Closed-form inverses for the mixed pixel/multipath interference problem in AMCW lidar

We present two new closed-form methods for mixed pixel/multipath interference separation in AMCW lidar systems. The mixed pixel/multipath interference problem arises from the violation of a standard range-imaging assumption that each pixel integrates over only a single, discrete backscattering source. While a numerical inversion method has previously been proposed, no close-form inverses have previously been posited. The first new method models reflectivity as a Cauchy distribution over range and uses four measurements at different modulation frequencies to determine the amplitude, phase and reflectivity distribution of up to two component returns within each pixel. The second new method uses attenuation ratios to determine the amplitude and phase of up to two component returns within each pixel. The methods are tested on both simulated and real data and shown to produce a significant improvement in overall error. While this paper focusses on the AMCW mixed pixel/multipath interference problem, the algorithms contained herein have applicability to the reconstruction of a sparse one dimensional signal from an extremely limited number of discrete samples of its Fourier transform

Extending AMCW lidar depth-of-field using a coded aperture

By augmenting a high resolution full-field Amplitude Modulated Continuous Wave lidar system with a coded aperture, we show that depth-of-field can be extended using explicit, albeit blurred, range data to determine PSF scale. Because complex domain range-images contain explicit range information, the aperture design is unconstrained by the necessity for range determination by depth-from-defocus. The coded aperture design is shown to improve restoration quality over a circular aperture. A proof-of-concept algorithm using dynamic PSF determination and spatially variant Landweber iterations is developed and using an empirically sampled point spread function is shown to work in cases without serious multipath interference or high phase complexity

Understanding and ameliorating non-linear phase and amplitude responses in AMCW Lidar

Amplitude modulated continuous wave (AMCW) lidar systems commonly suffer from non-linear phase and amplitude responses due to a number of known factors such as aliasing and multipath inteference. In order to produce useful range and intensity information it is necessary to remove these perturbations from the measurements. We review the known causes of non-linearity, namely aliasing, temporal variation in correlation waveform shape and mixed pixels/multipath inteference. We also introduce other sources of non-linearity, including crosstalk, modulation waveform envelope decay and non-circularly symmetric noise statistics, that have been ignored in the literature. An experimental study is conducted to evaluate techniques for mitigation of non-linearity, and it is found that harmonic cancellation provides a significant improvement in phase and amplitude linearity

Undue influence: Mitigating range-intensity coupling in AMCW ‘flash’ lidar using scene texture

We present a new algorithm for mitigating range-intensity coupling caused by scattered light in full-field amplitude modulated continuous wave lidar systems using scene texture. Full-field Lidar works using the time-of-flight principle to measure the range to thousands of points in a scene simultaneously. Mixed pixel are erroneous range measurements caused by pixels integrating light from more than one object at a time. Conventional optics suffer from internal reflections and light scattering which can result in every pixel being mixed with scattered light. This causes erroneous range measurements and range-intensity coupling. By measuring how range changes with intensity over local regions it is possible to determine the phase and intensity of the scattered light without the complex calibration inherent in deconvolution based restoration. The new method is shown to produce a substantial improvement in range image quality. An additional range from texture method is demonstrated which is resistant to scattered light. Variations of the algorithms are tested with and without segmentation - the variant without segmentation is faster, but causes erroneous ranges around the edges of objects which are not present in the segmented algorithm

Mixed pixel return separation for a full-field ranger

Full-field amplitude modulated continuous wave range imagers commonly suffer from the mixed pixel problem. This problem is caused by the integration of light from multiple sources by a single pixel, particularly around the edges of objects, resulting in erroneous range measurements. In this paper we present a method for identifying the intensity and range of multiple return values within each pixel, using the harmonic content of the heterodyne beat waveform. Systems capable of measurements at less than 90 degree phase shifts can apply these methods. Our paper builds on previous simulation based work and uses real range data. The method involves the application of the Levy-Fullagar algorithm and the use of the cyclic nature of the beat waveform to extract the mean noise power. We show that this method enables the separation of multiple range sources and also decreases overall ranging error by 30% in the single return case. Error in the two return case was found to increase substantially as relative intensity of the return decreased

Multiple return separation for a full-field ranger via continuous waveform modelling

We present two novel Poisson noise Maximum Likelihood based methods for identifying the individual returns within mixed pixels for Amplitude Modulated Continuous Wave rangers. These methods use the convolutional relationship between signal returns and the recorded data to determine the number, range and intensity of returns within a pixel. One method relies on a continuous piecewise truncated-triangle model for the beat waveform and the other on linear interpolation between translated versions of a sampled waveform. In the single return case both methods provide an improvement in ranging precision over standard Fourier transform based methods and a decrease in overall error in almost every case. We find that it is possible to discriminate between two light sources within a pixel, but local minima and scattered light have a significant impact on ranging precision. Discrimination of two returns requires the ability to take samples at less than 90 phase shifts

Ameliorating Systematic Errors in Full-Field AMCW Lidar

This thesis presents an analysis of systematic error in full-field amplitude modulated continuous wave range-imaging systems. The primary focus is on the mixed pixel/multipath interference problem, with digressions into defocus restoration, irregular phase sampling and the systematic phase perturbations introduced by random noise. As an integral part of the thesis, a detailed model of signal formation is developed, that models noise statistics not included in previously reported models. Prior work on the mixed pixel/multipath interference problem has been limited to detection and removal of perturbed measurements or partial amelioration using spatial information, such as knowledge of the spatially variant scattering point spread function, or raytracing using an assumption of Lambertian reflection. Furthermore, prior art has only used AMCW range measurements at a single modulation frequency. In contrast, in this thesis, by taking multiple measurements at different modulation frequencies with known ratio-of-integers frequency relationships, a range of new closed-form and lookup table based inversion and bounding methods are explored. These methods include: sparse spike train deconvolution based multiple return separation, a closed-form inverse using attenuation ratios and a normalisation based lookup table method that uses a new property we term the characteristic measurement. Other approaches include a Cauchy distribution based model for backscattering sources which are range-diffuse, like fog or hair. Novel bounding methods are developed using the characteristic measurement and attenuation ratios on relative intensity, relative phase and phase perturbutation. A detailed noise and performance analysis is performed of the characteristic measurement lookup table method and the bounding methods using simulated data. Experiments are performed using the University of Waikato Heterodyne range-imager, the Canesta XZ-422 and the Mesa Imaging Swissranger 4000 in order to demonstrate the performance of the lookup table method. The lookup table method is found to provide an order of magnitude improvement in ranging accuracy, albeit at the expense of ranging precision

A fast Maximum Likelihood method for improving AMCW lidar precision using waveform shape

Amplitude Modulated Continuous Wave imaging lidar systems use the time-of-flight principle to determine the range to objects in a scene. Typical systems use modulated illumination of a scene and a modulated sensor or image intensifier. By changing the relative phase of the two modulation signals it is possible to measure the phase shift induced in the illumination signal, thus the range to the scene. In practical systems, the resultant correlation waveform contains harmonics that typically result in a non-linear range response. Nevertheless, these harmonics can be used to improve range precision. We model a waveform continuously variable in phase and intensity as a linear interpolation. By approximating the problem as a Maximum Likelihood problem, an analytic solution for the problem is derived that enables an entire range image to be processed in a few seconds. A substantial improvement in overall RMS error and precision over the standard Fourier phase analysis approach results

Surface projection for mixed pixel restoration

Amplitude modulated full-field range-imagers are measurement devices that determine the range to an object simultaneously for each pixel in the scene, but due to the nature of this operation, they commonly suffer from the significant problem of mixed pixels. Once mixed pixels are identified a common procedure is to remove them from the scene; this solution is not ideal as the captured point cloud may become damaged. This paper introduces an alternative approach, in which mixed pixels are projected onto the surface that they should belong. This is achieved by breaking the area around an identified mixed pixel into two classes. A parametric surface is then fitted to the class closest to the mixed pixel, with this mixed pixel then being project onto this surface. The restoration procedure was tested using twelve simulated scenes designed to determine its accuracy and robustness. For these simulated scenes, 93% of the mixed pixels were restored to the surface to which they belong. This mixed pixel restoration process is shown to be accurate and robust for both simulated and real world scenes, thus provides a reliable alternative to removing mixed pixels that can be easily adapted to any mixed pixel detection algorithm

Defocus restoration for a full-field heterodyne ranger via multiple return separation

Full-field heterodyne time-of-flight range-imagers allow a large number of range measurements to be taken simultaneously across an entire scene; these range measurements may be corrupted due to limited depth of field. We propose a new method for deblurring heterodyne range images by identifying multiple signal returns within each pixel via deconvolution, thus reducing the spatially variant deblurring problem to a sequence of spatially invariant deconvolutions. We have applied this method to simulated data, showing significant improvement in the restored images