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The peak of star formation in the universe, the so-called ``cosmic noon," occurs around redshift 2. Therefore, to study the physical mechanisms driving galaxy assembly and star formation, and thus the bulk morphological appearances of present day galaxies, we must look to galaxies at this redshift and greater. Unfortunately, even with current space-based telescopes, the internal structures of these galaxies cannot be resolved. The point spread function of the Hubble Space Telescope (HST), for example, corresponds to scales of about 0.5 kpc at redshift 2. Even the next generation of telescopes (e.g., the James Webb Space Telescope, the Wide-Field Infrared Survey Telescope, and the new thirty meter class of ground-based telescopes) will not be able to access the spatial scales---tens of parsecs or less---on which star formation has been shown to occur in the local universe. Fortunately, strong gravitational lensing can magnify these spatial scales to angular scales comparable to, or larger than, the HST point spread function. However, this increased access to small scales comes at the cost of strong distortions of the underlying image. To deal with this, I use simulations to show that some morphological measurements (e.g., the Gini coefficient) are preserved by gravitational lensing and can be measured in the image plane. I further show how such measurements can aid image family identification and thus improve lens models and source reconstructions. I explore a method to measure the fraction of a lensed galaxy's light that is contained in star-forming clumps in the image plane, which would bypass the need for lens modeling and source reconstruction to carry out similar measurements. I present a proof of concept for a simple case, and show where the major uncertainties lie---uncertainties that will need to be dealt with in order to expand this technique for use on more image configurations and tighten the relationship between the intrinsic values and the measured values. I suggest several ways in which these uncertainties can be overcome. Finally, I discuss the potential for future application of these techniques, particularly in the context of explaining star formation processes across cosmic time, and the associated implications for galaxy mass assembly mechanisms and galaxy evolution.


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