Showing papers on "Optical transfer function published in 2019"

Metasurfaces with Asymmetric Optical Transfer Functions for Optical Signal Processing

Abstract: Metasurface thin films created from arrays of structured optical elements have been shown to perform spatial filtering of optical signals. To extend their usefulness it is important that the symmetry of their response with changes to the in-plane wave vector k_{p}→-k_{p} can be tailored or even dynamically tuned. In this Letter we use a general theory of metasurfaces constructed from nondiffracting arrays of coupled metal particles to derive the optical transfer function and identify the physical properties essential for asymmetry. We validate our theory experimentally showing how the asymmetric response of a two-dimensional (planar) metasurface can be optically tuned. Our results set the direction for future developments of metasurfaces for optical signal processing.

Design of foveated contact lens display for augmented reality.

Abstract: We present a design of a contact lens display, which features an array of collimated light-emitting diodes and a contact lens, for the augmented reality. By building the infrastructure directly on top of the eye, eye is allowed to move or rotate freely without the need of exit pupil expansion nor eye tracking. The resolution of light-emitting diodes is foveated to match with the density of cones on the retina. In this manner, the total number of pixels as well as the latency of image processing can be significantly reduced. Based on the simulation, the device performance is quantitatively analyzed. For the real image, modulation transfer functions is 0.669757 at 30 cycle/degree, contrast ratio is 5, and distortion is 10%. For the virtual image, the field of view is 82°, best angular resolution is 0.38′, modulation transfer function is above 0.999999 at 30 cycle/degree, contrast ratio is 4988, and distortion is 6%.

Ultra-thin near infrared camera enabled by a flat multi-level diffractive lens.

Abstract: We experimentally demonstrate a ∼1-mm-thick near infrared camera comprised of a multi-level diffractive lens coupled with a conventional monochrome image sensor. We performed careful measurements of the point-spread function, the modulation transfer function, focusing efficiency, aberrations, and the field of view of the camera.

Resolution characterization of a silicon-based, photon-counting computed tomography prototype capable of patient scanning.

Abstract: Photon-counting detectors are expected to bring a range of improvements to patient imaging with x-ray computed tomography (CT). One is higher spatial resolution. We demonstrate the resolution obtained using a commercial CT scanner where the original energy-integrating detector has been replaced by a single-slice, silicon-based, photon-counting detector. This prototype constitutes the first full-field-of-view silicon-based CT scanner capable of patient scanning. First, the pixel response function and focal spot profile are measured and, combining the two, the system modulation transfer function is calculated. Second, the prototype is used to scan a resolution phantom and a skull phantom. The resolution images are compared to images from a state-of-the-art CT scanner. The comparison shows that for the prototype 19 lp / cm are detectable with the same clarity as 14 lp / cm on the reference scanner at equal dose and reconstruction grid, with more line pairs visible with increasing dose and decreasing image pixel size. The high spatial resolution remains evident in the anatomy of the skull phantom and is comparable to that of other photon-counting CT prototypes present in the literature. We conclude that the deep silicon-based detector used in our study could provide improved spatial resolution in patient imaging without increasing the x-ray dose.

Extending the depth-of-field of imaging systems with a scattering diffuser.

Abstract: Large depth of field (DOF) is a longstanding goal in optical imaging field. In this paper we presented a simple but efficient method to extend the DOF of a diffraction-limited imaging system using a thin scattering diffuser. The DOF characteristic of the imaging system with random phase modulation was analyzed based on the analytical model of ambiguity function as a polar display of the optical transfer function (OTF). The results of numerical simulation showed that more high-frequency components existed in the defocused OTF curve when the exit pupil of the imaging system exhibited a random phase modulation. It proved the important role of the scattering diffuser in extending the DOF of imaging systems. For the reconstruction, a stack of point spread functions (PSFs) corresponding to different axial locations within a measurement range were superimposed to construct the stacked PSF. Then the large DOF image was recovered from a speckle pattern by deconvolution. In this proof-of-concept, we experimentally demonstrated the single-shot imaging with larger DOF using a thin glass scattering diffuser in both a single-lens imaging system and a microscopic imaging system.

Illumination conditions in microsphere-assisted microscopy.

Abstract: White-light microsphere-assisted microscopy is a full-field and label-free imaging promising technique making it possible to achieve a subdiffraction lateral resolution. However, performance of this technique depends not only on the geometrical parameters but also on the illumination conditions of the optical system. In the present work, experimental measurements and computer simulations have been performed in air in order to determine the influence of the two diaphragm apertures of the Kohler arrangement and the spectral width of the light source on both the depth-of-focus of the microsphere and the optimization of the imaging contrast. Furthermore, the super-resolution phenomenon is demonstrated and the cumulated optical aberrations are shown through the measurement of the optical transfer function for the different arrangements of the illumination part.

Rapid acquisition of the 3D MRI gradient impulse response function using a simple phantom measurement.

Abstract: Purpose To provide a simple tool for rapid measurement of the 3D gradient modulation transfer function (GMTF) of clinical MRI systems using a phantom. Knowledge of the transfer function is useful for gradient chain characterization, system calibration, and improvement of image reconstruction results. Methods Starting from the well-established thin slice method used for phantom-based measurement of the 1D GMTF, we add phase encoding to partition the thin slices into voxels that act as localized field probes. From the signal phase evolution measured at the 3D voxel positions, the GMTF can be derived for cross and higher order spatial terms represented by spherical harmonics up to 3rd order. Results Using spherical phantoms, 16 GMTFs representing all terms up to 3rd order harmonics can be determined in a scan time of 1 mL yields high SNR, enabling signal acquisition using the system's body coil. The method is applied for improving system calibration and for characterizing the effect of additional hardware in the bore. Conclusion The presented method seems well-suited for rapid measurement of the GMTF of a clinical system, as it delivers high-quality results in a short scan time.

Basic Spatial Resolution Metrics for Satellite Imagers

Abstract: Six basic criteria used to estimate the Ground Resolution Distance of satellite imagers are considered: Ground Sample Distance (GSD), Rayleigh diffraction limit, ground spot size, generalized Rayleigh resolution criterion, Sparrow limit, and the full-width at half-maximum (FWHM) of the Point/Line Spread Function (PSF/LSF). Theoretical arguments and experimental results that support the use of the LSF FWHM as a spatial resolution metric are presented. The procedure to compute the LSF FWHM from the system modulation transfer function is reviewed and is used to compute the FWHM of the three ideal sensors as a function of their optical factor, contrasting these theoretical results with 22 in orbit measurements. Within this context, the limited range of validity of the GSD and the Rayleigh diffraction limit as spatial resolution estimators is assessed. The limitations of the LSF FWHM as a resolution estimator are also noted.

Design of dual-band infrared zoom lens with multilayer diffractive optical elements.

Abstract: A mid-wave infrared (MWIR)/long-wave infrared (LWIR) dual-band zoom lens design with multilayer diffractive optical elements (MLDOEs) is presented. The mathematical relationship between the substrate material selection for dual-band MLDOE and polychromatic integral diffraction efficiency (PIDE) is deduced in the oblique incident situation, and further, a method for optimal selection of substrate material is proposed to obtain the high PIDE in an incident angle range. In the optimization process, the optimal substrate material combination is selected based on the proposed method, and the principle of lens material replacement is discussed. After optimization, the 5× hybrid dual-band infrared zoom system is obtained, which consists of seven lenses. The modulation transfer function values in all configurations are larger than 0.5 and 0.3 in MWIR and LWIR, respectively. The distortion values are less than 2% both in MWIR and LWIR for all configurations.

Dual energy imaging with a dual-layer flat panel detector

Abstract: Dual Energy (DE) imaging has been widely used in digital radiography and fluoroscopy, as has dual energy CT for various medical applications. In this study, the imaging performance of a dynamic dual-layer a-Si flat panel detector (FPD) prototype was characterized for dual energy imaging tasks. Dual energy cone beam CT (DE CBCT) scans were acquired and used to perform material decomposition in the projection domain, followed by reconstruction to generate material specific and virtual monoenergetic (VM) images. The dual-layer FPD prototype was built on a Varex XRD 4343RF detector by adding a 200 μm thick CsI scintillator and a-Si panel of 150 μm pixel size on top as a low energy detector. A 1 mm copper filter was added as a middle layer to increase energy separation with the bottom layer as a high energy detector. The imaging performance, such as Modulation Transfer Function (MTF), Conversion Factor (CF), and Detector Quantum Efficiency (DQE) of both the top and bottom detector layers were characterized and compared with those of the standard single layer XRD4343 RF detector. Several tissue equivalent cylinders (solid water, liquid water, bone, acrylic, polyethylene, etc.) were placed on a rotating stand, and two separate 450-projection CBCT scans were performed under continuous 120 kV and 80 kV X-ray beams. After an empirical material decomposition calibration, water and bone images were generated for each projection, and their respective volumes were reconstructed using Varex’s CBCT Software Tools (CST 2.0). A VM image, which maximized the contrast-to-noise ratio of water to polyethylene, was generated based on the water and bone images. The MTF at 1.0 lp/mm from the low energy detector was 32% and 22% higher than the high energy detector and the standard detector, respectively; the DQE of both high and low energy detectors is much lower than that of the standard XRD 4343RF detector. The CNR of water to polyethylene from the VM image improved by 50% over that from the low energy image alone at 120 kV, and by 80% at 80 kV. This study demonstrates the feasibility of using a dual-layer FPD in applications such as DE CBCT for contrast enhancement and material decomposition. Further evaluations are underway.

Modeling of full-field optical coherence tomography in scattering media.

Abstract: We develop a model of full-field optical coherence tomography (FF-OCT) that includes a description of partial temporal and spatial coherence, together with a mean-field scattering theory going beyond the Born approximation. Based on explicit expressions of the FF-OCT signal, we discuss essential features of FF-OCT imaging, such as the influence of partial coherence on the optical transfer function, and on the decay of the signal with depth. We derive the conditions under which the spatially averaged signal exhibits a pure exponential decay, providing a clear frame for the use of the Beer-Lambert law for quantitative measurements of the extinction length in scattering media.

Simulation and experimental validation of high-resolution test objects for evaluating a next-generation digital breast tomosynthesis prototype

Abstract: Star pattern test objects are used to evaluate the high-contrast performance of imaging systems. These objects were used to investigate alternative scanning geometries for a prototype next-generation tomosynthesis (NGT) system. The NGT system has 2D planar source motion and linear detector motion, and is capable of myriad acquisition geometries. We designed a virtual star pattern with a voxel size of 5𝜇m, and used it to evaluate the spatial resolution performance of the NGT system for three different acquisition geometries. The Open Virtual Clinical Trials (OpenVCT) framework was used to simulate virtual star patterns for acquisition geometries of the NGT system. Simulated x-ray projections of the virtual phantom were used to create super-sampled 3D image reconstructions. Using the same acquisition geometries on the NGT system, a physical star pattern was imaged to create experimental 3D image reconstructions. The simulated and physical data were compared qualitatively by visual inspection, and quantitatively using an in-house metric. This metric computes the Fourier transform radially for one quadrant of the star pattern to discern the limit of spatial resolution (LSR) and the existence of aliasing. The results exhibit the same characteristics in terms of super-resolution and Moire patterns (arising from aliasing) with visual inspection. The simulated LSR for the 12 conditions analyzed are all within 3% of the physical data. Aliasing was determined to be present in the same simulated image reconstructions as the experimental complements. Super-resolution is observed for two of the three NGT acquisition geometries in the experimental and simulated images.

Achromatic annular folded lens with reflective-diffractive optics.

Abstract: This paper proposes an achromatic annular folded lens (AFL) with a reflective-diffractive optical element (RDOE). We derive novel mathematical models of the diffraction efficiency and polychromatic integral diffraction efficiency (PIDE) of the RDOE and an expression for its microstructure height. An AFL with an RDOE made of an optical plastic substrate material is designed in the visible waveband. To minimize the influence of incident angle on the diffraction efficiency and PIDE, the microstructure height is optimized. The design results indicate that the lateral color of the AFL is corrected, the modulation transfer function considering the diffraction efficiency is larger than 0.25 at 111 cycles/mm for all field of views. The hybrid AFL outperforms the conventional refractive imaging system in terms of the system size, volume, and image quality under the same specifications. It can be used in new-generation miniaturized imaging systems.

Optimization of the size and shape of the scanning aperture in autocollimator-based deflectometric profilometers.

Abstract: Deflectometric profilometers based on industrial electronic autocollimators (ACs), as the ELCOMAT-3000, have become indispensable tools for precision form measurements of optical surfaces. A growing number of labs at synchrotron and free electron laser x-ray facilities are going for BESSY-II NOM-like versions of the AC-based profilometers. These tools have proven capable of characterizing state-of-the-art aspherical x-ray optics with an accuracy on the level of 100 nrad (root-mean-square) over the spatial frequency range limited by the size of the aperture used in the profilometer. Typically, a round aperture with a diameter of about 2.5 mm is used. Previous investigations have shown that with the optimally aligned 2.5-mm aperture, the spatial resolution of a NOM-like profilometer corresponding to the first zero-crossing of the optical transform function (OTF) is ∼1.2 mm. In this paper, we investigate the performance of an AC ELCOMAT-3000 for a slope profilometer with different aperture sizes and shapes. The results of angular calibration of the AC equipped with circular and rectangular apertures placed at different distances from the AC are discussed. The calibration was performed at the Physikalisch-Technische Bundesanstalt using the original experimental arrangements, also discussed in the paper. The OTF measurements with the specially developed test sample with chirped surface slope profiles were performed at the Advanced Light Source X-Ray Optics Laboratory (XROL) in application to a new optical surface measuring system under development at the XROL. In the OTF measurements, we have shown that application of a rectangular aperture with dimensions of 1.5 mm × 3 mm improves the spatial resolution in the tangential direction by a factor of ∼1.4 compared to that of the standard circular aperture of 2.5-mm diameter. We believe that the results of our investigations are crucial for reaching fundamental metrological limits in deflectometric profilometry utilizing state-of-the-art electronic autocollimators.

Practical edge-based modulation transfer function measurement.

Abstract: The accuracy and precision of the modulation transfer function (MTF) of a sampled imaging system are affected by the shift-variant nature of subpixel binning of the pixel values in edge-based methods. This study demonstrates that a binning phase selected from a small number of binning phases can achieve a practical precision criterion for the MTF measurement. Furthermore, the new method proposed in this paper approximates the non-aliased, fundamental MTF without edge angle estimation and the following subpixel binning. The algorithm simply averages the aliased MTFs calculated from the row-by-row edge gradients in the region of a bitonal edge image and removes an assumed aliasing component. This method is also applicable to an oblique and non-straight edge.

Imaging performance of a CaWO4/CMOS sensor

Abstract: The aim of this study was to investigate the modulation transfer function (MTF) and the effective gain transfer function (eGTF) of a non-destruc­­tive testing (NDT)/industrial inspection complementary metal oxide semi­conductor (CMOS) sensor in conjunction with a thin calcium tungstate (CaWO4) screen. Thin screen samples, with dimensions of 2.7x3.6 cm2 and thick­ness of 118.9 μm, estimated from scanning electron microscopy-SEM im­ages, were extracted from an Agfa Curix universal screen and coupled to the active area of an active pixel (APS) CMOS sensor. MTF was assessed using the slanted-edge method, following the IEC 62220-1-1:2015 method. MTF values were found high across the examined spatial frequency range. eGTF was found maximum when CaWO4 was combined with charge-coupled devices (CCD) of broadband anti-reflection (AR) coating (17.52 at 0 cycles/mm). The com­bi­nation of the thin CaWO4 screen with the CMOS sensor provided very pro­mis­ing image resolution and adequate efficiency properties, thus could be also con­sidered for use in CMOS based X-ray imaging devices, for various applications.

A novel method for fast image simulation of flat panel detectors.

Abstract: We have developed a novel method for fast image simulation of flat panel detectors, based on the photon energy deposition efficiency and the optical spread function (OSF). The proposed method, FastEPID, determines the photon detection using photon energy deposition and replaces particle transport within the detector with precalculated OSFs. The FastEPID results are validated against experimental measurement and conventional Monte Carlo simulation in terms of modulation transfer function (MTF), signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), contrast, and relative difference of pixel value, obtained with a slanted slit image, Las Vegas phantom, and anthropomorphic pelvis phantom. Excellent agreement is observed between simulation and measurement in all cases. Without degrading image quality, the FastEPID method is capable of reducing simulation time up to a factor of 150. Multiple applications, such as imager design optimization for planar and volumetric imaging, are expected to benefit from the implementation of the FastEPID method.

Wide-field off-axis telescope for the Mesospheric Airglow/Aerosol Tomography Spectroscopy satellite

Abstract: We present the development of a compact f/7.3 (D=35 mm) three-mirror reflective telescope for the atmospheric-research microsatellite Mesospheric Airglow/Aerosol Tomography Spectroscopy (MATS). The telescope design was driven by the end users’ need for a reflective wide-field (5.67°×0.91°) optic with high stray light rejection and six detection channels with separate image sensors, operating at wavelengths 270–772 nm. For the first time, a design method for wide-field off-axis telescopes—in which linear astigmatism is eliminated—was applied and tested in practice. Single-point diamond turning was used to produce two sets of 37–110 mm large free-form aluminum mirrors with surface figure errors and roughness values of 34–62 nm (RMS)/193–497 nm (PV) and 2.8–3.5 nm (RMS), respectively. A method that combines precise machining and geometry measurements (using a coordinate measuring machine) was employed to fabricate an aluminum structure to accurately position the mirrors without the need for manual alignment. The telescope was tested with a network of plate beamsplitters and filters, which define the spectral selection for the six detection channels. Imaging performance measurements were carried out using a reflective off-axis collimator, which projects imaging targets at infinite focus. A modulation transfer function (MTF) value of 0.45 at 20 lp/mm was measured at ∼760 nm (diffraction limit: 0.85) using a slanted edge target. By modeling the measured mirror surfaces in optical design software, a reoptimization of the mirror positions could be performed and an improved MTF of ∼0.75 at 20 lp/mm was predicted. The results demonstrate design- and building methods that can be utilized to make off-axis telescopes for a vast range of applications.

Fusion of interpolated frames superresolution in the presence of atmospheric optical turbulence

Abstract: An extension of the fusion of interpolated frames superresolution (FIF SR) method to perform SR in the presence of atmospheric optical turbulence is presented. The goal of such processing is to improve the performance of imaging systems impacted by turbulence. We provide an optical transfer function analysis that illustrates regimes where significant degradation from both aliasing and turbulence may be present in imaging systems. This analysis demonstrates the potential need for simultaneous SR and turbulence mitigation (TM). While the FIF SR method was not originally proposed to address this joint restoration problem, we believe it is well suited for this task. We propose a variation of the FIF SR method that has a fusion parameter that allows it to transition from traditional diffraction-limited SR to pure TM with no SR as well as a continuum in between. This fusion parameter balances subpixel resolution, needed for SR, with the amount of temporal averaging, needed for TM and noise reduction. In addition, we develop a model of the interpolation blurring that results from the fusion process, as a function of this tuning parameter. The blurring model is then incorporated into the overall degradation model that is addressed in the restoration step of the FIF SR method. This innovation benefits the FIF SR method in all applications. We present a number of experimental results to demonstrate the efficacy of the FIF SR method in different levels of turbulence. Simulated imagery with known ground truth is used for a detailed quantitative analysis. Three real infrared image sequences are also used. Two of these include bar targets that allow for a quantitative resolution enhancement assessment.

Lensless Wiener–Khinchin telescope based on second-order spatial autocorrelation of thermal light

Abstract: The resolution of a conventional imaging system based on first-order field correlation can be directly obtained from the optical transfer function. However, it is challenging to determine the resolution of an imaging system through random media, including imaging through scattering media and imaging through randomly inhomogeneous media, since the point-to-point correspondence between the object and the image plane in these systems cannot be established by the first-order field correlation anymore. In this Letter, from the perspective of ghost imaging, we demonstrate for the first time, to the best of our knowledge, that the point-to-point correspondence in these imaging systems can be quantitatively recovered from the second-order correlation of light fields, and the imaging capability, such as resolution, of such imaging schemes can thus be derived by analyzing second-order autocorrelation of the optical transfer function. Based on this theoretical analysis, we propose a lensless Wiener–Khinchin telescope based on second-order spatial autocorrelation of thermal light, which can acquire the image of an object by a snapshot via using a spatial random phase modulator. As an incoherent imaging approach illuminated by thermal light, the lensless Wiener–Khinchin telescope can be applied in many fields such as X-ray astronomical observations.

Integral diffraction efficiency model for multilayer diffractive optical elements with wide angles of incidence in case of polychromatic light.

Abstract: Oblique incidence is the normal working mode for diffractive optical elements (DOEs). The diffraction efficiency is very sensitive to the angle of incidence for multilayer diffractive optical elements (MLDOEs). Therefore, the design and diffraction efficiency analysis of MLDOEs with wide angles of incidence is of universal significance and practice. We propose an integral diffraction efficiency model for MLDOEs with wide angles of incidence in case of polychromatic light and then describe this corresponding optimal design in detail. It is shown that high diffraction efficiency can be realized by the surface micro-structure heights optimization, ensuring high modulation transfer function (MTF) for MLDOEs with wide angles of incidence in hybrid optical systems. On this basis, we present the optimal design process and simulation of an MLDOE working in visible waveband with optical plastic materials combination PMMA and POLYCARB as the two-layer substrates. The result shows that with this optimal design, we can achieve the maximum diffraction efficiency and minimum micro-structure heights, which makes the MLDOE design exactly over the entire waveband and wide angles of incidence especially for zoom hybrid optical system.

Design of high resolution panoramic annular lens system

Abstract: Panoramic annular lens (PAL) system consists of a panoramic head block unit and a relay lens system, adopting a plane cylindrical projection method to project a cylindrical field of view around the optical axis 360° into a two-dimensional planar annular region to realize super hemispherical imaging. PAL system requires large field of view imaging on a limited image plane, which inevitably results in lower image resolution and poor local detail imaging. However, the information processing speed gets faster with the development of 5G, which leads to a growing demand for better image quality and clarity. This paper presents a PAL system matching image sensors with 4K resolution, which can demonstrate the details about the object and get a smooth and ultra-high definition image. Unlike other sensors, it has large image faces and tiny pixels and the effective number of the pixel is about 24.3 million (4K × 6K). The proposed PAL system has 6 sets of 9 lenses with compact structure. The F-theta distortion of the full field of view is less than 1%, and the modulation transfer function value of each field of view is greater than 0.5 at the Nyquist spatial frequency of 130lp/mm which approaches diffraction limitation. The designed system has good imaging quality and meets the application requirements.

Influence of the System MTF on the On-Board Lossless Compression of Hyperspectral Raw Data

Abstract: A noticeable topic to be pursued in the field of on-board real-time data processing is the influence of the modulation transfer function (MTF) of the image acquisition system on the lossless compressibility of raw (that is, uncalibrated) hyperspectral data. Actually, notwithstanding the system device is constrained by several design and manufacturing requirements, the impact of the on-board MTF on the performance of data compressors is becoming remarkable. In particular, the aim of reducing both transmission bandwidth/power and mass storage can be efficiently pursued. Such an analysis is expected to be useful especially for systems employed in mini-satellites, whose payload must be compact and light. From this perspective, this paper investigates the performance of a typical imaging system that acquires low/medium-spatial-resolution images, by considering high-resolution reference data, which simulate the real scene to be imaged. To this end, standard Consultative Committee for Space Data Systems (CCSDS) Aviris 2006 data have been chosen, due to their spatial resolution of 17 m, which is adequate to be a reference for simulated data whose spatial resolution is foreseen between 50 and 150 m. MTF requirements are usually provided based on the cut-off value of the amplitude at the Nyquist frequency, which is defined as a half of the sampling frequency. Typically, a cut-off value between 0.2 and 0.3 ensures that a sufficient amount of information is delivered from the scene to the acquired image, by avoiding at the same time the degradation due to an excessive aliasing distortion. All the scores are achieved by running the standard lossless compression scheme CCSDS 1.2.3.0-B-1 for multispectral/hyperspectral data, as a function of the cut-off value and different noise acquisition levels. The final results, and related plots, show that this analysis can suggest a suitable choice for the cut-off value, to ensure both a sufficient quality and low bit rates for the transmitted data to the ground station.

Analysis of Dynamic Modulation Transfer Function for Complex Image Motion

Abstract: In remote-sensing imaging, the modulation transfer function (MTF) for image motion relevant to the mixing of multiple forms of motions is hard to calculate because of the complicated image motion expression. In this paper, a new method for calculating the MTF for complex image motion is proposed. The presented method makes it possible to obtain an analytical MTF expression derived from the mixing of linear motion and sinusoidal motion at an arbitrary frequency. On this basis, we used the summation of infinitely many terms involving the Bessel function to simplify the MTF expression. The truncation error obtained by the use of finite order sum approximations instead of infinite sums is investigated in detail. In order to verify the MTF calculation method, we proposed a simulation method to calculate the variation of MTF in an actual optical system caused by image motion. The mean value of the relative error between the calculation method and the simulation method is less than 5%. The experimental results are consistent with the MTF curve calculated by our method.

The Minimum Modulation Curve as a tool for specifying optical performance: application to surfaces with mid-spatial frequency errors.

Abstract: There are a variety of common situations in which specification of a one-dimensional modulation transfer function (MTF) or two orthogonal profiles of the 2D MTF are not adequate descriptions of the image quality performance of an optical system. These include systems with an asymmetric on-axis impulse response, systems with off-axis aberrations, systems with surfaces that include mid-spatial frequency errors, and freeform systems. In this paper, we develop the concept of the Minimum Modulation Curve (MMC). Starting with the two-dimensional MTF in polar form, the minimum MTF for any azimuth angle is plotted as a function of the radial spatial frequency. This can be presented in a familiar form similar to an MTF curve and is useful in the context of guaranteeing that a given MTF specification is met for any possible orientation of spatial frequencies in the image. In this way, an MMC may be of value in specifying the required performance of an optical system. We illustrate application of the MMC using profile data for surfaces with mid-spatial frequency errors.

Image Chain Simulation for Earth Observation Satellites

Abstract: We present a general-purpose end-to-end image chain simulation (ICS) that enables to assess the image quality of a satellite imager for Earth observations. The image chain consists of four main components: radiometry, atmosphere, optics, and detector. In particular, ICS first computes the input radiance from the reflectance values of a high-resolution input, and then calculates the image radiance by using the optical transfer function (OTF) of the overall system. This OTF contains all the distortion effects due to atmosphere, optics, and detector. Finally, the signal on the detector, including the noise term, is computed and converted to digital counts. To evaluate the overall image quality, metrics such as peak signal-to-noise ratio and minimum resolvable contrast are used. To illustrate the utility and versatility of the developed ICS, several analyses are also performed that demonstrate the system performance of a generic satellite imagery. Our development provides a unified framework for the ICS developers of spaceborne Earth-observing systems. Such a complete end-to-end ICS is crucial for the effective development of an Earth observation satellite, especially in the design and test phases.

Spatial Distortion Assessments of a Low-Cost Laboratory and Field Hyperspectral Imaging System.

Abstract: This article describes the adaptation of an existing aerial hyperspectral imaging system in a low-cost setup for collecting hyperspectral data in laboratory and field environment and spatial distortion assessments. The imaging spectrometer system consists of an ImSpector V9 hyperspectral pushbroom scanner, PixelFly high performance digital CCD camera, and a subsystem for navigation, position determination and orientation of the system in space, a sensor bracket and control system. The main objective of the paper is to present the system, with all its limitations, and a spatial calibration method. The results of spatial calibration and calculation of modulation transfer function (MTF) are reported along with examples of images collected and potential uses in agronomy. The distortion value rises drastically at the edges of the image in the near-infrared segment, while the results of MTF calculation showed that the image sharpness was equal for the bands from the visible part of the spectrum, and approached Nyquist’s theory of digitalization. In the near-infrared part of the spectrum, the MTF values showed a less sharp decrease in comparison with the visible part. Preliminary image acquisition indicates that this hyperspectral system has potential in agronomic applications.