Extended depth-of-focus (EDOF) diffractive lenses produce a narrow and long focusing region which have many applications on microscopy, laser focusing or contact and intraocular lenses. Several designs have been proposed to achieve EDOF by angularly modulating the focal length. Nevertheless, when the focus is highly elongated, some undesired intensity fluctuations are produced. To solve this problem, we have generalized this type of lenses by defining their focal length as a Fourier series. Moreover, we have used Particle Swarm Optimization algorithm to optimize its Fourier series coefficients and generate an enhanced design. The performance of our Fourier Series Diffractive Lens (FSDL) is parameterized through the Full Width at Half Maximum (FWHM) of the beam and the uniformity of the intensity along the optical axis. Our results prove that the FSDL beam on the focal region is narrower and much more uniform than previous EDOF designs, showing the enhancement of the proposed EDOF lens.
Diffraction gratings are one of the most used elements in optics and even in other fields of science. They are used also
like part of measurement devices in scientific and industrial applications. As it is well known, self-imaging effect
appears when a diffraction grating is illuminated with a coherent beam, such as a plane wave. This effect has been
analyzed in depth and its behavior is well known under ideal grating and illumination conditions. Usually, the
illumination beam is not perfectly collimated but presents a certain degree of aberration. The motivation of this work is
to try to explain the behavior of the self-images of an ideal amplitude grating when it is illuminated by a non-perfect
beam, that is, an aberrated beam. The known of this effect can help to understand how much the aberration of the light
beam affects to the diffraction pattern, and more in depth, to the self-imaging phenomenon. The results presented in this
work can be very useful in metrology applications, since sometimes the contrast obtained experimentally does not
correspond to the theoretical predictions, usually due to aberrations in the light beam. For this, we have used a
formalism based in the Rayleigh-Sommerfeld approach. We have modeled the aberrations by using the Zernike
polynomials. On the other hand, we have considered all kinds of aberrations, spherical, coma, tilt, astigmatism, etc. As it
is expected the contrast of the self-images decrease when the order of them increases and also when the aberration
degree increase. In some cases, contrast inversion is also produced for high aberrations.
Diffraction gratings have been successfully used in Optical Metrology for a long time. They can be found in scientific
and industrial applications, such as optical encoders for determining the linear or angular displacement, spectrometers,
robots, etc. Defects on the surface of the grating may occur due to the manufacturing process. Also dust particles, drops
of liquids, etc. can be deposited on its surface the devices are placed in a dirty industrial environment. This separation
from the ideal behaviour may produce a degradation of the self-images. In this work we analyze the effect produced by
an irregular distribution of surface defects on the grating, with different distribution densities. In particular, we focus
how the contrast of the self-images decreases when the defects density.
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