Theoretical study of optical systems

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Principal investigator: Miguel A. Alonso

Keywords: imaging; optical performance, mid-spatial frequency error, Strehl ratio, OTF, PDPD, ray-based methods, Wigner function.

The performance of imaging systems is hindered by manufacturing errors in the optical elements involved. These errors can be the standard aberrations, but also finer-scale imperfections known as mid-spatial frequency errors, resulting from the manufacturing/finishing process, particularly if sub-aperture tools are involved. A third possible cause of error is residual birefringence. We have proposed theoretical models for understanding the effects of these errors on standard optical performance metrics such as the Strehl ratio and the OTF. For this purpose, we have proposed a new quantity, the “pupil-difference probability density” (PDPD), which provides an intuitive connection between the surface/wavefront errors and the OTF.

Recent work in this area has also consisted of tutorial reviews of standard and novel mathematical models used to study optical systems, such as ray-based methods, linear canonical transformations (ABCD formalism), and Wigner functions.

Finally, this research includes theoretical studies of specific, unusual elements with interesting optical properties.


Exactly solvable model behind Bose-Hubbard dimers, Ince-Gauss beams, and aberrated optical cavities
R. Gutierrez-Cuevas, D.H.J. O’Dell, M.R. Dennis, and M.A. Alonso
Phys. Rev. A 107, L031502 (2023).
Using fluorescent beads to emulate single flurophores
L.A. Aleman-Castañeda, S.Y-T. Feng, R. Gutierrez-Cuevas, I. Herrera, T.G. Brown, S. Brasselet, and M.A. Alonso
J. Opt. Soc. Am. A 39, C167-C178 (2022)
(arXiv:2209.08950 (2022).)
Abstract spaces, mappings and geometry in the study of optical systems
M.A. Alonso
Proc. SPIE 12078, International Optical Design Conference 2021, 120780U (19 November 2021).
La théorie ondulatoire de fresnel a-t-elle tué les rayons ? Comment réconcilier les rayons et les ondes
M.A. Alonso
Photoniques pp. 29-33 (2020).
Effects on the OTF of MSF structures with random variations
K. Liang and M.A. Alonso
Opt. Express 27, 34665-34680 (2019).
Rapidly-Decaying Fourier-like bases
K. Liang, G.W. Forbes and M.A. Alonso
Opt. Express 27, 32263-32276 (2019).
Optimal birefringence distributions for imaging polarimetry
A. Vella and M.A. Alonso
Opt. Express 27, 36799-36814 (2019).
Study of reflectors for illumination via conformal maps
L.A. Alemán-Castañeda and M.A. Alonso
Opt. Lett. 44, 3809-3812 (2019).
Predictive models for the Strehl ratio of diamond-machined optics
H. Aryan, K. Liang, M.A. Alonso, and T.J. Suleski
Appl. Opt. 58, 3272-3276 (2019).
Validity of the perturbation model for the propagation of MSF structure in 2D
K. Liang, G.W. Forbes and M.A. Alonso
Opt. Express 27, 3390-3408 (2019).
Poincaré sphere representation for spatially varying birefringence
A. Vella and M.A. Alonso
Opt. Lett.43, 379-382 (2018).
Using the pupil-difference probability density to understand OTF
K. Liang, M.A. Alonso
Computational Optics II, Proc. SPIE 10694, 106940P (2018).
Birefringent distributions tailored for imaging and other applications
M.A. Alonso and A. Vella
17th Workshop on Information Optics (WIO), IEEE 1-3 (2018). doi: 10.1109/WIO.2018.8643458
Understanding the effects of groove structures on the MTF
K. Liang and M.A. Alonso
Opt. Express 25, 18827-18841 (2017).
Effects of defocus and other quadratic errors on OTF
K. Liang and M.A. Alonso
Opt. Lett.42, 5254-5257 (2017).
Strehl ratio as the Fourier transform of a probability density of error differences
M.A. Alonso and G.W. Forbes
Opt. Lett. 41, 3735-3738 (2016).
Foreword M.A. Alonso
Linear Canonical Transforms, Theory and Applications
Springer Series in Optical Sciences 198, 2016
eds. J.J. Healy, M.A. Kutay, H.M. Ozaktas, J.T. Sheridan.
Is the Maxwell-Shafer fish eye lens able to form super-resolved images?
M.A. Alonso
New J. Phys. 17, 073013 (2015).
Modern Optics
M.A. Alonso
The Princeton Companion to Applied Mathematics (Princeton U.P., 2015), ed. Nicholas J. Higham, pp. 673-680.
The Wigner function in optics
J.C. Petruccelli and M.A. Alonso
The Optics Encyclopedia (Wiley VCH, 2015), pp. 1-22.
Ray-based diffraction calculations using stable aggregates of flexible elements
M.A. Alonso
J. Opt. Soc. Am. A 30, 1223-1235 (2013).
Ray transer matrix for a spiral phase plate
M. Eggleston, T. Godat, E. Munro, M.A. Alonso, H. Shi, M. Bhattacharya
J. Opt. Soc. Am. A 30, 2526-2530 (2013).
The connection between rays and waves
M.A. Alonso
Proceedings of Fringe 2013, 7th International Workshop on Advanced Optical Imaging and Metrology, W. Osten, Ed. (Springer, Hiedelberg, 2013), pp. 457-466.
Imaging with complex ray-optical refractive-index interfaces between complex object and image distances
J. Courtial, B. Kirkpatrick, and M.A. Alonso
Opt. Lett. 37, 701-703 (2012).
Wigner functions in optics: describing beams as ray bundles and pulses as particle ensembles(review article)
M.A. Alonso
Adv. Opt. Phot. 3, 272-365 (2011).