We have used ultrafast optics, primarily focused on the nonlinear processes of Polarization Gating and of Optical Parametric Amplification, one for measurement and the other for imaging purposes. For measurement, we have demonstrated a robust method of measurement to simultaneously measure both optical pulses used in a pump-probe type configuration. We refer to this method of pulse measurement as Double Blind Polarization Gating FROG. We have demonstrated this single-shot method for measuring two unknown pulses using one device. In addition to pulse measurement, we have demonstrated the processes of Optical Parametric Amplification (OPA) applicability to imaging of complex objects. We have done this where the Fourier transform plane is used during the interaction. We have amplified and wavelength converted a complex image. We observe a gain of ~100, and, although our images were averaged over many shots, we used a single-shot geometry, capable of true single-shot OPA imaging. To our knowledge, this is the first Fourier-plane OPA imaging of more than a single spatial-frequency component of an image. We observe more than 30 distinct spatial frequency components in both our amplified image and our wavelength shifted image. We have demonstrated all-optical spatial filtering for these complex images. We have demonstrated that direct Fourier filtering of spatial features is possible by using a shaped pump beam. We can isolate certain portions of the image simply by rotating the crystal.

Many essential processes and interactions on atomic and molecular scales occur at ultrafast timescales. The ability to measure and manipulate ultrashort pulses hold the key to probing and understanding these key processes that physicists, engineers, chemists and biologists study today. Measuring ultrashort pulses means that we measure both the intensity (which is a function of time) and the phase of the pulse in time. Or alternately we might measure spectrum and spectral phase (in the corresponding Fourier domain). In the early 1990's, the invention of FROG opened up the field of ultrashort measurement with it's ability to measure the complete pulse. Since then, there have been a whole host of pulse measurement techniques that have been invented to measure all sorts of ultrashort pulses. However, no variation of FROG nor any other fs pulse measurement technique, for that matter, has yet been able to completely measure arbitrary ultraweak femtosecond light pulses such as those found in nature. In this thesis, we will explore a couple of highly sensitive methods in a quest to measure ultraweak ultrashort pulses. We explore the use of Spectral Interferometry, a known sensitive technique as one possibility. We find that it has certain drawbacks that make it not necessarily suitable to tackle this problem. But in the course of our quest, we find that this technique is highly suitable for measuring 10s of picosecond-long shaped pulses. We discuss a couple of developments which make SI highly practical to use for such shaped pulse-measurements. We also develop a new technique which is a variation of FROG, based on the non-linearity of Difference Frequency Generation and Optical Parametric Amplification, which can amplify pulses as weak as a few hundred attojoules to be able to spectrally resolve them and measure the full intensity and phase of these pulses. This technique offers great potential to measure generalized ultraweak ultrashort pulses.