisition speed in continuous DBT was also investigated, and a high speed of 0.753 mm/s was used. In step-and-shoot mode, the cutoff frequencies (10% MTF) in projection view (0°) and reconstructed DBT slices were 5.55 lp/mm and 4.95 lp/mm. Spatial resolution dropped in the continuous motion mode of the DBT due to the blur caused by the rotation of the stage and the cutoff frequencies reduced to 3.6 lp/mm and 3.18 lp/mm in the projection view (0o) and reconstructed DBT slices. At high rotational speed in continuous motion mode, the cutoff frequencies in the DBT slices dropped by 17 % to 2.65 lp/mm. Rotational speed of the rotation stage and spatial resolution are interconnected. Hence, reducing the motion blur in the continuous acquisition mode is important to maintain high spatial resolution for diagnostic purposes.

We present a simple technique which uses a random phase object for single-shot characterization of an optical system's phase transfer function. Existing methods for aberration measurement typically involve holography, requiring complicated wavefront sensing optics or through-focus measurements with known test objects (e.g. pinholes, fluorescent beads) for pupil recovery from the measured wavefront. Here, it is demonstrated that a weak diffuser can be used to recover the pupil of an imaging system in a single measurement, without exact knowledge of the diffuser's surface. Due to its stochastic nature, the diffuser scatters light to a wide range of spatial frequencies, thus probing the entire pupil plane. A linear theory based on the weak object approximations predicts the spectrum of the measured speckle intensity to depend directly on the pupil function. Numerical simulations of diffusers with varying strength confirm the validity of the theory and indicate sufficient conditions under which diffusers act as weak phase objects. Using index matching oils to modulate diffuser strength, experiments are shown to successfully recover aberrations from an optical system using coherent illumination. Additionally, this technique is applied to the recovery of defocus in images of a weak phase object obtained through a commercial microscope under partially coherent illumination.

Evaluating spatial resolution is an essential work for cone-beam computed tomography (CBCT) manufacturers, prototype designers or equipment users. To investigate the cross-sectional spatial resolution for different transaxial slices with CBCT, the slanted edge technique with a 3D slanted edge phantom are proposed and implemented on a prototype cone-beam micro-CT. Three transaxial slices with different cone angles are under investigation. An over-sampled edge response function (ERF) is firstly generated from the intensity of the slightly tiled air to plastic edge in each row of the transaxial reconstruction image. Then the oversampled ESF is binned and smoothed. The derivative of the binned and smoothed ERF gives the line spread function (LSF). At last the presampled modulation transfer function (MTF) is calculated by taking the modulus of the Fourier transform of the LSF. The spatial resolution is quantified with the spatial frequencies at 10% MTF level and full-width-half-maximum (FWHM) value. The spatial frequencies at 10% of MTFs are 3.1±0.08mm-1, 3.0±0.05mm-1, and 3.2±0.04mm-1 for the three transaxial slices at cone angles of 3.8°, 0°, and -3.8° respectively. The corresponding FWHMs are 252.8μm, 261.7μm and 253.6μm. Results indicate that cross-sectional spatial resolution has no much differences when transaxial slices being 3.8° away from z=0 plane for the prototype conebeam micro-CT.