Abcd matrix
As such, propagation through an optical system reduces to that of calculating the relevant matrix elements and substituting these into the expressions derived here. N2 - We demonstrate that within the paraxial ray approximation the propagation of light through a complex optical system can be formulated in terms of a Huygens principle expressed with the complete system’s ABCD-matrix elements. T1 - Complex-Valued ABCD Matrices and Speckle Metrology Specifically, scattering from rough surfaces not giving rise to a fully developed speckle field, various anemometers and systems for measuring rotational velocity have been treated in order to show the benefits of the complex ABCD matrices.",
#Abcd matrix series
In many cases (e.g., laser beam propagation and Gaussian optics) we have been able to derive simple analytical expressions for the optical field quantities at an observation plane.A series of laser-based optical measurement systems have been analyzed and analytical expressions for their main parameters have been given. We have introduced complex-valued matrix element to represent apertures, thus having diffraction properties inherent in the description.We have extended the treatments of Baues and Collins to include partially coherent light sources, optical elements of finite size, and distributed random inhomogeneity along the optical path. Specifically, scattering from rough surfaces not giving rise to a fully developed speckle field, various anemometers and systems for measuring rotational velocity have been treated in order to show the benefits of the complex ABCD matrices.Ībstract = "We demonstrate that within the paraxial ray approximation the propagation of light through a complex optical system can be formulated in terms of a Huygens principle expressed with the complete systems ABCD-matrix elements. In many cases (e.g., laser beam propagation and Gaussian optics) we have been able to derive simple analytical expressions for the optical field quantities at an observation plane.Ī series of laser-based optical measurement systems have been analyzed and analytical expressions for their main parameters have been given. We have extended the treatments of Baues and Collins to include partially coherent light sources, optical elements of finite size, and distributed random inhomogeneity along the optical path. We have introduced complex-valued matrix element to represent apertures, thus having diffraction properties inherent in the description. What is particularly noteworthy about the angle of the ray after the transformation?Īnd the answering of these questions should show you how the transfer matrix encodes the lens's collimating behavior for all points on the focal plane.We demonstrate that within the paraxial ray approximation the propagation of light through a complex optical system can be formulated in terms of a Huygens principle expressed with the complete system’s ABCD-matrix elements.So your task is to work out what the transfer matrix in (1) does to this state, i.e.
Before we begin, I believe your transfer matrix should be: In fact, you compute the image given the object position by using the unique, fixed transfer matrix characterizing an optical element. So it doesn't depend at all on where the object and image are. As such, it is meant to work for all cases, at least approximately, over a range of inputs. A transfer matrix is a representation of a homogeneous linear function that approximates a behavior.