The Deployable SpaceTelescope Project was started at Delft University of Technology in 2014. The projectaims to develop an ultra-high resolution Earth Observation telescope with aresolution of 0.25m, but with a much lower mass and volume than its competitorscurrently in operation. In order to meet the stringent mass requirements, adeployable primary and secondary mirror are used. However, it is expected thatthe deployment of the optics will introduce severe aberrations in the system,limiting the performance. This thesis project investigated the implementationof phase diversity algorithms as a method for correction of these aberrationsthat does not add additional mass and complexity to the system. Phase diversityalgorithms originate from the field of ground-based astronomy and are rarelyused in space systems. Even less is known about their behavior in EarthObservation telescopes, which typically suffer from larger aberrations thanground-based telescopes. Also, Earth Observation telescopes image extendedscenes instead of point objects. FORTA, a ray tracing application developed ir.D. Dolkens specifically for simulation of the Deployable Space TelescopeOptics, was used for the simulation of the telescope imaging process. A MATLABtoolbox, developed during this project, was then used for simulation of a broadrange of phase diversity algorithm configurations. These algorithmconfigurations numerous methods from the field of imaging, including aneffective method for mitigating wrap-around effects resulting from theapplication of the Fast Fourier Transform. First, the set of algorithmparameters resulting in the optimum configuration in the context of the DSTproject was determined through a large number of parametric studies. Afterthat, it was found through simulations that by using a novel method for theselection of the subframe to which phase diversity is applied a significantperformance increase could be obtained. An analysis of the open-loopperformance of the algorithm showed that the wavefront error in the exit pupilcould be estimated to within a Root Mean Square (RMS) error of 0.07 lambda_0 inover 75% of simulations, where lambda_0=450nm is the smallest wavelengthaccepted by the panchromatic channel, and that a Strehl ratio (SR) of above 0.8was achieved in over 80% of cases. Through the development of an innovativepost-processing method that exploits a priori knowledge of the expected errorshape, both these percentages could be increased to above 85%. Deconvolutionusing a Wiener filter subsequently resulted in the reconstruction of details ofsmaller than 0.25m, in accordance with requirements. In addition, an analysisof the closed-loop performance was done, in which the wavefront error estimateswere used for iterative control of the active optics. This analysis showed thatfor initial Strehl ratios of higher than 0.6, the method would consistentlyincrease the Strehl ratio to a value of around 0.8 or above. However, after anoptimum was reached the method would diverge again. For the reliableimplementation of phase diversity in a closed-loop configuration, an effectivetermination criterion should be developed. Phase Diversity methods showpotential for implementation in the DST project, and it is recommended thatfurther studies are performed. These studies should focus on making the methodmore reliable through identification of inaccurate estimations, as well as onthe joint implementation of phase diversity with other calibration methods sothat the strengths of phase diversity can be exploited and its weaknessescompensated.