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Different optical methods for phase recovering and therefore the wavefront are related with a set of direct techniques as interferometry, indirect ones like Shack-Hartmann sensing and iterative methods where an objective function is optimized. The aerospace industry has used techniques coming from optical metrology for the assembly and integration of instruments with optical properties. However, also other subjects use, involve and push the development of these kind of techniques, for example in microscopy. Currently, the wavefront retrieval techniques have been improved and strengthened by using algorithms coming from computer graphics. In addition, the design of filters and phase demodulation by using the theory of signals coming from electronic engineering and telecommunications. In addition to the improvements in algorithms, the experimental optical methods have triggered innovative developments considering the emergent technologies based on liquid crystal (spatial light modulators - SLMs) and its ability to modulate phase, amplitude or both easily. Furthermore, the performance in terms of response times, resolution and modulation capabilities, among others, of liquid crystal devices are improving constantly. This thesis proposes new methods and improvements in techniques for recovering the wavefront in order to be used in the corresponding processes of assembly and integration of optical instruments for space. A method able to recover the phase with abrupt differences of intensity in the incoming field is proposed from the conventional interferometry by using techniques coming from computer graphics and fringe normalization through filters described since the signal theory. A comparison between electronic speckle pattern interferometry (ESPI) and differential interferometry showing as a disadvantage that the last one does not recover the phase of an extended object. Moreover, the wavefront recovery in topographic applications is proposed in ESPI by using two wa, Los diferentes ḿetodos ́opticos para la recuperacíon de la fase y por tanto para el frente de onda pasan por una serie de t́ecnicas, como las interferoḿetricas y otras no directas entre las que destacan el sensado Shack-Hartmann y los ḿetodos iterativos en los que se minimiza una funcíon objetivo. La industria aeroespacial hace uso de estas t́ecnicas provenientes de la metroloǵıa ́optica para la integracíon de instrumentos esencialmente ́opticos. Sin embargo, no es la ́unica industria, ni ́area que hace uso de estas, un ejemplo es la microscopia, la cual tambíen ha aportado con nuevas t́ecnicas. Actualmente las t́ecnicas de recuperacíon del frente onda se han apropiado y robustecido desde la algoritmia de ́areas como la computacíon gŕafica, y desde el punto de vista del tratamiento de se˜nales provenientes de la ingenieŕıa electŕonica y de telecomunicaciones con el dise˜no de filtros y la demodulacíon de la fase en el espacio frecuencial. Por otro lado, no solo la algoritmia ha sido mejorada, los ḿetodos ́opticos experimentales han desencadenado en desarrollos novedosos con la aparicíon de tecnoloǵıas emergentes basadas en cristal-liquido (Moduladores espaciales de luz - SLMs). La gran ventaja de estos dispositivos es la capacidad de modular fase, amplitud o ambas con una relativa facilidad en su uso. Adicionalmente los nuevos dispositivos tienen cada vez mejor desempe˜nos en las capacidades de modulacíon, en los tiempos de respuesta, mayor resolucíon, entre otras. En resumen esta memoria de tesis propone ḿetodos novedosos e introduce mejoras en otros para las t́ecnicas de recuperacíon del frente de onda que son usados en los procesos de integracíon de instrumentos ́opticos para espacio. Desde la interferometŕıa convencional se propone un ḿetodo capaz de reconstruir la fase con diferencias de intensidad abruptas en el campo a reconstruir, usando t́ecnicas provenientes de la computacíon gŕafica y la normalizacíon de franjas a trav́es de fil

Different optical methods for phase recovering and therefore the wavefront are related with a set of direct techniques as interferometry, indirect ones like Shack-Hartmann sensing and iterative methods where an objective function is optimized. The aerospace industry has used techniques coming from optical metrology for the assembly and integration of instruments with optical properties. However, also other subjects use, involve and push the development of these kind of techniques, for example in microscopy. Currently, the wavefront retrieval techniques have been improved and strengthened by using algorithms coming from computer graphics. In addition, the design of filters and phase demodulation by using the theory of signals coming from electronic engineering and telecommunications. In addition to the improvements in algorithms, the experimental optical methods have triggered innovative developments considering the emergent technologies based on liquid crystal (spatial light modulators - SLMs) and its ability to modulate phase, amplitude or both easily. Furthermore, the performance in terms of response times, resolution and modulation capabilities, among others, of liquid crystal devices are improving constantly. This thesis proposes new methods and improvements in techniques for recovering the wavefront in order to be used in the corresponding processes of assembly and integration of optical instruments for space. A method able to recover the phase with abrupt differences of intensity in the incoming field is proposed from the conventional interferometry by using techniques coming from computer graphics and fringe normalization through filters described since the signal theory. A comparison between electronic speckle pattern interferometry (ESPI) and differential interferometry showing as a disadvantage that the last one does not recover the phase of an extended object. Moreover, the wavefront recovery in topographic applications is proposed in ESPI by using two wa