Article history: Received 13 December 2009 Received in revised form 26 July 2010 Accepted 1 October 2010 Based on a modified Huygens–Fresnel principle valid in the near field, we analytically verify the exponential wave decay of evanescent waves. This field decay along the propagation direction can be considered as the result of interference between elementary oscillating dipole sources rather ...

and Applied Analysis 3 Proof. Let ξ be fixed. If φ t is in S, then its diffraction Fresnel transform certainly exists. Moreover, differentiating the right-hand side of 2.3 with respect to ξ, under the integral sign, ktimes, yields a sum of polynomials, pk t ξ , say of combinations of t and ξ. That is, ∣ ∣ ∣ ∣ ∣ d dtk Fd ( φ ) ξ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ pk t ξ φ t exp ( i ( α1t 2 − 2tξ α2ξ ) 2γ1 )∣ ∣...

Modern optical telescopes are giving us unprecedented imaging of the Universe in order to probe into the nature of dark matter and dark energy. Large optical telescopes require complex optical systems—often involving multiple lenses and mirrors. Light diffraction patterns on the focal planes influence imaging resolution, so a good understanding of diffraction is required to ensure high precisio...

Free-space propagation can be described as a shearing of the Wigner distribution function in the spatial coordinate; this shearing is linear in paraxial approximation but assumes a more complex shape for wide-angle propagation. Integration in the frequency domain allows the determination of near-field diffraction, leading to the well known Fresnel diffraction when small angles are considered an...

The fractional Fourier transform can be optically defined through a phase-space coordinate rotation of the Wigner distribution function associated with the input signal. This operation can be achieved by performing three successive shearing processes, which are reduced to a free-space Fresnel diffraction originated by a scaled version of the input object illuminated with a spherical wave. This ...

Reliable application of spatial light modulators (SLMs) as programmable diffractive optical elements requires a thorough calibration. In this paper, we propose a method for calibrating SLMs based on the evaluation of Fresnel images. Fresnel images generated by a binary phase diffraction grating consist of binary irradiance distributions whose visibility depends on the phase modulation. By displ...

We demonstrate a flexible setup for holographic steering of laser tweezers in microscopy using a high resolution spatial light modulator (SLM). In contrast to other methods, hologram read-out is done in the off-axis Fresnel regime rather than in the typically used on-axis Fourier regime. The diffractive structure is calculated as a Fresnel hologram, such that after reflection at the SLM only th...

In this paper, the optimal Fresnel lenses are designed by Zemax software.The fundamental problem of the Fresnel lenses is the beam divergence, which wasresolved by decreeing the output stain diameter on the image plane. For this purpose,two types of radial and cylindrical Fresnel lenses are simulated with different groovesusing Global and Hammer optimization methods. The minimum output stain di...