Aplanatic Condition Research Articles

Synthesis and Analysis of Polyfocal Constrained Lenses

Three-dimensional problems of synthesis and analysis of polyfocal constrained lenses are considered. It is shown that such lenses can have up to five focal points on each side. The problem of synthesis of a pentafocal lens in the general case is reduced to three transcendental equations and, of a quadrifocal lens, to two transcendental equations. In the case of a pentafocal lens with three focuses in the symmetry plane of the lens, forming plane wave fronts at the output, the synthesis problem is reduced to one transcendental equation; in all other cases of plane front formation, an analytical solution of the problem is obtained. An analytical solution is also obtained for the problem of synthesis of a quadrifocal lens with three symmetry planes. An analytical solution is also found for the problem of synthesis of a quadrifocal lens with two symmetry planes forming in the plane of symmetry four plane fronts with simultaneous fulfillment of the aplanatic conditions (Abbe sines) in the orthogonal plane. Examples of solving the synthesis problems with the optimization of parameters in order to minimize the mean square aberration of the eikonal are given. In the two-dimensional case, the dependence of the mean square aberration of the eikonal on focal distances is studied and it is shown that there is an optimal ratio of focal distances providing its minimum.

Analytical solution of an afocal two freeform mirror design problem.

We investigate a new afocal two freeform mirror design problem in first order optics. The resulting first-order partial differential equations for the freeform two mirror system have an analytic solution with the sole condition that the x-y and x'-y' axes are parallel. Two selected solutions are presented. One of them is semiaplanatic (fulfilling the aplanatic condition only for the x-coordinates), while the other is, to our knowledge, the first example of an aplanatic two-mirror system without rotational symmetry.

Solid immersion lens at the aplanatic condition for enhancing the spectral bandwidth of a waveguide grating coupler

We report a technique to substantially boost the spectral bandwidth of a conventional waveguide grating coupler by using a solid immersion cylindrical lens at the aplanatic condition to create a highly anamorphic beam and reach a much larger numerical aperture, thus enhancing the spectral bandwidth of a free-space propagating optical beam coupled into a single-mode planar integrated optical waveguide (IOW). Our experimental results show that the broadband IOW spectrometer thus created almost doubles (94% enhancement) the coupled spectral bandwidth of a conventional configuration. To exemplify the benefits made possible by the developed approach, we applied the technique to the broadband spectroscopic characterization of a protein submonolayer; our experimental data confirm the enhanced spectral bandwidth (around 380-nm) and illustrate the potentials of the developed technology. Besides the enhanced bandwidth, the broadband coupler of the single-mode IOW spectrometer described here is more robust and user-friendly than those previously reported in the literature and is expected to have an important impact on spectroscopic studies of surface-adsorbed molecular layers and surface phenomena.

Optical Design for the Optimum Solid Immersion Lens with High Numerical Aperture and Large Tolerance

Super hemispherical solid immersion lens system becomes a matter of interest due to its high numerical aperture (NA) gain. However, because of the instability of the aplanatic condition, even small amount of alignment error can easily lower the optical performance. To overcome the instability while maintaining high NA gain, we suggest an optimum solid immersion lens (opti-SIL) system which combines the advantages of both super hemispherical SIL (hyper-SIL) and hemispherical SIL (hemi-SIL). Exemplary designs and simulation results of the tolerance analysis show that opti-SIL system has much higher tolerances to various performance-lowering factors than hyper-SIL, even with relatively small NA resignation.

Analysis of the applications of the Schwarzschild objective in the soft x-ray and VUV spectral ranges. 1.Conditions for fifth-order aplanatism

An analysis is reported of the use of the Schwarzschild objective in soft x-ray and VUV (2–20 nm) microscopy. The aplanatic conditions, including terms of the fifth order which ensure more accurate determination of the principal characteristics of the objective, are found for homocentric and heterocentric geometries.

Aplanatic unit‐magnification optical system

A modest aspheric deformation of a hemisphere refines a two-reflection whispering gallery to aplanatic image conditions.

Four-Spherical-Mirror Zoom Telescope Continuously Satisfying The Aplanatic Condition

The design of a four-spherical-mirror zoom telescope is presented. By use of third order aberration theory the system is determined to satisfy the aplanatic condition at every point on the zooming locus. From examination of spot diagrams, a system with Cassegrainian-Cassegrainian configuration is found satisfactory. The design data are presented.

Aplanatic condition required to reproduce jitter-free signals in an optical digital disk system

We present the optical condition required for precise reproduction of electric signals with digital data coded on an optical disk as a combination of the length of pits and the interval between them. We approximate the modulation of photocurrent by the interference between the zeroth- and first-order beams diffracted by the pits, and express the mean-squared waveform distortion of the readout signal as a function of the squared sum of the phase transfer function and the modulation transfer function. We established both by measurement and by prediction using waveform distortion (both measurement and theory agreeing well) that jitter is highest in the presence of tangential coma, next highest in the presence of spherical aberration. We conclude, therefore, that an optical digital disk system must be aplanatic for jitter-free reproduction of digital data.

Aplanatic Condition for Off-Axial Object Point

Aplanatic Condition for Off-Axial Object Point