Analysis tools for computational imaging systems

In the modern tactical imaging environment, new computational imaging (CI) systems and algorithms are being used to improve speed and accuracy for detection tasks. Therefore, a measurement technique is needed to predict the performance of complex non-shift invariant EO/IR imaging systems, including CI systems. Detection performance of traditional imaging systems can be modeled using current system metrics and measurements such as Modulation Transfer Function (MTF), Signal to Noise (SNR), and instantaneous Field of View (iFOV). In this correspondence, we propose a technique to experimentally measure a detection sensitivity metric for non-traditional CI systems. The detection sensitivity metric predicts the upper bound of linear algorithm performance though evaluation of a matched filter. The experimental results are compared with theoretical expected values though the Night Vision Integrated Performance Model (NV-IPM). Additionally, we demonstrate the experimental results for a variety of imaging systems (IR, visible, and color), target sizes and orientations, as well as SNR values. Our results demonstrate how this detection sensitivity metric can be measured to provide additional insight into the final system performance.

Optical imaging usually suffers from aberrations that are induced by various structures when imaging biological samples. Usually aberrations degrade the imaging system performances by broadening the point spread function (PSF). Unexpectedly we show that in spatially incoherent interferometry like full-filed optical coherence tomography (FFOCT), the system PSF width is almost insensitive to aberrations. Instead of considering the PSF of a classical imaging system such as a microscope, we specifically pay attention to the system PSF of interferometric imaging systems for which an undistorted wavefront from a reference beam interferes with the distorted wavefront of the object beam. By comparing the cases of scanning OCT with spatially coherent illumination, wide-field OCT with spatially coherent illumination and FFOCT with spatially incoherent illumination, we found that in FFOCT with spatially incoherent illumination the system PSF width is almost independent of the aberrations and only its amplitude varies. This is demonstrated by theoretical analysis as well as numerical calculations for different aberrations, and confirmed by experiments with a FFOCT system. It is the first time to the best of our knowledge that such specific merit of incoherent illumination in FFOCT has been demonstrated. Based on this, the signal level is used as metric in our adaptive optics FFOCT system for retinal imaging. Only the main aberrations (defocus and astigmatism) that are dominating in eye are corrected to improve the signal to noise ratio and the high order aberrations are skipped. This would increase the correction speed thus reducing the imaging time.

Computational imaging is a proven strategy for obtaining high-quality images with fast acquisition rates and simpler hardware. Metasurfaces provide exquisite control over electromagnetic fields, enabling the radiated field to be molded into unique patterns. The fusion of these two concepts can bring about revolutionary advances in the design of imaging systems for security screening. In the context of computational imaging, each field pattern serves as a single measurement of a scene; imaging a scene can then be interpreted as estimating the reflectivity distribution of a target from a set of measurements. As with any computational imaging system, the key challenge is to arrive at a minimal set of measurements from which a diffraction-limited image can be resolved. Here, we show that the information content of a frequency-diverse metasurface aperture can be maximized by design, and used to construct a complete millimeter-wave imaging system spanning a 2 m by 2 m area, consisting of 96 metasurfaces, capable of producing diffraction-limited images of human-scale targets. The metasurfacebased frequency-diverse system presented in this work represents an inexpensive, but tremendously flexible alternative to traditional hardware paradigms, offering the possibility of low-cost, real-time, and ubiquitous screening platforms.

Origami is the art of paper folding that allows a single flat piece of paper to assume different 3D shapes depending on the fold patterns and the sequence of folding. Using the principles of origami along with computation imaging technique the authors demonstrate a versatile shape‐morphing microwave imaging array with reconfigurable field‐of‐view and scene‐adaptive imaging capability. Microwave/millimeter‐wave based array imaging systems are expected to be the workhorse for sensory perception of future autonomous intelligent systems. The imaging capability of a planar array‐based systems operating in complex scattering conditions have limited field‐of‐view and lack the ability to adaptively reconfigure resolution. To overcome this, here, deviations from planarity and isometry are allowed, and a shape‐morphing computational imaging system is demonstrated. Implemented on a reconfigurable Waterbomb origami surface with 22 active metasurface panels that radiate near‐orthogonal modes across 17–27 GHz, capability to image complex 3D objects in full details minimizing the effects of specular reflections in diffraction‐limited sparse imaging with scene adaptability, reconfigurable cross‐range resolution, and field‐of‐view is demonstrated. Such electromagnetic origami surfaces, through simultaneous surface shape‐morphing ability (potentially with shape‐shifting electronic materials) and electromagnetic field programmability, opens up new avenues for intelligent and robust sensing and imaging systems for a wide range of applications.

One practical way to characterize the spatial performance of an in-flight satellite optical imaging system is to determine the modulation transfer function (MTF) from its remotely sensed images on the ground. Currently, there are many MTF measurement techniques designed to provide accurate measurements for high-resolution imaging systems. However, these existing techniques usually rely on the presence and manual identification of a well-separated characteristics target. We introduce an insight to effectively estimate a degradation function based on the MTF by analyzing the nonlocal self-similarity characteristics, namely the structural component, in the observed image. To this end, this paper presents several strategies to realize the aim of this work. First, we propose a segmentation method to select the ideal candidates for MTF estimation. Second, we develop an adaptive structure selection method that removes detrimental structures and selects useful information for point spread function (PSF) estimation. Finally, we put forward a robust estimation method by introducing a spatial prior that is able to simultaneously suppress noises while preserving the sparsity and continuity of the PSF kernels. For the experiments, datasets used in the analyses are synthetically blurred images simulated from level 2A product of IKONOS and real remotely sensed images from level 0 product of RazakSAT. The experimental results demonstrate that the proposed method is practical and effective, with <2.3 % of relative error at the Nyquist frequency as compared to the well-established edge method. This indicates that the proposed method can warrant a reliable result for on-orbit spatial characterization.

To obtain a high imaging frame rate, a computational ghost imaging system scheme is proposed based on optical fiber phased array (OFPA). Through high-speed electro-optic modulators, the randomly modulated OFPA can provide much faster speckle projection, which can be precomputed according to the geometry of the fiber array and the known phases for modulation. Receiving the signal light with a low-pixel APD array can effectively decrease the requirement on sampling quantity and computation complexity owing to the reduced data dimensionality while avoiding the image aliasing due to the spatial periodicity of the speckles. The results of analysis and simulation show that the frame rate of the proposed imaging system can be significantly improved compared with traditional systems.

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

The point spread function (PSF) of imaging system with coded mask is generally acquired by practical measure- ment with calibration light source. As the thermal radiation of coded masks are relatively severe than it is in visible imaging systems, which buries the modulation effects of the mask pattern, it is difficult to estimate and evaluate the performance of mask pattern from measured results. To tackle this problem, a model for infrared imaging systems with masks is presented in this paper. The model is composed with two functional components, the coded mask imaging with ideal focused lenses and the imperfection imaging with practical lenses. Ignoring the thermal radiation, the systems PSF can then be represented by a convolution of the diffraction pattern of mask with the PSF of practical lenses. To evaluate performances of different mask patterns, a set of criterion are designed according to different imaging and recovery methods. Furthermore, imaging results with inclined plane waves are analyzed to achieve the variation of PSF within the view field. The influence of mask cell size is also analyzed to control the diffraction pattern. Numerical results show that mask pattern for direct imaging systems should have more random structures, while more periodic structures are needed in system with image reconstruction. By adjusting the combination of random and periodic arrangement, desired diffraction pattern can be achieved.

Integrated, computational imaging systems are designed to maximally exploit system trade-offs for improved image quality. Applications of Fisher information to characterize the performance upper bounds of three specific integrated imaging systems will be discussed.

A recent study has shown that the double-pass method provides a good estimate of the ocular modulation transfer function (MTF) but that it does not yield the phase transfer function (PTF) [J. Opt. Soc. Am. A 12, 195 (1995)]. Therefore, one cannot recover the true retinal point-spread function (PSF). We present a modification of the double-pass method to overcome this problem. The key is to break the symmetry between the two passes. By using an unexpanded Gaussian input beam, we produce a diffraction-limited PSF for the first passes. Then, by using a large exit pupil, we get an aberrated PSF for the second pass. The double-pass aerial image is the cross correlation of both PSF's, so that the Fourier transform of such an aerial image directly provides the true retinal PTF, up to the cutoff frequency of the effective (small), diffraction-limited entrance pupil. The resulting double-pass aerial image is a blurred version of the true retinal PSF. Thus it shows the effect not only of even symmetric aberrations but also of odd and irregular aberrations such as coma. We have explored two different ways to retrieve the true retinal PSF: (a) deblurring of the aerial image and (b) PSF reconstruction combining PTF data with conventional double-pass MTF. We present promising initial results with both artificial and real eyes.

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.

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

Eddy-current imaging has been described in detail in previous publications [1,2,3]. As with other imaging systems, the image of an object represents blurring of the structures of the object by the system point spread function (PSF). Differing from other imaging systems, the PSF is very large and causes great spatial blurring of the object. This is because the eddy-current probe is a coil; its active area is much greater than the size of a beam of light, sound, or x-rays.

The burgeoning field of astrophotonics, the interface between astronomy and photonics, is redefining astronomical instrumentation to replace traditional bulk optical systems with integrated optics. This drives the development of a new promising photonics-integrated interferometric imaging technique, called the segmented planar imaging detector for electro-optical reconnaissance (SPIDER). Compared to conventional imaging systems, SPIDER can reduce the size, weight, and power (SWaP) by one to two orders of magnitude for an equivalent imaging resolution in virtue of photonics-integrated technology. However, SPIDER has a dense lens distribution and tens of separated narrow wavebands demultiplexed by array waveguide gratings. In this paper, we developed a new simplified sparse-aperture photonics-integrated interferometer (SPIN) imaging system. The SPIN imaging system was no more a Michelson configuration interferometer as SPIDER and was designed as a Fizeau configuration interferometer imaging system. This transfer of configuration type affords a more concise structure; the SPIN was designed with much less apertures and fewer wavebands than those of SPIDER. Further, the SPIN yields enhanced modulation transfer function and imaging quality with equivalent aperture diameter, compared with SPIDER. The main barrier of this transfer is the elimination of coupling restriction at the tip of a waveguide, namely the apodization effect. This effect, which is caused by the coupling effect between Fourier lens and waveguide, hinders SPIN imaging systems from getting finer resolution. However, a microscope could be used to eliminate this effect. Moreover, a waveguide array is used to receive these finer details and enlarges the field of view in SPIN. The coupling efficiency of the waveguides and crosstalk errors between waveguides of array were analyzed, which are important for proper parameters setting in SPIN imaging system. Based on these analyses, the imaging principle was derived and a hyper-Laplacian-based imaging reconstruction algorithm was developed. A simulation of the SPIN imaging system with seven apertures and one imaging waveband demonstrated the high imaging quality.

Purpose: To demonstrate a method of measuring the modulation transfer function (MTF) of digital imaging systems using the common star pattern test tool. The goal of this research is to develop a technique that brings precise and objective evaluation of spatial resolution to routine quality control in radiography and fluoroscopy. Method and Materials: Images of a 2‐degree star pattern were obtained on a variety of digital radiographic imaging systems, spanning a range of spatial resolution performance levels. One‐dimensional profiles from concentric circles around the center of the star were obtained from each star image. The circular profiles were unwrapped to produce a series of square waves, which were analyzed to produce the square wave response function (SWRF). Droege's method was used to compute the MTF from the SWRF. The MTF determined using the star pattern method was compared to published and quality control measurements of the MTF for several digital mammography and digital radiography systems. In implementing this method, important parameters that must be considered include the radial and angular sampling rates, the method for determining the zero‐frequency normalization and correction for beam nonuniformity. Results: The MTF computed from star pattern profile measurements closely matched the MTF obtained using other methods over the range of spatial frequencies between the Nyquist frequency and 1/3 of the Nyquist frequency. The star pattern MTF, which is a system measurement and includes the effects of detector and geometric unsharpness, was within 6–8% of reference values obtained from the scientific literature for two models digital mammography equipment. Conclusion: Images of a 2‐degree star pattern can produce estimates of the two‐dimensional system MTF. This method may offer a convenient means of assessing the spatial resolution of digital imaging systems for acceptance testing and quality control.