title: Extended depth-of-field imaging and ranging in microscopy
Creators: name: Zammit, Paul
Publisher: name: University of Glasgow
Year: 2017
Subjects: subject: Wavefront coding, extended depth-of-field, 3D imaging, ranging, optics, computational optics.

description: Conventional 3D imaging techniques such as laser scanning, focus-stacking and confocal microscopy either require scanning in all or a subset of the spatial dimensions, or else are limited by their depth of field (DOF). Scanning increases the acquisition time, therefore techniques which rely on it cannot be used to image moving scenes. In order to acquire both the intensity of the scene and its depth, extending the DOF without scanning is therefore necessary. This is traditionally achieved by stopping the system down (reducing the f/#). This, however, has the highly undesirable effect of lowering both the throughput and the lateral resolution of the system. In microscopy in particular, both these parameters are critical, therefore there is scope in breaking this trade-off. The objective of this work, therefore, is to develop a practical and simple 3D imaging technique which is capable of acquiring both the irradiance of the scene and its depth in a single snapshot over an extended DOF without incurring a reduction in optical throughput and lateral resolution. To this end, a new imaging technique, referred to as complementary Kernel Matching (CKM), is proposed in this thesis.

To extend the DOF, in CKM a hybrid imaging technique known as wavefront coding (WC) has been used. WC permits the DOF to be extended by an order of magnitude typically without reducing the efficiency and the resolution of the system. Moreover, WC only requires the introduction of a phase mask in the aperture of the system, hence it also has the benefit of simplicity and practicality. Unfortunately, in practice, WC systems are found to suffer from post-recovery artefacts and distortion, which substantially degrade the quality of the acquired image. To date, this long-standing problem has found no solution and is probably the cause for the lack of exploitation of this imaging technique by the industry.

In CKM, use of a largely ignored phenomenon associated with WC was made to measure the depth of the sample. This is the lateral translation of the scene in proportion to its depth. Furthermore, once the depth of the scene is known, the ensuing artefacts and distortion due to the introduction of the WC element can be compensated for. As a result, a high quality intensity image of the scene and its depth profile (referred to in stereo vision parlance as a depth map) is obtained over a DOF which is typically an order of magnitude larger than that of an equivalent clear-aperture system. This implies that, besides being a 3D imaging technique, CKM is also a solution to one of the longest standing problem in WC itself. By means of WC, therefore, the DOF was extended without scanning and without reducing the throughput and the optical resolution, allowing both an intensity image of the scene to be acquired and its depth map. In addition, CKM is inherently monocular, therefore it does not suffer from occlusion, which is a major problem affecting triangulation-based 3D imaging techniques such as the popular stereo vision. One therefore concludes that CKM fulfils the objectives set for this project.

In this work, various ways of implementing CKM were explored and compared; and the theory associated with them was developed. An experimental prototype was then built and the technique was demonstrated experimentally in microscopy. The results show that CKM eliminates WC artefacts and thus gives high quality images of the scene over an extended DOF. A DOF of ∼ 20μm was achieved on a 40×, 0.5NA system experimentally, however this can be increased if required. The experimental depth reconstructions of real samples (such as pollen grains and a silicon die) imaged in various modalities (reflection, transmission and fluorescence) were comparable to those given by a focus-stack. However, as with all other passive techniques, the performance of CKM depends on the texture and features in the scene itself. On a binary systematic scene consisting of regularly spaced dots with a linear depth gradient, an RMS error of ±0.15μm was obtained from an image signal-to-noise ratio of 60dB.

Finally, owing to its simplicity and large DOF, there is scope in investigating the possibility of using the same CKM setup for 3D point localisation applications such as super resolution. An initial investigation was therefore conducted by localising sub-resolution fluorescent beads. On a 40×, 0.5NA system, a mean precision of 148nm in depth and &lt; 30nm in the lateral dimensions was observed experimentally from 4, 000 photons per localisation over a DOF of 26μm. From these experimental values, a mean localisation precision of &lt; 34nm in depth and &lt; 13nm in the lateral dimensions from 2, 000 photons per localisation over a DOF of 3μm is expected on a more typical 100×, 1.4NA system. This compares favourably to the competition, therefore we conclude that there is scope in investigating this technique for 3D point localisation applications further.