It sounds as a very good idea, but in practice the Lytro camera has a very low resolution. In the first release camera the resolution is 11 × 11 × 380 × 380 pixels, where 11 x 11 is the resolution of the cell. Whether it is able to track the wavefront distortion and what the measurement accuracy we can get? Actually I have used only the first release camera and I know nothing about the second release (Lytro illum).

I can recommend this paper which  is accompanied by software release in MatLab. I believe this software is the best solution to date to deal with Lytro camera

http://www.cv-foundation.org/openaccess/content_cvpr_2013/papers/Dansereau_Decoding_Calibration_and_2013_CVPR_paper.pdf

http://www.mathworks.com/matlabcentral/fileexchange/41511-deprecated-light-field-toolbox-v0-2-v0-3-now-available

I have found that this idea is not original :(

R.M. Clare, R.G. Lane, Wave-front sensing from subdivision of the focal plane with a lenslet array, JOSA A, Vol. 22, Issue 1, pp. 117-125 (2005)

http://www.opticsinfobase.org/josaa/abstract.cfm?uri=josaa-22-1-117

L.F. Rodríguez-Ramos, Y. Martína, J.J. Díaza, J. Piquerasa, J.M. Rodríguez-Ramos, The Plenoptic Camera as a wavefront sensor for the European Solar Telescope (EST), Proc. SPIE 7439, Astronomical and Space Optical Systems, 74390I

http://www.cafadis.ull.es/data/7439B-17_Plenoptic_WFS.pdf

Dr. Chensheng Wu's work in University of Maryland, College Park is related to this.