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All atomic force microscope (AFM) images suffer from distortions, which are principally produced by the interaction between the measured sample and the AFM tip. If the three-dimensional shape of the tip is known, the distorted image can be processed and the original surface form ' restored' typically by deconvolution approaches. This restored image gives a better representation of the real 3D surface or the measured sample than the original distorted image. In this thesis, a quantitative investigation of using morphological deconvolution has been used to restore AFM images via computer simulation using various computer simulated tips and objects. This thesis also presents the systematic quantitative study of the blind tip estimation algorithm via computer simulation using various computer simulated tips and objects. This thesis proposes a new method for estimating the impulse response of the AFM by measuring a micro-cylinder with a-priori known dimensions using contact mode AFM. The estimated impulse response is then used to restore subsequent AFM images, when measured with the same tip, under similar measurement conditions. Significantly, an approximation to what corresponds to the impulse response of the AFM can be deduced using this method. The suitability of this novel approach for restoring AFM images has been confirmed using both computer simulation and also with real experimental AFM images. This thesis suggests another new approach (impulse response technique) to estimate the impulse response of the AFM. this time from a square pillar sample that is measured using contact mode AFM. Once the impulse response is known, a deconvolution process is carried out between the estimated impulse response and typical 'distorted' raw AFM images in order to reduce the distortion effects. The experimental results and the computer simulations validate the performance of the proposed approach, in which it illustrates that the AFM image accuracy has been significantly improved. A new approach has been implemented in this research programme for the restoration of AFM images enabling a combination of cantilever and feedback signals at different scanning speeds. In this approach, the AFM topographic image is constructed using values obtained by summing the height image that is used for driving the Z-scanner and the deflection image with a weight function oc that is close to 3. The value of oc has been determined experimentally using tri al and error. This method has been tested 3t ten different scanning speeds and it consistently gives more faithful topographic images than the original AFM images.

This thesis investigates ways for assessing the practical lateral resolution performance of imaging systems and explores the trade-off between lateral resolution and signal-to-noise ratio (SNR) in high resolution systems. Several authors have commented on the seemingly inherent inefficiency in which imaging systems use the available light when providing resolution enhancement beyond the Abbe limit, often due to the precise mechanism that enabled the resolution enhancement in the first place. Two methods for assessing the lateral resolution and noise performance of microscope systems were developed in this project: a probabilistic analysis based on two-point resolution which has the novelty of being able to deal with synthetic images and the stochastic transfer function (STF) which looks into the effect of noise in the Fourier domain. Results can be determined semi-analytically or by using Monte- Carlo simulations. These methods were applied to several microscope systems such as conventional widefield fluorescence microscopy (WFM) and structured illumination microscopy (SIM) and used to compare their noise performance. These techniques were also used to compare several post-reconstruction processing algorithms for SIM, showing the strengths and weaknesses of each strategy. SIM encodes high spatial frequency information into a senes of images and uses a reconstruction algorithm to yield a high resolution unage. Without further processing, the STF showed that SIM generates noise that is three times greater than that associated with a conventional fluorescence microscope and based on the two-point resolution analysis, the SIM SNR performance in 2D was only comparable with WFM, even though SIM has twice the theoretical bandwidth. However, the reconstruction processing of SIM introduces many redundancies in the form of overlapping spatial frequency orders which can be exploited to improve the SNR further. The STF showed a transition spatial frequency below which the WFM system outperforms SIM and it was shown that a simple WFM-SIM hybrid algorithm based on this observation can indeed significantly improve the SIM result. Common strategies which provide more complete treatments include the Wiener filter and the weighted- average approach. Based on the assumption of uncorrelated noise and a pre-defined goal transfer function, it was shown that the weighted-average method gives the minimum resultant variance statistically. For SIM, this condition is only met when the maximum fringe spatial frequency allowed by the illumination optics is used and the level of noise correlation increases with decreasing illumination grating frequency. The development of a general standardised metric which includes noise considerations can allow more realistic performance assessments of imaging systems and facilitate comparisons. Along with other considerations, such analysis can help practitioners select the most appropriate system for the intended tasks. Understanding the strength and weakness of existing systems will reveal areas of possible enhancements and also help with the development of new techniques.

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