TY - JOUR
T1 - Refracting and reflecting interfaces transforming a given wavefront into another one
AU - de Jesús Cabrera-Rosas, Omar
AU - Espíndola-Ramos, Ernesto
AU - González-Juárez, Adriana
AU - Julián-Macías, Israel
AU - Marciano-Melchor, Magdalena
AU - Ortega-Vidals, Paula
AU - Rickenstorff-Parrao, Carolina
AU - Román-Hernández, Edwin
AU - Silva-Ortigoza, Gilberto
AU - Silva-Ortigoza, Ramón
AU - Sosa-Sánchez, Citlalli Teresa
N1 - Publisher Copyright:
© 2021 Optical Society of America
PY - 2021/11
Y1 - 2021/11
N2 - The aim of this work is threefold. First, following Luneburg and using our own notation, we review the Cartesian ovals. Second, we obtain analytical expressions for the reflecting and refracting surfaces that transform a prescribed smooth two-dimensional wavefront into a spherical one. These results are applied to show that the reflecting surface that connects a plane wavefront to a spherical one is a parabolical surface, and we design a lens, with two freeform surfaces, that transforms a spherical wavefront into another spherical one. These examples show that our equations provide the well-known solution for these problems, which is given by the Cartesian ovals method. Third, we present a procedure to obtain exact expressions for the refracting and reflecting surfaces that connect two given arbitrary wavefronts; that is, by assuming that the optical path length between two points on the prescribed wavefronts is given by the designer the refracting and reflecting surfaces we are looking for are determined by a set of two algebraic equations, which in the general case have to be solved in a numerical way. These general results are applied to compute the analytical expressions for the reflecting and refracting surfaces that transform a parabolical initial wavefront into a plane one.
AB - The aim of this work is threefold. First, following Luneburg and using our own notation, we review the Cartesian ovals. Second, we obtain analytical expressions for the reflecting and refracting surfaces that transform a prescribed smooth two-dimensional wavefront into a spherical one. These results are applied to show that the reflecting surface that connects a plane wavefront to a spherical one is a parabolical surface, and we design a lens, with two freeform surfaces, that transforms a spherical wavefront into another spherical one. These examples show that our equations provide the well-known solution for these problems, which is given by the Cartesian ovals method. Third, we present a procedure to obtain exact expressions for the refracting and reflecting surfaces that connect two given arbitrary wavefronts; that is, by assuming that the optical path length between two points on the prescribed wavefronts is given by the designer the refracting and reflecting surfaces we are looking for are determined by a set of two algebraic equations, which in the general case have to be solved in a numerical way. These general results are applied to compute the analytical expressions for the reflecting and refracting surfaces that transform a parabolical initial wavefront into a plane one.
UR - http://www.scopus.com/inward/record.url?scp=85118659159&partnerID=8YFLogxK
U2 - 10.1364/JOSAA.431885
DO - 10.1364/JOSAA.431885
M3 - Artículo
C2 - 34807028
AN - SCOPUS:85118659159
SN - 1084-7529
VL - 38
SP - 1662
EP - 1672
JO - Journal of the Optical Society of America A: Optics and Image Science, and Vision
JF - Journal of the Optical Society of America A: Optics and Image Science, and Vision
IS - 11
ER -