System-level noise performance of coherent imaging systems.

We provide an in-depth analysis of noise considerations in coherent imaging, accounting for speckle and scintillation in addition to "conventional" image noise. Specifically, we formulate closed-form expressions for total effective noise in the presence of speckle only, scintillation only, and speckle combined with scintillation. We find analytically that photon shot noise is uncorrelated with both speckle and weak-to-moderate scintillation, despite their shared dependence on the mean signal. Furthermore, unmitigated speckle and scintillation noise tends to dominate coherent-imaging performance due to a squared mean-signal dependence. Strong coupling occurs between speckle and scintillation when both are present, and we characterize this behavior by fitting a scale factor capable of generating variances in closed form. We verify each of these claims through a series of wave-optics simulations, and we see strong agreement in general between numerical results and theoretical predictions. Our findings allow us to confidently gauge signal-to-noise ratio (SNR) expectations when active illumination produces coherent noise.

Active-tracking scaling laws using the noise-equivalent angle due to speckle.

It is well known to system engineers that speckle imposes a limitation on active-tracking performance, but scaling laws that quantify this limitation do not currently exist in the peer-reviewed literature. Additionally, existing models lack validation through either simulation or experimentation. With these points in mind, this paper formulates closed-form expressions that accurately predict the noise-equivalent angle due to speckle. The analysis separately treats both well-resolved and unresolved cases for circular and square apertures. When compared with the numerical results from wave-optics simulations, the analytical results show excellent agreement to a track-error limitation of (1/3)λ/D, where λ/D is the aperture diffraction angle. As a result, this paper creates validated scaling laws for system engineers that need to account for active-tracking performance.

Radiometry and contrast-to-noise ratio for continuous-wave and laser range-gated active imaging systems.

Resolution and sensitivity must be considered in the design of an active imaging system. System sensitivity is characterized by the signal-to-noise or contrast-to-noise ratio and is derived through radiometry. We present a tutorial for the radiometry associated with the contrast-to-noise ratio for active continuous-wave and laser range-gated imaging systems, giving a useful metric for determining reflective-band sensor performance against a target and background. A calculation of the full power and contrast-to-noise ratio terms is shown for an example case, and all relevant radiometric signal terms are covered while describing the assumptions made. Coherent effects on signal-to-noise ratio are excluded from this analysis.

Wave-optics simulation of dynamic speckle: I. In a pupil plane.

This two-part paper demonstrates the use of wave-optics simulations to model the effects of dynamic speckle. In Part I, we formulate closed-form expressions for the analytical irradiance correlation coefficient, specifically in the pupil plane of an optical system. These expressions are for square, circular, and Gaussian scattering spots and four different modes of extended-object motion, including in-plane and out-of-plane translation and rotation. Using a phase-screen approach, we then simulate the equivalent scattering from an optically rough extended object, where we assume that the surface heights are uniformly distributed and delta correlated from grid point to grid point. For comparison to the analytical irradiance correlation coefficient, we also calculate the numerical irradiance correlation coefficient from the dynamic speckle after propagation from the simulated object plane to the simulated pupil plane. Overall, the analytical and numerical results definitely demonstrate that, relative to theory, the dynamic speckle in the simulated pupil plane is properly correlated from one frame to the next. Such validated wave-optics simulations provide the framework needed to model more sophisticated setups and obtain accurate results for system-level studies.

Wave-optics simulation of dynamic speckle: II. In an image plane.

This two-part paper demonstrates the use of wave-optics simulations to model the effects of dynamic speckle. In Part II, we formulate closed-form expressions for the analytical irradiance correlation coefficient, specifically in the image plane of an optical system. These expressions are for square, circular, and Gaussian limiting apertures and four different modes of extended-object motion, including in-plane and out-of-plane translation and rotation. Using a phase-screen approach, we then simulate the equivalent scattering from an optically rough extended object, where we assume that the surface heights are uniformly distributed and delta correlated from grid point to grid point. For comparison to the analytical irradiance correlation coefficient, we also calculate the numerical irradiance correlation coefficient from the dynamic speckle after propagation from the simulated object plane to the simulated image plane. Overall, the analytical and numerical results definitely demonstrate that, relative to theory, the dynamic speckle in the simulated image plane is properly correlated from one frame to the next. Such validated wave-optics simulations provide the framework needed to model more sophisticated setups and obtain accurate results for system-level studies.

Performance of infrared systems in swimmer detection for maritime security.

The detection of swimmer activity in harbor areas around piers and ships is an important aspect of Anti-Terrorism/Force Protection (AT/FP) sensing efforts in the U.S. Navy and Coast Guard. A series of data collections and perception experiments were conducted to validate the use of thermal target acquisition models against swimmer targets. The results were analyzed to derive the discrimination criteria necessary for sensor design for maritime force protection.

Predicting range performance of sampled imagers by treating aliased signal as target-dependent noise.

This paper presents a new theory to predict the impact of sampling on target acquisition. The aliased signal that results from sampling is treated as noise. The aliased signal is different from detector noise in two ways. First, aliasing disappears as the target contrast decreases. Second, the image corruption due to aliasing gets worse with increased range. This is because sampling is constant in angle space, and targets become poorly sampled as range increases. The theory is presented, along with the results of three experiments. The match between model and experiment is excellent.

Predicting the probability of facial identification using a specific object model.

Many security and surveillance tasks involve either finding an object in a cluttered scene or discriminating between like objects. For example, an observer might look for a person of known height and weight in a crowd, or he might want to positively identify a specific face. The paper "Modeling target acquisition tasks associated with security and surveillance" [Appl. Opt. 46, 4209 (2007)] describes a specific-object model used to predict the probability of accomplishing this type of task. We describe four facial identification experiments and apply the specific-object model to predict the results. Facial identification is accurately predicted by the specific-object model.

Characteristics of infrared imaging systems that benefit from superresolution reconstruction.

There have been numerous applications of superresolution reconstruction algorithms to improve the range performance of infrared imagers. These studies show there can be a dramatic improvement in range performance when superresolution algorithms are applied to undersampled imager outputs. These occur when the imager is moving relative to the target, which creates different spatial samplings of the field of view for each frame. The degree of performance benefit is dependent on the relative sizes of the detector/spacing and the optical blur spot in focal plane space. The minimum blur spot size achievable on the focal plane is dependent on the system F/number. Hence, we provide a range of these sensor characteristics, for which there is a benefit from superresolution reconstruction algorithms. Additionally, we quantify the potential performance improvements associated with these algorithms. We also provide three infrared sensor examples to show the range of improvements associated with provided guidelines.

Adaptive deblurring of noisy images.

We propose a practical sensor deblurring filtering method for images that are contaminated with noise. A sensor blurring function is usually modeled via a Gaussian-like function having a bell shape. The straightforward inverse function results in the magnification of noise at high frequencies. To address this issue, we apply a special spectral window to the inverse blurring function. This special window is called the power window, which is a Fourier-based smoothing window that preserves most of the spatial frequency components in the passband and attenuates quickly at the transition band. The power window is differentiable at the transition point, which gives a desired smooth property and limits the ripple effect. Utilizing the properties of the power window, we design the deblurring filter adaptively by estimating the energy of the signal and the noise of the image to determine the passband and the transition band of the filter. The deblurring filter design criteria are (a) the filter magnitude is less than 1 at the frequencies where the noise is stronger than the desired signal (the transition band), and (b) the filter magnitude is greater than 1 at the other frequencies (the passband). Therefore the adaptively designed deblurring filter is able to deblur the image by a desired amount based on the estimated or known blurring function while suppressing the noise in the output image. The deblurring filter performance is demonstrated by a human perception experiment in which 10 observers are to identify 12 military targets with 12 aspect angles. The results of comparing target identification probabilities with blurred and deblurred images and adding two levels of noise to blurred and deblurred noisy images are reported.

Midwave infrared and visible sensor performance modeling: small craft identification discrimination criteria for maritime security.

The new emphasis on Anti-Terrorism and Force Protection (AT/FP), for both shore and sea platform protection, has resulted in a need for infrared imager design and evaluation tools that demonstrate field performance against U.S. Navy AT/FP requirements. In the design of infrared imaging systems for target acquisition, a discrimination criterion is required for successful sensor realization. It characterizes the difficulty of the task being performed by the observer and varies for different target sets. This criterion is used in both assessment of existing infrared sensor and in the design of new conceptual sensors. We collected 12 small craft signatures (military and civilian) in the visible band during the day and the long-wave and midwave infrared spectra in both the day and the night environments. These signatures were processed to determine the targets' characteristic dimension and contrast. They were also processed to band limit the signature's spatial information content (simulating longer range), and a perception experiment was performed to determine the task difficulty (N50 and V50). The results are presented and can be used for Navy and Coast Guard imaging infrared sensor design and evaluation.

Superresolution image reconstruction from a sequence of aliased imagery.

We present a superresolution image reconstruction from a sequence of aliased imagery. The subpixel shifts (displacement) among the images are unknown due to the uncontrolled natural jitter of the imager. A correlation method is utilized to estimate subpixel shifts between each low-resolution aliased image with respect to a reference image. An error-energy reduction algorithm is derived to reconstruct the high-resolution alias-free output image. The main feature of this proposed error-energy reduction algorithm is that we treat the spatial samples from low-resolution images that possess unknown and irregular (uncontrolled) subpixel shifts as a set of constraints to populate an oversampled (sampled above the desired output bandwidth) processing array. The estimated subpixel locations of these samples and their values constitute a spatial domain constraint. Furthermore, the bandwidth of the alias-free image (or the sensor imposed bandwidth) is the criterion used as a spatial frequency domain constraint on the oversampled processing array. The results of testing the proposed algorithm on the simulated low- resolution forward-looking infrared (FLIR) images, real-world FLIR images, and visible images are provided. A comparison of the proposed algorithm with a standard interpolation algorithm for processing the simulated low-resolution FLIR images is also provided.

Target-acquisition performance in undersampled infrared imagers: static imagery to motion video.

In this research we show that the target-acquisition performance of an undersampled imager improves with sensor or target motion. We provide an experiment designed to evaluate the improvement in observer performance as a function of target motion rate in the video. We created the target motion by mounting a thermal imager on a precision two-axis gimbal and varying the sensor motion rate from 0.25 to 1 instantaneous field of view per frame. A midwave thermal imager was used to permit short integration times and remove the effects of motion blur. It is shown that the human visual system performs a superresolution reconstruction that mitigates some aliasing and provides a higher (than static imagery) effective resolution. This process appears to be relatively independent of motion velocity. The results suggest that the benefits of superresolution reconstruction techniques as applied to imaging systems with motion may be limited.

Atmospheric modulation transfer function in the infrared.

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